Let's see what the experts have to say:
First and foremost, is it still "numerology" if you're right?
For instance, was Einstein a numerologist? Kepler? Ah, Kepler... a very easy target. But who will be the bold "expert" to grant Einstein his rightful due as mystic?
:-)
Best,
Raphie
P.S. Please spare us all the argument "even a broken clock is right twice a day." This is valid but irrelevant to the concept of "different ways of knowing." :-)
Let me give a very simple and clear example I alluded to in a recent post. Here are the triangular numbers:
0, 1, 3, 6, 10, 15, 21, 28...
It takes about an eight year old wit to see that any two successive numbers sum to a square number (1, 4, 9, etc...). Now let's say I came to the same recognition playing with, and arranging pebbles in the sand. The "fractal" relational mind might extrapolate from 49 pebbles to a zillion, understanding that the small square will just get bigger and bigger as the numbers increase in magnitude.
Is such knowledge any less valid for lacking an algebraic proof? Does such knowledge constitute "numerology"?
Best,
Raphie
0, 1, 3, 6, 10, 15, 21, 28...
It takes about an eight year old wit to see that any two successive numbers sum to a square number (1, 4, 9, etc...). Now let's say I came to the same recognition playing with, and arranging pebbles in the sand. The "fractal" relational mind might extrapolate from 49 pebbles to a zillion, understanding that the small square will just get bigger and bigger as the numbers increase in magnitude.
Is such knowledge any less valid for lacking an algebraic proof? Does such knowledge constitute "numerology"?
Best,
Raphie
QUOTE (Raphie Frank+Mar 4 2009, 12:00 PM)
Is such knowledge any less valid for lacking an algebraic proof? Does such knowledge constitute "numerology"?
Yes, because without algebraic proof it cannot be used for anything and cannot be known for certain.
For something as trivial as that (the proof is about 2 lines) it may be obvious, but if you start 'deducing' patterns which are obvious without proving them, you will make mistakes. Simple.
I don't think that example fits the dictionary definition of numerology but it is about as useful as numerology.
Yes, because without algebraic proof it cannot be used for anything and cannot be known for certain.
For something as trivial as that (the proof is about 2 lines) it may be obvious, but if you start 'deducing' patterns which are obvious without proving them, you will make mistakes. Simple.
I don't think that example fits the dictionary definition of numerology but it is about as useful as numerology.
Well actual numerology is saying Nick and Cusa have the same number of letters in their online names as the common US spelling of excrement, therefore their posts must have the property of being valued the same as waste products. It's why some buildings don't have a floor labelled with the number 13 and why Ataru Moroboshi has a number 4 on his track uniform.
Used somewhat metaphorically the term "numerology" could be when rough numerical agreement is taken as proof of a statement's connection with deep truth without a full analysis. For example, it's not an earth-shattering coincidence and a sign of divine blessing and great cosmic forces when Ikea sends you exactly the right number of screws to assemble your computer desk. In the physical sciences, Heim's "prediction" of the masses are not based on any physical theory with verified properties and indeed shows signs of being a post hoc fit to experimental data. I seem to remember someone being impressed that logarithms in the base of the golden ration of many quantities could be approximated well by integers or simple fractions. But since log base phi of 10 is 4.78+ then we have more coincidences than even with log base 2. But then you would miss the relation that phi^n is only phi^-n away from a whole number for sound algebraic principles.
Used somewhat metaphorically the term "numerology" could be when rough numerical agreement is taken as proof of a statement's connection with deep truth without a full analysis. For example, it's not an earth-shattering coincidence and a sign of divine blessing and great cosmic forces when Ikea sends you exactly the right number of screws to assemble your computer desk. In the physical sciences, Heim's "prediction" of the masses are not based on any physical theory with verified properties and indeed shows signs of being a post hoc fit to experimental data. I seem to remember someone being impressed that logarithms in the base of the golden ration of many quantities could be approximated well by integers or simple fractions. But since log base phi of 10 is 4.78+ then we have more coincidences than even with log base 2. But then you would miss the relation that phi^n is only phi^-n away from a whole number for sound algebraic principles.
QUOTE (rpenner+Mar 4 2009, 11:34 AM)
Well actual numerology is saying Nick and Cusa have the same number of letters in their online names
Good gosh, I had never noticed that... rather amazing. But why one vowel versus two? Do you suppose the aliens had anything to do with it? - RF
Good gosh, I had never noticed that... rather amazing. But why one vowel versus two? Do you suppose the aliens had anything to do with it? - RF
People have been assigning nonmathematical or pseudomathematical meaning to numbers, often supernatural stuff, ever since numbers were invented. Unfortunately this can cause trouble when taken seriously.
Wife and I assign a goofy meaning to certain numbers and sometimes use them just for grins. Trivial. Should take less than 5 seconds to figure out. Go
505, 1111, 926, 222, 858, 906, 252, 111, 1221, 659, 609, 808, 828, 619, 202, 515, 629, 101, 525, 956, 1001, 818, 916
Did I miss any?
Sporacle
does arithmetic real good
Wife and I assign a goofy meaning to certain numbers and sometimes use them just for grins. Trivial. Should take less than 5 seconds to figure out. Go
505, 1111, 926, 222, 858, 906, 252, 111, 1221, 659, 609, 808, 828, 619, 202, 515, 629, 101, 525, 956, 1001, 818, 916
Did I miss any?
Sporacle
does arithmetic real good
Pointless, except if you use one of those numbers to set the digital alarm clock, and whack it when it goes off and turn it upside down, it will read the same for a minute. You could ask why there are 23 and run with it, but I won't.
Seriously, mathematical operations are an integral aspect of reality. Which ones, sequences, combinations, etc are relevant (useful) and which are not, and how do we determine the difference? Sometimes people into "pure" mathematics make fun of physics mathematics.
Sporacle
tries stuff including trying to stay out of trouble
Seriously, mathematical operations are an integral aspect of reality. Which ones, sequences, combinations, etc are relevant (useful) and which are not, and how do we determine the difference? Sometimes people into "pure" mathematics make fun of physics mathematics.
Sporacle
tries stuff including trying to stay out of trouble
I don't see 212 in there.
Whoa! That makes 24... Now that's gotta mean something.
Whoa! That makes 24... Now that's gotta mean something.
Oops! Not a prime after all. It means you have to know how to count.
QUOTE (Raphie Frank+Mar 4 2009, 12:00 PM)
Is such knowledge any less valid for lacking an algebraic proof? Does such knowledge constitute "numerology"?
Yes, it is less valid. For instance, consider the sequence 41, 43, 47, 53, 61, ... Looks like a sequence of primes doesn't it. And notice how the difference keeps increasing by 2 each time. Heck, I'll add some more, 41, 43, 47, 53, 61, 71, 83, 97, 113, .... More primes! OMG, it's a sequence of primes! I'll add some more, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, more primes! Am I working with some kind of prime generating sequence? Can I find infinitely many primes using this "Increase the difference by 2 each time" rules? I've got a dozen primes so far, infact, I can give 40 consecutive primes.
But when I use algebra to work out that the formula is f(n) = n^2 + n + 41 I immediately see it cannot generate primes indefinitely because n=40 and n=41 are trivially not prime. A sequence of more than 3 dozen samples falls apart. And you, Raphie, only look at 6~12 terms in any of the sequences you talk about.
Yes, it is less valid. For instance, consider the sequence 41, 43, 47, 53, 61, ... Looks like a sequence of primes doesn't it. And notice how the difference keeps increasing by 2 each time. Heck, I'll add some more, 41, 43, 47, 53, 61, 71, 83, 97, 113, .... More primes! OMG, it's a sequence of primes! I'll add some more, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, more primes! Am I working with some kind of prime generating sequence? Can I find infinitely many primes using this "Increase the difference by 2 each time" rules? I've got a dozen primes so far, infact, I can give 40 consecutive primes.
But when I use algebra to work out that the formula is f(n) = n^2 + n + 41 I immediately see it cannot generate primes indefinitely because n=40 and n=41 are trivially not prime. A sequence of more than 3 dozen samples falls apart. And you, Raphie, only look at 6~12 terms in any of the sequences you talk about.
QUOTE (AlphaNumeric+Apr 8 2009, 08:39 AM)
Yes, it is less valid. For instance, consider the sequence 41, 43, 47, 53, 61, ... Looks like a sequence of primes doesn't it. And notice how the difference keeps increasing by 2 each time. Heck, I'll add some more, 41, 43, 47, 53, 61, 71, 83, 97, 113, .... More primes! OMG, it's a sequence of primes! I'll add some more, 41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, more primes! Am I working with some kind of prime generating sequence? Can I find infinitely many primes using this "Increase the difference by 2 each time" rules? I've got a dozen primes so far, infact, I can give 40 consecutive primes.
But when I use algebra to work out that the formula is f(n) = n^2 + n + 41 I immediately see it cannot generate primes indefinitely because n=40 and n=41 are trivially not prime. A sequence of more than 3 dozen samples falls apart. And you, Raphie, only look at 6~12 terms in any of the sequences you talk about.
In a general sense, you make a good point, Alphanumeric, but let me note that if one were predicting that all numbers in the x^2 + x + 41 series would be prime, this is eminently verifiable and falsifiable. In other words, a prediction is being made that can then be tested:
"Conjecture:"
x^2 + x + 41 = y | y is prime for all x
For values up to 39, all the numbers are prime, but now:
Let x = 40; y = 1681 = 41 * 41 (Conjecture is FALSE)
Let x = 41; y = 1763 = 41 * 43 (Conjecture is FALSE)
In many ways, this is a no-brainer, since for x = 40, you have a formula that reduces to n^2 + (2n+1), the formula for (n+1)^2, and for x = 41, you've a formula that reduces to n^2 + 2n, the formula for (n+1)^2 - 1, equal in all cases to (n)*(n+2)
In any case, funny you should post that particular formula as a basis by which to support claims of "lack of validity" since it is a quite famous formula in mathematical history. I will actually take the time to type out verbatim almost a full page from "The Music of the Primes" by Marcus du Sautoy (p. 45) as it a ) has bearing on your post, and b ) I believe will be informative for others:
[Note: Ah the wonders of the information age. I didn't have to type this all in as the full text can be found here: http://d.scribd.com/docs/174tfruz3w4l96sh0eej.pdf
===========================================================
Above all else, Euler loved calculating prime numbers. He produced tables of all the
primes up to 100,000 and a few beyond. In 1732, he was also the first to show that
Fermat's formula for primes, 2^2^n + 1, broke down when N = 5. Using new theoretical ideas,
he managed to show how to crack this ten-digit number into a product of two smaller
numbers. One of his most curious discoveries was a formula that seemed to generate an
uncanny number of primes. In 1772, he calculated all the answers that you get when you
feed the numbers from 0 to 39 into the formula x^2 + x + 41. He got the following list:
41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421,
461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971, 1,033, 1,097, 1,163, 1,231, 1,301,
1,373, 1,447, 1,523, 1,601
It seemed bizarre to Euler that you could generate so many primes with this formula. He
realised that the process would have to break down at some point. It might already be
clear to you that when you input 41, the output has to be divisible by 41. Also, for x = 40
you get a number which is not prime.
Nonetheless, Euler was quite struck by his formula's ability to produce so many primes. He
began to wonder what other numbers might work instead of 41. He discovered that in
addition to 41 you could also choose q = 2, 3, 5, 11, 17, and the formula x^2 + x + q would
spit out primes when fed numbers from 0 to q — 2.
But finding such a simple formula for generating all the primes was beyond even the great
Euler. As he wrote in 1751, 'There are some mysteries that the human mind will never
penetrate. To convince ourselves we have only to cast a glance at tables of primes and we
should perceive that there reigns neither order nor rule.' It seems paradoxical that the
fundamental objects on which we build our order-filled world of mathematics should
behave so wildly and unpredictably.
It would turn out that Euler had been sitting on an equation that would break the prime number deadlock. But it would take another hundred years, and another great mind, to show what Euler could not.
That mind belonged to Bernhard Riemann.
===========================================================
Now let me add the following:
If one could manage somehow to generate a similarly elegant and simple formula for Kissing Numbers as Euler did for primes (as you know I believe Kissing Numbers are related to the primes...), one would quadruple in one fell swoop the number of known kissing numbers, from 10 to 40. One might also be setting the stage for the next Riemann to come along 100 hundred years from now.
Just a thought.
Best,
Raphie
But when I use algebra to work out that the formula is f(n) = n^2 + n + 41 I immediately see it cannot generate primes indefinitely because n=40 and n=41 are trivially not prime. A sequence of more than 3 dozen samples falls apart. And you, Raphie, only look at 6~12 terms in any of the sequences you talk about.
In a general sense, you make a good point, Alphanumeric, but let me note that if one were predicting that all numbers in the x^2 + x + 41 series would be prime, this is eminently verifiable and falsifiable. In other words, a prediction is being made that can then be tested:
"Conjecture:"
x^2 + x + 41 = y | y is prime for all x
For values up to 39, all the numbers are prime, but now:
Let x = 40; y = 1681 = 41 * 41 (Conjecture is FALSE)
Let x = 41; y = 1763 = 41 * 43 (Conjecture is FALSE)
In many ways, this is a no-brainer, since for x = 40, you have a formula that reduces to n^2 + (2n+1), the formula for (n+1)^2, and for x = 41, you've a formula that reduces to n^2 + 2n, the formula for (n+1)^2 - 1, equal in all cases to (n)*(n+2)
In any case, funny you should post that particular formula as a basis by which to support claims of "lack of validity" since it is a quite famous formula in mathematical history. I will actually take the time to type out verbatim almost a full page from "The Music of the Primes" by Marcus du Sautoy (p. 45) as it a ) has bearing on your post, and b ) I believe will be informative for others:
[Note: Ah the wonders of the information age. I didn't have to type this all in as the full text can be found here: http://d.scribd.com/docs/174tfruz3w4l96sh0eej.pdf
===========================================================
Above all else, Euler loved calculating prime numbers. He produced tables of all the
primes up to 100,000 and a few beyond. In 1732, he was also the first to show that
Fermat's formula for primes, 2^2^n + 1, broke down when N = 5. Using new theoretical ideas,
he managed to show how to crack this ten-digit number into a product of two smaller
numbers. One of his most curious discoveries was a formula that seemed to generate an
uncanny number of primes. In 1772, he calculated all the answers that you get when you
feed the numbers from 0 to 39 into the formula x^2 + x + 41. He got the following list:
41, 43, 47, 53, 61, 71, 83, 97, 113, 131, 151, 173, 197, 223, 251, 281, 313, 347, 383, 421,
461, 503, 547, 593, 641, 691, 743, 797, 853, 911, 971, 1,033, 1,097, 1,163, 1,231, 1,301,
1,373, 1,447, 1,523, 1,601
It seemed bizarre to Euler that you could generate so many primes with this formula. He
realised that the process would have to break down at some point. It might already be
clear to you that when you input 41, the output has to be divisible by 41. Also, for x = 40
you get a number which is not prime.
Nonetheless, Euler was quite struck by his formula's ability to produce so many primes. He
began to wonder what other numbers might work instead of 41. He discovered that in
addition to 41 you could also choose q = 2, 3, 5, 11, 17, and the formula x^2 + x + q would
spit out primes when fed numbers from 0 to q — 2.
But finding such a simple formula for generating all the primes was beyond even the great
Euler. As he wrote in 1751, 'There are some mysteries that the human mind will never
penetrate. To convince ourselves we have only to cast a glance at tables of primes and we
should perceive that there reigns neither order nor rule.' It seems paradoxical that the
fundamental objects on which we build our order-filled world of mathematics should
behave so wildly and unpredictably.
It would turn out that Euler had been sitting on an equation that would break the prime number deadlock. But it would take another hundred years, and another great mind, to show what Euler could not.
That mind belonged to Bernhard Riemann.
===========================================================
Now let me add the following:
If one could manage somehow to generate a similarly elegant and simple formula for Kissing Numbers as Euler did for primes (as you know I believe Kissing Numbers are related to the primes...), one would quadruple in one fell swoop the number of known kissing numbers, from 10 to 40. One might also be setting the stage for the next Riemann to come along 100 hundred years from now.
Just a thought.
Best,
Raphie
Numerology is usually associated with mysticism. I remember back in the fifth grade or so, we had some formula to calculate the number of the beast 666. One would try to see if a person's name fit (added up to 666). If it did, that person was the Antichrist. I laugh about it now, but then we were dead serious. Henry Kissinger's name fit. That is an example of numerology.
Usually numerologists assign symbolic significance to certain numbers. 7 is holy. 6 is the number of man or sometimes an evil number. 4 symbolizes the earth or the material world. 5 is often associated with negativity or peril. 40 is a number of judgment, and so on. Often times it is not consistent as to which number is what. Cultures vary.
Except for certain people, it is not taken seriously now. It is true though that certain early mathematicians believed in this sort of mysticism. Pythagoras was big into mysticism. Geometry was something religious. He believed numbers were behind everything. He wasn't totally wrong, though, numbers did end up being the secrets of the universe. The math is just much more elaborate than they ever could have imagined. I suppose one could say numerology was to math/physics what alchemy was to chemistry.
...and people are still trying to calculate who the Antichrist is....
Usually numerologists assign symbolic significance to certain numbers. 7 is holy. 6 is the number of man or sometimes an evil number. 4 symbolizes the earth or the material world. 5 is often associated with negativity or peril. 40 is a number of judgment, and so on. Often times it is not consistent as to which number is what. Cultures vary.
Except for certain people, it is not taken seriously now. It is true though that certain early mathematicians believed in this sort of mysticism. Pythagoras was big into mysticism. Geometry was something religious. He believed numbers were behind everything. He wasn't totally wrong, though, numbers did end up being the secrets of the universe. The math is just much more elaborate than they ever could have imagined. I suppose one could say numerology was to math/physics what alchemy was to chemistry.
...and people are still trying to calculate who the Antichrist is....
People have been searching for the meaning of numbers and symbolic operations with them since the inventions of numbers. There have been countless assigned mystical meanings all along (numerology), but the tide turned when Kepler found a set of operations (algorithm) with real numbers which accounted for the motion of the planets.
An assumption of science is that there is no “supernatural”, and there is one reality.
There have been comparisons of the distribution of larger prime numbers and a random distribution of larger numbers, and pictures of the graphs look about the same. As said on this thread, algorithms have been found so far which predict the early part of the prime number sequence. Trial and error computer iteration has found far larger primes, but not with just specific algorithms (specific algorithms are used to streamline the search process).
Two questions:
1. Does the eventual distribution of increasingly larger primes approach a random number distribution?
2. Are ALL real numbers and ALL operations with them congruent with some aspect of physical reality?
Sporacle
been wondering a long time
An assumption of science is that there is no “supernatural”, and there is one reality.
There have been comparisons of the distribution of larger prime numbers and a random distribution of larger numbers, and pictures of the graphs look about the same. As said on this thread, algorithms have been found so far which predict the early part of the prime number sequence. Trial and error computer iteration has found far larger primes, but not with just specific algorithms (specific algorithms are used to streamline the search process).
Two questions:
1. Does the eventual distribution of increasingly larger primes approach a random number distribution?
2. Are ALL real numbers and ALL operations with them congruent with some aspect of physical reality?
Sporacle
been wondering a long time
A complication of question #1 above is so far there is no way to generate a truly random number sequence.
Right, Mitch. I don't believe in horoscope stuff. Sometimes works, but don't bet money on it. Fake random numbers, especially with stories attached that hide the odds, can mess things up, and if you're gambling, make sure you know the actual odds.
We can calculate the odds of events (depending on the data available), but so far we cannot generate a truly random number sequence for comparison with anything. (Countless researchers in every field use a compromise that is statistically acceptable for their studies.)
But I'm curious whether a way extended sequence of prime numbers approaches a random number distribution. The reason I'm curious is whether the distribution of primes demonstrates a natural spectrum from order to randomness.
Sporacle
betcha mathematics is reality
We can calculate the odds of events (depending on the data available), but so far we cannot generate a truly random number sequence for comparison with anything. (Countless researchers in every field use a compromise that is statistically acceptable for their studies.)
But I'm curious whether a way extended sequence of prime numbers approaches a random number distribution. The reason I'm curious is whether the distribution of primes demonstrates a natural spectrum from order to randomness.
Sporacle
betcha mathematics is reality
QUOTE (Cusa+Apr 19 2009, 04:40 AM)
Is randomness anti-pattern?
Our brains look for order by patterns.
What is something without pattern?
Mitch Raemsch
Thanks, Mitch!
Those three issues are crucial to understanding, and please forgive another long post.
People have been gradually making progress on the pattern/randomness thing but getting tangled up about it from the dawn of human communication including using symbolic operations.
There are lots of opinions about how the homeotherm brain works, but it is indeed a biological pattern finding system. Personal opinion is that the cerebral cortex finds specific relationships of input data (order), same as cold blooded creatures. But then in the present moment it can reiterate images of these and randomly recombine them in a search for interrelationships of these first order relationships and thus find much larger patterns. Then in the same way find where more of the first order relationships fit the patterns (look for order in patterns). These patterns of order we have found are obviously extremely useful for making predictions.
The evolution of a pattern finding brain helps avoiding getting eaten by something or other bad stuff, but there is a trade off. A false negative perception (not worrying enough) is way worse than a false positive (worrying unnecessarily). Random events are part of reality and when you’re not sure what is going on, it’s safer to assume they could get you. In general people fear unpredictability. Since ancient times, the essence of evil is unpredictability and chaos, always attacking our beloved, orderly patterns.
As I suggested elsewhere, the simplest possible set of operations that apply to everything is together and apart. Stuff together can be defined by relationships with the rest. An entity apart is random, cannot be defined, unpredictable. It is impossible to define random except with a negative term, in essence meaning not ordered or unpredictable. Random entities or events are without order or pattern, at least from our perspective, unless we come to understand more details of the situation that define some order involved.
