Hey TRoc,
Sorry TRoc, I should have qualified my previous post a bit more. The part the struck me as important was the possibility of constants changing, and had nothing in particular to do with the fine structure constant. The thought that I had upon reading the article was that your matrix is invariant to the assigned value of c.
David Argall,
I don't know if I can really be of any assistance...
There are certainly some alternative routes a person could take with quantities. 'One' can be very abstract: how can you define One tabula rasa? It seems that we always need "another One" to compare with / measure against in order to gain meaning.
When we name something, it becomes One of those somethings. However, if this "something" is made from other things, where does that "One" thing start? This is really the basis for particle & atomic physics: to find the Beginning of things is to find One "something" that is not measured against another in order to have an independent existence.
Why Not?,
Only at a centered, mirror symmetry is © derived. (it is important to note that the matrix was not built from the center out, with © as a goal; just a helical, 13 equal part spin from 1 to 2: the Fundamental Resonance)
As with any velocity, if you change time or distance, you change the speed. To find another common velocity, start with the 2 values in the diagonal positions x+1, y+10 and x+2, y+11. This (and any symmetrical pair from here) will give you the speed of sound (temperature dependent) ~320 m/s.
T.Roc
I don't know if I can really be of any assistance...
There are certainly some alternative routes a person could take with quantities. 'One' can be very abstract: how can you define One tabula rasa? It seems that we always need "another One" to compare with / measure against in order to gain meaning.
When we name something, it becomes One of those somethings. However, if this "something" is made from other things, where does that "One" thing start? This is really the basis for particle & atomic physics: to find the Beginning of things is to find One "something" that is not measured against another in order to have an independent existence.
Why Not?,
Only at a centered, mirror symmetry is © derived. (it is important to note that the matrix was not built from the center out, with © as a goal; just a helical, 13 equal part spin from 1 to 2: the Fundamental Resonance)
As with any velocity, if you change time or distance, you change the speed. To find another common velocity, start with the 2 values in the diagonal positions x+1, y+10 and x+2, y+11. This (and any symmetrical pair from here) will give you the speed of sound (temperature dependent) ~320 m/s.
T.Roc
Hey Troc,
When I mentioned the invariance to c, I had not thought of it that way (as in finding the helical relationship of any know velocity measured in m/s), but I believe it gets us to the same place. I was thinking more in terms of the units themselves.
I had tried finding the center for 186,282.397 and was unable to. The closest I could come was ~184,431. But when I changed 1.026709_ to 1.002474_ , it worked fine. So by setting R=1.00000, I can find both centers representing the speed of light and use ~1.026709^2 to convert to meters or ~1.002474^2 to convert to miles. The Fundamental Resonance seems to have a fundamental radius of one and from there the conversion factor gives us the units. Or maybe I'm just reading to much into this.
P.s. ~1.0020486^2 for feet.
When I mentioned the invariance to c, I had not thought of it that way (as in finding the helical relationship of any know velocity measured in m/s), but I believe it gets us to the same place. I was thinking more in terms of the units themselves.
I had tried finding the center for 186,282.397 and was unable to. The closest I could come was ~184,431. But when I changed 1.026709_ to 1.002474_ , it worked fine. So by setting R=1.00000, I can find both centers representing the speed of light and use ~1.026709^2 to convert to meters or ~1.002474^2 to convert to miles. The Fundamental Resonance seems to have a fundamental radius of one and from there the conversion factor gives us the units. Or maybe I'm just reading to much into this.
P.s. ~1.0020486^2 for feet.
Why Not?,
It's good to see you experimenting with the values; there are many interesting things possible.
Basically, you are right about the Fundamental Resonance. Cycles, or completion of a dualistic vibration, is what we're after. These can be measured in the number of cycles per distance, or the distance covered per cycle. All things being symmetrical, these two values have an inverse relationship that produces a constant velocity. Neither of these measurements can ever be zero.
The important part is the values that we are measuring these things against. Science has set the Meter, the Second, and Hertz, all at One, with each having its' own comparison.
1 Second = 299,792,458 Meters
1 Hertz = 1 Cycle per Second
1 Meter = 3.33_e-9 Seconds
Showing that Hz has the only 1:1 ratio.
Then, further defining the system with:
1 Wavelength = 1 Meters per 1 Cycle
1 Frequency = 1 Cycle per 1 Second
Showing either to have a possible 1:1 ratio, but not both.
So, completing the picture:
1 Wavelength = 299,792,458 Frequency per 1 Second
or
1 Frequency = 3.335640_e-9 Wavelength per 1 Second
I know this is all very basic, but I think its' worthwhile to put it all out like that to see the jostling of '1' unit to other units for comparison, or measurement. Time is the stable 1:1 factor in this version; later other parts were set to '1', and time set at other than '1', to compare "fundamental" length, etc. (Planck)
The speed of light (299,792,458 .. c ) was set because that is what was ALWAYS measured. No other reason. So, because velocity itself is a 2 part value (distance per time), then there are also 2 ways to describe this value. This is the 2 part, inverse relationship of F & W. When one gets smaller, the other gets bigger, and vice versa.
The reason I am repeating all of this is this:
The Matrix is one continuous set of discreet numbers, each value is the same ratio apart from the next. It has the capability of being infinitely small or large. We are mainly interested in the values in between.
You can start from '1' and move any integer # of steps and stop at a value. This value could be assigned "frequency", or "wavelength". Whichever you choose, its' inverse will also be found an integer number of steps from '1', but in the opposite direction. In this sense, the Matrix shows the F & W are more than inverse, they are naturally connected with a symmetrical rotation that has a center that can never be a point, both can not be from the same position.
This center is not '1'.
After the center is determined, you can define quadrants that, from any point, there exists a mirror symmetrical opposite point that will be frequency if you set the other to wavelength, or vice versa. Their product will always be c.
So the big question is: is c a constant of nature, and the way things work (Physics), or a constant of math, and the way we measure?
T.Roc
It's good to see you experimenting with the values; there are many interesting things possible.
Basically, you are right about the Fundamental Resonance. Cycles, or completion of a dualistic vibration, is what we're after. These can be measured in the number of cycles per distance, or the distance covered per cycle. All things being symmetrical, these two values have an inverse relationship that produces a constant velocity. Neither of these measurements can ever be zero.
The important part is the values that we are measuring these things against. Science has set the Meter, the Second, and Hertz, all at One, with each having its' own comparison.
1 Second = 299,792,458 Meters
1 Hertz = 1 Cycle per Second
1 Meter = 3.33_e-9 Seconds
Showing that Hz has the only 1:1 ratio.
Then, further defining the system with:
1 Wavelength = 1 Meters per 1 Cycle
1 Frequency = 1 Cycle per 1 Second
Showing either to have a possible 1:1 ratio, but not both.
So, completing the picture:
1 Wavelength = 299,792,458 Frequency per 1 Second
or
1 Frequency = 3.335640_e-9 Wavelength per 1 Second
I know this is all very basic, but I think its' worthwhile to put it all out like that to see the jostling of '1' unit to other units for comparison, or measurement. Time is the stable 1:1 factor in this version; later other parts were set to '1', and time set at other than '1', to compare "fundamental" length, etc. (Planck)
The speed of light (299,792,458 .. c ) was set because that is what was ALWAYS measured. No other reason. So, because velocity itself is a 2 part value (distance per time), then there are also 2 ways to describe this value. This is the 2 part, inverse relationship of F & W. When one gets smaller, the other gets bigger, and vice versa.
The reason I am repeating all of this is this:
The Matrix is one continuous set of discreet numbers, each value is the same ratio apart from the next. It has the capability of being infinitely small or large. We are mainly interested in the values in between.
You can start from '1' and move any integer # of steps and stop at a value. This value could be assigned "frequency", or "wavelength". Whichever you choose, its' inverse will also be found an integer number of steps from '1', but in the opposite direction. In this sense, the Matrix shows the F & W are more than inverse, they are naturally connected with a symmetrical rotation that has a center that can never be a point, both can not be from the same position.
This center is not '1'.
After the center is determined, you can define quadrants that, from any point, there exists a mirror symmetrical opposite point that will be frequency if you set the other to wavelength, or vice versa. Their product will always be c.
So the big question is: is c a constant of nature, and the way things work (Physics), or a constant of math, and the way we measure?
T.Roc
Hey TRoc,
The beauty (at least part of it) that I see in your model (your Matrix, it's formulation, the role of beat frequency, etc.) is that it shows that c is both. Mathematically the model provides a dimensionless formulation providing the inverse relationship of f and w. Naturally it allows us to find harmonious values, regardless of the measuring devices we choose.
I am surprised that none of the others have chimed in...
QUOTE
So the big question is: is c a constant of nature, and the way things work (Physics), or a constant of math, and the way we measure?
The beauty (at least part of it) that I see in your model (your Matrix, it's formulation, the role of beat frequency, etc.) is that it shows that c is both. Mathematically the model provides a dimensionless formulation providing the inverse relationship of f and w. Naturally it allows us to find harmonious values, regardless of the measuring devices we choose.
I am surprised that none of the others have chimed in...
Why Not?,
I agree: it is both. It would be very hard for it to be one or the other. In just asking the question, however, much depth can be seen.
As far as the others, I do believe that you are the first person who actually constructed my matrix per my easy instructions. Many people have commented, but without having the full spread in front of you, there is just too much to imagine, and it is too different from what is out there. A few people asked for a copy of it, and I devised a smaller version; but I don't think it does it justice.
Since you like to play with the numbers a bit, try this: Take any number (~3.86 is a good one), at any point in the chart. Mark it somehow (I found small cuts of post-its work well), and then start to mark everywhere else this number appears. You will have to accept +/- 10 (ie 3.76 to 3.96) approximations, and, of course, you will be covering exponents of 10 (3.8e-7, 3.8e-6, 3.8e-5, etc). Keep in mind that this "deca" mapping would be closer to our 0-9 system, with the "resonance" at 10, than the matrix, which just extends the Primary Resonance (1, 2) recursively.
T.Roc
I agree: it is both. It would be very hard for it to be one or the other. In just asking the question, however, much depth can be seen.
As far as the others, I do believe that you are the first person who actually constructed my matrix per my easy instructions. Many people have commented, but without having the full spread in front of you, there is just too much to imagine, and it is too different from what is out there. A few people asked for a copy of it, and I devised a smaller version; but I don't think it does it justice.
Since you like to play with the numbers a bit, try this: Take any number (~3.86 is a good one), at any point in the chart. Mark it somehow (I found small cuts of post-its work well), and then start to mark everywhere else this number appears. You will have to accept +/- 10 (ie 3.76 to 3.96) approximations, and, of course, you will be covering exponents of 10 (3.8e-7, 3.8e-6, 3.8e-5, etc). Keep in mind that this "deca" mapping would be closer to our 0-9 system, with the "resonance" at 10, than the matrix, which just extends the Primary Resonance (1, 2) recursively.
T.Roc
Hey TRoc,
You can lead them to water...
With regard to you suggestion... First off, the numbers (the first 3 digits, +/- 10) tend to repeat ever 10 rows. Likewise, they tend to repeat every 3 and 1/3 rotations (1200 degrees). However, ~386 (+/- 10) is the only number that is one "octave" (360 degrees) off center with it's partner (center being c). As such, the product of the two is always 1/2 c. So me thinks this has something to do with Planck?
When are you going to get around to posting your theory? I am particularly interested in how you see gravity "fitting" in...
You can lead them to water...
With regard to you suggestion... First off, the numbers (the first 3 digits, +/- 10) tend to repeat ever 10 rows. Likewise, they tend to repeat every 3 and 1/3 rotations (1200 degrees). However, ~386 (+/- 10) is the only number that is one "octave" (360 degrees) off center with it's partner (center being c). As such, the product of the two is always 1/2 c. So me thinks this has something to do with Planck?
When are you going to get around to posting your theory? I am particularly interested in how you see gravity "fitting" in...
Deleted.
Hey guys,
What happened to RealityCheck, anybody know? TRoc, I haven't worked out your matrix yet, but reading your conversation with Why Not, I find it intriguing. Especially since the number 10 is the sum of 1, 2, 3, and 4, and these, in turn, are connected to the fundamental harmonics within the octave, the fourth and, its inverse, the fifth.
Now, it turns out also that these are related to 1D, 2D, and 3D geometry; that is, they are all mathematically equivalent expansions of 1, 2, 3, and 4, in the form of the reciprocal number (1D) "geometry," fractal (2D) geometry, and Euclidean (3D) geometry. This is seen in the basic ratio of 3/4 (the fourth harmonic), where the ratio of the number of poles in the RN, to the total units of motion in these poles, and the ratio of the length of the Koch curve initiator, to the number of units in its generator, and the ratio of the number of points in a rotated line, to the number of line segments in the resulting plane and cube, are all a function of dimension:
f(x) = (p/l)^d = (3/4)^d
where p is the number of poles, l is the units of motion or length, and d is the dimension of the geometry. If we take the ratio of the log of p, to the log of x, or the log of l, to the log of x, and solve for p or l, the dimension need not be an integer. This definition of dimension is called a Hausdorff dimension and occurs in descriptions of natural objects and evaluations of the trajectories of dynamic systems.
It would be interesting to look at your matrices in this light.
What happened to RealityCheck, anybody know? TRoc, I haven't worked out your matrix yet, but reading your conversation with Why Not, I find it intriguing. Especially since the number 10 is the sum of 1, 2, 3, and 4, and these, in turn, are connected to the fundamental harmonics within the octave, the fourth and, its inverse, the fifth.