Over about the past century people have been including terms of probability (randomness) into algorithms to describe the activity of small stuff. This has made many people nervous, but the predictions have obvious utility, and a question now is extending the methods to the big stuff. However there are at least four basic problems in the continuing exploration.
1. As the complexity of mathematical models increases (always great fun and important), including combined probability factors, the odds these will fit reality on the larger scale become increasingly unpredictable, even if the complex models appear consistent (a pattern).
2. Observations of the big stuff are showing patterns that don’t fit our models very well and the speculation is there must be some other stuff involved. And of course whatever it is must be interrelated with the small stuff we observe and define.
3. A basic, standard problem at any scale is that the physical entities and their activity studied are interrelated with everything else involved, and the system boundaries necessary in the studies and the mathematical models are limited and also complicated by probability factors. There has been steady progress requiring extensive grunt work.
4. As I suggested elsewhere, the assumed geometry of what is taking place (Standard Model) is outside in. (It is suggested that by turning the Standard Model inside out and assuming there is an unlimited entity and the simplest possible set of operations, the geometry of the interactions of all entities can be defined and understood.
Sporacle is betting that randomness and order are integral aspects of all reality. (doesn’t help figure out what to do with the sliding 401k)
Our brains look for order by patterns.
What is something without pattern?
Mitch Raemsch
Thanks, Mitch!
Those three issues are crucial to understanding, and please forgive another long post.
People have been gradually making progress on the pattern/randomness thing but getting tangled up about it from the dawn of human communication including using symbolic operations.
There are lots of opinions about how the homeotherm brain works, but it is indeed a biological pattern finding system. Personal opinion is that the cerebral cortex finds specific relationships of input data (order), same as cold blooded creatures. But then in the present moment it can reiterate images of these and randomly recombine them in a search for interrelationships of these first order relationships and thus find much larger patterns. Then in the same way find where more of the first order relationships fit the patterns (look for order in patterns). These patterns of order we have found are obviously extremely useful for making predictions.
The evolution of a pattern finding brain helps avoiding getting eaten by something or other bad stuff, but there is a trade off. A false negative perception (not worrying enough) is way worse than a false positive (worrying unnecessarily). Random events are part of reality and when you’re not sure what is going on, it’s safer to assume they could get you. In general people fear unpredictability. Since ancient times, the essence of evil is unpredictability and chaos, always attacking our beloved, orderly patterns.
As I suggested elsewhere, the simplest possible set of operations that apply to everything is together and apart. Stuff together can be defined by relationships with the rest. An entity apart is random, cannot be defined, unpredictable. It is impossible to define random except with a negative term, in essence meaning not ordered or unpredictable. Random entities or events are without order or pattern, at least from our perspective, unless we come to understand more details of the situation that define some order involved.
Over about the past century people have been including terms of probability (randomness) into algorithms to describe the activity of small stuff. This has made many people nervous, but the predictions have obvious utility, and a question now is extending the methods to the big stuff. However there are at least four basic problems in the continuing exploration.
1. As the complexity of mathematical models increases (always great fun and important), including combined probability factors, the odds these will fit reality on the larger scale become increasingly unpredictable, even if the complex models appear consistent (a pattern).
2. Observations of the big stuff are showing patterns that don’t fit our models very well and the speculation is there must be some other stuff involved. And of course whatever it is must be interrelated with the small stuff we observe and define.
3. A basic, standard problem at any scale is that the physical entities and their activity studied are interrelated with everything else involved, and the system boundaries necessary in the studies and the mathematical models are limited and also complicated by probability factors. There has been steady progress requiring extensive grunt work.
4. As I suggested elsewhere, the assumed geometry of what is taking place (Standard Model) is outside in. (It is suggested that by turning the Standard Model inside out and assuming there is an unlimited entity and the simplest possible set of operations, the geometry of the interactions of all entities can be defined and understood.
Sporacle is betting that randomness and order are integral aspects of all reality. (doesn’t help figure out what to do with the sliding 401k)
QUOTE (sporacle+Apr 20 2009, 09:30 AM)
4. As I suggested elsewhere, the assumed geometry of what is taking place (Standard Model) is outside in. (It is suggested that by turning the Standard Model inside out and assuming there is an unlimited entity and the simplest possible set of operations, the geometry of the interactions of all entities can be defined and understood.
This is meaningless BS and obviously you don't even know the SM you just want to make it seem like you do.
This is meaningless BS and obviously you don't even know the SM you just want to make it seem like you do.
QUOTE (AlphaNumeric+Apr 20 2009, 10:16 AM)
This is meaningless BS and obviously you don't even know the SM you just want to make it seem like you do.
Sporacle doesn't care what anybody thinks about him and will never quit asking questions. What he knows or doesn't know is irrelevant. Don't hesitate to ask questions and say what you think about anything.
For anyone who thinks eversion (maintaining all the same small scale relationships) of the Standard Model is dangerous BS, DO NOT consider the possibility there is an unlimited entity and DO NOT explore the simplest possible set of operations. It might cause mental distress. Take care.
Sporacle doesn't care what anybody thinks about him and will never quit asking questions. What he knows or doesn't know is irrelevant. Don't hesitate to ask questions and say what you think about anything.
For anyone who thinks eversion (maintaining all the same small scale relationships) of the Standard Model is dangerous BS, DO NOT consider the possibility there is an unlimited entity and DO NOT explore the simplest possible set of operations. It might cause mental distress. Take care.
QUOTE
What he knows or doesn't know is irrelevant
Fits right in with the rest of the cranks.
Sounds like you guys know you have the knowledge of the way reality operates, so you're cool and the rest of us are not. Sounds like the rest of us are supposed to learn that real science is based on the authority of those who have the knowledge and that speculating about anything else is crazy.
Please explain for the rest of us kooks out here why the jet or whatever it is in the Chandra images of Pictor A show a straight line for 800 thousand light years.
BTW flaming somebody with no real explanation makes you sound like insecure grad students trying to look cool. There are plenty of serious people here exploring puzzling questions. If something is truly BS it should be really easy to falsify, and a good falsification of an idea is far more helpful for everyone.
Sporacle
Please explain for the rest of us kooks out here why the jet or whatever it is in the Chandra images of Pictor A show a straight line for 800 thousand light years.
BTW flaming somebody with no real explanation makes you sound like insecure grad students trying to look cool. There are plenty of serious people here exploring puzzling questions. If something is truly BS it should be really easy to falsify, and a good falsification of an idea is far more helpful for everyone.
Sporacle
QUOTE (sporacle+Apr 21 2009, 02:00 AM)
Sounds like you guys know you have the knowledge of the way reality operates, so you're cool and the rest of us are not. Sounds like the rest of us are supposed to learn that real science is based on the authority of those who have the knowledge and that speculating about anything else is crazy.
Please explain for the rest of us kooks out here why the jet or whatever it is in the Chandra images of Pictor A show a straight line for 800 thousand light years.
BTW flaming somebody with no real explanation makes you sound like insecure grad students trying to look cool. There are plenty of serious people here exploring puzzling questions. If something is truly BS it should be really easy to falsify, and a good falsification of an idea is far more helpful for everyone.
Sporacle
You mean the traffic jam of gases piling onto a black hole - it gets so crowded that some of the gas gets thrown into space.
Bitchin! http://www.ast.cam.ac.uk/~regan/quasar.jpg
"There is man then there is Beer w/Straw" Thus said Therathustra (quoting Beer w/Straw)
Please explain for the rest of us kooks out here why the jet or whatever it is in the Chandra images of Pictor A show a straight line for 800 thousand light years.
BTW flaming somebody with no real explanation makes you sound like insecure grad students trying to look cool. There are plenty of serious people here exploring puzzling questions. If something is truly BS it should be really easy to falsify, and a good falsification of an idea is far more helpful for everyone.
Sporacle
You mean the traffic jam of gases piling onto a black hole - it gets so crowded that some of the gas gets thrown into space.
Bitchin! http://www.ast.cam.ac.uk/~regan/quasar.jpg
"There is man then there is Beer w/Straw" Thus said Therathustra (quoting Beer w/Straw)
QUOTE (sporacle+Apr 21 2009, 02:00 AM)
Sounds like you guys know you have the knowledge of the way reality operates, so you're cool and the rest of us are not. Sounds like the rest of us are supposed to learn that real science is based on the authority of those who have the knowledge and that speculating about anything else is crazy.
BTW flaming somebody with no real explanation makes you sound like insecure grad students trying to look cool. There are plenty of serious people here exploring puzzling questions. If something is truly BS it should be really easy to falsify, and a good falsification of an idea is far more helpful for everyone.
33 posts into your Physorg posting career and you sound like your whining because nobody will pick you for kickball. Give 'em a reason to pick you. Don't step up to the plate unless you can hit the ball every once in a while.
And is it really necessary to end your post by "signing" it with the same pseudonym that you use to post? It's redundant ... ya know?
BTW flaming somebody with no real explanation makes you sound like insecure grad students trying to look cool. There are plenty of serious people here exploring puzzling questions. If something is truly BS it should be really easy to falsify, and a good falsification of an idea is far more helpful for everyone.
33 posts into your Physorg posting career and you sound like your whining because nobody will pick you for kickball. Give 'em a reason to pick you. Don't step up to the plate unless you can hit the ball every once in a while.
And is it really necessary to end your post by "signing" it with the same pseudonym that you use to post? It's redundant ... ya know?
Thanks, Beer w//Straw
Beer is an integrally related part of reality. Like countless other things, usually considered insignificant and ignored in speculations about the big picture. Any theory of everything must account for every detail of everything including beer (and petunias, black holes and Methusela) on all scales and systems without exception. Any theory of everything can be falsified by identifying any entity or process that doesn't fit.
If something is putting out gas on any scale, it's way hard to keep it going on way out there in a straight line. Also really hard to do it with leptons, hadrons and photons. Maybe there is something else in that way long straight whatever it is besides the gas and those x-rays in the Pictor A example. Cosmic jets are neat.
Here comes another strange idea guys, so watch out (not gas and not from beer). Maybe something is taking place at the same time all along the straight "jet" configuration and producing hadrons, electrons, photons, etc in situ. A speculation is that maybe quarks are intergalactic size circular standing waves of precise local configuration (as the activity of a single unlimited entity, and forget the limit of light speed) and linked as hadrons in a spinning black hole (big star). Their collective quark locus describes an intergalactic size torus, and the center of the torus is an axis of quarks perpendicular to the spin of the black hole and could be extremely long.
The quarks continue to randomly recombine toward maximum interrelatedness as hadrons in the black hole, and the hadrons continue to accelerate together (gravity). But at some point in the increasing density, the randomness in the process exceeds the stability of the quark (hadron) interactions, and the quarks disassociate, further disrupting the stability of other hadron interactions nearby. In ordinary terms it goes blooey. Then the configuration of quarks on the axis of the black hole spin is no longer stable and they randomly recombine as hadrons all along the axis, producing high energy leptons and photons. Gravitational energy of the "black hole" is converted to the mass of the "jet".
Don't think to hard about petunias
Cheers
Sporacle
Beer is an integrally related part of reality. Like countless other things, usually considered insignificant and ignored in speculations about the big picture. Any theory of everything must account for every detail of everything including beer (and petunias, black holes and Methusela) on all scales and systems without exception. Any theory of everything can be falsified by identifying any entity or process that doesn't fit.
If something is putting out gas on any scale, it's way hard to keep it going on way out there in a straight line. Also really hard to do it with leptons, hadrons and photons. Maybe there is something else in that way long straight whatever it is besides the gas and those x-rays in the Pictor A example. Cosmic jets are neat.
Here comes another strange idea guys, so watch out (not gas and not from beer). Maybe something is taking place at the same time all along the straight "jet" configuration and producing hadrons, electrons, photons, etc in situ. A speculation is that maybe quarks are intergalactic size circular standing waves of precise local configuration (as the activity of a single unlimited entity, and forget the limit of light speed) and linked as hadrons in a spinning black hole (big star). Their collective quark locus describes an intergalactic size torus, and the center of the torus is an axis of quarks perpendicular to the spin of the black hole and could be extremely long.
The quarks continue to randomly recombine toward maximum interrelatedness as hadrons in the black hole, and the hadrons continue to accelerate together (gravity). But at some point in the increasing density, the randomness in the process exceeds the stability of the quark (hadron) interactions, and the quarks disassociate, further disrupting the stability of other hadron interactions nearby. In ordinary terms it goes blooey. Then the configuration of quarks on the axis of the black hole spin is no longer stable and they randomly recombine as hadrons all along the axis, producing high energy leptons and photons. Gravitational energy of the "black hole" is converted to the mass of the "jet".
Don't think to hard about petunias
Cheers
Sporacle
QUOTE (uaafanblog+Apr 21 2009, 03:50 AM)
33 posts into your Physorg posting career and you sound like your whining because nobody will pick you for kickball. Give 'em a reason to pick you. Don't step up to the plate unless you can hit the ball every once in a while.
And is it really necessary to end your post by "signing" it with the same pseudonym that you use to post? It's redundant ... ya know?
Looks like when somebody trashes you, the usual procedure is to reply. Pain in the butt, but guess I gotta do one more.
I learned a long time ago that whining never works, including with boss and wife. Gonna keep saying what I think, and if you don't like it, please don't lose sleep over it.
Most people here are not interested in games or winning, and it's about trying to figure out how things work. The fun is exploring ideas, and it makes no difference who is who or how much you know. BS is an integral aspect of reality and everybody does it and we point it out to each other in detail. There is a typical BS ratio here, and we all know it already so if you can't handle it and aren't willing to explain the details, shut up about it so you don't waste our time.
And hey, you never said anything about your thoughts about the 800 thousand light year long straight line thing in the Chandra image of Pictor A.
My name is Don, aka donnyboy, space cadet, geek, *** face, news freak, icky, animal, old fart and hey you. I use Sporacle because my fun is searching for the simplest ideas with the widest application and broadcasting them. Hope I maintain identity (redundant) until my brain bails. In my work before I retired if I didn't sign all the stuff I cranked out, I would be in deep trouble. Old habit.
Sporacle
And is it really necessary to end your post by "signing" it with the same pseudonym that you use to post? It's redundant ... ya know?
Looks like when somebody trashes you, the usual procedure is to reply. Pain in the butt, but guess I gotta do one more.
I learned a long time ago that whining never works, including with boss and wife. Gonna keep saying what I think, and if you don't like it, please don't lose sleep over it.
Most people here are not interested in games or winning, and it's about trying to figure out how things work. The fun is exploring ideas, and it makes no difference who is who or how much you know. BS is an integral aspect of reality and everybody does it and we point it out to each other in detail. There is a typical BS ratio here, and we all know it already so if you can't handle it and aren't willing to explain the details, shut up about it so you don't waste our time.
And hey, you never said anything about your thoughts about the 800 thousand light year long straight line thing in the Chandra image of Pictor A.
My name is Don, aka donnyboy, space cadet, geek, *** face, news freak, icky, animal, old fart and hey you. I use Sporacle because my fun is searching for the simplest ideas with the widest application and broadcasting them. Hope I maintain identity (redundant) until my brain bails. In my work before I retired if I didn't sign all the stuff I cranked out, I would be in deep trouble. Old habit.
Sporacle
QUOTE (sporacle+Apr 21 2009, 05:00 AM)
Thanks, Beer w//Straw
Beer is an integrally related part of reality. Like countless other things, usually considered insignificant and ignored in speculations about the big picture. Any theory of everything must account for every detail of everything including beer (and petunias, black holes and Methusela) on all scales and systems without exception. Any theory of everything can be falsified by identifying any entity or process that doesn't fit.
If something is putting out gas on any scale, it's way hard to keep it going on way out there in a straight line. Also really hard to do it with leptons, hadrons and photons. Maybe there is something else in that way long straight whatever it is besides the gas and those x-rays in the Pictor A example. Cosmic jets are neat.
Here comes another strange idea guys, so watch out (not gas and not from beer). Maybe something is taking place at the same time all along the straight "jet" configuration and producing hadrons, electrons, photons, etc in situ. A speculation is that maybe quarks are intergalactic size circular standing waves of precise local configuration (as the activity of a single unlimited entity, and forget the limit of light speed) and linked as hadrons in a spinning black hole (big star). Their collective quark locus describes an intergalactic size torus, and the center of the torus is an axis of quarks perpendicular to the spin of the black hole and could be extremely long.
The quarks continue to randomly recombine toward maximum interrelatedness as hadrons in the black hole, and the hadrons continue to accelerate together (gravity). But at some point in the increasing density, the randomness in the process exceeds the stability of the quark (hadron) interactions, and the quarks disassociate, further disrupting the stability of other hadron interactions nearby. In ordinary terms it goes blooey. Then the configuration of quarks on the axis of the black hole spin is no longer stable and they randomly recombine as hadrons all along the axis, producing high energy leptons and photons. Gravitational energy of the "black hole" is converted to the mass of the "jet".
Don't think to hard about petunias
Cheers
Sporacle
Are you coming on to me?
Beer is an integrally related part of reality. Like countless other things, usually considered insignificant and ignored in speculations about the big picture. Any theory of everything must account for every detail of everything including beer (and petunias, black holes and Methusela) on all scales and systems without exception. Any theory of everything can be falsified by identifying any entity or process that doesn't fit.
If something is putting out gas on any scale, it's way hard to keep it going on way out there in a straight line. Also really hard to do it with leptons, hadrons and photons. Maybe there is something else in that way long straight whatever it is besides the gas and those x-rays in the Pictor A example. Cosmic jets are neat.
Here comes another strange idea guys, so watch out (not gas and not from beer). Maybe something is taking place at the same time all along the straight "jet" configuration and producing hadrons, electrons, photons, etc in situ. A speculation is that maybe quarks are intergalactic size circular standing waves of precise local configuration (as the activity of a single unlimited entity, and forget the limit of light speed) and linked as hadrons in a spinning black hole (big star). Their collective quark locus describes an intergalactic size torus, and the center of the torus is an axis of quarks perpendicular to the spin of the black hole and could be extremely long.
The quarks continue to randomly recombine toward maximum interrelatedness as hadrons in the black hole, and the hadrons continue to accelerate together (gravity). But at some point in the increasing density, the randomness in the process exceeds the stability of the quark (hadron) interactions, and the quarks disassociate, further disrupting the stability of other hadron interactions nearby. In ordinary terms it goes blooey. Then the configuration of quarks on the axis of the black hole spin is no longer stable and they randomly recombine as hadrons all along the axis, producing high energy leptons and photons. Gravitational energy of the "black hole" is converted to the mass of the "jet".
Don't think to hard about petunias
Cheers
Sporacle
Are you coming on to me?
QUOTE (sporacle+Apr 21 2009, 06:47 AM)
And hey, you never said anything about your thoughts about the 800 thousand light year long straight line thing in the Chandra image of Pictor A.
I find the quote feature works best for readers when one only includes the parts to which one is responding.
The last thing I like to see here (as a reader) is someone quote an 300 line original post when they just want to call the originator a dummy.
I've got a fancy ultra fast computer but scrolling is a pain. Great for HALO though.
I find the quote feature works best for readers when one only includes the parts to which one is responding.
The last thing I like to see here (as a reader) is someone quote an 300 line original post when they just want to call the originator a dummy.
I've got a fancy ultra fast computer but scrolling is a pain. Great for HALO though.
QUOTE (sporacle+Apr 21 2009, 03:00 AM)
If something is truly BS it should be really easy to falsify, and a good falsification of an idea is far more helpful for everyone.
Photons are all carried by tiny little pixies which are too small for us to see.
Obviously BS, but if you can falsify that you're a genius.
Think before you post
Photons are all carried by tiny little pixies which are too small for us to see.
Obviously BS, but if you can falsify that you're a genius.
Think before you post
Good thought, but it doesn’t require a genius to falsify BS.
A now retired airline pilot who ferried a most important VIP around sometimes explains (after a couple beers) how airplanes actually fly because of “lifties”, teeny invisible entities not detectable by ordinary means. Forget Bernoulli and Coanda. His model is internally consistent in great detail (and hilarious).
Reality is a unity, an integrally related system, and a BS model is easily demonstrated by comparison with entities outside the system boundaries of the proposed model. Entities that do not fit falsify the system and generally scientists tend to accept this. Another perspective is that a model that is not testable (falsifiable by comparisons) may or may not be BS but is not useful and currently odds are it will eventually be falsified.
It has taken millennia for people to figure out how to falsify models. Truly knowing something requires demonstrating there are no other possibilities in relationships of it` with all entities in an unbounded system. Sorting BS will remain grunt work for a long time.
Spo…
A now retired airline pilot who ferried a most important VIP around sometimes explains (after a couple beers) how airplanes actually fly because of “lifties”, teeny invisible entities not detectable by ordinary means. Forget Bernoulli and Coanda. His model is internally consistent in great detail (and hilarious).
Reality is a unity, an integrally related system, and a BS model is easily demonstrated by comparison with entities outside the system boundaries of the proposed model. Entities that do not fit falsify the system and generally scientists tend to accept this. Another perspective is that a model that is not testable (falsifiable by comparisons) may or may not be BS but is not useful and currently odds are it will eventually be falsified.
It has taken millennia for people to figure out how to falsify models. Truly knowing something requires demonstrating there are no other possibilities in relationships of it` with all entities in an unbounded system. Sorting BS will remain grunt work for a long time.
Spo…
http://scienceblogs.com/mikethemadbiologis...ullsh-t_and.php
It doesn't take a genius to correctly label something as obvious BS. But proving it to be BS to non-experts requires a generous effort of the writer and reader both to communicate that proof.
Which is why for the May Day party I won't feel obligated to convince the award winners that they richly and fully deserve their awards. Details to be announced.
It doesn't take a genius to correctly label something as obvious BS. But proving it to be BS to non-experts requires a generous effort of the writer and reader both to communicate that proof.
Which is why for the May Day party I won't feel obligated to convince the award winners that they richly and fully deserve their awards. Details to be announced.
QUOTE (sporacle+Apr 23 2009, 02:20 AM)
Good thought, but it doesn’t require a genius to falsify BS.
Come on, less BS and more substance; how would you go about falsifying my obviously absurd assertion?
Come on, less BS and more substance; how would you go about falsifying my obviously absurd assertion?
"lifties”, teeny invisible entities not detectable by ordinary means"
Sound suspiciously like anti-gravitons !!
Sound suspiciously like anti-gravitons !!
QUOTE (bm1957+Apr 22 2009, 11:10 AM)
Photons are all carried by tiny little pixies which are too small for us to see.
Obviously BS, but if you can falsify that you're a genius.
Pixies of any type have never been observed (using current scientific method) interacting in any way in systems outside the photon system. The model of non observable pixies carrying photons cannot be falsified. Most people who understand scientific method tend to categorize models that cannot be falsified as BS.
Obviously BS, but if you can falsify that you're a genius.
Pixies of any type have never been observed (using current scientific method) interacting in any way in systems outside the photon system. The model of non observable pixies carrying photons cannot be falsified. Most people who understand scientific method tend to categorize models that cannot be falsified as BS.
QUOTE (Edward 3+Apr 23 2009, 10:53 AM)
"lifties”, teeny invisible entities not detectable by ordinary means"
Sound suspiciously like anti-gravitons !!
There are lots of alternative models nowadays of things that are not understood.
The intention of the experienced pilot describing "lifties" was an internally consistent model of how planes fly that was total BS for entertainment. The fun part was how he got almost all of the details integrally related in his "lifty" system.
Pilots (and their passengers) rely on the details of their understanding of how planes fly. Their understanding is effective but never totally complete. Old pilots understand humility.
Spo
Sound suspiciously like anti-gravitons !!
There are lots of alternative models nowadays of things that are not understood.
The intention of the experienced pilot describing "lifties" was an internally consistent model of how planes fly that was total BS for entertainment. The fun part was how he got almost all of the details integrally related in his "lifty" system.
Pilots (and their passengers) rely on the details of their understanding of how planes fly. Their understanding is effective but never totally complete. Old pilots understand humility.
Spo
bm 1957
"Photons are all carried by nothing but themselves.
Obviously BS, but if you can falsify that you're a genius."
"Photons are all carried by nothing but themselves.
Obviously BS, but if you can falsify that you're a genius."
QUOTE (sporacle+Apr 24 2009, 12:14 AM)
The model of non observable pixies carrying photons cannot be falsified. Most people who understand scientific method tend to categorize models that cannot be falsified as BS.
My point exactly.
So why suggest that falsifying BS would be more helpful than deriding it?
BS does not count as "exploring puzzling questions".
Never really thought it through, did you?
My point exactly.
So why suggest that falsifying BS would be more helpful than deriding it?
BS does not count as "exploring puzzling questions".
QUOTE
There are plenty of serious people here exploring puzzling questions. If something is truly BS it should be really easy to falsify, and a good falsification of an idea is far more helpful for everyone.
Never really thought it through, did you?
QUOTE (bm1957+Apr 24 2009, 11:19 AM)
BS does not count as "exploring puzzling questions".
Does the below qualify as "numerology" or "exploration."?
======================================================================
"What if" the 9D Kissing Number was 306 and the D10 Kissing Number was 504?
======================================================================
Where...
P_x:n = n-th Polygonal Number of side number x
K_n = n-th Kissing Number
T_n = n-th Triangular Number ( = P_3:n)
a = 1, 0, 1, 0, 1, 0, 1, 0... = (1 - (-1)^n)/2
b = 0, 1, 0, 1, 0, 1, 0, 1... = (1 + (-1)^n)/2
m = 1, 1, 2, 2, 3, 3, 4, 4... = sigma_(a) = ((2*n - 1) - (-1)^n)/4
And where...
K_1 = 2
K_2 = 6
K_3 = 12
K_4 = 24
K_5 = 40
K_6 = 72
K_7 = 126
K_8 = 240
K_9 = 306* (Highest known Non-Lattice Kissing Number = 306)
K_10 = 504* (Highest known Kissing Number for D10 = 500)
* hypothetical values
The "KISSING TRIANGLE"
====================================================================================
ROW ---------------------------------------------ROW SUM ----------TRIANGLE SUM
0 -----0002 ---------------------------------------- 0002 -------------- 0002 = 2*T_1
1 -----0006 0012 ---------------------------------- 0018 -------------- 0020 = 2*T_4
2 -----0024 0040 0072 ---------------------------- 0136 -------------- 0156 = 2*T_12
3 -----0126 0240 0306 0504 ---------------------- 1176 -------------- 1332 = 2*T_36
====================================================================================
ROW SUM
----------------------
ROW SUM_0 = (P_4:02)/2 = (P_4:(1*K_1))/2
ROW SUM_1 = (P_4:06)/2 = (P_4:(1*K_2))/2
ROW SUM_2 = (P_3:16)/1 = (P_3:(8*K_1))/1
ROW SUM_3 = (P_3:48)/1 = (P_3:(8*K_2))/1
==========================================
ROW SUM_(n-1) = ((P_(5-m) : ( 8^(m-1)* K_(1+ b ))))/(3-m)
==========================================
TRIANGLE SUM
----------------------
TRIANGLE SUM_0 = 2*(P_3:01) = 2 * 1
TRIANGLE SUM_1 = 2*(P_3:04) = 2 * 10
TRIANGLE SUM_2 = 2*(P_3:12) = 2 * 78
TRIANGLE SUM_3 = 2*(P_3:36) = 2 * 666
==========================================
TRIANGLE SUM_(n-1) = 2*T_(1 + (sigma_(x^2-1))
==========================================
x = some number progression containing the integers (1, 2, 3, 5 )
(i.e. Unity plus Primes, Fibonacci_(n+1), Partition Numbers_(n)...)
Note that:
K_(T_1) = 2... is equal to (1 * 2) = (1 * K_(T_(1) - 0) --- [ROW 0 - Right to Left Edge Value Ratio = 1]
K_(T_2) = 12... is equal to (2 * 6) = (2 * K_(T_(2) - 1) --- [ROW 1 - Right to Left Edge Value Ratio = 2]
K_(T_3) = 72... is equal to (3 * 24) = (3 * K_(T_(3) - 2) --- [ROW 2 - Right to Left Edge Value Ratio = 3]
K_(T_4) = 504*... is equal to (4 * 126) = (4 * K_(T_(4) - 3) --- [ROW 3 - Right to Left Edge Value Ratio = 4]
Also note that:
K_(T_2) * 10 = K_3 * 10 = 5!
K_(T_3) * 10 = K_6 * 10 = 6!
K_(T_4) * 10 = K_10 * 10 = 7!
The next value in the series?
K_(T_5) * 10 = 8!
... If and only if the D15 Kissing Number is 4032.
Related Thread:
Mersenne Primes & The 15d Kissing Number, equal to 4032?
http://www.physforum.com/index.php?showtop...ndpost&p=391847
Best,
Raphie
P.S. Please forgive in advance any typos that may have been made above...
P.P.S. As an afterthought, it occurs to me: There is a symbol to denote "some unknown value." Perhaps I will betray ignorance, but is there an equivalent symbol in mathematics to denote "some unknown progression"? TIA. Best, RF
Does the below qualify as "numerology" or "exploration."?
======================================================================
"What if" the 9D Kissing Number was 306 and the D10 Kissing Number was 504?
======================================================================
Where...
P_x:n = n-th Polygonal Number of side number x
K_n = n-th Kissing Number
T_n = n-th Triangular Number ( = P_3:n)
a = 1, 0, 1, 0, 1, 0, 1, 0... = (1 - (-1)^n)/2
b = 0, 1, 0, 1, 0, 1, 0, 1... = (1 + (-1)^n)/2
m = 1, 1, 2, 2, 3, 3, 4, 4... = sigma_(a) = ((2*n - 1) - (-1)^n)/4
And where...
K_1 = 2
K_2 = 6
K_3 = 12
K_4 = 24
K_5 = 40
K_6 = 72
K_7 = 126
K_8 = 240
K_9 = 306* (Highest known Non-Lattice Kissing Number = 306)
K_10 = 504* (Highest known Kissing Number for D10 = 500)
* hypothetical values
The "KISSING TRIANGLE"
====================================================================================
ROW ---------------------------------------------ROW SUM ----------TRIANGLE SUM
0 -----0002 ---------------------------------------- 0002 -------------- 0002 = 2*T_1
1 -----0006 0012 ---------------------------------- 0018 -------------- 0020 = 2*T_4
2 -----0024 0040 0072 ---------------------------- 0136 -------------- 0156 = 2*T_12
3 -----0126 0240 0306 0504 ---------------------- 1176 -------------- 1332 = 2*T_36
====================================================================================
ROW SUM
----------------------
ROW SUM_0 = (P_4:02)/2 = (P_4:(1*K_1))/2
ROW SUM_1 = (P_4:06)/2 = (P_4:(1*K_2))/2
ROW SUM_2 = (P_3:16)/1 = (P_3:(8*K_1))/1
ROW SUM_3 = (P_3:48)/1 = (P_3:(8*K_2))/1
==========================================
ROW SUM_(n-1) = ((P_(5-m) : ( 8^(m-1)* K_(1+ b ))))/(3-m)
==========================================
TRIANGLE SUM
----------------------
TRIANGLE SUM_0 = 2*(P_3:01) = 2 * 1
TRIANGLE SUM_1 = 2*(P_3:04) = 2 * 10
TRIANGLE SUM_2 = 2*(P_3:12) = 2 * 78
TRIANGLE SUM_3 = 2*(P_3:36) = 2 * 666
==========================================
TRIANGLE SUM_(n-1) = 2*T_(1 + (sigma_(x^2-1))
==========================================
x = some number progression containing the integers (1, 2, 3, 5 )
(i.e. Unity plus Primes, Fibonacci_(n+1), Partition Numbers_(n)...)
Note that:
K_(T_1) = 2... is equal to (1 * 2) = (1 * K_(T_(1) - 0) --- [ROW 0 - Right to Left Edge Value Ratio = 1]
K_(T_2) = 12... is equal to (2 * 6) = (2 * K_(T_(2) - 1) --- [ROW 1 - Right to Left Edge Value Ratio = 2]
K_(T_3) = 72... is equal to (3 * 24) = (3 * K_(T_(3) - 2) --- [ROW 2 - Right to Left Edge Value Ratio = 3]
K_(T_4) = 504*... is equal to (4 * 126) = (4 * K_(T_(4) - 3) --- [ROW 3 - Right to Left Edge Value Ratio = 4]
Also note that:
K_(T_2) * 10 = K_3 * 10 = 5!
K_(T_3) * 10 = K_6 * 10 = 6!
K_(T_4) * 10 = K_10 * 10 = 7!
The next value in the series?
K_(T_5) * 10 = 8!
... If and only if the D15 Kissing Number is 4032.
Related Thread:
Mersenne Primes & The 15d Kissing Number, equal to 4032?
http://www.physforum.com/index.php?showtop...ndpost&p=391847
Best,
Raphie
P.S. Please forgive in advance any typos that may have been made above...
P.P.S. As an afterthought, it occurs to me: There is a symbol to denote "some unknown value." Perhaps I will betray ignorance, but is there an equivalent symbol in mathematics to denote "some unknown progression"? TIA. Best, RF
How many times does this have to be explained to you? Forget calling things "kissing numbers" etc, because you're not doing any mathematics relating to their origin. From your clueless perspective, you have a few short lists of numbers you've found on the internet:
a_1, a_2, a_3, a_4, ... , a_P
b_1, b_2, b_3, b_4, ... , b_Q
c_1, c_2, c_3, c_4, ... , c_R
where P,Q,R are small integers. I have told you, and have even given you proof, that there are infinitely many algebraic relationships between these sets of numbers. As such, it is utterly stupid to identify just 1 or 2 or 1,000,000 different relationships between them and use it to form a conjecture for "the next number in the sequence" game. Do you not get it? I could, right now, produce 1000s of different relationships of the form a[n]= F(b[n],c[n]), and it would mean nothing. Hell, I've already given you an uncountable collection of formulae that match the "next number in the sequence" game!
How can you not understand?
a_1, a_2, a_3, a_4, ... , a_P
b_1, b_2, b_3, b_4, ... , b_Q
c_1, c_2, c_3, c_4, ... , c_R
where P,Q,R are small integers. I have told you, and have even given you proof, that there are infinitely many algebraic relationships between these sets of numbers. As such, it is utterly stupid to identify just 1 or 2 or 1,000,000 different relationships between them and use it to form a conjecture for "the next number in the sequence" game. Do you not get it? I could, right now, produce 1000s of different relationships of the form a[n]= F(b[n],c[n]), and it would mean nothing. Hell, I've already given you an uncountable collection of formulae that match the "next number in the sequence" game!
How can you not understand?
QUOTE (Euler+Apr 25 2009, 09:23 AM)
you're not doing any mathematics relating to their origin...
How can you not understand?
I understand quite well Euler. The entire point over time is to a) demonstrate that there is more than one route to knowledge, or at the very least to valuable hypothesis generation, and b ) imply that the Kissing Numbers are, in their own manner, quite sensible and as rational as Pascal's Triangle.
I need know very little mathematics if this is the case. The key, instead, is to find the right "rule" or heuristic to determine "what number comes next."
To give you an example you may be able to conceptualize a bit better, as I understand you, while not "utterly stupid," to be more than a bit conceptually challenged, I will refer to Pascal's Triangle:
===========================================================
POLYGONAL "NUMBER DNA"
Huh? What on earth has Pascal's Triangle to do with any other Polygon than the triangle?
Well, want to know the maximal number of areas of an n-sided Polygon? Just add up the 3rd, 4th and 5th diagonals in Pascal's Triangle corresponding to the (n-1)-th row. The maximal number of connections between those points? Add up the 2nd and 3rd diagonals. The number of points from which the polygon may be constructed? Add up the 1st and 2nd diagonals. The maximal number of internal vertices? Add up the 4th and 5th diagonals.
In other words, all the "DNA" of any Polygon from the henagon to the circle is contained within those 1st five diagonals.
Now, maybe it helps if you know that those diagonals correspond with, in order,
a) the unity series
b ) the digonal series
c) the triangular series
d) the tetrahedral series
e) the hyper-tetrahedral series
... especially since it then becomes a simple matter to create a formula to derive the information without reference to Pascal's triangle, but it's certainly not necessary to know the underlying mathematics in order to derive the correct answer related to, say, the Pentagon.
=============
ROW 4 = 1 4 6 4 1
=============
p = points = 1 + 4 = 5
i = intersections = 4 + 1 = 5
c = connections = 4 + 6 = 10
a = areas = 6 + 4 + 1 = 11
The sum total?
p + i + c + a = 31
===========================================================
Notice, Euler, I have not done mathematics any more complicated than basic addition, and that 31 total up above is no less valid for it than if I had simply entered the number 4 into the following equation:
1/12 * ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0)
(1 / 12) * ((1 * (4^4)) - (2 * (4^3)) + (11 * (4^2)) + (14 * (4^1)) + (12 * (4^0))) = 31
Now, let's go in reverse:
1/12 ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0)
What on earth has that to do with Pascal's Triangle or anything else!?! There are an INFINITE number of formulas that could generate 31. Quite true.
Just as there an an infinite number of ways to express the following number series in algebraic form:
1, 3, 7, 15, 31, 61, 113, 197, 325, 511 ...
But in reference to p + i + c + a, there is one and only one number progression that applies, however one might formulate it.
The above formula is just one way to do that and it's nothing more than the sum of the first five diagonals of Pascal's triangle * 2 less one, which helps explain why those first five terms, along with the 10th term are all Mersenne Numbers, as the row sum of Pascal's Triangle is always equal to a power of 2.
The point being:
1/12 * ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0) seems like nonsense algebraic chicanery, but it expresses something very rational and geometric. Conversely, summing entries in Pascal's Triangle may seem very simple, but it masks an underlying hidden sophistication.
In terms of Kissing Numbers, I am operating from the premise that Kissing Numbers are far simpler than we are making them out to be. If I am wrong, then so be it. But if I am right, it will be no more a "lucky" guess than Mersenne's list of Mersenne Primes. He was incorrect on many of those guesses. But he was also correct on many of them.
Most importantly, the following list is FALSIFIABLE.
Conjectured Kissing Numbers:
K_10 = 504
K_11 = 660
K_12 = 1056
K_13 = 1378
K_14 = 1764
K_15 = 4032
K_16 = 6480
To disprove these guesses, all you or anyone need do is construct a sphere packing for any of those dimensions with but one more equidistant sphere from the origin...
Best,
Raphie
How can you not understand?
I understand quite well Euler. The entire point over time is to a) demonstrate that there is more than one route to knowledge, or at the very least to valuable hypothesis generation, and b ) imply that the Kissing Numbers are, in their own manner, quite sensible and as rational as Pascal's Triangle.
I need know very little mathematics if this is the case. The key, instead, is to find the right "rule" or heuristic to determine "what number comes next."
To give you an example you may be able to conceptualize a bit better, as I understand you, while not "utterly stupid," to be more than a bit conceptually challenged, I will refer to Pascal's Triangle:
===========================================================
POLYGONAL "NUMBER DNA"
Huh? What on earth has Pascal's Triangle to do with any other Polygon than the triangle?
Well, want to know the maximal number of areas of an n-sided Polygon? Just add up the 3rd, 4th and 5th diagonals in Pascal's Triangle corresponding to the (n-1)-th row. The maximal number of connections between those points? Add up the 2nd and 3rd diagonals. The number of points from which the polygon may be constructed? Add up the 1st and 2nd diagonals. The maximal number of internal vertices? Add up the 4th and 5th diagonals.
In other words, all the "DNA" of any Polygon from the henagon to the circle is contained within those 1st five diagonals.
Now, maybe it helps if you know that those diagonals correspond with, in order,
a) the unity series
b ) the digonal series
c) the triangular series
d) the tetrahedral series
e) the hyper-tetrahedral series
... especially since it then becomes a simple matter to create a formula to derive the information without reference to Pascal's triangle, but it's certainly not necessary to know the underlying mathematics in order to derive the correct answer related to, say, the Pentagon.
=============
ROW 4 = 1 4 6 4 1
=============
p = points = 1 + 4 = 5
i = intersections = 4 + 1 = 5
c = connections = 4 + 6 = 10
a = areas = 6 + 4 + 1 = 11
The sum total?
p + i + c + a = 31
===========================================================
Notice, Euler, I have not done mathematics any more complicated than basic addition, and that 31 total up above is no less valid for it than if I had simply entered the number 4 into the following equation:
1/12 * ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0)
(1 / 12) * ((1 * (4^4)) - (2 * (4^3)) + (11 * (4^2)) + (14 * (4^1)) + (12 * (4^0))) = 31
Now, let's go in reverse:
1/12 ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0)
What on earth has that to do with Pascal's Triangle or anything else!?! There are an INFINITE number of formulas that could generate 31. Quite true.
Just as there an an infinite number of ways to express the following number series in algebraic form:
1, 3, 7, 15, 31, 61, 113, 197, 325, 511 ...
But in reference to p + i + c + a, there is one and only one number progression that applies, however one might formulate it.
The above formula is just one way to do that and it's nothing more than the sum of the first five diagonals of Pascal's triangle * 2 less one, which helps explain why those first five terms, along with the 10th term are all Mersenne Numbers, as the row sum of Pascal's Triangle is always equal to a power of 2.
The point being:
1/12 * ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0) seems like nonsense algebraic chicanery, but it expresses something very rational and geometric. Conversely, summing entries in Pascal's Triangle may seem very simple, but it masks an underlying hidden sophistication.
In terms of Kissing Numbers, I am operating from the premise that Kissing Numbers are far simpler than we are making them out to be. If I am wrong, then so be it. But if I am right, it will be no more a "lucky" guess than Mersenne's list of Mersenne Primes. He was incorrect on many of those guesses. But he was also correct on many of them.
Most importantly, the following list is FALSIFIABLE.
Conjectured Kissing Numbers:
K_10 = 504
K_11 = 660
K_12 = 1056
K_13 = 1378
K_14 = 1764
K_15 = 4032
K_16 = 6480
To disprove these guesses, all you or anyone need do is construct a sphere packing for any of those dimensions with but one more equidistant sphere from the origin...
Best,
Raphie
QUOTE (Raphie Frank+Apr 25 2009, 05:32 PM)
The key, instead, is to find the right "rule" or heuristic to determine "what number comes next."
How can anyone be this stupid? How can you not get this? There are infinitely many rules which match your sequences. Get that? In addition, there are infinitely many relationships which you can construct between these small sets of integers.
I have tried to explain this in to you in very simple terms. I honestly don't see how a human being could be incapable of understanding what I've pointed out to you. What is it you don't understand?
How can anyone be this stupid? How can you not get this? There are infinitely many rules which match your sequences. Get that? In addition, there are infinitely many relationships which you can construct between these small sets of integers.
I have tried to explain this in to you in very simple terms. I honestly don't see how a human being could be incapable of understanding what I've pointed out to you. What is it you don't understand?
Euler, do you think it a "coincidence" that for dimensions 0, 1, 2, 3, 6 and 8 the following constructions apply for Kissing Numbers?