Now, it turns out also that these are related to 1D, 2D, and 3D geometry; that is, they are all mathematically equivalent expansions of 1, 2, 3, and 4, in the form of the reciprocal number (1D) "geometry," fractal (2D) geometry, and Euclidean (3D) geometry. This is seen in the basic ratio of 3/4 (the fourth harmonic), where the ratio of the number of poles in the RN, to the total units of motion in these poles, and the ratio of the length of the Koch curve initiator, to the number of units in its generator, and the ratio of the number of points in a rotated line, to the number of line segments in the resulting plane and cube, are all a function of dimension:
f(x) = (p/l)^d = (3/4)^d
where p is the number of poles, l is the units of motion or length, and d is the dimension of the geometry. If we take the ratio of the log of p, to the log of x, or the log of l, to the log of x, and solve for p or l, the dimension need not be an integer. This definition of dimension is called a Hausdorff dimension and occurs in descriptions of natural objects and evaluations of the trajectories of dynamic systems.
It would be interesting to look at your matrices in this light.
Why not?,
Actually, all numbers produced in the matrix have this feature (not just 3.86), that's why I said "pick any number"; it has a built in intuitive hint when you compare 3.88e-7, in the UV, to 3.85e+14, in the IR. They are 1 octave less than equally spaced from the center, and have the product of 1/2c, as you said.
What I wanted you to think of was extending this pattern still further: at some point, any number will drift all the way across the columns to return to the "other side", or vertical octave. The 'horizontal' octave is the standard 1n to 2n in 13 left to right steps. The 'vertical' octave moves (staying with the ~3.86 example) from the 3 # 'set' 3.77e-40, 3.86e-37, and 3.95e-34 in the 13th column (each 10 rows apart, or *2^10), and staggers it's way through the matrix, until reaching the 1st column, with the 3 # set 3.75e+47, 3.84e+50, and 3.93e+53. This may be the effective size limit of the Resonance Matrix; the ‘Planck’ similarities are obvious.
3.77e-40 * 3.75e+47 = 1/2c
Z*R^1896 = 3.7513432849367840643122882481166e+47
x
Z/R^1572 = 3.771534337855930815479689876855e-40
= 141483200.12224346289928411624845
x
2
= 2.8296640024448692579856823249698e+8
x
1.059463094355929526456182529494
= 2.9979245800178257169113036420939e+8
so,
x+6, y-143 * x+6, y+145 = ˝c with 0 rotation
is the same thing as saying
x-6, y-144 * x+6, y+145 = c with full rotation
but, either way, the symmetry is broken. (both x & y canceling as in all other pairs)
I am still a couple weeks from posting part 1 of my theory on its' own thread. Hang in there. Gravity will be there, but not in the first parts.
Excal,
Nice to see you back.
Don't know anything about RC. Also Tor?
I don't have time to do your post justice, but I am interested as well. The Koch curve would seem to be a special case in my matrix, and resonance as well. Equal thirds produces a completely different kind of resonant chord; I believe it to show the fundamental difference between the Proton vibration, and the electron vibration.
I think recursive geometries will be important to the autopoeitic nature of the 'common nodes' of fundamental resonances from quantum vibrations. You might read a few of my last posts in "puzzling questions" sub-forum: The nature of electricity.. are bubbles the answer?
ciao!
T.Roc
Actually, all numbers produced in the matrix have this feature (not just 3.86), that's why I said "pick any number"; it has a built in intuitive hint when you compare 3.88e-7, in the UV, to 3.85e+14, in the IR. They are 1 octave less than equally spaced from the center, and have the product of 1/2c, as you said.
What I wanted you to think of was extending this pattern still further: at some point, any number will drift all the way across the columns to return to the "other side", or vertical octave. The 'horizontal' octave is the standard 1n to 2n in 13 left to right steps. The 'vertical' octave moves (staying with the ~3.86 example) from the 3 # 'set' 3.77e-40, 3.86e-37, and 3.95e-34 in the 13th column (each 10 rows apart, or *2^10), and staggers it's way through the matrix, until reaching the 1st column, with the 3 # set 3.75e+47, 3.84e+50, and 3.93e+53. This may be the effective size limit of the Resonance Matrix; the ‘Planck’ similarities are obvious.
3.77e-40 * 3.75e+47 = 1/2c
Z*R^1896 = 3.7513432849367840643122882481166e+47
x
Z/R^1572 = 3.771534337855930815479689876855e-40
= 141483200.12224346289928411624845
x
2
= 2.8296640024448692579856823249698e+8
x
1.059463094355929526456182529494
= 2.9979245800178257169113036420939e+8
so,
x+6, y-143 * x+6, y+145 = ˝c with 0 rotation
is the same thing as saying
x-6, y-144 * x+6, y+145 = c with full rotation
but, either way, the symmetry is broken. (both x & y canceling as in all other pairs)
I am still a couple weeks from posting part 1 of my theory on its' own thread. Hang in there. Gravity will be there, but not in the first parts.
Excal,
Nice to see you back.
Don't know anything about RC. Also Tor?
I don't have time to do your post justice, but I am interested as well. The Koch curve would seem to be a special case in my matrix, and resonance as well. Equal thirds produces a completely different kind of resonant chord; I believe it to show the fundamental difference between the Proton vibration, and the electron vibration.
I think recursive geometries will be important to the autopoeitic nature of the 'common nodes' of fundamental resonances from quantum vibrations. You might read a few of my last posts in "puzzling questions" sub-forum: The nature of electricity.. are bubbles the answer?
ciao!
T.Roc
Hey TRoc,
I guess I should state this another way. While any number is one octave off center with its "partner", ~386 is the only number where it's "partner" is also ~386. For example, (x1, y6) and (x-1, y-5) or (x5, y13) and (x-5, y -12) (admittedly, I have not looked at all of the numbers, but ~386 looks like the only one that pairs one octave off from it's partner that also is ~386. - Either that, or I have somehow screwed up the spreadsheet!) It almost looked like another level of symmetry.
With regard to what you were trying to point out (vertical and horizontal octaves), I have not been able to go past 15 decimal places (I guess it's time I figured out how to in Excel) so I have not been able to extend your Matrix more than about 60 rows +/- from center. But from what I do have, I think I see your point.
One last question though, have you run the coordinates for all of the quark and lepton masses and do they show a pattern?
I look forward to you thread.
QUOTE
However, ~386 (+/- 10) is the only number that is one "octave" (360 degrees) off center with it's partner (center being c). As such, the product of the two is always 1/2 c. So me thinks this has something to do with Planck?
I guess I should state this another way. While any number is one octave off center with its "partner", ~386 is the only number where it's "partner" is also ~386. For example, (x1, y6) and (x-1, y-5) or (x5, y13) and (x-5, y -12) (admittedly, I have not looked at all of the numbers, but ~386 looks like the only one that pairs one octave off from it's partner that also is ~386. - Either that, or I have somehow screwed up the spreadsheet!) It almost looked like another level of symmetry.
With regard to what you were trying to point out (vertical and horizontal octaves), I have not been able to go past 15 decimal places (I guess it's time I figured out how to in Excel) so I have not been able to extend your Matrix more than about 60 rows +/- from center. But from what I do have, I think I see your point.
One last question though, have you run the coordinates for all of the quark and lepton masses and do they show a pattern?
I look forward to you thread.
Why Not?,
Don't rely on the math that Excel produces, I had too many problems, given that I needed near 35 digits for the RM (resonance matrix) to work. Now I always calculate the actual number with the scientific calculator that comes with windows. The actual printout that I have is just used for loose reference. The positions are the same, the numbers are just 'approximate'.
Yes, I have ran all the numbers for the leptons and quarks. They came out very good. I'm not so much looking for a 'geometrical' pattern, that would appear from the positions of the values on the matrix as I am looking for a repetitive mathematical pattern. The electron neutrino is sort of an oddball so far, as its' mass (in Hz) is so close to the visible light band of frequencies. Still more to do...
--~~~~~~~--
T.Roc
Don't rely on the math that Excel produces, I had too many problems, given that I needed near 35 digits for the RM (resonance matrix) to work. Now I always calculate the actual number with the scientific calculator that comes with windows. The actual printout that I have is just used for loose reference. The positions are the same, the numbers are just 'approximate'.
Yes, I have ran all the numbers for the leptons and quarks. They came out very good. I'm not so much looking for a 'geometrical' pattern, that would appear from the positions of the values on the matrix as I am looking for a repetitive mathematical pattern. The electron neutrino is sort of an oddball so far, as its' mass (in Hz) is so close to the visible light band of frequencies. Still more to do...
--~~~~~~~--
T.Roc
Hey TRoc, Excal, et al,
TRoc, still patiently waiting for your thread...
I ran across this paper today and thought you may find it interesting.
http://music.princeton.edu/%7Edmitri/voiceleading.pdf
My knowledge of music theory is minimal (ok, it is as close to zero as one can get), but I found the paper interesting and possibly of relavance.
TRoc, still patiently waiting for your thread...
I ran across this paper today and thought you may find it interesting.
http://music.princeton.edu/%7Edmitri/voiceleading.pdf
My knowledge of music theory is minimal (ok, it is as close to zero as one can get), but I found the paper interesting and possibly of relavance.
Why Not?,
Yes, for certain, Dmitri Tymoczko's paper is very relevant and interesting. You may have read that it was published by the journal Science, and that it was the first paper concerning Music it their 137 year history. While the scope of his paper is limited to Music (chord voicing), it's broad importance will become more apparent with several related papers due to be published this year. The math that supports his chord scale is the same that supports the individual frequencies that the Resonance Matrix uses. I will be using it as a key reference in my work. I will be posting soon, in parts so not to delay.
Did you see the links to SGS that I posted earlier in this thread? There is some similarity there, if you can picture a helical geometry with discreet rotation. Having a scaled ratio of symmetrical vibrations is critical in producing a constant measured velocity.
Ciao!
T.Roc
Yes, for certain, Dmitri Tymoczko's paper is very relevant and interesting. You may have read that it was published by the journal Science, and that it was the first paper concerning Music it their 137 year history. While the scope of his paper is limited to Music (chord voicing), it's broad importance will become more apparent with several related papers due to be published this year. The math that supports his chord scale is the same that supports the individual frequencies that the Resonance Matrix uses. I will be using it as a key reference in my work. I will be posting soon, in parts so not to delay.
Did you see the links to SGS that I posted earlier in this thread? There is some similarity there, if you can picture a helical geometry with discreet rotation. Having a scaled ratio of symmetrical vibrations is critical in producing a constant measured velocity.
Ciao!
T.Roc
You really cannot do without e and pi.
Don't worry about i, just think of complexland as a place to go to get rid of i's and then back again:-)
The complex field "completes" the reals.
Above links e and pi (circles and spirals).
Don't worry about i, just think of complexland as a place to go to get rid of i's and then back again:-)
The complex field "completes" the reals.
Above links e and pi (circles and spirals).
Damn!
How to post math? Try again with ML.
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msup>
<mi>i</mi>
<mi>i</mi>
</msup>
<mo>=</mo>
<msup>
<mi>e</mi>
<mo>−</mo>
</msup>
<mfrac>
<mi>Π</mi>
<mn>2</mn>
</mfrac>
<mo>=</mo>
<mn>0.21</mn>
<mfenced>
<mrow>
<mi>a</mi>
<mi>p</mi>
<mi>x</mi>
</mrow>
</mfenced>
</mrow>
</math>
How to post math? Try again with ML.
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block">
<mrow>
<msup>
<mi>i</mi>
<mi>i</mi>
</msup>
<mo>=</mo>
<msup>
<mi>e</mi>
<mo>−</mo>
</msup>
<mfrac>
<mi>Π</mi>
<mn>2</mn>
</mfrac>
<mo>=</mo>
<mn>0.21</mn>
<mfenced>
<mrow>
<mi>a</mi>
<mi>p</mi>
<mi>x</mi>
</mrow>
</mfenced>
</mrow>
</math>
Big as I can get it..duh!
Why Not?,
I have had to change my idea about posting my thread in parts: I was going to just add the parts to the first posting with the "edit" function, which is now no longer available (after x time).
I think I can do something similar with "links" to different parts of the thread. The point is to keep the flow of information going, but to encourage comments and discussion along the way.
Give me your opinion (and everyone else that is reading this) on this: what do you think about posting "answers" first, and then explanations? Meaning post "the math" and then "the model"? I think that, without seeing what the simple math does, the model, or verbal explanation, seems too abstract, or even "cranky".
Anyway, something soon!
Contrarian: you got the symbol posted (which is more than i can do), are you going to discuss its' meaning?
ciao!
T.Roc
I have had to change my idea about posting my thread in parts: I was going to just add the parts to the first posting with the "edit" function, which is now no longer available (after x time).
I think I can do something similar with "links" to different parts of the thread. The point is to keep the flow of information going, but to encourage comments and discussion along the way.
Give me your opinion (and everyone else that is reading this) on this: what do you think about posting "answers" first, and then explanations? Meaning post "the math" and then "the model"? I think that, without seeing what the simple math does, the model, or verbal explanation, seems too abstract, or even "cranky".
Anyway, something soon!
Contrarian: you got the symbol posted (which is more than i can do), are you going to discuss its' meaning?
ciao!
T.Roc
It's been a while since I posted, but I've been looking at ways that the simple evolution from a random network could actually have many characteristics similar to lossless, lightspeed medium.
I won't go into detail, so as not to bias others insights into this, but consider how the evolution of information flow through a collection of random computational elements could occur.
The lossless medium and ideas of conservation of energy need not actually be true. If it's a closed system (or at least for the most part closed), then the only pieces of information and pathways retained would be necessarily lossless.
As a simple example, if you have two data loops and one has an element that isn't lossless (say a fixed binary 0 output), then that loop isn't detectable and the elements in it would become static values. You could compare this to the physical possibility of something begin truly destroyed and not being conserved - whatever energies had the possibility of passing through this channel would not be present later (you might compare this to the rapid cooling or inflationary period after the Big Bang), whereas information cycling through lossless pathways would be retained. Likely this would be observed along the lines of a distribution of inherent 'half lifes' to things, though some things could potentially have this value infinite (or at least very large, if the system isn't entirely closed but slowly changing over time).
Also the equivalent of a rather uniform light speed medium could be constructed. The delays between elements of this network would correlate with light speed delays and the shortest path between two points would be the equivalent light speed delay.
Now you might think such a network would act diffusively and not contain wave fronts, but all information in this network would have cyclic features (to the extent it was closed) and equivalent wavelike properties and the reason why only the fastest path between two points is ultimately retained is because if a secondary path existed that took longer an effective phase cancellation could occur. This cancellation would also act destructively and in a non-lossless manner and only be able to occur once. The remaining cyclic information would need to have this secondary pathway act only in some phase lagged multiple of a 2pi or 360 deg phase shift. These requirements construct the pathways for spacetime.
Let me give an example here:
Let's say we have one path with 6 cycles delay, and these are elements in a chain A, B, C, D, E and F.
Now if we route a "wormhole" from A to D and only some logic operation to occur between A and D before proceednig to E, and watch what occurs, we'll find that this places a restriction on the possible contents of this system. Before any possible combination of 6 values could cycle through the system losslessly, but now at a distance of 3, only lossless operations are supported and though the system may have started with 6 distinct value it quickly evolves into more limited modes.
Let's say all elements shift right (A to B, B to C, etc.) each time step but in a ring that goes back from F to A. Now if we make the D to E step include an AND operation with the A element, we can no longer support any elements at a distance of 3 than aren't either both 0 or both 1 (assuming binary values, if A is 0 and D is 1 then E will be 0 and effectively destroy the content of D, which occurs only once but from then on is seen as losslessly propogating information but with "strange action at a distance" and other fine correlations to properties distributed throughout space).
Now, because we inevitably make observations from within the network, we can't see this outside perspective of a small closed system, instead we see time delays as distances. Let's start from time 0 and reconstruct things from the perspective of F, and see what it looks like as a 1-D string of information:
Each of these is the value present in node F at each time step.
F,E,D&A,C&F,B&E,A&D,F&C,E&B,D&A... etc.
If we assume some intelligence parsing of this information, the repetitions are the only static frame of reference to make measurements from so it would be parsed like this:
F, E (one shot, Big Bang events)
D&A, C&F, B&E,
D&A, C&F, B&E, (ANDing is commutative like addition so you can reverse the operations)
D&A, C&F, B&E ...
Now if the operation hadn't been commutative it could have supported a 6 cycle space. Since only the ANDed values are available after after the first couple time steps, there is no need to indicate the AND operations in the observed data (the values prior to this aren't witnessable and might be perceived as intangible absolutes describing the process behind the observation, but not physically verifiable)
So this ends up as a repetitive spacetime though could either be interpreted as infinite in length, though with repetition and texture on a smaller scale:
Either:
X,Y,Z,X,Y,Z,X,Y,Z.... (infinite in space but only 1 time)
or
X,Y,Z
X,Y,Z
X,Y,Z
...
(infinite in time but in a finite space of 3 elements)
The actual underlying grouping in space would be:
X,Y,Z,X,Y,Z
X,Y,Z,X,Y,Z
...
But unless some physical manner of accessing and differentiating these additional nodes wasn't available then it would be an arbitrary and confusing way of perceiving things.
But consider how these match in character the quantum observations of underlying quantized units that can be traded off in various ways of time, distance, velocity and equivalent angular representations.
Let me point out how the faster pathway from A to D effectively overrode the longer pathway of 6 elements and substituted itself as the equivalent lightspeed mode of propogation. And to emphasize some equivalencies, a "wavelength" of 5 would not "resonate" losslessly within this pathway.
Now consider how multiple pathways interacting at a point could appear. If we had pathways of lengths 3, 4 and 5 intersecting at some node or computational element, the total cyclic period of this could potentially be up to 3*4*5 = 60 units of time long before an indentical repetition would be experienced, though smaller and shortwavelength characteristics would be apparent at the actual sizes of 3, 4 and 5.
If space were composed of such loops, then though the total distance in this dimension might be physically perceived at a cycle 60 repetition, attempting to actually interact on these distance would reveal in interdependency at various distances and linkage of properties distributed through space and no physical chain of 60 independent elements would actually exist, though the period of this space would potentially support up to that length (just as a 10 bit binary counter only has 10 digits but counts and repeats over a cycle of 1024 ... but if you change the count at one location it affects results at other locations as well because these spaces aren't physically independent).
Let's say that a second truely independent ring of 60 units was attached to this merged 3,4,5 structure and look at the characteristics. Though both would exihibit 60 cycle periods, one dimension could be influenced in a spacially independent manner (the 60 unit chain) and perceived as such, whereas the tightly convoluted 3,4,5 structure would act as a smearing across the larger dimension and would give it periodic structure. Now if instead these 3,4,5 structures were actually replicated 60 times and only one element of each of these 3,4,5 structures was visible as part of a 60 unit chain, then space would exhibit a small scale "memory", similar to inertia - if you held one location of the larger 60 unit chain at a fixed value, over a period of time this value would propogate within the 3,4,5 chains and fill them, but if you attempted to remove this, these elements would serve similar to mirrored copies that would tend to retain this value over time and require energy (or equiavlently force over time) to alter signifcantly.
There was another thread where I believe you can actually map some of these into the equivalent of magnetic field lines. (If you interprete things in a 2 dimensional space but watch the cycles over time, it becomes a 3D toroidal structure that follows the form of the fields we see as electromagnetic forces), the reason these field lines are parrallel and don't intersect, is because whenever intersections have occured the information is destroyed (I just had a funny thought, does anyone remember Ghostbusters and the warning against crossing the streams? Anyway it's just a cute analogy)
I believe the reason we intuitively perceive most of space as being rather uniform and not tightly convoluted or warped is because these structures are small and the vast number of small repetitions that occur tend to blur out on larger scales. For example, though a crystal might be seen as a large solid single object, it's because the crystal is a repetitive structure at a small scale and we're also not in a position to see outside this network to actually measure the size, so repetitions simply appear to expand out into space. Just as how only a single AND gate in the above 6 element "space" appeared to exist at all location in space - all paths passed through the same element and were exposed to the same processing so a singular element, from an external perspective, can appear in a reciprocal sense, all encompassing from an internal perspective (though truly other than for the "Big Bang" of that 6 element chain, the AND gate is actually invisible, though additional pathways would allow for it to be detected in a relative manner).
I don't want to add much more (and truly I didn't want to give this much detail because I'm looking for new input) but I hope this stimulates some creative tastebuds for you guys.
Have fun.
BTW for some of the resonant views, if you go back the example of a 6 stage chain, if the bypassed interaction was of a length that was relatively prime to the larger length, the chain would degrade into a single state for all 6 elements. In this way space could be seen to support harmonic structures with wavelengths of 1/k or reciprocally integral units of energy. If the bypass had been length 1 or 5, the system would have degraded into a single shared state for example, but a spacing of 2 or 4 would have resulted in a 2 state repetition. Basically a pathway in space to both interact with other energies and be assured to be lossless must reinforce itself at either no delay or some integer number of cycles delay, because spreading slightly and coming back in to interact in a phase shifted manner causes cancellation and for a closed system this can only be a one time event.
The really interesting part would be to find how macroscopic observations similar to gravity, inertia and mass would result from a rather random collection of computational elements. (One thing I didn't consider here is how a subjective frame of reference could shift depending on the information passing through a node ... the interpretation of motion and forces could be not directly embedded in the network but in the manner in which the information is interpreted, but that's just a suggestion).
I won't go into detail, so as not to bias others insights into this, but consider how the evolution of information flow through a collection of random computational elements could occur.
The lossless medium and ideas of conservation of energy need not actually be true. If it's a closed system (or at least for the most part closed), then the only pieces of information and pathways retained would be necessarily lossless.
As a simple example, if you have two data loops and one has an element that isn't lossless (say a fixed binary 0 output), then that loop isn't detectable and the elements in it would become static values. You could compare this to the physical possibility of something begin truly destroyed and not being conserved - whatever energies had the possibility of passing through this channel would not be present later (you might compare this to the rapid cooling or inflationary period after the Big Bang), whereas information cycling through lossless pathways would be retained. Likely this would be observed along the lines of a distribution of inherent 'half lifes' to things, though some things could potentially have this value infinite (or at least very large, if the system isn't entirely closed but slowly changing over time).
Also the equivalent of a rather uniform light speed medium could be constructed. The delays between elements of this network would correlate with light speed delays and the shortest path between two points would be the equivalent light speed delay.
Now you might think such a network would act diffusively and not contain wave fronts, but all information in this network would have cyclic features (to the extent it was closed) and equivalent wavelike properties and the reason why only the fastest path between two points is ultimately retained is because if a secondary path existed that took longer an effective phase cancellation could occur. This cancellation would also act destructively and in a non-lossless manner and only be able to occur once. The remaining cyclic information would need to have this secondary pathway act only in some phase lagged multiple of a 2pi or 360 deg phase shift. These requirements construct the pathways for spacetime.
Let me give an example here:
Let's say we have one path with 6 cycles delay, and these are elements in a chain A, B, C, D, E and F.
Now if we route a "wormhole" from A to D and only some logic operation to occur between A and D before proceednig to E, and watch what occurs, we'll find that this places a restriction on the possible contents of this system. Before any possible combination of 6 values could cycle through the system losslessly, but now at a distance of 3, only lossless operations are supported and though the system may have started with 6 distinct value it quickly evolves into more limited modes.
Let's say all elements shift right (A to B, B to C, etc.) each time step but in a ring that goes back from F to A. Now if we make the D to E step include an AND operation with the A element, we can no longer support any elements at a distance of 3 than aren't either both 0 or both 1 (assuming binary values, if A is 0 and D is 1 then E will be 0 and effectively destroy the content of D, which occurs only once but from then on is seen as losslessly propogating information but with "strange action at a distance" and other fine correlations to properties distributed throughout space).
Now, because we inevitably make observations from within the network, we can't see this outside perspective of a small closed system, instead we see time delays as distances. Let's start from time 0 and reconstruct things from the perspective of F, and see what it looks like as a 1-D string of information:
Each of these is the value present in node F at each time step.
F,E,D&A,C&F,B&E,A&D,F&C,E&B,D&A... etc.
If we assume some intelligence parsing of this information, the repetitions are the only static frame of reference to make measurements from so it would be parsed like this:
F, E (one shot, Big Bang events)
D&A, C&F, B&E,
D&A, C&F, B&E, (ANDing is commutative like addition so you can reverse the operations)
D&A, C&F, B&E ...
Now if the operation hadn't been commutative it could have supported a 6 cycle space. Since only the ANDed values are available after after the first couple time steps, there is no need to indicate the AND operations in the observed data (the values prior to this aren't witnessable and might be perceived as intangible absolutes describing the process behind the observation, but not physically verifiable)
So this ends up as a repetitive spacetime though could either be interpreted as infinite in length, though with repetition and texture on a smaller scale:
Either:
X,Y,Z,X,Y,Z,X,Y,Z.... (infinite in space but only 1 time)
or
X,Y,Z
X,Y,Z
X,Y,Z
...
(infinite in time but in a finite space of 3 elements)
The actual underlying grouping in space would be:
X,Y,Z,X,Y,Z
X,Y,Z,X,Y,Z
...
But unless some physical manner of accessing and differentiating these additional nodes wasn't available then it would be an arbitrary and confusing way of perceiving things.
But consider how these match in character the quantum observations of underlying quantized units that can be traded off in various ways of time, distance, velocity and equivalent angular representations.
Let me point out how the faster pathway from A to D effectively overrode the longer pathway of 6 elements and substituted itself as the equivalent lightspeed mode of propogation. And to emphasize some equivalencies, a "wavelength" of 5 would not "resonate" losslessly within this pathway.
Now consider how multiple pathways interacting at a point could appear. If we had pathways of lengths 3, 4 and 5 intersecting at some node or computational element, the total cyclic period of this could potentially be up to 3*4*5 = 60 units of time long before an indentical repetition would be experienced, though smaller and shortwavelength characteristics would be apparent at the actual sizes of 3, 4 and 5.
If space were composed of such loops, then though the total distance in this dimension might be physically perceived at a cycle 60 repetition, attempting to actually interact on these distance would reveal in interdependency at various distances and linkage of properties distributed through space and no physical chain of 60 independent elements would actually exist, though the period of this space would potentially support up to that length (just as a 10 bit binary counter only has 10 digits but counts and repeats over a cycle of 1024 ... but if you change the count at one location it affects results at other locations as well because these spaces aren't physically independent).
Let's say that a second truely independent ring of 60 units was attached to this merged 3,4,5 structure and look at the characteristics. Though both would exihibit 60 cycle periods, one dimension could be influenced in a spacially independent manner (the 60 unit chain) and perceived as such, whereas the tightly convoluted 3,4,5 structure would act as a smearing across the larger dimension and would give it periodic structure. Now if instead these 3,4,5 structures were actually replicated 60 times and only one element of each of these 3,4,5 structures was visible as part of a 60 unit chain, then space would exhibit a small scale "memory", similar to inertia - if you held one location of the larger 60 unit chain at a fixed value, over a period of time this value would propogate within the 3,4,5 chains and fill them, but if you attempted to remove this, these elements would serve similar to mirrored copies that would tend to retain this value over time and require energy (or equiavlently force over time) to alter signifcantly.