CASE A
========
BASE 3
9^n - 3^n
========
. = 0 = K_0
20 = 6 = K_2
2200 = 72 = K_6
222000 = 702
22220000 = 6480 = K_16*
* Hypothetical Value
CASE B
========
BASE 2
4^n - 2^n
========
. = 0 = K_0
10 = 2 = K_1
1100 = 12 = K_3
111000 = 56
11110000 = 240 = K_6
Do you furthermore believe it a "coincidence" that the partial sums of those dimensions add to...
0, 1, 3, 6, 12, 20
that when multiplied by 2 equal...
0, 2, 6, 12, 24, 40
In order, the 0th, 1st, 2nd, 3rd, 4th and 5th Kissing Numbers?
[Note: If 6480 is the D-16 Kissing Number, 0, 1, 3, 6, 12, 20 would become 0, 1, 3, 6, 12, 20, 36 that when multiplied by 2 equal 0, 2, 6, 12, 24, 40, 72, the 0th, 1st, 2nd, 3rd, 4th, 5th and 6th Kissing Numbers]
Do you furthermore believe it a "coincidence that all remaining known Kissing Numbers that are twice a triangular number follow the form:
CASE C
========
BASE 2
4^n + 2^n
========
10 = 2 = K_1
110 = 6 = K_2
10100 = 20
1001000 = 72 = K_6
100010000 = 272 = K_9 (lattice construction)
10000100000 = 1056 = K_12*
* Hypothetical Value
Well, I do not not believe it to be a coincidence and so I am not running through "infinite fields" of possibility. If, of course, this IS coincidence, then I am most surely wasting my time...
Incidentally, Euler, the "Case B" Construction ties in directly with Geometry in a very simple, and I believe, elegant manner. All numbers of that form are equal to the Perimeter of a Primitive Triangle with edge lengths:
a = 2^n - 1
b = ((2^n - 1)^2 - 1)/2
c = ((2^n - 1)^2 + 1)/2
a^2 + b^2 = c^2
The area of such a Triangle is 6* the (n-1)/2 Sum of Squares
Surely, one would be stretching the limits of credulity to suggest that the Pythagorean Theorem has anything to do in any manner whatsoever with Kissing Numbers...
Best,
Raphie
CASE A
========
BASE 3
9^n - 3^n
========
. = 0 = K_0
20 = 6 = K_2
2200 = 72 = K_6
222000 = 702
22220000 = 6480 = K_16*
* Hypothetical Value
CASE B
========
BASE 2
4^n - 2^n
========
. = 0 = K_0
10 = 2 = K_1
1100 = 12 = K_3
111000 = 56
11110000 = 240 = K_6
Do you furthermore believe it a "coincidence" that the partial sums of those dimensions add to...
0, 1, 3, 6, 12, 20
that when multiplied by 2 equal...
0, 2, 6, 12, 24, 40
In order, the 0th, 1st, 2nd, 3rd, 4th and 5th Kissing Numbers?
[Note: If 6480 is the D-16 Kissing Number, 0, 1, 3, 6, 12, 20 would become 0, 1, 3, 6, 12, 20, 36 that when multiplied by 2 equal 0, 2, 6, 12, 24, 40, 72, the 0th, 1st, 2nd, 3rd, 4th, 5th and 6th Kissing Numbers]
Do you furthermore believe it a "coincidence that all remaining known Kissing Numbers that are twice a triangular number follow the form:
CASE C
========
BASE 2
4^n + 2^n
========
10 = 2 = K_1
110 = 6 = K_2
10100 = 20
1001000 = 72 = K_6
100010000 = 272 = K_9 (lattice construction)
10000100000 = 1056 = K_12*
* Hypothetical Value
Well, I do not not believe it to be a coincidence and so I am not running through "infinite fields" of possibility. If, of course, this IS coincidence, then I am most surely wasting my time...
Incidentally, Euler, the "Case B" Construction ties in directly with Geometry in a very simple, and I believe, elegant manner. All numbers of that form are equal to the Perimeter of a Primitive Triangle with edge lengths:
a = 2^n - 1
b = ((2^n - 1)^2 - 1)/2
c = ((2^n - 1)^2 + 1)/2
a^2 + b^2 = c^2
The area of such a Triangle is 6* the (n-1)/2 Sum of Squares
Surely, one would be stretching the limits of credulity to suggest that the Pythagorean Theorem has anything to do in any manner whatsoever with Kissing Numbers...
Best,
Raphie
Oh for the love of God! How can anyone be so utterly inept.
Do you not understand that there are infinitely many "next numbers"? How can you not get this? In addition, there are infinitely many "relationships" between the first X,Y,Z of the collection of numbers you're randomly looking at.
How can you not get this? If someone is reading my posts and would be good enough to point out which point is unclear, please speak up.
Do you not understand that there are infinitely many "next numbers"? How can you not get this? In addition, there are infinitely many "relationships" between the first X,Y,Z of the collection of numbers you're randomly looking at.
How can you not get this? If someone is reading my posts and would be good enough to point out which point is unclear, please speak up.
QUOTE (Euler+Apr 25 2009, 08:17 PM)
Do you not understand that there are infinitely many "next numbers"?
You are absolutely correct there are an infinite number of possible next numbers. Exactly why heuristics can be useful. They can help provide guidance as to where to look within that infinity.
You are absolutely correct there are an infinite number of possible next numbers. Exactly why heuristics can be useful. They can help provide guidance as to where to look within that infinity.
QUOTE (Euler+Apr 25 2009, 08:17 PM)
Oh for the love of God! How can anyone be so utterly inept.
Do you not understand that there are infinitely many "next numbers"? How can you not get this? In addition, there are infinitely many "relationships" between the first X,Y,Z of the collection of numbers you're randomly looking at.
How can you not get this? If someone is reading my posts and would be good enough to point out which point is unclear, please speak up.
That would presuppose that someone was reading Raphie's posts as well.
Do you not understand that there are infinitely many "next numbers"? How can you not get this? In addition, there are infinitely many "relationships" between the first X,Y,Z of the collection of numbers you're randomly looking at.
How can you not get this? If someone is reading my posts and would be good enough to point out which point is unclear, please speak up.
That would presuppose that someone was reading Raphie's posts as well.
QUOTE (Raphie Frank+Apr 25 2009, 08:24 PM)
You are absolutely correct there are an infinite number of possible next numbers. Exactly why heuristics can be useful. They can help provide guidance as to where to look within that infinity,
Are you joking? This is insane - how can you not understand this? Give me any collection of numbers, whether they're the first 100 primes, the first 1,058 perfect numbers, the first 18,928 numbers that pop up in Pascal's triangle, the first 1,000,001 numbers that randomly fall into your tiny head - I can construct infinitely many relationships between each of these sets of numbers, and the set of numbers you are considering.
For instance, you've mentioned triangular numbers. There are infinitely many relationships between the first X of these numbers, and the first Y Kissing numbers. I can write down, in a matter of minutes, an infinite collection of such relationships, as I've already shown you.
What don't you understand?
Are you joking? This is insane - how can you not understand this? Give me any collection of numbers, whether they're the first 100 primes, the first 1,058 perfect numbers, the first 18,928 numbers that pop up in Pascal's triangle, the first 1,000,001 numbers that randomly fall into your tiny head - I can construct infinitely many relationships between each of these sets of numbers, and the set of numbers you are considering.
For instance, you've mentioned triangular numbers. There are infinitely many relationships between the first X of these numbers, and the first Y Kissing numbers. I can write down, in a matter of minutes, an infinite collection of such relationships, as I've already shown you.
What don't you understand?
QUOTE (Raphie Frank+Apr 25 2009, 09:24 PM)
You are absolutely correct there are an infinite number of possible next numbers. Exactly why heuristics can be useful. They can help provide guidance as to where to look within that infinity.
You are trying to claim that there's some sequences which are 'better' than others, that you're led to them via heuristics. Heuristics is you simply looking for familiar or simplistic patterns. There's no 'better' or 'worse' sequences. 1,2,4,8,15 is not 'worse' than 1,2,4,8,16, it's just a less simplistic pattern.
Saying "Oh I think the next number in the sequence is 45 because....." is completely pointless because you can provide a reason for ANY number.
Saying "Let's look at it heuristically" implies the pattern is more likely to be a simplistic one or one which is close to familiar patterns. Why? Plenty of things in maths have turned out to be horrifically unpleasant and unfamiliar and unlike anything else.
Now if you were saying "I've got 10 numbers and I want the simplest formula to generate each of them" and you rigorously defined what you mean by 'simplest' (such as lowest order polynomial) then perhaps a bit of intuition would help rather than applying some brute force algorithm to the problem but that's different from what you're doing. You're not doing anything more than just listing two lots of half a dozen numbers and then going "Oh look, a coincidence". There's dozens, if not hundreds, of 'well known formulae' like triangular numbers, squares, primes, Fibonacci, etc. Sloane's list is enormous, so the probability of finding a formula or combination of formula which relate 2 sets of 6 numbers less than 100 is pretty high.
You're engaging in pointless navel gazing. Rather than doing actual number theory or working with formula, not short lists of small numbers, you just waste time going "Wow, isn't 1,2,4,8 amazingly like 2,4,6,8, do powers of 2 related to even numbers?!".
Now if you want to do something useful with Kissing numbers showing there's a lower bound on K(n) as a function of n is very useful. Postulating a list based on nothing more than "I think I saw this pattern" is worthless. If its falsified you just pick another pattern you thought you saw. Then another and another. You achieve nothing. A correct guess is worthless because its impossible to show it's right. Justification, proof, rigour. They are the fundamental, essential, critical foundation and cornerstone of maths. If you can't justify your answer with something then you might as well have just used a random number generator. You said "All anyone needs to do to disprove this....". NO. That is NOT how maths works. You aren't 'right until proven wrong'. You're assumed wrong until proven right. Except with the very very very VERY hardest problems like the Riemann hypothesis noone will build on your results if you can't prove it, because it's building on a house without foundations. It's a worthless mathematician who says "Well prove me wrong".
You are trying to claim that there's some sequences which are 'better' than others, that you're led to them via heuristics. Heuristics is you simply looking for familiar or simplistic patterns. There's no 'better' or 'worse' sequences. 1,2,4,8,15 is not 'worse' than 1,2,4,8,16, it's just a less simplistic pattern.
Saying "Oh I think the next number in the sequence is 45 because....." is completely pointless because you can provide a reason for ANY number.
Saying "Let's look at it heuristically" implies the pattern is more likely to be a simplistic one or one which is close to familiar patterns. Why? Plenty of things in maths have turned out to be horrifically unpleasant and unfamiliar and unlike anything else.
Now if you were saying "I've got 10 numbers and I want the simplest formula to generate each of them" and you rigorously defined what you mean by 'simplest' (such as lowest order polynomial) then perhaps a bit of intuition would help rather than applying some brute force algorithm to the problem but that's different from what you're doing. You're not doing anything more than just listing two lots of half a dozen numbers and then going "Oh look, a coincidence". There's dozens, if not hundreds, of 'well known formulae' like triangular numbers, squares, primes, Fibonacci, etc. Sloane's list is enormous, so the probability of finding a formula or combination of formula which relate 2 sets of 6 numbers less than 100 is pretty high.
You're engaging in pointless navel gazing. Rather than doing actual number theory or working with formula, not short lists of small numbers, you just waste time going "Wow, isn't 1,2,4,8 amazingly like 2,4,6,8, do powers of 2 related to even numbers?!".
Now if you want to do something useful with Kissing numbers showing there's a lower bound on K(n) as a function of n is very useful. Postulating a list based on nothing more than "I think I saw this pattern" is worthless. If its falsified you just pick another pattern you thought you saw. Then another and another. You achieve nothing. A correct guess is worthless because its impossible to show it's right. Justification, proof, rigour. They are the fundamental, essential, critical foundation and cornerstone of maths. If you can't justify your answer with something then you might as well have just used a random number generator. You said "All anyone needs to do to disprove this....". NO. That is NOT how maths works. You aren't 'right until proven wrong'. You're assumed wrong until proven right. Except with the very very very VERY hardest problems like the Riemann hypothesis noone will build on your results if you can't prove it, because it's building on a house without foundations. It's a worthless mathematician who says "Well prove me wrong".
The inevitable typo correction(s)...
CASE B
========
BASE 2
4^n - 2^n
========
. = 0 = K_0
10 = 2 = K_1
1100 = 12 = K_3
111000 = 56
11110000 = 240 = K_6
The above should have read...
CASE B
========
BASE 2
4^n - 2^n
========
. = 0 = K_0
10 = 2 = K_1
1100 = 12 = K_3
111000 = 56
11110000 = 240 = K_8
8 replaces 6 on the last line...
Also...
"Well, want to know the maximal number of areas of an n-sided Polygon?"
... should have read...
"Well, want to know the maximal number of areas created by connecting all the edges and diagonals of an n-sided Polygon?"
Best,
Raphie
P.S. Alphanumeric, I appreciated your critique, as much as I may not agree with it. I will give it some thought before responding.
QUOTE (Raphie Frank+Apr 25 2009, 08:09 PM)
CASE B
========
BASE 2
4^n - 2^n
========
. = 0 = K_0
10 = 2 = K_1
1100 = 12 = K_3
111000 = 56
11110000 = 240 = K_6
The above should have read...
CASE B
========
BASE 2
4^n - 2^n
========
. = 0 = K_0
10 = 2 = K_1
1100 = 12 = K_3
111000 = 56
11110000 = 240 = K_8
8 replaces 6 on the last line...
Also...
"Well, want to know the maximal number of areas of an n-sided Polygon?"
... should have read...
"Well, want to know the maximal number of areas created by connecting all the edges and diagonals of an n-sided Polygon?"
Best,
Raphie
P.S. Alphanumeric, I appreciated your critique, as much as I may not agree with it. I will give it some thought before responding.
Hi Raphie
When Monstrous Moonshine hypothesis appeared it was based on numerology within special field of knowledge.
Any usage of differential equations of the same type for different phenomena is numerology just of slightly different type, more complicated ( or so it is made to look).
Consider someone saying : to calculate this and that we will start with diff equation for similar system and than perturb it a bit and see what happens.
That is pure numerology, although sophisticated one as it does presume some understanding of underlaying process but it DOES not presume knowledge about the underlaying process as then perturbations would not be needed.
When Monstrous Moonshine hypothesis appeared it was based on numerology within special field of knowledge.
Any usage of differential equations of the same type for different phenomena is numerology just of slightly different type, more complicated ( or so it is made to look).
Consider someone saying : to calculate this and that we will start with diff equation for similar system and than perturb it a bit and see what happens.
That is pure numerology, although sophisticated one as it does presume some understanding of underlaying process but it DOES not presume knowledge about the underlaying process as then perturbations would not be needed.
QUOTE (Ivars+Apr 30 2009, 09:40 AM)
When Monstrous Moonshine hypothesis appeared it was based on numerology within special field of knowledge.
Hi Ivars,
Although I disagree with your use of the term "numerology," you are absolutely correct that Monster Moonshine was discovered because serious, open-minded mathematicians noted a series of numerical coincidences that they recognized as unlikely to be mere coincidence and investigated further.
[Paragraph break added for clarity]
=============================================================
MOONSHINE
from the website of Mark Ronan
The original moonshine observation was made by John McKay. He knew that the first non-trivial dimension in which the Monster might operate was 196,883, and was astonished to find 196,884 appearing in a quite different branch of mathematics, as the first in a sequence of numbers expressing an important formula in number theory. This had to be more than a chance coincidence, and McKay wrote to John Thompson, who then found further numerical evidence, and was convinced something mysterious was going on.
Thompson communicated his observations to John Conway who had complete data on the Monster at the Cambridge mathematics department. It appeared that the numbers in the sequence — which were coefficients in a formula for something called the j?function — were related to dimensions in which the Monster could operate, and in a 1979 paper they called Monstrous Moonshine, Conway and Simon Norton proved there was a relationship, though no-one quite understood why.
http://www.math.uic.edu/~ronan/moonshine
=============================================================
Apparently, some mathematicians are not against the "evidentiary" approach as a first step to something that can then be later proved.
Interestingly, it was while reading the book "Symmetry and the Monster," written by Mark Ronan and excerpted above ( http://www.math.uic.edu/~ronan/symmetryandthemonster), that I noted that 196560, the D_24 Kissing Number, divided by its dimension number equals 8190, the 5th Mersenne Prime less 1. Finding this odd, given that I was specifically interested in possible relationships between the number 8191 and 24 [btw, 8191 also equals DIVISOR SUM (sqrt 2)^24 + 1], I looked further and noted that the following relationship holds for dimensions 0, 1, 4 and 8, as well as 24:
Let...
K_x = the x-th Kissing Number
Z_n = Unity + the Mersenne Primes
d# = Dimension Number
x = d#
Then, for n = 0, 1, 2, 3, 5
K_d# = d# * (Z_n - 1)
0 * (1 - 1) = 0 = K_0
1 * (3 - 1) = 2 = K_1
4 * (7 - 1) = 24 = K_4
8 * (31 - 1) = 240 = K_8
24 * (8191 - 1) = 196560 = K_24
I do not personally believe this numerical relationship between Mersenne Primes and Kissing Numbers to be mere coincidence.
Only one of the first five Mersenne Primes, 127, is excluded (but would not be if 1764 were found to be the 14-Dimensional Kissing Number), and with the exception of 0, those dimension numbers are generated very simply by the equation 2^(n-1) + 2*(n-1) for n = 1, 2, 3, 5. Furthermore, those specific Dimensions are not just trivial dimensions. While I understand it to be a "cardinal sin" to cite Wikipedia, nevertheless Dimensions 1, 8 and 24 are considered at least by some, to be the three most important examples of Unimodular Lattices, while Dimension 4 is associated with the 24-cell.
Unimodular Lattice
http://en.wikipedia.org/wiki/Unimodular_lattice
24-cell
http://en.wikipedia.org/wiki/24-cell
Rather ironically, given some of the critiques positing that that I am only working with "small numbers," my explorations into Kissing Numbers began with the largest known one of all, 196560, associated with the number of vertices in the Leech Lattice. To offer a bit of perspective, while 196560 may be a small number in Universal terms, 196560 days ago, Columbus had not even yet sailed the ocean blue and most people still thought the world flat.
Best,
Raphie
Hi Ivars,
Although I disagree with your use of the term "numerology," you are absolutely correct that Monster Moonshine was discovered because serious, open-minded mathematicians noted a series of numerical coincidences that they recognized as unlikely to be mere coincidence and investigated further.
[Paragraph break added for clarity]
=============================================================
MOONSHINE
from the website of Mark Ronan
The original moonshine observation was made by John McKay. He knew that the first non-trivial dimension in which the Monster might operate was 196,883, and was astonished to find 196,884 appearing in a quite different branch of mathematics, as the first in a sequence of numbers expressing an important formula in number theory. This had to be more than a chance coincidence, and McKay wrote to John Thompson, who then found further numerical evidence, and was convinced something mysterious was going on.
Thompson communicated his observations to John Conway who had complete data on the Monster at the Cambridge mathematics department. It appeared that the numbers in the sequence — which were coefficients in a formula for something called the j?function — were related to dimensions in which the Monster could operate, and in a 1979 paper they called Monstrous Moonshine, Conway and Simon Norton proved there was a relationship, though no-one quite understood why.
http://www.math.uic.edu/~ronan/moonshine
=============================================================
Apparently, some mathematicians are not against the "evidentiary" approach as a first step to something that can then be later proved.
Interestingly, it was while reading the book "Symmetry and the Monster," written by Mark Ronan and excerpted above ( http://www.math.uic.edu/~ronan/symmetryandthemonster), that I noted that 196560, the D_24 Kissing Number, divided by its dimension number equals 8190, the 5th Mersenne Prime less 1. Finding this odd, given that I was specifically interested in possible relationships between the number 8191 and 24 [btw, 8191 also equals DIVISOR SUM (sqrt 2)^24 + 1], I looked further and noted that the following relationship holds for dimensions 0, 1, 4 and 8, as well as 24:
Let...
K_x = the x-th Kissing Number
Z_n = Unity + the Mersenne Primes
d# = Dimension Number
x = d#
Then, for n = 0, 1, 2, 3, 5
K_d# = d# * (Z_n - 1)
0 * (1 - 1) = 0 = K_0
1 * (3 - 1) = 2 = K_1
4 * (7 - 1) = 24 = K_4
8 * (31 - 1) = 240 = K_8
24 * (8191 - 1) = 196560 = K_24
I do not personally believe this numerical relationship between Mersenne Primes and Kissing Numbers to be mere coincidence.
Only one of the first five Mersenne Primes, 127, is excluded (but would not be if 1764 were found to be the 14-Dimensional Kissing Number), and with the exception of 0, those dimension numbers are generated very simply by the equation 2^(n-1) + 2*(n-1) for n = 1, 2, 3, 5. Furthermore, those specific Dimensions are not just trivial dimensions. While I understand it to be a "cardinal sin" to cite Wikipedia, nevertheless Dimensions 1, 8 and 24 are considered at least by some, to be the three most important examples of Unimodular Lattices, while Dimension 4 is associated with the 24-cell.
Unimodular Lattice
http://en.wikipedia.org/wiki/Unimodular_lattice
24-cell
http://en.wikipedia.org/wiki/24-cell
Rather ironically, given some of the critiques positing that that I am only working with "small numbers," my explorations into Kissing Numbers began with the largest known one of all, 196560, associated with the number of vertices in the Leech Lattice. To offer a bit of perspective, while 196560 may be a small number in Universal terms, 196560 days ago, Columbus had not even yet sailed the ocean blue and most people still thought the world flat.
Best,
Raphie
I cannot believe you still don't get this. You are staggeringly stupid - congratulations.
When did Raphie Frank stop believing in K_2 ?
Why does Raphie Frank ignore the existence of K_5 ?
Why does Raphie Frank ignore the existence of K_5 ?
QUOTE (rpenner+May 3 2009, 09:53 AM)
When did Raphie Frank stop believing in K_2 ?
Why does Raphie Frank ignore the existence of K_5 ?
The values of K_2 and K_5, RPenner, along with those for K_0 and K_7 are Pentagonal Pyramid numbers (1/2 (n^3 + n^2)). Only a "staggeringly stupid" "ignoramus" (other posters' words, not mine...) would expect them to fit into any framings geared towards twice Triangular numbers (n^2 + n), a bill which fits dimensions 0,1,2,3,6,8 and 9.
In fact, all known Kissing Numbers, with some overlap, fit into one of three categories:
A ) The Pentagonal Pyramid Set [0,2,5,7]
B ) The Double Triangle Set [0,1,2,3,6,8,9]
C ) The Ramanujan-Nagell Set [0,1,4,8,24]*
* associated with the Ramanujan-Nagell Triangular Numbers 0, 1, 3, 15, 4095
Gosh golly forbid, one might suggest that "Kissing Spaces" have anything to do with Geometry or Polygonal Numbers...
Bottom line in case you missed it:
I quite believe in K_2 and K_5
Best Regards,
Raphie
P.S. It "accidentally" so happens that the first 8 values for:
floor ({Unity + Mersenne Prime Exponents] - 1) /2)
are...
0, 0, 1, 2, 3, 6, 8, 9
... which also happen to be the complete set of dimension numbers for Kissing Numbers that are twice a Triangular Number. Considering those dimension numbers are not only presumably quite "random," but were also stumbled upon quite "randomly," I would imagine a responsible scientist would at the very least raise an eyebrow. The imagination, alas, is quite undependable...
Why does Raphie Frank ignore the existence of K_5 ?
The values of K_2 and K_5, RPenner, along with those for K_0 and K_7 are Pentagonal Pyramid numbers (1/2 (n^3 + n^2)). Only a "staggeringly stupid" "ignoramus" (other posters' words, not mine...) would expect them to fit into any framings geared towards twice Triangular numbers (n^2 + n), a bill which fits dimensions 0,1,2,3,6,8 and 9.
In fact, all known Kissing Numbers, with some overlap, fit into one of three categories:
A ) The Pentagonal Pyramid Set [0,2,5,7]
B ) The Double Triangle Set [0,1,2,3,6,8,9]
C ) The Ramanujan-Nagell Set [0,1,4,8,24]*
* associated with the Ramanujan-Nagell Triangular Numbers 0, 1, 3, 15, 4095
Gosh golly forbid, one might suggest that "Kissing Spaces" have anything to do with Geometry or Polygonal Numbers...
Bottom line in case you missed it:
I quite believe in K_2 and K_5
Best Regards,
Raphie
P.S. It "accidentally" so happens that the first 8 values for:
floor ({Unity + Mersenne Prime Exponents] - 1) /2)
are...
0, 0, 1, 2, 3, 6, 8, 9
... which also happen to be the complete set of dimension numbers for Kissing Numbers that are twice a Triangular Number. Considering those dimension numbers are not only presumably quite "random," but were also stumbled upon quite "randomly," I would imagine a responsible scientist would at the very least raise an eyebrow. The imagination, alas, is quite undependable...
QUOTE (Euler+May 3 2009, 09:24 AM)
I cannot believe you still don't get this. You are staggeringly stupid - congratulations.
Congratulate me, Euler, after I take the GRE's again and improve upon the the rather embarrassing 720 I scored in mathematics this past October. I would have hoped at the very least least to match the 740 I received on my SAT's 25 years ago. But, c'est la vie, fate favors not the "staggeringly stupid."
Best,
Raphie
Congratulate me, Euler, after I take the GRE's again and improve upon the the rather embarrassing 720 I scored in mathematics this past October. I would have hoped at the very least least to match the 740 I received on my SAT's 25 years ago. But, c'est la vie, fate favors not the "staggeringly stupid."
Best,
Raphie
It's not even in question - you are a staggeringly stupid person who has been unable to understand the umpteen explanations given to you.
Anywho - I'll bite. Let's see you in action.
Anywho - I'll bite. Let's see you in action.
What a surprise...
Still nothing...
QUOTE (Euler+May 15 2009, 11:05 PM)
Still nothing...
Euler, I have nothing to prove to you. So, yes... of course "nothing."
Euler, I have nothing to prove to you. So, yes... of course "nothing."
So just to make the situation clear: you have claimed:
In fact, all known Kissing Numbers, with some overlap, fit into one of three categories:
A ) The Pentagonal Pyramid Set [0,2,5,7]
B ) The Double Triangle Set [0,1,2,3,6,8,9]
C ) The Ramanujan-Nagell Set [0,1,4,8,24]*
* associated with the Ramanujan-Nagell Triangular Numbers 0, 1, 3, 15, 4095
Gosh golly forbid, one might suggest that "Kissing Spaces" have anything to do with Geometry or Polygonal Numbers...
In the interests of accuracy...
"A ) The Pentagonal Pyramid Set [0,2,5,7]"
should have read...
"A ) The Pentagonal Pyramid Set [4,1,0,0,2,5,7]"
At the time of the prior posting, I had neglected to include negative numbers (or a floating point zero). Where T_n = Triangular Number ((n^2 + n)/2), and K_n = Kissing Number...
|-4* T__-4| = 024 = K_4
|-2* T__-2| = 002 = K_1
|-0* T__-0| = 000 = K_0
|+0* T__+0| = 000 = K_0
|+2* T__+2| = 006 = K_2
|+4* T__+4| = 040 = K_5
|+6* T__+6| = 126 = K_7
The dimensions of those Kissing Numbers, incidentally, are, in order, quite easy to derive, based on Number Progressions previously posted to this forum. But I won't spoil the fun, as I am quite "certain" one quick search upon OEIS will reveal all, at least as certain posters upon this thread would have you believe...
Search OEIS for 4, 1, 0, 0, 2, 5, 7
Best,
Raphie
P.S. @ Alphanumeric. Please note how short, length-wise, the above number sequence is and how small the value of the terms. Also, please do consider my posts to Ivars, Rpenner and now, this one, to be background for a response to your eminently reasonable, but I believed yet flawed, critique some time back... Best, RF
P.P.S. Pentagonal Pyramid Numbers follow the form (n^3 + n^2)/2. Alternatively, they can also be conceived of as Polygonal Numbers "slicing" though through the "Polygonal Number Field" at a 45 degree pitch... e.g. 0 = P_4:0; 1 = P_5:1; 6 = P_6:2; 18 = P_7:3; 40 = P_8:4, etc.
QUOTE (Raphie Frank+May 13 2009, 09:31 AM)
...after I take the GRE's again and improve upon the the rather embarrassing 720 I scored in mathematics this past October...
And yet, when presented with such a test, you're unwilling to demonstrate any level of competency.
Like I said, you're an idiot. This latest episode just indicates you're dishonest.
And yet, when presented with such a test, you're unwilling to demonstrate any level of competency.
Like I said, you're an idiot. This latest episode just indicates you're dishonest.
QUOTE (Raphie Frank+May 13 2009, 08:40 AM)
In fact, all known Kissing Numbers, with some overlap, fit into one of three categories:
A ) The Pentagonal Pyramid Set [0,2,5,7]
B ) The Double Triangle Set [0,1,2,3,6,8,9]
C ) The Ramanujan-Nagell Set [0,1,4,8,24]*
* associated with the Ramanujan-Nagell Triangular Numbers 0, 1, 3, 15, 4095
Gosh golly forbid, one might suggest that "Kissing Spaces" have anything to do with Geometry or Polygonal Numbers...
In the interests of accuracy...
"A ) The Pentagonal Pyramid Set [0,2,5,7]"
should have read...
"A ) The Pentagonal Pyramid Set [4,1,0,0,2,5,7]"
At the time of the prior posting, I had neglected to include negative numbers (or a floating point zero). Where T_n = Triangular Number ((n^2 + n)/2), and K_n = Kissing Number...
|-4* T__-4| = 024 = K_4
|-2* T__-2| = 002 = K_1
|-0* T__-0| = 000 = K_0
|+0* T__+0| = 000 = K_0
|+2* T__+2| = 006 = K_2
|+4* T__+4| = 040 = K_5
|+6* T__+6| = 126 = K_7
The dimensions of those Kissing Numbers, incidentally, are, in order, quite easy to derive, based on Number Progressions previously posted to this forum. But I won't spoil the fun, as I am quite "certain" one quick search upon OEIS will reveal all, at least as certain posters upon this thread would have you believe...
Search OEIS for 4, 1, 0, 0, 2, 5, 7
Best,
Raphie
P.S. @ Alphanumeric. Please note how short, length-wise, the above number sequence is and how small the value of the terms. Also, please do consider my posts to Ivars, Rpenner and now, this one, to be background for a response to your eminently reasonable, but I believed yet flawed, critique some time back... Best, RF
P.P.S. Pentagonal Pyramid Numbers follow the form (n^3 + n^2)/2. Alternatively, they can also be conceived of as Polygonal Numbers "slicing" though through the "Polygonal Number Field" at a 45 degree pitch... e.g. 0 = P_4:0; 1 = P_5:1; 6 = P_6:2; 18 = P_7:3; 40 = P_8:4, etc.
Hmmm... Raphie...
Speaking of numerology I think Euler has your number.
Anywho - I'll bite. Let's see you in action.
This does indeed weaken your boast to the level of a facile lie.
Numerology was quite an important folklore in the Middle Ages and it is something I know quite a bit about... however it has little to do with what you are doing now, which is nothing other than navel gazing.
Speaking of numerology I think Euler has your number.
QUOTE
after I take the GRE's again and improve upon the the rather embarrassing 720 I scored in mathematics this past October...
QUOTE (->
| QUOTE |
| after I take the GRE's again and improve upon the the rather embarrassing 720 I scored in mathematics this past October... |
Anywho - I'll bite. Let's see you in action.
This does indeed weaken your boast to the level of a facile lie.
Numerology was quite an important folklore in the Middle Ages and it is something I know quite a bit about... however it has little to do with what you are doing now, which is nothing other than navel gazing.
OFF-TOPIC
QUOTE (RobDegraves+Jun 17 2009, 06:21 AM)
This does indeed weaken your boast to the level of a facile lie.
RPenner has the means (as of about a week ago), by private email, to begin the process of confirmation or not. In the meantime, I will ask you kindly to refrain from unintentional libel.
Care to call the 720 Verbal on the SAT's (790 adjusted after recentering) a "facile lie" as well?
I am losing patience with those who speak from their ar*es...
Best,
Raphie
P.S. To offer a bit of "I told you so" solace to my detractors... on the GRE's this past October, after but one go-around, I but barely scored 620 Verbal, for a 1340 combined, almost 200 points down combined (after recentering) from my SAT scores 24/25 years ago. Before you gloat, however, check out average admittance scores to the Ivies... Best, RF
RPenner has the means (as of about a week ago), by private email, to begin the process of confirmation or not. In the meantime, I will ask you kindly to refrain from unintentional libel.
Care to call the 720 Verbal on the SAT's (790 adjusted after recentering) a "facile lie" as well?
I am losing patience with those who speak from their ar*es...
Best,
Raphie
P.S. To offer a bit of "I told you so" solace to my detractors... on the GRE's this past October, after but one go-around, I but barely scored 620 Verbal, for a 1340 combined, almost 200 points down combined (after recentering) from my SAT scores 24/25 years ago. Before you gloat, however, check out average admittance scores to the Ivies... Best, RF
Yeah, lots of talk - and still no attempt to show any level of competency. In fact, at every opportunity, you make posts that indicate a staggering amount of incompetency.
To go back on-topic...
In the interests of accuracy...
"A ) The Pentagonal Pyramid Set [0,2,5,7]"
should have read...
"A ) The Pentagonal Pyramid Set [4,1,0,0,2,5,7]"
At the time of the prior posting, I had neglected to include negative numbers (or a floating point zero). Where T_n = Triangular Number ((n^2 + n)/2), and K_n = Kissing Number...
|-4* T__-4| = 024 = K_4
|-2* T__-2| = 002 = K_1
|-0* T__-0| = 000 = K_0
|+0* T__+0| = 000 = K_0
|+2* T__+2| = 006 = K_2
|+4* T__+4| = 040 = K_5
|+6* T__+6| = 126 = K_7
The dimensions of those Kissing Numbers, incidentally, are, in order, quite easy to derive, based on Number Progressions previously posted to this forum. But I won't spoil the fun, as I am quite "certain" one quick search upon OEIS will reveal all, at least as certain posters upon this thread would have you believe...
Search OEIS for 4, 1, 0, 0, 2, 5, 7
Best,
Raphie
P.S. @ Alphanumeric. Please note how short, length-wise, the above number sequence is and how small the value of the terms. Also, please do consider my posts to Ivars, Rpenner and now, this one, to be background for a response to your eminently reasonable, but I believed yet flawed, critique some time back... Best, RF
P.P.S. Pentagonal Pyramid Numbers follow the form (n^3 + n^2)/2. Alternatively, they can also be conceived of as Polygonal Numbers "slicing" though through the "Polygonal Number Field" at a 45 degree pitch... e.g. 0 = P_4:0; 1 = P_5:1; 6 = P_6:2; 18 = P_7:3; 40 = P_8:4, etc.
Rpenner can, via his moderator capacity, settle the rest or not. In the meantime, arguments related to the topic at hand, "mathematics" vs, "numerology," are of course most welcome...
Best,
Raphie
QUOTE (Raphie Frank+Jun 17 2009, 05:01 AM)
In the interests of accuracy...
"A ) The Pentagonal Pyramid Set [0,2,5,7]"
should have read...
"A ) The Pentagonal Pyramid Set [4,1,0,0,2,5,7]"
At the time of the prior posting, I had neglected to include negative numbers (or a floating point zero). Where T_n = Triangular Number ((n^2 + n)/2), and K_n = Kissing Number...
|-4* T__-4| = 024 = K_4
|-2* T__-2| = 002 = K_1
|-0* T__-0| = 000 = K_0
|+0* T__+0| = 000 = K_0
|+2* T__+2| = 006 = K_2
|+4* T__+4| = 040 = K_5
|+6* T__+6| = 126 = K_7
The dimensions of those Kissing Numbers, incidentally, are, in order, quite easy to derive, based on Number Progressions previously posted to this forum. But I won't spoil the fun, as I am quite "certain" one quick search upon OEIS will reveal all, at least as certain posters upon this thread would have you believe...
Search OEIS for 4, 1, 0, 0, 2, 5, 7
Best,
Raphie
P.S. @ Alphanumeric. Please note how short, length-wise, the above number sequence is and how small the value of the terms. Also, please do consider my posts to Ivars, Rpenner and now, this one, to be background for a response to your eminently reasonable, but I believed yet flawed, critique some time back... Best, RF
P.P.S. Pentagonal Pyramid Numbers follow the form (n^3 + n^2)/2. Alternatively, they can also be conceived of as Polygonal Numbers "slicing" though through the "Polygonal Number Field" at a 45 degree pitch... e.g. 0 = P_4:0; 1 = P_5:1; 6 = P_6:2; 18 = P_7:3; 40 = P_8:4, etc.
Rpenner can, via his moderator capacity, settle the rest or not. In the meantime, arguments related to the topic at hand, "mathematics" vs, "numerology," are of course most welcome...
Best,
Raphie
[edit]
[edit]
QUOTE (Raphie Frank+May 13 2009, 08:40 AM)
P.S. It "accidentally" so happens that the first 8 values for:
floor ({Unity + Mersenne Prime Exponents] - 1) /2)
are...
0, 0, 1, 2, 3, 6, 8, 9
... which also happen to be the complete set of dimension numbers for Kissing Numbers that are twice a Triangular Number. Considering those dimension numbers are not only presumably quite "random," but were also stumbled upon quite "randomly," I would imagine a responsible scientist would at the very least raise an eyebrow. The imagination, alas, is quite undependable...
Dear RPenner,
In the interests of clarity, and at least partly as a a response to those who charge "navel gazing," let me specify what I mean when I state that those dimension numbers, 0, 0, 1, 2, 3, 6, 8, 9 were "randomly" stumbled upon.
Let...
A_k = (2^|k - 1| + 2*(k-1))
Z_k = 2*(2^(D_k) - 1) = (Unity + the first 5 Mersenne Primes, less 1)
Where...
D_k = {Unity + Mersenne Prime Exponents} - 1
K_k = Kissing Number
For k = 0, 1, 2, 3, 4, 5
A_k = 0, 1, 4, 8, 14, 24
Z_k = 0, 2, 6, 30, 126, 8190
==============================
A_k * Z_k = K_(A_k)*
= 0, 2, 24, 240, 1764, 196560
= K_0, K_1, K_4, K_8, K_14**, K_24
* holds for k = 0, 1, 2, 3, 5 and for k = 0, 1, 2, 3, 4, 5, if and only if 1764 is the 14-D Kissing Number
** hypothetical value
==============================
Now, where...
T = Triangular Number
==============================
for k = 0, 1, 2, 3
2*T_(Z_k/2^(+1)) U 2*T_(A_k/2^(-1))
= 2*T_0, 2 *T_0, 2*T_1, 2 *T_2, 2*T_3, 2*T_8, , 2*T_15, , 2*T_16
= 0, 0, 2, 6, 12, 72, 240, 272
= K_0, K_0, K_1, K_2, K_3, K_6, K_8, K_9*
* laminated lattice value
= K_(floor D_k/2)
In other words...
K_(({Unity + Mersenne Prime Exponents} - 1)/2)
for k = 0 --> 7
==============================
Rather "coincidental," and frankly, "random" don't you think, that not only does A_k*Z*k yield Kissing Numbers (for dimensions 0, 1, 4, 8, 24 and possible 14), but that the component parts, when inserted in to the n^2 + n (Twice Triangular) form, also yield Kissing Numbers, the dimensions of which are directly related to Mersenne Prime Exponents?
Especially considering the initial observation was simply that (K_24 + 24)/24 = 8191, the 5th Mersenne Prime?
Feel free to search OEIS for the number series 0, 0, 1, 2, 3, 6, 8, 9
A hint, you will NOT find it there, although if you drop the first two zeroes, a few results will indeed come up... Search OEIS for 1,2,3,6,8,9
Best,
Raphie
===============
RELATED PAPER:
===============
Mersenne Primes, Polygonal Anomalies and String Theory Classification
http://arxiv.org/abs/hep-th/9904212
Paul H. Frampton, Thomas W. Kephart
(Submitted on 29 Apr 1999)
It is pointed out that the Mersenne primes $M_p=(2^p-1)$ and associated perfect numbers ${\cal M}_p=2^{p-1}M_p$ play a significant role in string theory; this observation may suggest a classification of consistent string theories.
floor ({Unity + Mersenne Prime Exponents] - 1) /2)
are...
0, 0, 1, 2, 3, 6, 8, 9
... which also happen to be the complete set of dimension numbers for Kissing Numbers that are twice a Triangular Number. Considering those dimension numbers are not only presumably quite "random," but were also stumbled upon quite "randomly," I would imagine a responsible scientist would at the very least raise an eyebrow. The imagination, alas, is quite undependable...
Dear RPenner,
In the interests of clarity, and at least partly as a a response to those who charge "navel gazing," let me specify what I mean when I state that those dimension numbers, 0, 0, 1, 2, 3, 6, 8, 9 were "randomly" stumbled upon.
Let...
A_k = (2^|k - 1| + 2*(k-1))
Z_k = 2*(2^(D_k) - 1) = (Unity + the first 5 Mersenne Primes, less 1)
Where...
D_k = {Unity + Mersenne Prime Exponents} - 1
K_k = Kissing Number
For k = 0, 1, 2, 3, 4, 5
A_k = 0, 1, 4, 8, 14, 24
Z_k = 0, 2, 6, 30, 126, 8190
==============================
A_k * Z_k = K_(A_k)*
= 0, 2, 24, 240, 1764, 196560
= K_0, K_1, K_4, K_8, K_14**, K_24
* holds for k = 0, 1, 2, 3, 5 and for k = 0, 1, 2, 3, 4, 5, if and only if 1764 is the 14-D Kissing Number
** hypothetical value
==============================
Now, where...
T = Triangular Number
==============================
for k = 0, 1, 2, 3
2*T_(Z_k/2^(+1)) U 2*T_(A_k/2^(-1))
= 2*T_0, 2 *T_0, 2*T_1, 2 *T_2, 2*T_3, 2*T_8, , 2*T_15, , 2*T_16
= 0, 0, 2, 6, 12, 72, 240, 272
= K_0, K_0, K_1, K_2, K_3, K_6, K_8, K_9*
* laminated lattice value
= K_(floor D_k/2)
In other words...
K_(({Unity + Mersenne Prime Exponents} - 1)/2)
for k = 0 --> 7
==============================
Rather "coincidental," and frankly, "random" don't you think, that not only does A_k*Z*k yield Kissing Numbers (for dimensions 0, 1, 4, 8, 24 and possible 14), but that the component parts, when inserted in to the n^2 + n (Twice Triangular) form, also yield Kissing Numbers, the dimensions of which are directly related to Mersenne Prime Exponents?
Especially considering the initial observation was simply that (K_24 + 24)/24 = 8191, the 5th Mersenne Prime?
Feel free to search OEIS for the number series 0, 0, 1, 2, 3, 6, 8, 9
A hint, you will NOT find it there, although if you drop the first two zeroes, a few results will indeed come up... Search OEIS for 1,2,3,6,8,9
Best,
Raphie
===============
RELATED PAPER:
===============
Mersenne Primes, Polygonal Anomalies and String Theory Classification
http://arxiv.org/abs/hep-th/9904212
Paul H. Frampton, Thomas W. Kephart
(Submitted on 29 Apr 1999)
It is pointed out that the Mersenne primes $M_p=(2^p-1)$ and associated perfect numbers ${\cal M}_p=2^{p-1}M_p$ play a significant role in string theory; this observation may suggest a classification of consistent string theories.