There was another thread where I believe you can actually map some of these into the equivalent of magnetic field lines. (If you interprete things in a 2 dimensional space but watch the cycles over time, it becomes a 3D toroidal structure that follows the form of the fields we see as electromagnetic forces), the reason these field lines are parrallel and don't intersect, is because whenever intersections have occured the information is destroyed (I just had a funny thought, does anyone remember Ghostbusters and the warning against crossing the streams? Anyway it's just a cute analogy)
I believe the reason we intuitively perceive most of space as being rather uniform and not tightly convoluted or warped is because these structures are small and the vast number of small repetitions that occur tend to blur out on larger scales. For example, though a crystal might be seen as a large solid single object, it's because the crystal is a repetitive structure at a small scale and we're also not in a position to see outside this network to actually measure the size, so repetitions simply appear to expand out into space. Just as how only a single AND gate in the above 6 element "space" appeared to exist at all location in space - all paths passed through the same element and were exposed to the same processing so a singular element, from an external perspective, can appear in a reciprocal sense, all encompassing from an internal perspective (though truly other than for the "Big Bang" of that 6 element chain, the AND gate is actually invisible, though additional pathways would allow for it to be detected in a relative manner).
I don't want to add much more (and truly I didn't want to give this much detail because I'm looking for new input) but I hope this stimulates some creative tastebuds for you guys.
Have fun.
BTW for some of the resonant views, if you go back the example of a 6 stage chain, if the bypassed interaction was of a length that was relatively prime to the larger length, the chain would degrade into a single state for all 6 elements. In this way space could be seen to support harmonic structures with wavelengths of 1/k or reciprocally integral units of energy. If the bypass had been length 1 or 5, the system would have degraded into a single shared state for example, but a spacing of 2 or 4 would have resulted in a 2 state repetition. Basically a pathway in space to both interact with other energies and be assured to be lossless must reinforce itself at either no delay or some integer number of cycles delay, because spreading slightly and coming back in to interact in a phase shifted manner causes cancellation and for a closed system this can only be a one time event.
The really interesting part would be to find how macroscopic observations similar to gravity, inertia and mass would result from a rather random collection of computational elements. (One thing I didn't consider here is how a subjective frame of reference could shift depending on the information passing through a node ... the interpretation of motion and forces could be not directly embedded in the network but in the manner in which the information is interpreted, but that's just a suggestion).
Troc
Assume you have Tymoczko's program?
http://music.princeton.edu/%7Edmitri/ChordGeometriesPC11.zip
(BTW, at risk of starting a riot, I consider e, pi (phi as well) to be "natural" but not i; i is simply an "operator")
Gez
Assume you have Tymoczko's program?
http://music.princeton.edu/%7Edmitri/ChordGeometriesPC11.zip
(BTW, at risk of starting a riot, I consider e, pi (phi as well) to be "natural" but not i; i is simply an "operator")
Gez
Contrarian,
I did download the program, but, although it does load up, it shuts down when I try to use the 'visualizer' (the point of geometry!). I think I have a video card problem.
I would not argue against your statement "I consider e, pi (phi as well) to be "natural" but not i; i is simply an "operator" .
StevenA,
Thanks for the post, I think you will like what I have done.
T.Roc
I did download the program, but, although it does load up, it shuts down when I try to use the 'visualizer' (the point of geometry!). I think I have a video card problem.
I would not argue against your statement "I consider e, pi (phi as well) to be "natural" but not i; i is simply an "operator" .
StevenA,
Thanks for the post, I think you will like what I have done.
T.Roc
Hey TRoc,
I think posting the math followed by the model is a novel idea - at least on this site. It would certainly help to avoid a lot of confusion and misunderstanding. The math would serve as a cornerstone for comments regarding the model and would allow for more cogent comment and critique of the model.
Best...
I think posting the math followed by the model is a novel idea - at least on this site. It would certainly help to avoid a lot of confusion and misunderstanding. The math would serve as a cornerstone for comments regarding the model and would allow for more cogent comment and critique of the model.
Best...
Why not first the list of assumptions (starting principles) that are contained implicitly or explicitly in the theory.
Then go from there once they are understood.
Then go from there once they are understood.
Whew! After 2 hours of going through this thread, I am puzzled why no one has brought up the duality that exists in tetrahedral modeling..(.Bucky Fuller's number games in this geometry were interesting...)
BTW, the "rational geometry" was a new arena for me.. Thanks, StevenA (if I remember correctly). I have struggled with the concept of there are many points on a line and its "dual", there are many angles between two lines and the spread appears to resolve the "brick wall" I encountered in in classical geometry. A duality appears feasible between these concepts.
BTW, the "rational geometry" was a new arena for me.. Thanks, StevenA (if I remember correctly). I have struggled with the concept of there are many points on a line and its "dual", there are many angles between two lines and the spread appears to resolve the "brick wall" I encountered in in classical geometry. A duality appears feasible between these concepts.
QUOTE (TRoc+Oct 6 2005, 05:55 AM)
If the the function of an entity (wave, particle, energy, or mass) has the operating "code" built in, would "plus one" be used by the fastest thing in the Universe? It is my belief that it would not.
So, while I'm not suggesting that we toss out the common set, I am wondering if there are other naturally produced (or self replicating) sets of quantities that could be used to describe "the way things work." (physics)
Infinity is divisible and multipliable (and not + 1 or – 1), but it wouldn't be considered "the fastest thing in the universe", because time would be infinite as well. How about the "efficient coefficient"?
The common (finite) set gives us "event horizons", which are secondary to the built-in code. Event horizons are a nice touch (here & there/then & now/this & that/sunrise & sunset/night & day/etc.), but they are just a "tangible duality" that appear to form a "surface". The built-in code doesn't actually have a surface.
So, while I'm not suggesting that we toss out the common set, I am wondering if there are other naturally produced (or self replicating) sets of quantities that could be used to describe "the way things work." (physics)
Infinity is divisible and multipliable (and not + 1 or – 1), but it wouldn't be considered "the fastest thing in the universe", because time would be infinite as well. How about the "efficient coefficient"?
The common (finite) set gives us "event horizons", which are secondary to the built-in code. Event horizons are a nice touch (here & there/then & now/this & that/sunrise & sunset/night & day/etc.), but they are just a "tangible duality" that appear to form a "surface". The built-in code doesn't actually have a surface.
Eric England,
I think infinity is a pipe dream; a simple limitation to the observer's thinking based on what he sees AROUND himself. I believe that the Universe is finite in size and quantity (of what it contains).
When I mention "+/- one", I am talking about math, not anything physical. I'm not sure where you saw the word "surface" in my writing.
Because of the fixed speed of light (in vacuo), the "gears" that are used can not be "plus 1", they must use a scalable method. Of course, I don't mean real gears either, I am talking about the wave interactions.
ciao!
T.Roc
I think infinity is a pipe dream; a simple limitation to the observer's thinking based on what he sees AROUND himself. I believe that the Universe is finite in size and quantity (of what it contains).
When I mention "+/- one", I am talking about math, not anything physical. I'm not sure where you saw the word "surface" in my writing.
Because of the fixed speed of light (in vacuo), the "gears" that are used can not be "plus 1", they must use a scalable method. Of course, I don't mean real gears either, I am talking about the wave interactions.
ciao!
T.Roc
Hey Troc, England used "surface" because of my thinking.
I love the "dimensionless constant" of S^3/V^2 (or its inverse) to describe geometrical structures that may apply in considering the problem of TOE. Who is mathematically proficient (not me, I can only "approximate, like an engineer) to look at the following.
Been reviewing my paper of 1989 on spheres and regular tetraedrons as related to my 4 magnetic marbles in at least 3 stable configurations. Three marbles make a triangle (introduced elsewhere) with 4 edges that compromize their magnetic fields, i.e. 3 "edges". Now adding the 4th must cause 3 more "edges" that must compromise and stabilize with the other 3. It appears that there are at least 3 ways that a stable configuration in equilibrium can be established. (I can see it and feel it, but not enough of a mathemetician to describe it with an equation. Anyone?
Lately I have extended my thinking to include the "dimensionless constant" of S^3/V^2 (or its inverse, V^2/S^3) to prolate and oblate spheroids. It would seem that this would represent the connection of a "surface" to "volume, or content" as it relates to a geometric structure.
So, in order of regular tetrahedron, sphere, prolate spheroid, and oblate spheroid: )below)
Note f=r/R where prolate is considered as a round pencil of radius r and length R while for the oblate is considred as a round plate of thickness r and radius R. ( R>>r so higher ordrs of r ignored)
S^3/V^2 values are:
374, 113. 25.2 f. and 1.57 f^2
or inverse, V^2/S^3
.00267, .00885, .0397/f, and .637/f^2
I find it significant that the "f" value to equal value for a tetrahedron is ~15 for BOTH prolate and oblate, while the "f" value to equal that of a sphere is ~4.5 for prolate and 0.014 for oblate.
Seems as if geometric "structure" is involved some way...??? Tetrhedrons have discrete "edges" while spherical "edges" are continuous, i.e. blurry. SO WHAT?
I love the "dimensionless constant" of S^3/V^2 (or its inverse) to describe geometrical structures that may apply in considering the problem of TOE. Who is mathematically proficient (not me, I can only "approximate, like an engineer) to look at the following.
Been reviewing my paper of 1989 on spheres and regular tetraedrons as related to my 4 magnetic marbles in at least 3 stable configurations. Three marbles make a triangle (introduced elsewhere) with 4 edges that compromize their magnetic fields, i.e. 3 "edges". Now adding the 4th must cause 3 more "edges" that must compromise and stabilize with the other 3. It appears that there are at least 3 ways that a stable configuration in equilibrium can be established. (I can see it and feel it, but not enough of a mathemetician to describe it with an equation. Anyone?
Lately I have extended my thinking to include the "dimensionless constant" of S^3/V^2 (or its inverse, V^2/S^3) to prolate and oblate spheroids. It would seem that this would represent the connection of a "surface" to "volume, or content" as it relates to a geometric structure.
So, in order of regular tetrahedron, sphere, prolate spheroid, and oblate spheroid: )below)
Note f=r/R where prolate is considered as a round pencil of radius r and length R while for the oblate is considred as a round plate of thickness r and radius R. ( R>>r so higher ordrs of r ignored)
S^3/V^2 values are:
374, 113. 25.2 f. and 1.57 f^2
or inverse, V^2/S^3
.00267, .00885, .0397/f, and .637/f^2
I find it significant that the "f" value to equal value for a tetrahedron is ~15 for BOTH prolate and oblate, while the "f" value to equal that of a sphere is ~4.5 for prolate and 0.014 for oblate.
Seems as if geometric "structure" is involved some way...??? Tetrhedrons have discrete "edges" while spherical "edges" are continuous, i.e. blurry. SO WHAT?
QUOTE (TRoc+Aug 6 2006, 03:50 PM)
I think infinity is a pipe dream; a simple limitation to the observer's thinking based on what he sees AROUND himself. I believe that the Universe is finite in size and quantity (of what it contains).
When I mention "+/- one", I am talking about math, not anything physical. I'm not sure where you saw the word "surface" in my writing.
I don't agree. I think finite is a pipe dream. The observable universe is the limitation we see around us.
I didn't mean to imply you said "surface". My attempt was to include "the way things work (physics)". Math (quantity) is not the only aspect. Physics (quality) is the other one. Surface is applicable to the discussion.
Infinity is a self-replicating concept, which is I think, what you asked for. +/– 1 is fininite and not self-replicating. Divisible/multipliable is self-replicating. Not infinity divided or mulitplied by infinity, but by any one of its components.
If you don't agree, then maybe I'm wrong or you could take a closer look at infinity.
When I mention "+/- one", I am talking about math, not anything physical. I'm not sure where you saw the word "surface" in my writing.
I don't agree. I think finite is a pipe dream. The observable universe is the limitation we see around us.
I didn't mean to imply you said "surface". My attempt was to include "the way things work (physics)". Math (quantity) is not the only aspect. Physics (quality) is the other one. Surface is applicable to the discussion.
Infinity is a self-replicating concept, which is I think, what you asked for. +/– 1 is fininite and not self-replicating. Divisible/multipliable is self-replicating. Not infinity divided or mulitplied by infinity, but by any one of its components.
If you don't agree, then maybe I'm wrong or you could take a closer look at infinity.
Eric England,
Of course, in theory, a self replicating system could extend to infinity. Unless the recursive beginning quantity was itself a harmonic of the entire system (the Universe). This is simply represented through a vibration in a cavity: the size of the cavity dictates the size of the smallest harmonic, as well as the total number of modes.
In the end, in Scientific terms, Finite is provable, and Infinite is not. I will stick with what we can observe/measure/prove. To me, infinite simply means "everything", in a statistical manner, where the true total is not known.
Infinities poke their heads up and tend to ruin mathematical formalisms. I feel they shouldn't be there in the first place.
regards,
T.Roc
Of course, in theory, a self replicating system could extend to infinity. Unless the recursive beginning quantity was itself a harmonic of the entire system (the Universe). This is simply represented through a vibration in a cavity: the size of the cavity dictates the size of the smallest harmonic, as well as the total number of modes.
In the end, in Scientific terms, Finite is provable, and Infinite is not. I will stick with what we can observe/measure/prove. To me, infinite simply means "everything", in a statistical manner, where the true total is not known.