Hmmm... Raphie...
I am a bit confused by all your lofty claims.
You claim to have taken the GRE in mathematics. You said...
Let me get this straight...
1. The GRE and the SAT are different tests. The scores are not directly equivalent. (Keep in mind that I am not American... our tests are differently scored).
2. You did the SAT's 25 years ago... I assume you would have had to have been 18 or so at the time. That would make you about 43 at least. Why are you doing your GRE now? Is it to impress people?
3.
Let me get this straight...
1. The GRE and the SAT are different tests. The scores are not directly equivalent. (Keep in mind that I am not American... our tests are differently scored).
2. You did the SAT's 25 years ago... I assume you would have had to have been 18 or so at the time. That would make you about 43 at least. Why are you doing your GRE now? Is it to impress people?
3. Care to call the 720 Verbal on the SAT's (790 adjusted after recentering) a "facile lie" as well?
Apparently it's no longer called the Verbal but the Critical Reading.... which leads me to my next question.
4.
So... you scored 1340 combined on the GRE... 200 points down from your SAT scores?
Let's look at the scoring scheme for both...
GRE...
So... you scored 1340 combined on the GRE... 200 points down from your SAT scores?
Let's look at the scoring scheme for both...
GRE...
An official GRE score report consists of three parts:
* Verbal Scaled Score (on a scale from 200 to 800)
* Quantitative Scaled Score (on a scale from 200 to 800)
* Analytical Writing Score (on a scale from 0 to 6)
So... no combined score at all then.
The SAT...
That apparently is a very simplified summation of a complex scoring system.
However...
The GRE scoring system and the SAT scoring system are not actually directly comparable.... especially when you consider that the analytical writing score is form 0 to 6 while the SAT ones are all from 200 to 800.
Quite frankly I cannot prove that you are lying since I do not have the in depth knowledge required to gauge that. However....
My BS meter is going off the scales.
Oh... and comments on your numerology?
It's silly.
I am a bit confused by all your lofty claims.
You claim to have taken the GRE in mathematics. You said...
QUOTE
Congratulate me, Euler, after I take the GRE's again and improve upon the the rather embarrassing 720 I scored in mathematics this past October. I would have hoped at the very least least to match the 740 I received on my SAT's 25 years ago.
Let me get this straight...
1. The GRE and the SAT are different tests. The scores are not directly equivalent. (Keep in mind that I am not American... our tests are differently scored).
2. You did the SAT's 25 years ago... I assume you would have had to have been 18 or so at the time. That would make you about 43 at least. Why are you doing your GRE now? Is it to impress people?
3.
QUOTE (->
| QUOTE |
| Congratulate me, Euler, after I take the GRE's again and improve upon the the rather embarrassing 720 I scored in mathematics this past October. I would have hoped at the very least least to match the 740 I received on my SAT's 25 years ago. |
Let me get this straight...
1. The GRE and the SAT are different tests. The scores are not directly equivalent. (Keep in mind that I am not American... our tests are differently scored).
2. You did the SAT's 25 years ago... I assume you would have had to have been 18 or so at the time. That would make you about 43 at least. Why are you doing your GRE now? Is it to impress people?
3. Care to call the 720 Verbal on the SAT's (790 adjusted after recentering) a "facile lie" as well?
Apparently it's no longer called the Verbal but the Critical Reading.... which leads me to my next question.
4.
QUOTE
on the GRE's this past October, after but one go-around, I but barely scored 620 Verbal, for a 1340 combined, almost 200 points down combined (after recentering) from my SAT scores 24/25 years ago
So... you scored 1340 combined on the GRE... 200 points down from your SAT scores?
Let's look at the scoring scheme for both...
GRE...
QUOTE (->
| QUOTE |
| on the GRE's this past October, after but one go-around, I but barely scored 620 Verbal, for a 1340 combined, almost 200 points down combined (after recentering) from my SAT scores 24/25 years ago |
So... you scored 1340 combined on the GRE... 200 points down from your SAT scores?
Let's look at the scoring scheme for both...
GRE...
An official GRE score report consists of three parts:
* Verbal Scaled Score (on a scale from 200 to 800)
* Quantitative Scaled Score (on a scale from 200 to 800)
* Analytical Writing Score (on a scale from 0 to 6)
So... no combined score at all then.
The SAT...
QUOTE
The exam consists of three parts: Critical Reading, Mathematics and Writing. The scores from each section can range from 200 to 800, so the best possible total score is 2400. The average score for each section is roughly 500, so the average total score is about 1500.
That apparently is a very simplified summation of a complex scoring system.
However...
The GRE scoring system and the SAT scoring system are not actually directly comparable.... especially when you consider that the analytical writing score is form 0 to 6 while the SAT ones are all from 200 to 800.
Quite frankly I cannot prove that you are lying since I do not have the in depth knowledge required to gauge that. However....
My BS meter is going off the scales.
Oh... and comments on your numerology?
It's silly.
QUOTE (RobDegraves+Jun 18 2009, 07:35 AM)
Hmmm... Raphie...
I am a bit confused by all your lofty claims.
OFF-TOPIC
Let's be crystal clear, Rob. I am not making "claims," but stating FACTS, in response to repeated harassment and false character assassination which threatens my future earnings potential insofar as it jeopardizes my admittance to an Ivy Leage calibre school (I am 41, and want to get a PhD. in Network Theory; I took the SAT's as a 16 and 17 year old...). Although case law is very much yet in process both internationally, and within the online realm, I am responding, in general, to public written statements that arguably constitute libel.
So... let's be CRYSTAL CLEAR...
In the 1980's I scored 720 Verbal, 740 Mathematics on the SAT's, back when there were only two sections. This is 1460 combined. This score correlates in 2008 terms, and to the best of my knowledge, with 790 Verbal, 740 Math, which is 1530 combined.
In 2008, I scored 620 Verbal, 720 Math on the GRE's, which is 1340 combined. Do the math. This is not complicated and is provable well beyond any reasonable doubt in a court of law, although a very undesirable lawsuit would likely be necessary in order to gain access to my high school and College Academic records via "discovery," a point I have already made in passing (privately) to RPenner.
Since the likely possibility of legal action borders on absurdity, a time and money drain for all concerned, I have provided RPenner with a credible source by which to judge my veracity. Should RPenner not be satisfied with this source, I will gladly, but privately, offer him more information.
FACT: I was the captain of my high school chess team, a "sport" not generally associated with "stupidity," although I consider myself a merely competent chess player. The Maret school, in Washington, D.C. may not be the best school in the world, but it was good enough to be one of the three schools the Obamas considered sending their children to.
FACT: I graduated from Vassar College in 1990 with a double degree in Psychology (3.3 GPA) and Dramatic Writing (3.5 GPA).
FACT: I am a triple legacy of Princeton University (Father, Mother, Sister), which means zilch unless one assumes that intelligence is hereditary. Ditto for the fact that I am the son of a former Princeton Professor (tenured at age 31) and the grandson of a former NYU Professor.
FACT: In 2009, Columbia University recruited me for their Continuing Education Program on the basis of my GRE's. In April, by invitation, I attended a seminar on the University Campus. (Interesting Note: According to the Speaker at the Seminar, the average time from decision to return to grad school to actual matriculation is 6 years, at least for top level schools...)
=============================
BOTTOM LINE...
=============================
When simply stated OBJECTIVE FACTS are fodder for "BS meters," one wanders perilously close to the realm of what many might term "delusional." All the more disturbing is when those who are entering such a realm are supposedly the caretakers of "scientific truth."
Best,
Raphie
P.S. On one point, Rob, I generally agree. It is difficult to directly compare GRE's to SAT's. That said, both can be correlated with IQ, and by this measure I have become considerably "dumber" in my "old age."
I am a bit confused by all your lofty claims.
OFF-TOPIC
Let's be crystal clear, Rob. I am not making "claims," but stating FACTS, in response to repeated harassment and false character assassination which threatens my future earnings potential insofar as it jeopardizes my admittance to an Ivy Leage calibre school (I am 41, and want to get a PhD. in Network Theory; I took the SAT's as a 16 and 17 year old...). Although case law is very much yet in process both internationally, and within the online realm, I am responding, in general, to public written statements that arguably constitute libel.
So... let's be CRYSTAL CLEAR...
In the 1980's I scored 720 Verbal, 740 Mathematics on the SAT's, back when there were only two sections. This is 1460 combined. This score correlates in 2008 terms, and to the best of my knowledge, with 790 Verbal, 740 Math, which is 1530 combined.
In 2008, I scored 620 Verbal, 720 Math on the GRE's, which is 1340 combined. Do the math. This is not complicated and is provable well beyond any reasonable doubt in a court of law, although a very undesirable lawsuit would likely be necessary in order to gain access to my high school and College Academic records via "discovery," a point I have already made in passing (privately) to RPenner.
Since the likely possibility of legal action borders on absurdity, a time and money drain for all concerned, I have provided RPenner with a credible source by which to judge my veracity. Should RPenner not be satisfied with this source, I will gladly, but privately, offer him more information.
FACT: I was the captain of my high school chess team, a "sport" not generally associated with "stupidity," although I consider myself a merely competent chess player. The Maret school, in Washington, D.C. may not be the best school in the world, but it was good enough to be one of the three schools the Obamas considered sending their children to.
FACT: I graduated from Vassar College in 1990 with a double degree in Psychology (3.3 GPA) and Dramatic Writing (3.5 GPA).
FACT: I am a triple legacy of Princeton University (Father, Mother, Sister), which means zilch unless one assumes that intelligence is hereditary. Ditto for the fact that I am the son of a former Princeton Professor (tenured at age 31) and the grandson of a former NYU Professor.
FACT: In 2009, Columbia University recruited me for their Continuing Education Program on the basis of my GRE's. In April, by invitation, I attended a seminar on the University Campus. (Interesting Note: According to the Speaker at the Seminar, the average time from decision to return to grad school to actual matriculation is 6 years, at least for top level schools...)
=============================
BOTTOM LINE...
=============================
When simply stated OBJECTIVE FACTS are fodder for "BS meters," one wanders perilously close to the realm of what many might term "delusional." All the more disturbing is when those who are entering such a realm are supposedly the caretakers of "scientific truth."
Best,
Raphie
P.S. On one point, Rob, I generally agree. It is difficult to directly compare GRE's to SAT's. That said, both can be correlated with IQ, and by this measure I have become considerably "dumber" in my "old age."
Ahem...
QUOTE (Euler+May 13 2009, 09:46 AM)
Let's see you in action.
MORE OFF-TOPIC...
@ Rob
P.P.S. For any who would suggest I should have responded to Euler's challenge, keep in mind that before one takes the GRE's one studies for them. I've no intention of cramming for a day simply to respond to spurious challenges by those who have repeatedly expressed ill intent towards me.
And by "ill intent," I mean, for instance, one who has publicly stated his desire to "prove" me a "cretin."
Cretin? Consider...
RELATED FACT: While at Vassar College, I was a charter member of the President Frances Fergusson's Advisory Committee on Public Service. Feel free to contact Raymond Parker, Executive Director of Campus Activities at Vassar, to learn more...
RELATED FACT: While in Prague, the Czech Republic in the early 1990's, I was the Co-Director of a Culture House, Asylum, that Dr. Gwen Orel, in her Doctoral dissertation, described as follows:
=============================================================
Community Theatre in Prague: Asylum
-----------------------------------------------
In it’s mission to “provide space to disenfranchised groups” Asylum was perhaps the one English-language theatrical organization in Prague during the 1990’s that fits the definition of “Community Theatre” by Jacqueline Lo and Helen Gilbert:
Community theatre is characterized by social engagement; it is theatre primarily committed to bringing about actual change in specific communities… The constitution of the performance group and the subject matter may be organized around common interests (such as gender, ethnicity, or shared social experience) or defined in terms of geographical location. Multicultural community theatre generally incorporates a range of languages and cultural resources, including performing traditions, drawn from the community.
From PERFORMING CULTURES: ENGLISH-LANGUAGE THEATRES IN POST-COMMUNIST PRAGUE by Dr. Gwen Orel (AB English, AB Classics, 1987, AM English 1987 from Stanford University; Doctor of Philosophy from the University of Pittsburgh, 2005)
=============================================================
Manage to "prove" me a "cretin," Rob, and we will surely have entered the world Orwell spoke of back in 1948 when he wrote 1984. (This, statement, of course, and by way of contrast, merely "opinion," not "fact" ...)
Best,
Raphie
P.S. Speaking of 1984, I don't just make this analogy lightly...
via Political Cortex...
What NOT to do if the Secret Service Comes Calling...
By Raphie Frank
05/02/2007 10:47:47 PM EST
http://www.politicalcortex.com/story/2007/5/2/224747/5946
@ Rob
QUOTE (Raphie Frank+May 15 2009, 11:23 PM)
P.P.S. For any who would suggest I should have responded to Euler's challenge, keep in mind that before one takes the GRE's one studies for them. I've no intention of cramming for a day simply to respond to spurious challenges by those who have repeatedly expressed ill intent towards me.
And by "ill intent," I mean, for instance, one who has publicly stated his desire to "prove" me a "cretin."
Cretin? Consider...
RELATED FACT: While at Vassar College, I was a charter member of the President Frances Fergusson's Advisory Committee on Public Service. Feel free to contact Raymond Parker, Executive Director of Campus Activities at Vassar, to learn more...
RELATED FACT: While in Prague, the Czech Republic in the early 1990's, I was the Co-Director of a Culture House, Asylum, that Dr. Gwen Orel, in her Doctoral dissertation, described as follows:
=============================================================
Community Theatre in Prague: Asylum
-----------------------------------------------
In it’s mission to “provide space to disenfranchised groups” Asylum was perhaps the one English-language theatrical organization in Prague during the 1990’s that fits the definition of “Community Theatre” by Jacqueline Lo and Helen Gilbert:
Community theatre is characterized by social engagement; it is theatre primarily committed to bringing about actual change in specific communities… The constitution of the performance group and the subject matter may be organized around common interests (such as gender, ethnicity, or shared social experience) or defined in terms of geographical location. Multicultural community theatre generally incorporates a range of languages and cultural resources, including performing traditions, drawn from the community.
From PERFORMING CULTURES: ENGLISH-LANGUAGE THEATRES IN POST-COMMUNIST PRAGUE by Dr. Gwen Orel (AB English, AB Classics, 1987, AM English 1987 from Stanford University; Doctor of Philosophy from the University of Pittsburgh, 2005)
=============================================================
Manage to "prove" me a "cretin," Rob, and we will surely have entered the world Orwell spoke of back in 1948 when he wrote 1984. (This, statement, of course, and by way of contrast, merely "opinion," not "fact" ...)
Best,
Raphie
P.S. Speaking of 1984, I don't just make this analogy lightly...
via Political Cortex...
What NOT to do if the Secret Service Comes Calling...
By Raphie Frank
05/02/2007 10:47:47 PM EST
http://www.politicalcortex.com/story/2007/5/2/224747/5946
Ahem, ahem...
QUOTE (Euler+May 13 2009, 09:46 AM)
Anywho - I'll bite. Let's see you in action.
QUOTE (RobDegraves+Jun 18 2009, 07:35 AM)
Oh... and comments on your numerology?
It's silly.
ON TOPIC.
How so, Rob?
The below is not conjecture, but fact. Whether this "fact" is meaningful or not is clearly open to debate:
K = Kissing Number
Mp = Mersenne Prime
(K_24 + 24)/24 = 8191 = (2^13 - 1) = Mp_5
(K_8 + 8)/8 = 31 = (2^5 - 1) = Mp_3
(K_4 + 4)/4 = 7 = (2^3 - 1) = Mp_2
(K_1 + 1)/1 = 3 = (2^2 - 1) = Mp_1
For good measure in terms of the 2^x - 1 form, where...
d(x) = divisors of x
then...
d(2^n - 1) = 1, 4, 8, 24
Are the above statements really any more bold than if I were to state that for x = 0, 1, 3, 15, 4095 (the Ramaujan-Nagell Triangular Numbers), then 8x + 1 = the Ramaujan-Nagell Square Numbers?... a number series which, incidentally, you will, rather surprisingly, not find on OEIS.
Best,
Raphie
It's silly.
ON TOPIC.
How so, Rob?
The below is not conjecture, but fact. Whether this "fact" is meaningful or not is clearly open to debate:
K = Kissing Number
Mp = Mersenne Prime
(K_24 + 24)/24 = 8191 = (2^13 - 1) = Mp_5
(K_8 + 8)/8 = 31 = (2^5 - 1) = Mp_3
(K_4 + 4)/4 = 7 = (2^3 - 1) = Mp_2
(K_1 + 1)/1 = 3 = (2^2 - 1) = Mp_1
For good measure in terms of the 2^x - 1 form, where...
d(x) = divisors of x
then...
d(2^n - 1) = 1, 4, 8, 24
Are the above statements really any more bold than if I were to state that for x = 0, 1, 3, 15, 4095 (the Ramaujan-Nagell Triangular Numbers), then 8x + 1 = the Ramaujan-Nagell Square Numbers?... a number series which, incidentally, you will, rather surprisingly, not find on OEIS.
Best,
Raphie
QUOTE (Raphie Frank+Jun 18 2009, 11:22 AM)
The below is not conjecture, but fact. Whether this "fact" is meaningful or not is clearly open to debate...
Many people have now explained to you, countless times, that there are infinitely many such relationships, and even a child could produce them. How a human being could not grasp this fact, and its consequences, is utterly mind boggling.
But seriously though - let's see you in action.
Many people have now explained to you, countless times, that there are infinitely many such relationships, and even a child could produce them. How a human being could not grasp this fact, and its consequences, is utterly mind boggling.
But seriously though - let's see you in action.
QUOTE (Euler+Jun 18 2009, 11:26 AM)
Many people have now explained to you, countless times, that there are infinitely many such relationships, and even a child could produce them. How a human being could not grasp this fact, and its consequences, is utterly mind boggling.
But seriously though - let's see you in action.
Please do not confuse "many people" with one person, you (with an assist from AN), stating the same point over and over and over again, even as the recipient of that message has already acknowledged both its validity and, yet at times, absolute irrelevance.
By your logic, we should throw all science to the wayside because our interpretations of the data are but one of an infinitude that could possibly fit that data...
In any case, and any infinities aside, there IS, for instance, a 14 Dimensional Kissing Number, Euler. It already exists, but we have simply not identified it thus far. Furthermore our imaginings of it are necessarily finite, not infinite, given that there are known bounds to where it lies upon the integral number line. That number lies somewhere between 1,582 and 3,183. (http://en.wikipedia.org/wiki/Kissing_number_problem)
My reasoned guess, as you know, is that it is 1764, based on a hypothesized relationship between Mersenne Primes (at least the first five) and Kissing Numbers that is grounded within a conceptual framework of "fully packed states."
If (K_14 + 14)/14 = Mp_4, then since Mp_4 equals 127, then K_14 would equal 1764.
Almost too bloody simple and obvious to be true, I dare say.
- Raphie
But seriously though - let's see you in action.
Please do not confuse "many people" with one person, you (with an assist from AN), stating the same point over and over and over again, even as the recipient of that message has already acknowledged both its validity and, yet at times, absolute irrelevance.
By your logic, we should throw all science to the wayside because our interpretations of the data are but one of an infinitude that could possibly fit that data...
In any case, and any infinities aside, there IS, for instance, a 14 Dimensional Kissing Number, Euler. It already exists, but we have simply not identified it thus far. Furthermore our imaginings of it are necessarily finite, not infinite, given that there are known bounds to where it lies upon the integral number line. That number lies somewhere between 1,582 and 3,183. (http://en.wikipedia.org/wiki/Kissing_number_problem)
My reasoned guess, as you know, is that it is 1764, based on a hypothesized relationship between Mersenne Primes (at least the first five) and Kissing Numbers that is grounded within a conceptual framework of "fully packed states."
If (K_14 + 14)/14 = Mp_4, then since Mp_4 equals 127, then K_14 would equal 1764.
Almost too bloody simple and obvious to be true, I dare say.
- Raphie
No, you clearly don't understand. You are not doing any sort of mathematics relevant to "Kissing Numbers", and such like. You are simply trying to construct relationships between sets of numbers. All you are doing is this:
Here is a set of numbers: X = {1, 4, 6, 23, 3434, 564332}.
Here is another set of numbers: Y = {0, 2, 5, 7, 15, 1233}.
I've identified one, of infinitely many maps {f}, such that the image of f|_X (i.e. the restriction of f to X) exactly coincides with Y.
How can you not understand this? How can someone not get this, and still operate a keyboard?
Here is a set of numbers: X = {1, 4, 6, 23, 3434, 564332}.
Here is another set of numbers: Y = {0, 2, 5, 7, 15, 1233}.
I've identified one, of infinitely many maps {f}, such that the image of f|_X (i.e. the restriction of f to X) exactly coincides with Y.
How can you not understand this? How can someone not get this, and still operate a keyboard?
Again.... just to clarify a few things.
1. I find Euler's argument so far to be quite convincing. After looking at your numbers, I do see how you could see a relationship... however, you could find a similar relationship between any complicated set of numbers. I could give you endless examples of this, particularly from the middle ages, which is my specialty, but I doubt you would care. What you are doing is more in the way of superstition than it is math.
Furthermore...
You statements about yourself continue to be contradictory.
1. Fact.
I did. This is not how the GRE is scored. Look it up.
I did. This is not how the GRE is scored. Look it up.