Infinities poke their heads up and tend to ruin mathematical formalisms. I feel they shouldn't be there in the first place.
regards,
T.Roc
Infinities and irrational values don't represent any specific tangible properties or finite numbers of interactions, IMO.
Instead these represent systems and processes and more "wholistic" traits, rather than fundamental physical units.
So if you need pi, think a process, not a particle or individual wave.
BTW, I've got some good ideas going here:
http://forum.physorg.com/index.php?showtop...=0&#entry113847
Diffusion seems to be the key.
Instead these represent systems and processes and more "wholistic" traits, rather than fundamental physical units.
So if you need pi, think a process, not a particle or individual wave.
BTW, I've got some good ideas going here:
http://forum.physorg.com/index.php?showtop...=0&#entry113847
Diffusion seems to be the key.
TRoc, are you saying that infinity might have a theoretical beginning and end quantity?
Also, are you saying that "extend to infinity" means that infinite could theoretically have an arrival (and departure) point? Same question, actually.
"Where the true total is not known" supposes that "total" is applicable or important.
... "infinite simply means everything" can just as easily imply that if we are looking for a theory of "everything", then infinite is not something to dismiss, but to truly understand.
StevenA, when you say "Instead these represent systems and processes and more "wholistic" traits, rather than fundamental physical units."... are we to assume there are physical units?
A "TOE", if it is to be found, requires no assumptions be made. All needs to be included and thoroughly understood, and then "dismissed" as a starting point. What is the starting point?
All propensities towards one viewpoint or another, have not yet, been able to dismiss the opposite viewpoint.
When I said "finite is a pipe dream", I am not dismissing finite, but just saying that it's an "event horizon", that is historical and not necessarily actual. A mathematical or physical "ship" that goes over the horizon, does not mean that is its end.
To find a TOE, mathematics and physics needs to climb up to the top of a philosophical tower, and take a higher view of the horizon. Mathematics and physics came from philosophy, and need to recognize and revisit their roots.
Also, are you saying that "extend to infinity" means that infinite could theoretically have an arrival (and departure) point? Same question, actually.
"Where the true total is not known" supposes that "total" is applicable or important.
... "infinite simply means everything" can just as easily imply that if we are looking for a theory of "everything", then infinite is not something to dismiss, but to truly understand.
StevenA, when you say "Instead these represent systems and processes and more "wholistic" traits, rather than fundamental physical units."... are we to assume there are physical units?
A "TOE", if it is to be found, requires no assumptions be made. All needs to be included and thoroughly understood, and then "dismissed" as a starting point. What is the starting point?
All propensities towards one viewpoint or another, have not yet, been able to dismiss the opposite viewpoint.
When I said "finite is a pipe dream", I am not dismissing finite, but just saying that it's an "event horizon", that is historical and not necessarily actual. A mathematical or physical "ship" that goes over the horizon, does not mean that is its end.
To find a TOE, mathematics and physics needs to climb up to the top of a philosophical tower, and take a higher view of the horizon. Mathematics and physics came from philosophy, and need to recognize and revisit their roots.
QUOTE (TRoc+Aug 6 2006, 03:50 PM)
I think infinity is a pipe dream; a simple limitation to the observer's thinking based on what he sees AROUND himself. I believe that the Universe is finite in size and quantity (of what it contains).
It's the other way around. Historically speaking, people have generally thought of the universe as being finite in size. It is really not so long ago people thought the world was flat and had an end. Until recently, we didn't know how small particles could be either. Personally, I think the universe is infinitely large and can be 'broken down' to infinitely small parts. The way it really works is far beyond our imagination. Make a TOE that predicts the creation and evolution of life with formulas (don't forget the soul aspect as well - the component that differs you from me), and you'll receive the Nobel prize for sure. There's no TOE without this. Compared to this seemingly impossible task, the question of 'infinity or not' turns pale.. The only thing we know is that nothing lives forever in the same state. Therefore we shall die one day. What will happen then is a question of belief. Life has an end, it has a finite length, so I guess it's only natural that we prefer to think of the universe as having limits as well..
It's the other way around. Historically speaking, people have generally thought of the universe as being finite in size. It is really not so long ago people thought the world was flat and had an end. Until recently, we didn't know how small particles could be either. Personally, I think the universe is infinitely large and can be 'broken down' to infinitely small parts. The way it really works is far beyond our imagination. Make a TOE that predicts the creation and evolution of life with formulas (don't forget the soul aspect as well - the component that differs you from me), and you'll receive the Nobel prize for sure. There's no TOE without this. Compared to this seemingly impossible task, the question of 'infinity or not' turns pale.. The only thing we know is that nothing lives forever in the same state. Therefore we shall die one day. What will happen then is a question of belief. Life has an end, it has a finite length, so I guess it's only natural that we prefer to think of the universe as having limits as well..
all,
Because I agree with so much of what you have said, I will try a different approach.
I can buy the word "immeasurably" small or large.
I don't have a problem with the Philosophical side of infinite, or the soul.
Just that (this is a mathematical thread) I would need a number to include infinity in a mathematical theory. Can you give me a number that uses the 0-9 symbols? I've been to +/- 100 digits and back; it was the same as the first octave! The point there is that we don't need to go nearly as far as you might imagine to meet the values of everything we know so far.
I should point out that I don't believe in time as a construct either. You could say that time is infinite.
BTW, GR, we don't need to establish the evolution of life forms, it's been done well enough. I can offer no help on "predicting" the soul; but that would require an established/accepted definition, which we don't have yet (or for consciousness).
I can offer a "predictive" mathematical statement that produces all known particles and elements; that should be enough to get "life" going. According to Science, just a few compounds and some energy is enough. This same mathematical iteration can shed light (not prove) on the workings of the "electron based" human mind, and how it perceives things like color, sound, smells and thoughts. Stay tuned...
Ciao!
T.Roc
Because I agree with so much of what you have said, I will try a different approach.
I can buy the word "immeasurably" small or large.
I don't have a problem with the Philosophical side of infinite, or the soul.
Just that (this is a mathematical thread) I would need a number to include infinity in a mathematical theory. Can you give me a number that uses the 0-9 symbols? I've been to +/- 100 digits and back; it was the same as the first octave!
The point there is that we don't need to go nearly as far as you might imagine to meet the values of everything we know so far.I should point out that I don't believe in time as a construct either. You could say that time is infinite.
BTW, GR, we don't need to establish the evolution of life forms, it's been done well enough. I can offer no help on "predicting" the soul; but that would require an established/accepted definition, which we don't have yet (or for consciousness).
I can offer a "predictive" mathematical statement that produces all known particles and elements; that should be enough to get "life" going. According to Science, just a few compounds and some energy is enough. This same mathematical iteration can shed light (not prove) on the workings of the "electron based" human mind, and how it perceives things like color, sound, smells and thoughts. Stay tuned...
Ciao!
T.Roc
QUOTE (TRoc+Aug 9 2006, 02:57 PM)
Just that (this is a mathematical thread) I would need a number to include infinity in a mathematical theory. Can you give me a number that uses the 0-9 symbols? I've been to +/- 100 digits and back; it was the same as the first octave! The point there is that we don't need to go nearly as far as you might imagine to meet the values of everything we know so far.
TRoc, this is why like this forum, progress is possible.
I'm a generalist, so I can only hope to give a satisfactory mathematical description that can lead to further discussion. Also, correct me if I'm wrong about the ones that are already mathematical givens.
In the philosophical viewpoint I'm taking, there are four sets of quantities to be considered. The finite, relative, relatively absolute, and absolute (each > the previous).
Each set has a its own particular rendition of 0/1.
1. Finite – 0 is meaningless and 1 is +/–.
2. Relative – 0 is relatively nothing and 1 is something relative.
3. Relatively absolute – 0 is no-thing and 1 is everything.
4. Absolute – 0 is in perfect respect to 1.
In all four cases 0 is inside (not spatially) 1. The only exception is #2, where 0 & 1 are infinitely inside and outside of each other.
I'll skip any further explanation for now, except to expound a bit on #4. There is self-evident logical proof of absolute 0/1, but I'll skip that also and speak to them as givens, if I may.
There is no outside to 1 and no inside to 0. All lesser forms of 0/1 fall between them. These two can equally be said to be 0/False inside 1/True. "In perfect respect to" means reflects.
Imagine them as a point within a point, without getting into defining "point". 0/False sits at the center of 1/True reflecting what it is in respect to. All else is in the reflection.
See if this makes any sense to you. I know it's far from "normal".
The point there is that we don't need to go nearly as far as you might imagine to meet the values of everything we know so far.TRoc, this is why like this forum, progress is possible.
I'm a generalist, so I can only hope to give a satisfactory mathematical description that can lead to further discussion. Also, correct me if I'm wrong about the ones that are already mathematical givens.
In the philosophical viewpoint I'm taking, there are four sets of quantities to be considered. The finite, relative, relatively absolute, and absolute (each > the previous).
Each set has a its own particular rendition of 0/1.
1. Finite – 0 is meaningless and 1 is +/–.
2. Relative – 0 is relatively nothing and 1 is something relative.
3. Relatively absolute – 0 is no-thing and 1 is everything.
4. Absolute – 0 is in perfect respect to 1.
In all four cases 0 is inside (not spatially) 1. The only exception is #2, where 0 & 1 are infinitely inside and outside of each other.
I'll skip any further explanation for now, except to expound a bit on #4. There is self-evident logical proof of absolute 0/1, but I'll skip that also and speak to them as givens, if I may.
There is no outside to 1 and no inside to 0. All lesser forms of 0/1 fall between them. These two can equally be said to be 0/False inside 1/True. "In perfect respect to" means reflects.
Imagine them as a point within a point, without getting into defining "point". 0/False sits at the center of 1/True reflecting what it is in respect to. All else is in the reflection.
See if this makes any sense to you. I know it's far from "normal".
QUOTE (TRoc+Nov 6 2005, 05:15 PM)
(here: to 5 decimal points for brevity; for the complete story: allow for 15 per column, 13 columns, and start with 1.0267093)
[b]{1.02670, 1.08776, 1.15244, 1.22097, 1.29357, 1.37049, 1.45198, 1.53832, 1.62979, 1.72671, 1.82938, 1.93816, 2.05341}
The "operator" is the 12th square root of 2. (1.059463094355929526456182529494)
An harmonic scale can be defined as H[N] = 2^((N-1)/S), N = [1..S], where S is the number of notes in the scale
Now, if we choose 12 notes in our scale, we get the following series:
1, 1.059463094, 1.122462048, 1.189207115, 1.25992105, 1.33483985, 1.414213562, 1.498307077, 1.587401052, 1.681792831, 1.781797436, 1.887748625
Adding octave selection to the formula: H[N,O] = 2^(N/S) * 2^O = 2^((N-1+S*O)/S)
Harmonic relation; You can multiply any number of note values derived from the formula, the result will always be another note value on the scale.
H1(N1,O1) * H2(N2,O2) = 2^((N1-1+S*O1)/S) * 2^((N2-1+S*O2)/S) = 2^((N1+N2-2+S*(O1+O2))/S)
The harmonic relation holds for division as well.
You can introduce a base value (E) that represents the note value for N=0 and O=0 :
H[N,O] = (E + 2^(N-1/S)) * 2^O
By using the above formula you can create a scale of any dimension with any base value suitable. In your example, you used a base value of 1.0267093. Any particular reason you chose this base value for the scale? Finding the 'speed of light' shouldn't be too difficult to find someplace on the scale if you can adjust the base in any way you wish. In fact, you could just set the base value to the speed of light!
[b]{1.02670, 1.08776, 1.15244, 1.22097, 1.29357, 1.37049, 1.45198, 1.53832, 1.62979, 1.72671, 1.82938, 1.93816, 2.05341}
The "operator" is the 12th square root of 2. (1.059463094355929526456182529494)
An harmonic scale can be defined as H[N] = 2^((N-1)/S), N = [1..S], where S is the number of notes in the scale
Now, if we choose 12 notes in our scale, we get the following series:
1, 1.059463094, 1.122462048, 1.189207115, 1.25992105, 1.33483985, 1.414213562, 1.498307077, 1.587401052, 1.681792831, 1.781797436, 1.887748625
Adding octave selection to the formula: H[N,O] = 2^(N/S) * 2^O = 2^((N-1+S*O)/S)
Harmonic relation; You can multiply any number of note values derived from the formula, the result will always be another note value on the scale.
H1(N1,O1) * H2(N2,O2) = 2^((N1-1+S*O1)/S) * 2^((N2-1+S*O2)/S) = 2^((N1+N2-2+S*(O1+O2))/S)
The harmonic relation holds for division as well.
You can introduce a base value (E) that represents the note value for N=0 and O=0 :
H[N,O] = (E + 2^(N-1/S)) * 2^O
By using the above formula you can create a scale of any dimension with any base value suitable. In your example, you used a base value of 1.0267093. Any particular reason you chose this base value for the scale? Finding the 'speed of light' shouldn't be too difficult to find someplace on the scale if you can adjust the base in any way you wish. In fact, you could just set the base value to the speed of light!
QUOTE (GR+Aug 11 2006, 12:58 AM)
In your example, you used a base value of 1.0267093.
E=0.0267093 in the formula.
E=0.0267093 in the formula.