Three scores are reported on the General Test:
*
a Verbal Reasoning score reported on a 200-800 score scale, in 10-point increments
*
a Quantitative Reasoning score reported on a 200-800 score scale, in 10-point increments
*
an Analytical Writing score reported on a 0 to 6 score scale in half-point increments.
There is no "Math" section as such. Verbal, Quantitative Reasoning and Analytical writing. Furthermore, the scores are not combined in the report, nor would any institution look for that particular score.
I could understand that sort of vagueness from someone who was not claiming to be as brilliant as you... but in this case it does sound like an elaborate falsehood. It's likely more along the lines of ignorance and confusion when trying to make elaborate claims about yourself... but quite frankly the truth is more interesting.
As an aside...
For someone with such an interest in Math, that is an odd combo for a degree. However... why not indeed.
Let's see.... you went from Vassar College with a degree (I would have to assume a BA ) in psychology and creative writing then went to Prague to do community theater.
A look at your personal website is quite interesting and leads to a bit of a contradiction itself.
This is from your own website....
For someone with such an interest in Math, that is an odd combo for a degree. However... why not indeed.
Let's see.... you went from Vassar College with a degree (I would have to assume a BA ) in psychology and creative writing then went to Prague to do community theater.
A look at your personal website is quite interesting and leads to a bit of a contradiction itself.
This is from your own website....
At heart, however, he considers himself a storyteller with the desire to tell reality-based stories with “happy, hopeful” endings. He is currently engaged in a process to create the stories he wants to write about within a business context and plans a return to graduate school to study economic sociology.
Contrasted with...
I don't think those are exactly the same kind of subject.
However....
Let's recap.
You got a BA in psych and creative writing. Even assuming that this is true, which you pointed out would be nigh impossible to verify...
I don't think those are exactly the same kind of subject.
However....
Let's recap.
You got a BA in psych and creative writing. Even assuming that this is true, which you pointed out would be nigh impossible to verify...
This is not complicated and is provable well beyond any reasonable doubt in a court of law, although a very undesirable lawsuit would likely be necessary in order to gain access to my high school and College Academic records via "discovery," a point I have already made in passing (privately) to RPenner.
It's not overwhelmingly impressive, you have to admit.
Then you bummed around Prague for a while... a time you describe yourself as ...
Now you intend to go back to school. Very nice for you.
You are described in the blog you refer to as....
Now you intend to go back to school. Very nice for you.
You are described in the blog you refer to as....
Raphie Frank, Senior Producer at swandivedigital, has been known to act upon the stage (badly, but energetically by all accounts), argue passionately in defense of positions he doesn't agree with, and sing original songs on European streets for spare change to buy cabbage and eggs.
It's actually fascinating.
Lastly.... As to your repeated mentions of legal reprisals....
I absolutely dare you to try. I will even provide you with my real name and such info that you might need.
It is hardly a crime to point out the truth.
BTW... if you wish to discuss numerology in the sense of folklore and history, I would be more than happy to do so. However, your current belief in it is not scientific, it's just navel gazing.
1. I find Euler's argument so far to be quite convincing. After looking at your numbers, I do see how you could see a relationship... however, you could find a similar relationship between any complicated set of numbers. I could give you endless examples of this, particularly from the middle ages, which is my specialty, but I doubt you would care. What you are doing is more in the way of superstition than it is math.
Furthermore...
You statements about yourself continue to be contradictory.
1. Fact.
QUOTE
In 2008, I scored 620 Verbal, 720 Math on the GRE's, which is 1340 combined. Do the math
I did. This is not how the GRE is scored. Look it up.
QUOTE (->
| QUOTE |
| In 2008, I scored 620 Verbal, 720 Math on the GRE's, which is 1340 combined. Do the math |
I did. This is not how the GRE is scored. Look it up.
Three scores are reported on the General Test:
*
a Verbal Reasoning score reported on a 200-800 score scale, in 10-point increments
*
a Quantitative Reasoning score reported on a 200-800 score scale, in 10-point increments
*
an Analytical Writing score reported on a 0 to 6 score scale in half-point increments.
There is no "Math" section as such. Verbal, Quantitative Reasoning and Analytical writing. Furthermore, the scores are not combined in the report, nor would any institution look for that particular score.
I could understand that sort of vagueness from someone who was not claiming to be as brilliant as you... but in this case it does sound like an elaborate falsehood. It's likely more along the lines of ignorance and confusion when trying to make elaborate claims about yourself... but quite frankly the truth is more interesting.
As an aside...
QUOTE
FACT: I graduated from Vassar College in 1990 with a double degree in Psychology (3.3 GPA) and Dramatic Writing (3.5 GPA).
For someone with such an interest in Math, that is an odd combo for a degree. However... why not indeed.
Let's see.... you went from Vassar College with a degree (I would have to assume a BA ) in psychology and creative writing then went to Prague to do community theater.
A look at your personal website is quite interesting and leads to a bit of a contradiction itself.
This is from your own website....
QUOTE (->
| QUOTE |
| FACT: I graduated from Vassar College in 1990 with a double degree in Psychology (3.3 GPA) and Dramatic Writing (3.5 GPA). |
For someone with such an interest in Math, that is an odd combo for a degree. However... why not indeed.
Let's see.... you went from Vassar College with a degree (I would have to assume a BA ) in psychology and creative writing then went to Prague to do community theater.
A look at your personal website is quite interesting and leads to a bit of a contradiction itself.
This is from your own website....
At heart, however, he considers himself a storyteller with the desire to tell reality-based stories with “happy, hopeful” endings. He is currently engaged in a process to create the stories he wants to write about within a business context and plans a return to graduate school to study economic sociology.
Contrasted with...
QUOTE
I am 41, and want to get a PhD. in Network Theory;
I don't think those are exactly the same kind of subject.
However....
Let's recap.
You got a BA in psych and creative writing. Even assuming that this is true, which you pointed out would be nigh impossible to verify...
QUOTE (->
| QUOTE |
| I am 41, and want to get a PhD. in Network Theory; |
I don't think those are exactly the same kind of subject.
However....
Let's recap.
You got a BA in psych and creative writing. Even assuming that this is true, which you pointed out would be nigh impossible to verify...
This is not complicated and is provable well beyond any reasonable doubt in a court of law, although a very undesirable lawsuit would likely be necessary in order to gain access to my high school and College Academic records via "discovery," a point I have already made in passing (privately) to RPenner.
It's not overwhelmingly impressive, you have to admit.
Then you bummed around Prague for a while... a time you describe yourself as ...
QUOTE
as a crazed Bacchanalian Warholesquian happening, even if, public nipple piercings and simulated urination aside, a generally less explicitly sexual version.
Now you intend to go back to school. Very nice for you.
You are described in the blog you refer to as....
QUOTE (->
| QUOTE |
| as a crazed Bacchanalian Warholesquian happening, even if, public nipple piercings and simulated urination aside, a generally less explicitly sexual version. |
Now you intend to go back to school. Very nice for you.
You are described in the blog you refer to as....
Raphie Frank, Senior Producer at swandivedigital, has been known to act upon the stage (badly, but energetically by all accounts), argue passionately in defense of positions he doesn't agree with, and sing original songs on European streets for spare change to buy cabbage and eggs.
It's actually fascinating.
Lastly.... As to your repeated mentions of legal reprisals....
I absolutely dare you to try. I will even provide you with my real name and such info that you might need.
It is hardly a crime to point out the truth.
BTW... if you wish to discuss numerology in the sense of folklore and history, I would be more than happy to do so. However, your current belief in it is not scientific, it's just navel gazing.
ON-TOPIC
Dear Rob,
I would be quite pleased, and I imagine others would be as well, to have you offer your insights on numerology and the Middle Ages. It seems to me it could only enrich everyone's understanding of the topic.
OFF-TOPIC
Regarding the disparity between what I originally intended to study, Economic Sociology, and what I currently state as my Academic Interest, Network Theory, I see this as a point being worthy of response.
In fact, this disparity was specifically addressed in my unsuccessful appplication to an Ivy League School this past year. Below is an excerpt from my Personal Statement to [University X]. Because I am uncertain if such statements are expected to be confidential, I have removed any obvious identifying markers.
=======================================================
Dear Members of the Admissions Committee,
When first I approached the [University X] Sociology Department about one and a half years ago, my stated desire was to study Economic Sociology. In furtherance of that end, in the hopes that I might demonstrate scholarship through action and innovation, I had spent considerable time developing the broad outline of an admittedly quixotic, but I still believe, workable, social entrepreneurial business model I call Business Artivism, intended as a hybrid for-profit / not-for profit blending of Business, Art and Non-Partisan Activism.
I was drawn, specifically, to [University X] at that time primarily because the scholarship of [SCHOLAR A] in relation to the Arts, Cultural Capital and Organizational Isomorphisms, I felt, presented a good match with my own interests; and also because I was interested in multi-disciplinary collaborations in the spirit of Consilience (aka “The Unity of Knowledge.”) and many of my intellectual heroes, ranging from [SCHOLAR B] to [SCHOLAR C], [SCHOLAR D] and [SCHOLAR E], are [University X] scholars.
While, of course, I would not expect to have direct contact with such prominent figures, I was nevertheless excited at the prospect of interacting with those studying under them, in particular since, as a student, I would hope to begin an informal lecture series I call the “Consilience Roundtable” intended as a means by which to cross-pollinate ideas between various disciplines.
One and a half years later, knowing now what I did not know then, much has changed. No longer is my primary anticipated focus Economic Sociology, as much as I’ve yet a passion for it. Rather, the study of A ) Network Theory: The Dynamics of Social Change, B ) Network Theory: Societal Implications of Information “Flow” and “Access” in the Digital Age, and C ) Applied Network Theory: Hidden Populations, now top my list as desired areas of academic inquiry.
Additionally, while [SCHOLAR A] is still one of my main attractors to [University X], as I view cultural capital to be the “exchange currency” of human dynamic, I can now add to my list of attractors to [University X], [SCHOLAR F]. In particular, I view [SCHOLAR F]’s work on the Butterfly Effect and Hidden Populations / Respondent Driven Sampling to be seminal in nature, with great import of social value.
=======================================================
Suffice it to say, Rob, that if, in fact, I am applying to Graduate Schools, to publicly and knowlingly state false information regarding personal background (i.e. test scores, where I went to school, degrees received, etc.), would be tantamount to academic suicide (given that they have the means to verify or falsify this information...), so think what you will.
Best,
Raphie
TYPO CORRECTION: Pertaining to factual statements, and given that "academic suicide" is not at all desirable, I just noted a typo from a previous post. My GPA in Psychology at Vassar, was 3.2, not 3.3, for a combined 3.35 (roughly) GPA for the Psychology/Dramatic Writing Double Major. While I would not typically split hairs on such a detail, in this particular instance, it is important to correct the record...
Dear Rob,
I would be quite pleased, and I imagine others would be as well, to have you offer your insights on numerology and the Middle Ages. It seems to me it could only enrich everyone's understanding of the topic.
OFF-TOPIC
Regarding the disparity between what I originally intended to study, Economic Sociology, and what I currently state as my Academic Interest, Network Theory, I see this as a point being worthy of response.
In fact, this disparity was specifically addressed in my unsuccessful appplication to an Ivy League School this past year. Below is an excerpt from my Personal Statement to [University X]. Because I am uncertain if such statements are expected to be confidential, I have removed any obvious identifying markers.
=======================================================
Dear Members of the Admissions Committee,
When first I approached the [University X] Sociology Department about one and a half years ago, my stated desire was to study Economic Sociology. In furtherance of that end, in the hopes that I might demonstrate scholarship through action and innovation, I had spent considerable time developing the broad outline of an admittedly quixotic, but I still believe, workable, social entrepreneurial business model I call Business Artivism, intended as a hybrid for-profit / not-for profit blending of Business, Art and Non-Partisan Activism.
I was drawn, specifically, to [University X] at that time primarily because the scholarship of [SCHOLAR A] in relation to the Arts, Cultural Capital and Organizational Isomorphisms, I felt, presented a good match with my own interests; and also because I was interested in multi-disciplinary collaborations in the spirit of Consilience (aka “The Unity of Knowledge.”) and many of my intellectual heroes, ranging from [SCHOLAR B] to [SCHOLAR C], [SCHOLAR D] and [SCHOLAR E], are [University X] scholars.
While, of course, I would not expect to have direct contact with such prominent figures, I was nevertheless excited at the prospect of interacting with those studying under them, in particular since, as a student, I would hope to begin an informal lecture series I call the “Consilience Roundtable” intended as a means by which to cross-pollinate ideas between various disciplines.
One and a half years later, knowing now what I did not know then, much has changed. No longer is my primary anticipated focus Economic Sociology, as much as I’ve yet a passion for it. Rather, the study of A ) Network Theory: The Dynamics of Social Change, B ) Network Theory: Societal Implications of Information “Flow” and “Access” in the Digital Age, and C ) Applied Network Theory: Hidden Populations, now top my list as desired areas of academic inquiry.
Additionally, while [SCHOLAR A] is still one of my main attractors to [University X], as I view cultural capital to be the “exchange currency” of human dynamic, I can now add to my list of attractors to [University X], [SCHOLAR F]. In particular, I view [SCHOLAR F]’s work on the Butterfly Effect and Hidden Populations / Respondent Driven Sampling to be seminal in nature, with great import of social value.
=======================================================
Suffice it to say, Rob, that if, in fact, I am applying to Graduate Schools, to publicly and knowlingly state false information regarding personal background (i.e. test scores, where I went to school, degrees received, etc.), would be tantamount to academic suicide (given that they have the means to verify or falsify this information...), so think what you will.
Best,
Raphie
TYPO CORRECTION: Pertaining to factual statements, and given that "academic suicide" is not at all desirable, I just noted a typo from a previous post. My GPA in Psychology at Vassar, was 3.2, not 3.3, for a combined 3.35 (roughly) GPA for the Psychology/Dramatic Writing Double Major. While I would not typically split hairs on such a detail, in this particular instance, it is important to correct the record...
QUOTE (Raphie Frank+Jun 18 2009, 11:22 AM)
For good measure in terms of the 2^x - 1 form, where...
d(x) = divisors of x
then...
d(2^n - 1) = 1, 4, 8, 24
==================
Those blasted typos...
==================
The above should have read...
For good measure in terms of the 2^x - 1 form, where...
o'(x) = sum of the divisors of x (including x)
then...
o'(2^n - 1) = 1, 4, 8, 24
d(x) = divisors of x
then...
d(2^n - 1) = 1, 4, 8, 24
==================
Those blasted typos...
==================
The above should have read...
For good measure in terms of the 2^x - 1 form, where...
o'(x) = sum of the divisors of x (including x)
then...
o'(2^n - 1) = 1, 4, 8, 24
This is yet another instance in which I have outlined, in detail, why your numerology is trivial and meaningless, and you've conveniently chosen not to respond to my points. I know, the readers know, and you know, that you don't respond because the points I make illuminate your utter stupidity.
I'm actually beginning to sway my opinion: previously I've simply thought you were some idiot who has a very high opinion of his own misunderstandings. And yet now, I'm actually beginning to feel sorry for you. You're actually applying for PhDs in Network theory, and yet previously you've shown that your mathematics is so lacking that you're unable to expand out the expression n(n+1). As we've witnessed so many times on this forum: it is the most incompetent who grossly over estimate their own ability and achievements.
Seriously - sort your life out.
I'm actually beginning to sway my opinion: previously I've simply thought you were some idiot who has a very high opinion of his own misunderstandings. And yet now, I'm actually beginning to feel sorry for you. You're actually applying for PhDs in Network theory, and yet previously you've shown that your mathematics is so lacking that you're unable to expand out the expression n(n+1). As we've witnessed so many times on this forum: it is the most incompetent who grossly over estimate their own ability and achievements.
Seriously - sort your life out.
Just to correct the record.
I take it that you are no longer used to academia and how it works.
I could come on this forum and claim to be the King of Siam, with 70 PHD's and the love of the Queen of Fairies (which would be cool indeed)... and my University would not care a whit. I have my degrees, my scores, etc. That is all that matters. When you apply to wherever you are going, I don't think they are going to ask whether you made false claims on an internet forum.
Now... if I were to publish something under false pretenses, or try to make money based on fake credentials (which happens a lot anyway), that would be different. However, this place is for discussion... and the only measure of your worth is your own words.
I do place a certain amount of importance on someone having actual knowledge and training in a field. This is usually self evident, or not, by the quality of what they are saying. A good example is Rpenner and Alphanumeric, both of whom have actual qualifications in their field and it shows.
However, that is not the only measure of an argument. In the end, facts speak louder than words.
PS
In the next post I will address medieval numerology if anyone wishes.
QUOTE
Suffice it to say, Rob, that if, in fact, I am applying to Graduate Schools, to publicly and knowlingly state false information regarding personal background (i.e. test scores, where I went to school, degrees received, etc.), would be tantamount to academic suicide (given that they have the means to verify or falsify this information...), so think what you will.
I take it that you are no longer used to academia and how it works.
I could come on this forum and claim to be the King of Siam, with 70 PHD's and the love of the Queen of Fairies (which would be cool indeed)... and my University would not care a whit. I have my degrees, my scores, etc. That is all that matters. When you apply to wherever you are going, I don't think they are going to ask whether you made false claims on an internet forum.
Now... if I were to publish something under false pretenses, or try to make money based on fake credentials (which happens a lot anyway), that would be different. However, this place is for discussion... and the only measure of your worth is your own words.
I do place a certain amount of importance on someone having actual knowledge and training in a field. This is usually self evident, or not, by the quality of what they are saying. A good example is Rpenner and Alphanumeric, both of whom have actual qualifications in their field and it shows.
However, that is not the only measure of an argument. In the end, facts speak louder than words.
PS
In the next post I will address medieval numerology if anyone wishes.
And now my conscience has kicked in.
Raphie Frank: I'm sure you're a nice guy, and you're probably guilty of little more than a sub-standard grasp of mathematics. What you must understand, is that there are people with lots more knowledge and ability in this particular area. If your posts contained any sort of mathematics that was in the least bit interesting or non-trivial, I would be very keen to discuss it with you. I gain nothing by telling you, over and over, that your posts are nothing more than low-brow numerology. I am telling you, that as someone who regularly publishes papers in mathematical journals, that all this "work" (and I use the term loosely) that you continue to harp on about, is utter drivel.
If you'd genuinely like to do a PhD in Network theory, then I would recommend you spend your time a little more productively by going over some high-school work.
Raphie Frank: I'm sure you're a nice guy, and you're probably guilty of little more than a sub-standard grasp of mathematics. What you must understand, is that there are people with lots more knowledge and ability in this particular area. If your posts contained any sort of mathematics that was in the least bit interesting or non-trivial, I would be very keen to discuss it with you. I gain nothing by telling you, over and over, that your posts are nothing more than low-brow numerology. I am telling you, that as someone who regularly publishes papers in mathematical journals, that all this "work" (and I use the term loosely) that you continue to harp on about, is utter drivel.
If you'd genuinely like to do a PhD in Network theory, then I would recommend you spend your time a little more productively by going over some high-school work.
QUOTE (Euler+Jun 18 2009, 08:44 PM)
your mathematics is so lacking that you're unable to expand out the expression n(n+1).
The above quoted statement takes the cake, Euler, as indicative of what I believe to be continued expressions of utter nonsense and bad faith on your part. Below, for example, is a very simple formula for Polygonal Numbers (P_s:k):
P_s:k = k * (s-2)*T_(k-1)
where...
s = # of sides of an n-gon
k = kth number of Polygonal Progression
T = Triangular Number = (n^2 + n)/2
n * (n+1)/2, the formula for Triangular Numbers (T_n), and one half the value of the quoted formula you refer to, n(n+1), is but a sliver of the entirety of what one might term the "Polygonal Number Field," which in turn is a sliver so small as to constitute "nothingness" in relation to Rational Numbers, and so on...
Alternatively, of course, we could include the triangular numbers as part of the n-hedral set.
(n)/1!
(n * (n+1))/2!
(n * (n+1) * (n+2))/3!
(n * (n+1) * (n+2) * (n+3))/4!
And so on...
That such slivers of the numerical entirety as Polygonal Numbers and n-Hedral Numbers, and in fact slivers of those slivers (i.e. P_s:(s-4), (P:4:k - 1)):, slivers so small as to constitute "nothingness upon nothingness" rather "seem" at the very least to be related to one of the "Seven Staggering Sequences" http://www.research.att.com/~njas/doc/g4g7.pdf as put forth by N. J. A. Sloane, might be considered perhaps of interest to some.
That they are not of interest to you is your business, but neither this lack of interest, nor your rather "wrong-headed" beliefs regarding my character, intelligence and honesty, justify such silly and absurd statements as you make.
Best,
Raphie
P.S. Feel free to "feel sorry" for me, Euler, but there are many others to feel far more sorry for than one invited by an Ivy League, Columbia University, to consider entry into their Continuing Education program by way of stepping stone to further Advanced Graduate Studies.
The above quoted statement takes the cake, Euler, as indicative of what I believe to be continued expressions of utter nonsense and bad faith on your part. Below, for example, is a very simple formula for Polygonal Numbers (P_s:k):
P_s:k = k * (s-2)*T_(k-1)
where...
s = # of sides of an n-gon
k = kth number of Polygonal Progression
T = Triangular Number = (n^2 + n)/2
n * (n+1)/2, the formula for Triangular Numbers (T_n), and one half the value of the quoted formula you refer to, n(n+1), is but a sliver of the entirety of what one might term the "Polygonal Number Field," which in turn is a sliver so small as to constitute "nothingness" in relation to Rational Numbers, and so on...
Alternatively, of course, we could include the triangular numbers as part of the n-hedral set.
(n)/1!
(n * (n+1))/2!
(n * (n+1) * (n+2))/3!
(n * (n+1) * (n+2) * (n+3))/4!
And so on...
That such slivers of the numerical entirety as Polygonal Numbers and n-Hedral Numbers, and in fact slivers of those slivers (i.e. P_s:(s-4), (P:4:k - 1)):, slivers so small as to constitute "nothingness upon nothingness" rather "seem" at the very least to be related to one of the "Seven Staggering Sequences" http://www.research.att.com/~njas/doc/g4g7.pdf as put forth by N. J. A. Sloane, might be considered perhaps of interest to some.
That they are not of interest to you is your business, but neither this lack of interest, nor your rather "wrong-headed" beliefs regarding my character, intelligence and honesty, justify such silly and absurd statements as you make.
Best,
Raphie
P.S. Feel free to "feel sorry" for me, Euler, but there are many others to feel far more sorry for than one invited by an Ivy League, Columbia University, to consider entry into their Continuing Education program by way of stepping stone to further Advanced Graduate Studies.
QUOTE (Euler+Jun 18 2009, 09:29 PM)
And now my conscience has kicked in.
Raphie Frank: I'm sure you're a nice guy, and you're probably guilty of little more than a sub-standard grasp of mathematics. What you must understand, is that there are people with lots more knowledge and ability in this particular area. If your posts contained any sort of mathematics that was in the least bit interesting or non-trivial, I would be very keen to discuss it with you. I gain nothing by telling you, over and over, that your posts are nothing more than low-brow numerology. I am telling you, that as someone who regularly publishes papers in mathematical journals, that all this "work" (and I use the term loosely) that you continue to harp on about, is utter drivel.
If you'd genuinely like to do a PhD in Network theory, then I would recommend you spend your time a little more productively by going over some high-school work.
In spite of the condescension, Euler, the above quoted post was actually bordering on constructive. This is progress.
Raphie Frank: I'm sure you're a nice guy, and you're probably guilty of little more than a sub-standard grasp of mathematics. What you must understand, is that there are people with lots more knowledge and ability in this particular area. If your posts contained any sort of mathematics that was in the least bit interesting or non-trivial, I would be very keen to discuss it with you. I gain nothing by telling you, over and over, that your posts are nothing more than low-brow numerology. I am telling you, that as someone who regularly publishes papers in mathematical journals, that all this "work" (and I use the term loosely) that you continue to harp on about, is utter drivel.
If you'd genuinely like to do a PhD in Network theory, then I would recommend you spend your time a little more productively by going over some high-school work.
In spite of the condescension, Euler, the above quoted post was actually bordering on constructive. This is progress.
QUOTE (RobDegraves+Jun 18 2009, 09:06 PM)
I could come on this forum and claim to be the King of Siam, with 70 PHD's and the love of the Queen of Fairies (which would be cool indeed)... and my University would not care a whit.
You may well be on mark, Rob. Perhaps I idealize the Academy's commitment to honesty and integrity. But, hopefully, I do not believe I mischaracterize the ideals of the Academy.
You may well be on mark, Rob. Perhaps I idealize the Academy's commitment to honesty and integrity. But, hopefully, I do not believe I mischaracterize the ideals of the Academy.
QUOTE (Raphie Frank+Jun 18 2009, 09:32 PM)
The above quoted statement takes the cake, Euler, as indicative of what I believe to be continued expressions of utter nonsense and bad faith on your part.
===========================================================
It should be a matter of simple algebraic manipulation to show that those two expressions:
(s-2)*T_(n-1) + N_n = P_s:n
AND
(s-2)*T_(n) - (s-3)*N_n = P_s:n
... are equivalencies.
===========================================================
(s-3) replaces 4.
From here on out, I'm sure some high schooler, perhaps of age 13 or thereabouts, can either further revise or prove the above.
QUOTE (Raphie Frank+Aug 1 2008, 06:27 AM)
===========================================================
It should be a matter of simple algebraic manipulation to show that those two expressions:
(s-2)*T_(n-1) + N_n = P_s:n
AND
(s-2)*T_(n) - (s-3)*N_n = P_s:n
... are equivalencies.
===========================================================
(s-3) replaces 4.
From here on out, I'm sure some high schooler, perhaps of age 13 or thereabouts, can either further revise or prove the above.
QUOTE (Euler+Aug 1 2008, 06:48 AM)
Do it then! This, quite literally, would be expected of the average 13yr old who attends school.
QUOTE (Raphie Frank+Aug 1 2008, 07:11 AM)
YOU do it, you little elitest prick.
Don't you remember that one? Where you needed help because you couldn't answer a question that was tantamount to expanding n(n+1). How quickly we forget...
Seriously though. You are making a fool of yourself on this forum, and you will be making a fool of yourself if you are applying for PhDs in network theory. You look stupid. You are convincing people, including myself, that you are utterly incompetent.
I gain nothing by telling you this. I think it is sad that someone would do this to themselves. Please stop.
Don't you remember that one? Where you needed help because you couldn't answer a question that was tantamount to expanding n(n+1). How quickly we forget...
Seriously though. You are making a fool of yourself on this forum, and you will be making a fool of yourself if you are applying for PhDs in network theory. You look stupid. You are convincing people, including myself, that you are utterly incompetent.
I gain nothing by telling you this. I think it is sad that someone would do this to themselves. Please stop.
QUOTE (Raphie Frank+Jun 18 2009, 09:34 PM)
In spite of the condescension, Euler, the above quoted post was actually bordering on constructive. This is progress.
And yet you persist...
And yet you persist...
First, Euler, post-facto apologies for the name-calling. Given that I am rather adamantly opposed to such, that was hypocritical -- no matter how "justified" -- behavior on my part.
Second, please do not confuse your interpretation of my replies with that which actually IS. If I were as algebraically inept as you seem to believe, I would not be able to derive equations such as the one quoted below, which I do not believe you will find anywhere else but upon this forum:
Second, please do not confuse your interpretation of my replies with that which actually IS. If I were as algebraically inept as you seem to believe, I would not be able to derive equations such as the one quoted below, which I do not believe you will find anywhere else but upon this forum:
QUOTE (Raphie Frank+Apr 25 2009, 05:32 PM)
Notice, Euler, I have not done mathematics any more complicated than basic addition, and that 31 total up above is no less valid for it than if I had simply entered the number 4 into the following equation:
1/12 * ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0)
(1 / 12) * ((1 * (4^4)) - (2 * (4^3)) + (11 * (4^2)) + (14 * (4^1)) + (12 * (4^0))) = 31
Now, let's go in reverse:
1/12 ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0)
What on earth has that to do with Pascal's Triangle or anything else!?! There are an INFINITE number of formulas that could generate 31. Quite true.
Just as there an an infinite number of ways to express the following number series in algebraic form:
1, 3, 7, 15, 31, 61, 113, 197, 325, 511 ...
Best,
Raphie
P.S. @ Rob Degraves
The above formula is an expansion not just of n*(n+1), but of the {(first five diagonals of Pascal's Triangle * 2) - 1), of which (n*(n+1) is but merely one component. Rather "miraculous," don't you think, that I can expand the entirety, but, if Euler is to be found "convincing," not the part? This formula, incidentally, gives the maximal number of combined points, intersections, connections and areas created when one "connects the dots" of any n-gon. Best, RF
1/12 * ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0)
(1 / 12) * ((1 * (4^4)) - (2 * (4^3)) + (11 * (4^2)) + (14 * (4^1)) + (12 * (4^0))) = 31
Now, let's go in reverse:
1/12 ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0)
What on earth has that to do with Pascal's Triangle or anything else!?! There are an INFINITE number of formulas that could generate 31. Quite true.
Just as there an an infinite number of ways to express the following number series in algebraic form:
1, 3, 7, 15, 31, 61, 113, 197, 325, 511 ...
Best,
Raphie
P.S. @ Rob Degraves
The above formula is an expansion not just of n*(n+1), but of the {(first five diagonals of Pascal's Triangle * 2) - 1), of which (n*(n+1) is but merely one component. Rather "miraculous," don't you think, that I can expand the entirety, but, if Euler is to be found "convincing," not the part? This formula, incidentally, gives the maximal number of combined points, intersections, connections and areas created when one "connects the dots" of any n-gon. Best, RF
We can only judge your ability by what we can infer from your posts. Your mathematical ability is below what I would expect from the average 15yr old in the UK.
I interview lots of young students for admission onto our undergraduate course. I can categorically say that the ability you have displayed on this forum is light-years below the poorest student I have ever encountered.
Of course, you could display your mathematical aptitude by explaining to us how to answer a few of the questions on that maths GRE paper - but it seems you're unable to do so. This is no surprise to me, or other readers it would appear.
Like I said - you're making a fool of yourself.
I interview lots of young students for admission onto our undergraduate course. I can categorically say that the ability you have displayed on this forum is light-years below the poorest student I have ever encountered.
Of course, you could display your mathematical aptitude by explaining to us how to answer a few of the questions on that maths GRE paper - but it seems you're unable to do so. This is no surprise to me, or other readers it would appear.
Like I said - you're making a fool of yourself.
QUOTE (Raphie Frank+Jun 18 2009, 10:04 PM)
The above formula is an expansion not just of n*(n+1), but of the {(first five diagonals of Pascal's Triangle * 2) - 1), of which (n*(n+1) is but merely one component. Rather "miraculous," don't you think, that I can expand the entirety, but, if Euler is to be found "convincing," not the part?
On a human scale, Euler, you continue to speak abhorrent "NOISE" as RPenner might term it. For this reason alone I must say that I quite sympathize with him in his moderator capacity. To paraphrase said moderator, please do not confuse the vigour with which you present your claims as a substitution for "truth."
Best,
Raphie
On a human scale, Euler, you continue to speak abhorrent "NOISE" as RPenner might term it. For this reason alone I must say that I quite sympathize with him in his moderator capacity. To paraphrase said moderator, please do not confuse the vigour with which you present your claims as a substitution for "truth."
Best,
Raphie
We can yadda-yadda all day about how you believe your mathematical ability is better than my informed assessment. The fact is, people respect my mathematical opinion; whilst you're some guy on an internet forum who insists he knows what he's on about because his mum and dad were smart, and because he got some mediocre grades in a dramatic writing (giggle) course!
The fact remains that you struggle with basic mathematical concepts, you are unable to see the utter ineptitude of your continual ramblings and you refuse to display any sign of mathematical competence by answering questions to a test you've claimed to score well on.
Prove me wrong.
The fact remains that you struggle with basic mathematical concepts, you are unable to see the utter ineptitude of your continual ramblings and you refuse to display any sign of mathematical competence by answering questions to a test you've claimed to score well on.
Prove me wrong.
(I should add, for completeness, that we all see that you've once again chosen to avoid responding to the points in which people have criticized your attempts at mathematics)
QUOTE (Euler+Jun 18 2009, 10:36 PM)
(I should add, for completeness, that we all see that you've once again chosen to avoid responding to the points in which people have criticized your attempts at mathematics)
Says the one who publicly states that this poster can not expand n*(n+1)?
You are simply, at times, too funny!
1/12 * ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0)
Not brain surgery, Euler, but in order to derive this, it was necessary, as a rather trivial operation, to perform the elementary school mathematics you have quite confidently stated I am incapable of.
Why on this good earth would I ever try to "prove" anything, much less objective facts, to someone so apparently impervious to what many might term "reality"? Ought I to waste valuable time "proving" to you also that there are, as of 2009, 50 States in the United States of America?"
Get real, but, to your credit, I am confident you could also make a quite convincing case that there are not actually 50 States in the United States of America.
Best,
Raphie
Says the one who publicly states that this poster can not expand n*(n+1)?
You are simply, at times, too funny!
1/12 * ( 1*k^4 - 2*k^3 + 11*k^2 + 14*k^1 + 12*k^0)
Not brain surgery, Euler, but in order to derive this, it was necessary, as a rather trivial operation, to perform the elementary school mathematics you have quite confidently stated I am incapable of.
Why on this good earth would I ever try to "prove" anything, much less objective facts, to someone so apparently impervious to what many might term "reality"? Ought I to waste valuable time "proving" to you also that there are, as of 2009, 50 States in the United States of America?"
Get real, but, to your credit, I am confident you could also make a quite convincing case that there are not actually 50 States in the United States of America.
Best,
Raphie
Again, you have failed to respond appropriately. If you can now do the kiddie level operation of expanding some brackets, then I'm happy for you. But let's see you respond to:
QUOTE (Euler+Jun 18 2009, 10:33 PM)
The fact remains that you struggle with basic mathematical concepts, you are unable to see the utter ineptitude of your continual ramblings and you refuse to display any sign of mathematical competence by answering questions to a test you've claimed to score well on.
Prove me wrong.
What if you saw it twice? 
Prove me wrong.
QUOTE (Euler+Jun 18 2009, 12:08 PM)
No, you clearly don't understand. You are not doing any sort of mathematics relevant to "Kissing Numbers", and such like. You are simply trying to construct relationships between sets of numbers. All you are doing is this:
Here is a set of numbers: X = {1, 4, 6, 23, 3434, 564332}.
Here is another set of numbers: Y = {0, 2, 5, 7, 15, 1233}.
I've identified one, of infinitely many maps {f}, such that the image of f|_X (i.e. the restriction of f to X) exactly coincides with Y.
How can you not understand this? How can someone not get this, and still operate a keyboard?
The fact that you continue to avoid refering to the GRE mathematics test I've linked, speaks volumes.
I cannot stress this enough: you are making a fool of yourself.
Here is a set of numbers: X = {1, 4, 6, 23, 3434, 564332}.
Here is another set of numbers: Y = {0, 2, 5, 7, 15, 1233}.
I've identified one, of infinitely many maps {f}, such that the image of f|_X (i.e. the restriction of f to X) exactly coincides with Y.
How can you not understand this? How can someone not get this, and still operate a keyboard?
The fact that you continue to avoid refering to the GRE mathematics test I've linked, speaks volumes.
I cannot stress this enough: you are making a fool of yourself.
OK...
With permission hopefully from Euler... I would like to move beyond the qualifications level. I think we know where things stand at this time.
It's not a question of intelligence or learning... it's a question of the thread itself.
You say you have identified relationships between numbers.
We say that such relationships are common and have nothing to do with the real world.
Here is the main question.
What is your point?
The OP does not really have a point as far as I can tell. People have always seen symbols and parallels in sets of numbers. Numerology is common now as it has always been, however it is never been seen as predictive nor significant by anyone except people who hold it as a superstition.
So...
Why the number show.... what are you trying to say?
With permission hopefully from Euler... I would like to move beyond the qualifications level. I think we know where things stand at this time.
It's not a question of intelligence or learning... it's a question of the thread itself.
You say you have identified relationships between numbers.
We say that such relationships are common and have nothing to do with the real world.
Here is the main question.
What is your point?
The OP does not really have a point as far as I can tell. People have always seen symbols and parallels in sets of numbers. Numerology is common now as it has always been, however it is never been seen as predictive nor significant by anyone except people who hold it as a superstition.
So...
Why the number show.... what are you trying to say?
QUOTE (Euler+Jun 18 2009, 11:02 PM)
Again, you have failed to respond appropriately. If you can now do the kiddie level operation of expanding some brackets, then I'm happy for you. But let's see you respond to:
The fact that you continue to avoid refering to the GRE mathematics test I've linked, speaks volumes.
I cannot stress this enough: you are making a fool of yourself.
I suggest, Euler, in order to follow through on your certainty, that you contact the Columbia University School of Continuing Education and alert them to the fact that the GRE Recruiting Service they rely upon for student recruitment has somehow become compromised/corrupted, apparently recording false test scores for at least one test-taker.
It is uncertain whether this corruption was achieved via alien intervention, astral projection, or some form of material/immaterial quantum entanglement that has broken the heretofore inviolable border between reality and wishful thinking.
Good luck, Euler. One can only imagination the powerful forces that will be arrayed against you in your quest to alert the Guardians of the Academy to this grand conspiracy directed against the Scientific and Academic Establishment.
- RF
The fact that you continue to avoid refering to the GRE mathematics test I've linked, speaks volumes.
I cannot stress this enough: you are making a fool of yourself.
I suggest, Euler, in order to follow through on your certainty, that you contact the Columbia University School of Continuing Education and alert them to the fact that the GRE Recruiting Service they rely upon for student recruitment has somehow become compromised/corrupted, apparently recording false test scores for at least one test-taker.
It is uncertain whether this corruption was achieved via alien intervention, astral projection, or some form of material/immaterial quantum entanglement that has broken the heretofore inviolable border between reality and wishful thinking.
Good luck, Euler. One can only imagination the powerful forces that will be arrayed against you in your quest to alert the Guardians of the Academy to this grand conspiracy directed against the Scientific and Academic Establishment.
- RF
Hmmm... how about leaving it and answering my question then?
There is an extraordinarily simple solution to the debate ongoing within this thread...
Raphie, take the test Euler offered you.
Here's the link again.
Just post your answers and we can all see that you're as good as you claim to be. You've said you have nothing to prove, but that's not true. You claimed to have scored a 720 on a GRE. Neither Euler nor any others here believe that, therefore the burden of proof is on you. If you won't prove it, you cannot complain when no-one believes you and you find yourself called a liar.
Raphie, take the test Euler offered you.
Here's the link again.
Just post your answers and we can all see that you're as good as you claim to be. You've said you have nothing to prove, but that's not true. You claimed to have scored a 720 on a GRE. Neither Euler nor any others here believe that, therefore the burden of proof is on you. If you won't prove it, you cannot complain when no-one believes you and you find yourself called a liar.
Perhaps rephrasing the original question, and maybe moving beyond arguments about qualifications so the rest of us might learn something.
Consider these three categories:
1. Numerology
2. Mathematics
3. Mathematical models of physical entities and processes.
Is there a straightforward definition of the differences among these categories?
(BTW saw a number posted on a car window. 333. Half evil.)
Consider these three categories:
1. Numerology
2. Mathematics
3. Mathematical models of physical entities and processes.
Is there a straightforward definition of the differences among these categories?
(BTW saw a number posted on a car window. 333. Half evil.)
What if you saw it twice?
No problem, the observer is not the same as what is observed. I'm 99.543% certain I'm no more evil than anybody else. (Just don't ask my wife.)
QUOTE (MjolnirPants+Jun 18 2009, 11:59 PM)
There is an extraordinarily simple solution to the debate ongoing within this thread...
Raphie, take the test Euler offered you.
Here's the link again.
Just post your answers and we can all see that you're as good as you claim to be. You've said you have nothing to prove, but that's not true. You claimed to have scored a 720 on a GRE. Neither Euler nor any others here believe that, therefore the burden of proof is on you. If you won't prove it, you cannot complain when no-one believes you and you find yourself called a liar.
It is is very easy to not respond to or accept spurious and rather inane challenges when one has, so to speak, "truth" on one's side.
If I speak "truth", which I do, I have nothing to gain from accepting such challenges.
To provide context, however, it takes great effort for the unconventional thinker-type, a category I believe most would agree applies to me, to force him/her -self into the "standardized" box of accepted learning. The question is not one of native intelligence, but of how one applies that intelligence. In other words, it's an issue of "emphasis."
Given all this, taking the GRE's was extremely stressful for me, and required intense short term concentration and "cramming." I basically had to alter my entire reference frame, diagnosed ADHD and all, for a week or so, committing to rote memory mathematical "tricks" and "shortcuts" that had held little to no interest for me. Not an experience I wish to repeat, especially to satisfy the absurd and rather delusional ravings of any who would challenge what passes for most as "objective reality."
Best,
Raphie
P.S. For the record, I did not request nor did I receive any time handicap on the GRE's, in case anyone is wondering.
P.P.S. Keep in mind that the "challenger" is one who has publicly posited that I cannot even multiply out n*(n+1). Good lord, just who's credibility ought to be in question here?
Raphie, take the test Euler offered you.
Here's the link again.
Just post your answers and we can all see that you're as good as you claim to be. You've said you have nothing to prove, but that's not true. You claimed to have scored a 720 on a GRE. Neither Euler nor any others here believe that, therefore the burden of proof is on you. If you won't prove it, you cannot complain when no-one believes you and you find yourself called a liar.
It is is very easy to not respond to or accept spurious and rather inane challenges when one has, so to speak, "truth" on one's side.
If I speak "truth", which I do, I have nothing to gain from accepting such challenges.
To provide context, however, it takes great effort for the unconventional thinker-type, a category I believe most would agree applies to me, to force him/her -self into the "standardized" box of accepted learning. The question is not one of native intelligence, but of how one applies that intelligence. In other words, it's an issue of "emphasis."
Given all this, taking the GRE's was extremely stressful for me, and required intense short term concentration and "cramming." I basically had to alter my entire reference frame, diagnosed ADHD and all, for a week or so, committing to rote memory mathematical "tricks" and "shortcuts" that had held little to no interest for me. Not an experience I wish to repeat, especially to satisfy the absurd and rather delusional ravings of any who would challenge what passes for most as "objective reality."
Best,
Raphie
P.S. For the record, I did not request nor did I receive any time handicap on the GRE's, in case anyone is wondering.
P.P.S. Keep in mind that the "challenger" is one who has publicly posited that I cannot even multiply out n*(n+1). Good lord, just who's credibility ought to be in question here?
PhysOrg scientific forums are totally dedicated to science, physics, and technology. Besides topical forums such as nanotechnology, quantum physics, silicon and III-V technology, applied physics, materials, space and others, you can also join our news and publications discussions. We also provide an off-topic forum category. If you need specific help on a scientific problem or have a question related to physics or technology, visit the PhysOrg Forums. Here you’ll find experts from various fields online every day.
To quit out of "lo-fi" mode and return to the regular forums, please click here.