QUOTE (GR+Aug 11 2006, 12:58 AM)
H[N,O] = (E + 2^(N-1/S)) * 2^O
The formula is better written like this:
H[N,O] = E * 2^((N-1+S*O)/S)
S = number of notes in the scale, any positive integer
N = note number, [1..S]
O = octave number, any integer
E = base value for N=1, O=0
The formula is better written like this:
H[N,O] = E * 2^((N-1+S*O)/S)
S = number of notes in the scale, any positive integer
N = note number, [1..S]
O = octave number, any integer
E = base value for N=1, O=0
Eric England,
"Normal" is not necessary. I get the gist of your last post, but have no idea where you want to go with it ?
GR,
I would recommend registering into the forum if you plan on having conversations with others; anybody can log in as 'GR' and continue for you. (you may not like what they say!)
First, you are forgetting a crucial part of the scale: the octave itself. This means that you need 13 steps, or iterations of 1.059.. , to complete the doubling of the fundamental note. So the last value produced by this series of ratios is 1.9999..
I think I have already gone into why not start at One, basically it is Philosophical. However, after completing the mathematical part of the model, you see that is is absolutely necessary to produce a match with empirical values. That answers your question "Any particular reason you chose this base value for the scale? "
The actual value is 1.02670931(1); with an uncertainty of 1 on the last digit. You are right in that is wasn't "too difficult" to produce c from the base and the operator. The answer is:
1.02670930^2 * 1.0594630943559295264561825294946^337 = 299,792,457.99..
I write that as Z^2 * R^337=c
Care to come up with another?
Actually, as far as c goes, the fact that the symmetry in the matrix (produced recursively from the series) sets all values of symmetrical products equal to c is much more significant. This sets up natural "resonant nodes", where we are likely to find measurements of our World. It also derives the inverse relationship, most obviously of frequency & wavelength, but also distance (space) and velocity (movement) measured in units of time.
I think that you might be a musician, so I'll throw this in too:
Z * R^84 = 131.41.. and it's octave, 262.82.. "middle c" on the piano.
for now,
Ciao!
T.Roc
"Normal" is not necessary. I get the gist of your last post, but have no idea where you want to go with it ?
GR,
I would recommend registering into the forum if you plan on having conversations with others; anybody can log in as 'GR' and continue for you. (you may not like what they say!)
First, you are forgetting a crucial part of the scale: the octave itself. This means that you need 13 steps, or iterations of 1.059.. , to complete the doubling of the fundamental note. So the last value produced by this series of ratios is 1.9999..
I think I have already gone into why not start at One, basically it is Philosophical. However, after completing the mathematical part of the model, you see that is is absolutely necessary to produce a match with empirical values. That answers your question "Any particular reason you chose this base value for the scale? "
The actual value is 1.02670931(1); with an uncertainty of 1 on the last digit. You are right in that is wasn't "too difficult" to produce c from the base and the operator. The answer is:
1.02670930^2 * 1.0594630943559295264561825294946^337 = 299,792,457.99..
I write that as Z^2 * R^337=c
Care to come up with another?
Actually, as far as c goes, the fact that the symmetry in the matrix (produced recursively from the series) sets all values of symmetrical products equal to c is much more significant. This sets up natural "resonant nodes", where we are likely to find measurements of our World. It also derives the inverse relationship, most obviously of frequency & wavelength, but also distance (space) and velocity (movement) measured in units of time.
I think that you might be a musician, so I'll throw this in too:
Z * R^84 = 131.41.. and it's octave, 262.82.. "middle c" on the piano.
for now,
Ciao!
T.Roc
QUOTE (TRoc+Aug 11 2006, 05:23 PM)
"Normal" is not necessary. I get the gist of your last post, but have no idea where you want to go with it ?
Hi TRoc,
Good to hear that normal is not necessary. Gist is good, very good. I laid out the math as close as a generalist can.
The absolute 1 I referred to, is where a TOE or in my opinion, an ACT (a complete theory) needs to begin. You'll notice in #3 that "everything" is only relatively absolute. The goal is to establish an absolute. Re-normalization of GR and Quantum, is one example of two relatives that are looking for an absolute. Something from nothing is another one. All the biggies boil down to this.
So, to begin an ACT requires establishing "1 something", that does not have a cause (an outside) whatsoever. Looking inside the universe will not result in this.
What could possibly be outside this absolute, that would keep it from being the starting point? It would be absolute 0 or absolutely nothing. In essence, non-existence.
Now the simplest of all ideas, and maybe to some, the hardest to grasp – is that if non-existence EXISTED, there wouldn't be non-existence. If absolutely nothing EXISTED, there wouldn't be absolutely nothing. No matter how it's described, it's simply impossible.
So what is there since there isn't absolutely nothing? Something absolute. But there's one other thing to cover, to make sure it has no cause (outside). Even "absolutely nothing is impossible" is inside the absolute. Not even a fact, is outside of it. I think this could be called "externally consistent".
This simple self-evident logic, is where an ACT needs to begin. I ran across this by "experience", but have subsequently found out, that the recognized but forgotten father of all western philosophy, physics, and math established it 2,500 years ago – Parmenides. (long story)
In respect (inside) to this absolute 1/True, is an internally consistent 0/False. They are dimensionless points (no spatial extent), that have no position in regard to a greater or lesser spatial extent – either inside 0 or outside 1, or in between the two.
Substance, space, and time along with the rest of #1-3, are only the illusion of dimension. This is explainable, along with force and gravity. It all boils down to understanding "center". I won't elaborate at this juncture.
As Einstein said – "Reality is merely an illusion, albeit a very persistent one."
I hope this gives a good gist, of where I want to go with it.
Actually, I'm so burned out from working on it, I want to go on vacation with it. But I'm so broke from doing it, I can't. A relative conundrum, of immense personal proportion.
Hi TRoc,
Good to hear that normal is not necessary. Gist is good, very good. I laid out the math as close as a generalist can.
The absolute 1 I referred to, is where a TOE or in my opinion, an ACT (a complete theory) needs to begin. You'll notice in #3 that "everything" is only relatively absolute. The goal is to establish an absolute. Re-normalization of GR and Quantum, is one example of two relatives that are looking for an absolute. Something from nothing is another one. All the biggies boil down to this.
So, to begin an ACT requires establishing "1 something", that does not have a cause (an outside) whatsoever. Looking inside the universe will not result in this.
What could possibly be outside this absolute, that would keep it from being the starting point? It would be absolute 0 or absolutely nothing. In essence, non-existence.
Now the simplest of all ideas, and maybe to some, the hardest to grasp – is that if non-existence EXISTED, there wouldn't be non-existence. If absolutely nothing EXISTED, there wouldn't be absolutely nothing. No matter how it's described, it's simply impossible.
So what is there since there isn't absolutely nothing? Something absolute. But there's one other thing to cover, to make sure it has no cause (outside). Even "absolutely nothing is impossible" is inside the absolute. Not even a fact, is outside of it. I think this could be called "externally consistent".
This simple self-evident logic, is where an ACT needs to begin. I ran across this by "experience", but have subsequently found out, that the recognized but forgotten father of all western philosophy, physics, and math established it 2,500 years ago – Parmenides. (long story)
In respect (inside) to this absolute 1/True, is an internally consistent 0/False. They are dimensionless points (no spatial extent), that have no position in regard to a greater or lesser spatial extent – either inside 0 or outside 1, or in between the two.
Substance, space, and time along with the rest of #1-3, are only the illusion of dimension. This is explainable, along with force and gravity. It all boils down to understanding "center". I won't elaborate at this juncture.
As Einstein said – "Reality is merely an illusion, albeit a very persistent one."
I hope this gives a good gist, of where I want to go with it.
Actually, I'm so burned out from working on it, I want to go on vacation with it. But I'm so broke from doing it, I can't. A relative conundrum, of immense personal proportion.
QUOTE (TRoc+Aug 11 2006, 05:23 PM)
I would recommend registering into the forum if you plan on having conversations with others; anybody can log in as 'GR' and continue for you. (you may not like what they say!)
Alright, this is my first post as a registered user!
Not quite right.. If our scale has 12 different notes (which is our normal musical scale), then note 13 would be the first note on the 2nd octave. Let's use the simplest form of the formula:
H[N] = 2^(N/12)
Two first notes on the base octave:
H[0] = 2^(0/12) = 1
H[1] = 2^(1/12) = 1.059463094
Last note on the base octave:
H[11] = 2^(11/12) = 1.887748625
Two first notes on the next octave (above the base):
H[12] = 2^(12/12) = 2
H[13] = 2^(13/12) = 2,118926189
The confusion is likely caused by the fact that you need to treat N=0 as a note index. This gives the base note, which will be 1 without any tuning factor.
Not quite right.. If our scale has 12 different notes (which is our normal musical scale), then note 13 would be the first note on the 2nd octave. Let's use the simplest form of the formula:
H[N] = 2^(N/12)
Two first notes on the base octave:
H[0] = 2^(0/12) = 1
H[1] = 2^(1/12) = 1.059463094
Last note on the base octave:
H[11] = 2^(11/12) = 1.887748625
Two first notes on the next octave (above the base):
H[12] = 2^(12/12) = 2
H[13] = 2^(13/12) = 2,118926189
The confusion is likely caused by the fact that you need to treat N=0 as a note index. This gives the base note, which will be 1 without any tuning factor.
I think I have already gone into why not start at One, basically it is Philosophical. However, after completing the mathematical part of the model, you see that is is absolutely necessary to produce a match with empirical values. That answers your question "Any particular reason you chose this base value for the scale? "
Let's talk about the speed of light. c is a definition; the distance, in meters light is traveling in one second. A second is defined as the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K. From this, one meter is defined as the distance light is traveling in 1/c of a second. Now, if we changed our definitions of one meter and one second, such that the speed of light became one meter per second. Strictly speaking, we wouldn't need to call it 'a meter' or 'a second' - it's enough that the speed of light equates to 1 distance per time unit. Then, mathematically, consider E=m*c^2 and what effect it would have on nature and reality..
The note C you're looking for is vibrating with a speed of 261.6255653 Hz (if the instrument is perfectly tuned to the standard tuning; A=440 Hz):
H[N,O] = 440 * 2^((N+(O*12))/12) = H[3,-1] = 440 * 2^((3+(-1*12))/12) = 261.6255653
And you're right about music! I play guitar and keyboard, although not professionally. I do some composing from time to time as well. 15 years ago I created some computer music software. It was fun to refresh the mathematical principles
Alright, this is my first post as a registered user!
QUOTE
First, you are forgetting a crucial part of the scale: the octave itself. This means that you need 13 steps, or iterations of 1.059.. , to complete the doubling of the fundamental note. So the last value produced by this series of ratios is 1.9999..
Not quite right.. If our scale has 12 different notes (which is our normal musical scale), then note 13 would be the first note on the 2nd octave. Let's use the simplest form of the formula:
H[N] = 2^(N/12)
Two first notes on the base octave:
H[0] = 2^(0/12) = 1
H[1] = 2^(1/12) = 1.059463094
Last note on the base octave:
H[11] = 2^(11/12) = 1.887748625
Two first notes on the next octave (above the base):
H[12] = 2^(12/12) = 2
H[13] = 2^(13/12) = 2,118926189
The confusion is likely caused by the fact that you need to treat N=0 as a note index. This gives the base note, which will be 1 without any tuning factor.
QUOTE (->
| QUOTE |
| First, you are forgetting a crucial part of the scale: the octave itself. This means that you need 13 steps, or iterations of 1.059.. , to complete the doubling of the fundamental note. So the last value produced by this series of ratios is 1.9999.. |
Not quite right.. If our scale has 12 different notes (which is our normal musical scale), then note 13 would be the first note on the 2nd octave. Let's use the simplest form of the formula:
H[N] = 2^(N/12)
Two first notes on the base octave:
H[0] = 2^(0/12) = 1
H[1] = 2^(1/12) = 1.059463094
Last note on the base octave:
H[11] = 2^(11/12) = 1.887748625
Two first notes on the next octave (above the base):
H[12] = 2^(12/12) = 2
H[13] = 2^(13/12) = 2,118926189
The confusion is likely caused by the fact that you need to treat N=0 as a note index. This gives the base note, which will be 1 without any tuning factor.
I think I have already gone into why not start at One, basically it is Philosophical. However, after completing the mathematical part of the model, you see that is is absolutely necessary to produce a match with empirical values. That answers your question "Any particular reason you chose this base value for the scale? "
Let's talk about the speed of light. c is a definition; the distance, in meters light is traveling in one second. A second is defined as the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. This definition refers to a caesium atom at rest at a temperature of 0 K. From this, one meter is defined as the distance light is traveling in 1/c of a second. Now, if we changed our definitions of one meter and one second, such that the speed of light became one meter per second. Strictly speaking, we wouldn't need to call it 'a meter' or 'a second' - it's enough that the speed of light equates to 1 distance per time unit. Then, mathematically, consider E=m*c^2 and what effect it would have on nature and reality..
QUOTE
Z * R^84 = 131.41.. and it's octave, 262.82.. "middle c" on the piano.
The note C you're looking for is vibrating with a speed of 261.6255653 Hz (if the instrument is perfectly tuned to the standard tuning; A=440 Hz):
H[N,O] = 440 * 2^((N+(O*12))/12) = H[3,-1] = 440 * 2^((3+(-1*12))/12) = 261.6255653
And you're right about music! I play guitar and keyboard, although not professionally. I do some composing from time to time as well. 15 years ago I created some computer music software. It was fun to refresh the mathematical principles
Hi Eric,
I follow you now. A fellow walked up to me the other day and asked if I thought there was a beginning, or "big bang". I said "do we need to know?" He rather liked that answer.
Somewhere there will always be a line between knowledge and faith.
geirlade,
Congratulations on being "in" the forum!
I hate to "bicker", but even though I'm sure you understand the system, we are seemingly not on the same page.
When I said
I follow you now. A fellow walked up to me the other day and asked if I thought there was a beginning, or "big bang". I said "do we need to know?" He rather liked that answer.
Somewhere there will always be a line between knowledge and faith.
geirlade,
Congratulations on being "in" the forum!
I hate to "bicker", but even though I'm sure you understand the system, we are seemingly not on the same page.
When I said
QUOTE
"First, you are forgetting a crucial part of the scale: the octave itself. This means that you need 13 steps, or iterations of 1.059.. , to complete the doubling of the fundamental note. So the last value produced by this series of ratios is 1.9999.. "
That was in response to your post QUOTE (->
| QUOTE |
| "First, you are forgetting a crucial part of the scale: the octave itself. This means that you need 13 steps, or iterations of 1.059.. , to complete the doubling of the fundamental note. So the last value produced by this series of ratios is 1.9999.. " |
That was in response to your post " Now, if we choose 12 notes in our scale, we get the following series:
1, 1.059463094, 1.122462048, 1.189207115, 1.25992105, 1.33483985, 1.414213562, 1.498307077, 1.587401052, 1.681792831, 1.781797436, 1.887748625 "
Your series never gets to the octave: double the tonic. You need to end at 2 (or 1.999). You are right in having 12 separate notes, but you still need 13 steps to get from 1 to 2 in the interval series. The tonic, 1, is the "same" as the octave, 2, and there are 11 other notes between them, for a total of 13.
I know you understand the idea because this (your statement) is correct "
However, your formula is not working.
However, your formula is not working.
Two first notes on the base octave:
H[0] = 2^(0/12) = 1
H[1] = 2^(1/12) = Two first notes on the base octave:
H[0] = 2^(0/12) = 1
H[1] = 2^(1/12) = 1.059463094
Neither of those are mathematically valid. 0/12 does not equal 1, and 1/12 does not equal 1.05946309. That is why, in the end, your statement "
does not work either. The 12th note (starting with C) is B; and the octave is C' . You are making the 12th note "2", or double, and the 13th note more than double (2.118).
The 12th note is the "leading" note (1.887..), and the 13th is the octave (1.999..).
Yes, in exact A440 tuning, the middle C is 261.6255653 , however, it certainly is more common to call that 262, as you will see it referred to in all music books (that are not of primarily mathematical nature). This tuning is totally subjective, as I'm sure you are aware. Also "standard" (even on my "standard" tuner) is A443, and around the world, "standard" tuning is still debated within a few Hz.
YOU (musician & composer) MIGHT be able to discern a difference between 261.6 and 262.8, but 99.9% of the world can not. That is part of the problem. The main thing is for all oscillators to be in tune with each other; if the symphony is tuned as a whole to A442, they will sound just as good as A440.
The human brain needs a certain RATIO between sounds to identify them as separate, otherwise it "disregards" the beat frequencies that exist. Sound exists because of electron vibrations, the same as for light. This is a large part of the premise for VRT (vibrational resonance theory), which puts all vibrations on equal footing. The same RATIO exists between colors, in order for us to identify them as separate.
The WAY we defined sound to be consonant at ~A440 Hz was arbitrary, yet totally NATURAL. The WAY we defined color, although Science is behind in this idea, is the same. The base for the 261.6 Hz would be 1.021974864453125, so you can see it is very close to my Z = 1.02670931 (1) base for my resonance matrix. Here is where they differ:
as I said, Z * R^84 = 131.41.. for a C note, and the entire scale that it produces for SOUND.
Now, here is the "scale", or spectrum of visible light:
Position.......Equation..........Value.......................................................Observed as
x-2, y-35___Z*R^581 = 3.857593416366057036060893838683e+14 : Infra-Red
x-1, y-35___Z*R^582 = 4.086977857670244421953202204508e+14 : Red
x+1, y-35___Z*R^583 = 4.3300022076514848805362545893036e+14: R/O
x+2, y-35___Z*R^584 = 4.5874775374864482805507786128818e+14: Orange
x+3, y-35___Z*R^585 = 4.8602631471537121859292338082802e+14: Y/O
x+4, y-35___Z*R^586 = 5.1492694332675603665089454795232e+14: Yellow
x+5, y-35___Z*R^587 = 5.455460927442053066711559503955e+14 : Green
x+6, y-35___Z*R^588 = 5.779859515325626672275073543563e+14 : Cyan
x-6, y-36____Z*R^589 = 6.1235478470494515119705844064778e+14: "sky"
x-5, y-36____Z*R^590 = 6.4876729504716021553074207138354e+14: Blue
x-4, y-36____Z*R^591 = 6.8734500592759067396630103593148e+14: Indigo
x-3, y-36____Z*R^592 = 7.2821666687013993787771186960934e+14: Violet
x-2, y-36____Z*R^593 = 7.7151868324379956819347694377182e+14 : Ultra-Violet
Of course, you can get a very similar spectrum using 1.02197.. for a base, but the product of those frequencies will not equal c when multiplied by their respective wavelengths. Here, from the same base, are the wavelengths:
x+2, y+36___Z/R^256 = 3.8857446294093126434933258105629e-7: Ultra-Violet
x+3, y+36___Z/R^255 = 4.1168030289509250115640690548051e-7: Violet
x+4, y+36___Z/R^254 = 4.3616008759062103395215350158364e-7: Indigo
x+5, y+36___Z/R^253 = 4.6209551603331261944764443543237e-7: Blue
x+6, y+36___Z/R^252 = 4.895731453046534330685082067968e-7 : "sky"
x-6, y+35____Z/R^251 = 5.1868467943803323657043275656108e-7: Cyan
x-5, y+35____Z/R^250 = 5.4952727547243206642420064252574e-7: Green
x-4, y+35____Z/R^249 = 5.8220386770500617173225604322764e-7: Yellow
x-3, y+35____Z/R^248 = 6.1682351122473606492575211474075e-7: Y/O
x-2, y+35____Z/R^247 = 6.5350174587364830093688231242627e-7 : Orange
x-1, y+35____Z/R^246 = 6.9236098185029772892552860854157e-7: R/O
x+1, y+35___Z/R^245 = 7.3353090824242599311532789282972e-7: Red
x+2, y+35___Z/R^244 = 7.7714892585223605354368815016556e-7: Infra-Red
You will note the mirror symmetry in the position on the matrix between the values of any colors' frequency and wavelength, and most importantly, their product equals c.
An example:
5.1492694332675603665089454795232e+14: Yellow
x
5.8220386770500617173225604322764e-7: Yellow
=
299792457.99035388214033317614916
This will not work with any other number besides Z, a resonant "constant".
So, when humans set ~A440 tuning as "consonant", they did so with INSTINCT, and it was arguably EXACTLY "in tune" with what Science came up with much later. This resonant constant gives a REASON for c to be what it is; something that Science did not have. Of course, our eyes, ears and brains are electron based as well, and are able to detect these differences with speeds that do not allow for complex computations. The same can be said for pair production, orbital state changes, etc. in Physics. This is what VRT is about.
If that is not enough for you, I have also "predicted" the masses of all the particles in the standard model, as well as for all the elements in the periodic table with this same resonant constant. Z also produces Planck's constant h = 6.626 0693(11) × 10-34 J•s :
1.02670932 Hz = 6.8030471e-34 J / 1.02670932 = 6.62606929..e-34
(Dirac's h-bar is even more precisely produced)
Again, giving mathematical REASON to previously AD HOC constants.
Regards,
T.Roc
"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality." – Albert Einstein
Mathematics is an appoximation. A perfect circle or line, are made up of dimensionless points that are given a dimension of location. Until a dimensionless point that has no location is found, there is no chance for mathematics to establish anything other than approximate location.
So in that regard, the point, the circle, and the line are blurry.
Just like the "surface" between mass, space, and time.
1, 1.059463094, 1.122462048, 1.189207115, 1.25992105, 1.33483985, 1.414213562, 1.498307077, 1.587401052, 1.681792831, 1.781797436, 1.887748625 "
Your series never gets to the octave: double the tonic. You need to end at 2 (or 1.999). You are right in having 12 separate notes, but you still need 13 steps to get from 1 to 2 in the interval series. The tonic, 1, is the "same" as the octave, 2, and there are 11 other notes between them, for a total of 13.
I know you understand the idea because this (your statement) is correct "
QUOTE
If our scale has 12 different notes (which is our normal musical scale), then note 13 would be the first note on the 2nd octave."
However, your formula is not working.
QUOTE (->
| QUOTE |
| If our scale has 12 different notes (which is our normal musical scale), then note 13 would be the first note on the 2nd octave." |
However, your formula is not working.
Two first notes on the base octave:
H[0] = 2^(0/12) = 1
H[1] = 2^(1/12) = Two first notes on the base octave:
H[0] = 2^(0/12) = 1
H[1] = 2^(1/12) = 1.059463094
Neither of those are mathematically valid. 0/12 does not equal 1, and 1/12 does not equal 1.05946309. That is why, in the end, your statement "
QUOTE
Two first notes on the next octave (above the base):
H[12] = 2^(12/12) = 2
H[13] = 2^(13/12) = 2,118926189
H[12] = 2^(12/12) = 2
H[13] = 2^(13/12) = 2,118926189
does not work either. The 12th note (starting with C) is B; and the octave is C' . You are making the 12th note "2", or double, and the 13th note more than double (2.118).
The 12th note is the "leading" note (1.887..), and the 13th is the octave (1.999..).
Yes, in exact A440 tuning, the middle C is 261.6255653 , however, it certainly is more common to call that 262, as you will see it referred to in all music books (that are not of primarily mathematical nature). This tuning is totally subjective, as I'm sure you are aware. Also "standard" (even on my "standard" tuner) is A443, and around the world, "standard" tuning is still debated within a few Hz.
YOU (musician & composer) MIGHT be able to discern a difference between 261.6 and 262.8, but 99.9% of the world can not. That is part of the problem. The main thing is for all oscillators to be in tune with each other; if the symphony is tuned as a whole to A442, they will sound just as good as A440.
The human brain needs a certain RATIO between sounds to identify them as separate, otherwise it "disregards" the beat frequencies that exist. Sound exists because of electron vibrations, the same as for light. This is a large part of the premise for VRT (vibrational resonance theory), which puts all vibrations on equal footing. The same RATIO exists between colors, in order for us to identify them as separate.
The WAY we defined sound to be consonant at ~A440 Hz was arbitrary, yet totally NATURAL. The WAY we defined color, although Science is behind in this idea, is the same. The base for the 261.6 Hz would be 1.021974864453125, so you can see it is very close to my Z = 1.02670931 (1) base for my resonance matrix. Here is where they differ:
as I said, Z * R^84 = 131.41.. for a C note, and the entire scale that it produces for SOUND.
Now, here is the "scale", or spectrum of visible light:
Position.......Equation..........Value.......................................................Observed as
x-2, y-35___Z*R^581 = 3.857593416366057036060893838683e+14 : Infra-Red
x-1, y-35___Z*R^582 = 4.086977857670244421953202204508e+14 : Red
x+1, y-35___Z*R^583 = 4.3300022076514848805362545893036e+14: R/O
x+2, y-35___Z*R^584 = 4.5874775374864482805507786128818e+14: Orange
x+3, y-35___Z*R^585 = 4.8602631471537121859292338082802e+14: Y/O
x+4, y-35___Z*R^586 = 5.1492694332675603665089454795232e+14: Yellow
x+5, y-35___Z*R^587 = 5.455460927442053066711559503955e+14 : Green
x+6, y-35___Z*R^588 = 5.779859515325626672275073543563e+14 : Cyan
x-6, y-36____Z*R^589 = 6.1235478470494515119705844064778e+14: "sky"
x-5, y-36____Z*R^590 = 6.4876729504716021553074207138354e+14: Blue
x-4, y-36____Z*R^591 = 6.8734500592759067396630103593148e+14: Indigo
x-3, y-36____Z*R^592 = 7.2821666687013993787771186960934e+14: Violet
x-2, y-36____Z*R^593 = 7.7151868324379956819347694377182e+14 : Ultra-Violet
Of course, you can get a very similar spectrum using 1.02197.. for a base, but the product of those frequencies will not equal c when multiplied by their respective wavelengths. Here, from the same base, are the wavelengths:
x+2, y+36___Z/R^256 = 3.8857446294093126434933258105629e-7: Ultra-Violet
x+3, y+36___Z/R^255 = 4.1168030289509250115640690548051e-7: Violet
x+4, y+36___Z/R^254 = 4.3616008759062103395215350158364e-7: Indigo
x+5, y+36___Z/R^253 = 4.6209551603331261944764443543237e-7: Blue
x+6, y+36___Z/R^252 = 4.895731453046534330685082067968e-7 : "sky"
x-6, y+35____Z/R^251 = 5.1868467943803323657043275656108e-7: Cyan
x-5, y+35____Z/R^250 = 5.4952727547243206642420064252574e-7: Green
x-4, y+35____Z/R^249 = 5.8220386770500617173225604322764e-7: Yellow
x-3, y+35____Z/R^248 = 6.1682351122473606492575211474075e-7: Y/O
x-2, y+35____Z/R^247 = 6.5350174587364830093688231242627e-7 : Orange
x-1, y+35____Z/R^246 = 6.9236098185029772892552860854157e-7: R/O
x+1, y+35___Z/R^245 = 7.3353090824242599311532789282972e-7: Red
x+2, y+35___Z/R^244 = 7.7714892585223605354368815016556e-7: Infra-Red
You will note the mirror symmetry in the position on the matrix between the values of any colors' frequency and wavelength, and most importantly, their product equals c.
An example:
5.1492694332675603665089454795232e+14: Yellow
x
5.8220386770500617173225604322764e-7: Yellow
=
299792457.99035388214033317614916
This will not work with any other number besides Z, a resonant "constant".
So, when humans set ~A440 tuning as "consonant", they did so with INSTINCT, and it was arguably EXACTLY "in tune" with what Science came up with much later. This resonant constant gives a REASON for c to be what it is; something that Science did not have. Of course, our eyes, ears and brains are electron based as well, and are able to detect these differences with speeds that do not allow for complex computations. The same can be said for pair production, orbital state changes, etc. in Physics. This is what VRT is about.
If that is not enough for you, I have also "predicted" the masses of all the particles in the standard model, as well as for all the elements in the periodic table with this same resonant constant. Z also produces Planck's constant h = 6.626 0693(11) × 10-34 J•s :
1.02670932 Hz = 6.8030471e-34 J / 1.02670932 = 6.62606929..e-34
(Dirac's h-bar is even more precisely produced)
Again, giving mathematical REASON to previously AD HOC constants.
Regards,
T.Roc
QUOTE (TRoc+Aug 12 2006, 07:37 PM)
Neither of those are mathematically valid. 0/12 does not equal 1, and 1/12 does not equal 1.05946309. That is why, in the end, your statement "
does not work either. The 12th note (starting with C) is B; and the octave is C' . You are making the 12th note "2", or double, and the 13th note more than double (2.118).
You just have to read the formula correctly, as well as understanding the basic power rules of mathematics.
A^0 = 1
A^1 = A
A^2 = A*A
A^N1 * A^N2 = A^(N1+N2)
A^(1/2) = A^0.5 = root of A
A^(1/N) = Nth root of A
A^(1/N) * A^(1/N) = A^(1/N + 1/N) = A^(2/N)
2^(0/12) = 2^0 = 1
2^(1/12) = 12th root of 2 = 1.059463094
2^(1/12) * 2^(1/12) = 2^(2/12) = 1.122462048
2^(1/12) * 2^(1/12) * 2^(1/12) = 2^(3/12) = 1.189207115
2^(12/12) = 2^1 = 2
does not work either. The 12th note (starting with C) is B; and the octave is C' . You are making the 12th note "2", or double, and the 13th note more than double (2.118).
You just have to read the formula correctly, as well as understanding the basic power rules of mathematics.
A^0 = 1
A^1 = A
A^2 = A*A
A^N1 * A^N2 = A^(N1+N2)
A^(1/2) = A^0.5 = root of A
A^(1/N) = Nth root of A
A^(1/N) * A^(1/N) = A^(1/N + 1/N) = A^(2/N)
2^(0/12) = 2^0 = 1
2^(1/12) = 12th root of 2 = 1.059463094
2^(1/12) * 2^(1/12) = 2^(2/12) = 1.122462048
2^(1/12) * 2^(1/12) * 2^(1/12) = 2^(3/12) = 1.189207115
2^(12/12) = 2^1 = 2
geirlade,
My apologies, you are correct: I did not read your formula correctly. For some reason, I was taking it as a literal, interval based approach.
Perhaps, now we are on the same page!
Did you have any comments on the rest of my post?
Also, maybe you can shed some light on this complex? power series??
Z^.5*R^84.25 = sq rt (sq rt c) [131.58463366739101187893721378354]
Z^1*R^168.5 = sq rt c
Z^2*R^337 = c
Z^4*R^674 = c^2
Z^8*R^1348 = c^4 [8.0776087120228701375974276847492e+33]
Does this seem normal?
ciao!
T.Roc
My apologies, you are correct: I did not read your formula correctly. For some reason, I was taking it as a literal, interval based approach.
Perhaps, now we are on the same page!
Did you have any comments on the rest of my post?
Also, maybe you can shed some light on this complex? power series??
Z^.5*R^84.25 = sq rt (sq rt c) [131.58463366739101187893721378354]
Z^1*R^168.5 = sq rt c
Z^2*R^337 = c
Z^4*R^674 = c^2
Z^8*R^1348 = c^4 [8.0776087120228701375974276847492e+33]
Does this seem normal?
ciao!
T.Roc
QUOTE (TRoc+Aug 12 2006, 07:37 PM)
Neither of those are mathematically valid. 0/12 does not equal 1, and 1/12 does not equal 1.05946309. That is why, in the end, your statement "
does not work either. The 12th note (starting with C) is B; and the octave is C' . You are making the 12th note "2", or double, and the 13th note more than double (2.118).
So to sum up, the basic formula can be written as:
H[N] = 2^(N/S)
S = number of notes in scale (dimension), S>0
N = note index, any number.
Keep in mind that N=0 for note number 1 in the first octave. Then it comes by logic that N=S-1 for the last note in the first octave.
The formula can be modified to support octave selection:
H[N,O] = B * 2^((N+O*S)/S)
The octave (O) can be any number. N = [0..S-1]. B is the base value.
This formula simplifies the creation of an Excel sheet to render the values. I took the time to make it:
http://home.online.no/~ladehaug/harmonicscale.xls
About the Excel file:
The index value of each octave is indicated with red background. The octave number is indicated with blue background on the left. The values on blue background to the right is the octave number multiplied with the dimension.
3 parameters can be modified (green background). The dimension of the scale can be changed (field B1), although for dimensions larger than 12, you'll only see the first 12 values. A base (field B2) can be set to any desirable value. The 'from octave' value (field B3) is what octave and values you want on the first row. There are 100 octaves in the list (more can be made, but it should suffice).
does not work either. The 12th note (starting with C) is B; and the octave is C' . You are making the 12th note "2", or double, and the 13th note more than double (2.118).
So to sum up, the basic formula can be written as:
H[N] = 2^(N/S)
S = number of notes in scale (dimension), S>0
N = note index, any number.
Keep in mind that N=0 for note number 1 in the first octave. Then it comes by logic that N=S-1 for the last note in the first octave.
The formula can be modified to support octave selection:
H[N,O] = B * 2^((N+O*S)/S)
The octave (O) can be any number. N = [0..S-1]. B is the base value.
This formula simplifies the creation of an Excel sheet to render the values. I took the time to make it:
http://home.online.no/~ladehaug/harmonicscale.xls
About the Excel file:
The index value of each octave is indicated with red background. The octave number is indicated with blue background on the left. The values on blue background to the right is the octave number multiplied with the dimension.
3 parameters can be modified (green background). The dimension of the scale can be changed (field B1), although for dimensions larger than 12, you'll only see the first 12 values. A base (field B2) can be set to any desirable value. The 'from octave' value (field B3) is what octave and values you want on the first row. There are 100 octaves in the list (more can be made, but it should suffice).
QUOTE (TRoc+Aug 13 2006, 01:07 AM)
Z^.5*R^84.25 = sq rt (sq rt c) [131.58463366739101187893721378354]
Z^1*R^168.5 = sq rt c
Z^2*R^337 = c
Z^4*R^674 = c^2
Z^8*R^1348 = c^4 [8.0776087120228701375974276847492e+33]
Does this seem normal?
(Z*R^a) * (Z/R^b) = c
Z^2 * (R^a / R^b) = c
Z^2 * R^(a-b) = c
a = b + 337
Z^2 * R^(b+337-b) = c
Z^2 * R^337 = c
R= 2^(1/12)
Z^2 * (2^(1/12))^337) = c
Z^2 * 2^(337/12) = c
Z^2 = c / 2^(337/12)
Z = sqrt (c / 2^(337/12))
c = 299792458
Z = sqrt (299792458 / 2^28.083333333333)
Z = 1,0267092994669238122487866214354
Hope this helps!
--
GR
Z^1*R^168.5 = sq rt c
Z^2*R^337 = c
Z^4*R^674 = c^2
Z^8*R^1348 = c^4 [8.0776087120228701375974276847492e+33]
Does this seem normal?
(Z*R^a) * (Z/R^b) = c
Z^2 * (R^a / R^b) = c
Z^2 * R^(a-b) = c
a = b + 337
Z^2 * R^(b+337-b) = c
Z^2 * R^337 = c
R= 2^(1/12)
Z^2 * (2^(1/12))^337) = c
Z^2 * 2^(337/12) = c
Z^2 = c / 2^(337/12)
Z = sqrt (c / 2^(337/12))
c = 299792458
Z = sqrt (299792458 / 2^28.083333333333)
Z = 1,0267092994669238122487866214354
Hope this helps!
--
GR
geirlade,
Very nice, thank you for the time spent!
So far, using a different approach, I had come to limit --> 1.02670932699999999993632085457 , but because of some other calculations, have resigned to 1.02670931 (1) . BTW, I am manipulating WHOLE integer steps of irrational quantities, so 28.083 isn't as tidy.
Are you as handy with QM as you are with math?
ciao!
T.Roc
Very nice, thank you for the time spent!
So far, using a different approach, I had come to limit --> 1.02670932699999999993632085457 , but because of some other calculations, have resigned to 1.02670931 (1) . BTW, I am manipulating WHOLE integer steps of irrational quantities, so 28.083 isn't as tidy.
Are you as handy with QM as you are with math?
ciao!
T.Roc
QUOTE (TRoc+Aug 12 2006, 07:37 PM)
Hi Eric,
I follow you now. A fellow walked up to me the other day and asked if I thought there was a beginning, or "big bang". I said "do we need to know?" He rather liked that answer.
Somewhere there will always be a line between knowledge and faith.
Hi T.Roc,
But where is that line? I don't think it's as far "in", as the question of the big bang. To me, that's easily explainable and isn't a line between knowledge and faith.
I'm actually of the well-considered belief, that there are no lines (boundaries) that can not be surmounted. This does not mean however, that we can predict by our own devices alone.
One can arrive at the Absolute (which is what we are looking for/science included), and see right through it, to why and how it has no cause.
How is this possible? Because it's invisible.
"Faith" is not involved in what we can know about existence. Faith is in the knowledge that we can not control outcomes, ourselves, or others and that this is how it's meant to be.
I follow you now. A fellow walked up to me the other day and asked if I thought there was a beginning, or "big bang". I said "do we need to know?" He rather liked that answer.
Somewhere there will always be a line between knowledge and faith.
Hi T.Roc,
But where is that line? I don't think it's as far "in", as the question of the big bang. To me, that's easily explainable and isn't a line between knowledge and faith.
I'm actually of the well-considered belief, that there are no lines (boundaries) that can not be surmounted. This does not mean however, that we can predict by our own devices alone.
One can arrive at the Absolute (which is what we are looking for/science included), and see right through it, to why and how it has no cause.
How is this possible? Because it's invisible.
"Faith" is not involved in what we can know about existence. Faith is in the knowledge that we can not control outcomes, ourselves, or others and that this is how it's meant to be.
TRoc
I have trouble with understanding your approach because I'm the guy in the choir that is told to lip sing.
Maybe this link would be helpfull. It might have something usefull knowledge or have some explanatory powers.
http://sonic-arts.org/td/erlich/intropblock1.htm
Dig around in his different links.
jal
I have trouble with understanding your approach because I'm the guy in the choir that is told to lip sing.
Maybe this link would be helpfull. It might have something usefull knowledge or have some explanatory powers.
http://sonic-arts.org/td/erlich/intropblock1.htm
Dig around in his different links.
jal
I think a mathematical insight from the TOE project, needs to be an absolute 1 & 0.
I am not a mathematician, but I think the following is a fair assessment. Please correct me if I'm mistaken.
All mathematics is an approximation. A finite extrapolation of one kind or another, along an infinite scale that is not yet defined. All extrapolations being first and foremost infinite, but given a workable approximation for the sake of observation.
I think an absolute 1 & 0 is the only way to define those pesky infinites and give those finites a concise reference point.
I am not a mathematician, but I think the following is a fair assessment. Please correct me if I'm mistaken.
All mathematics is an approximation. A finite extrapolation of one kind or another, along an infinite scale that is not yet defined. All extrapolations being first and foremost infinite, but given a workable approximation for the sake of observation.
I think an absolute 1 & 0 is the only way to define those pesky infinites and give those finites a concise reference point.
QUOTE (Eric England+Oct 6 2006, 03:22 AM)
All mathematics is an approximation.
Approximation of what? Mathematics is an abstract mental construct and as such is far more 'perfect' or exact than reality can be. Perfect circles and straight lines exist in maths, they don't in reality.
Approximation of what? Mathematics is an abstract mental construct and as such is far more 'perfect' or exact than reality can be. Perfect circles and straight lines exist in maths, they don't in reality.
QUOTE
Approximation of what? Mathematics is an abstract mental construct and as such is far more 'perfect' or exact than reality can be. Perfect circles and straight lines exist in maths, they don't in reality.
"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality." – Albert Einstein
Mathematics is an appoximation. A perfect circle or line, are made up of dimensionless points that are given a dimension of location. Until a dimensionless point that has no location is found, there is no chance for mathematics to establish anything other than approximate location.
So in that regard, the point, the circle, and the line are blurry.
Just like the "surface" between mass, space, and time.
QUOTE (Eric England+Oct 6 2006, 05:51 PM)
"As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality." – Albert Einstein
Exactly, Einstein is saying that while you can use maths to model reality, that doesn't mean they influence one another.
Does it mean that because a perfect circle doesn't exist in reality that you can't imagine it or find some abstract way to represent the concept of a perfect circle? Of course not. That's what maths is, it can talk about the concepts of perfection even if they can't be physically realised.
Exactly, Einstein is saying that while you can use maths to model reality, that doesn't mean they influence one another.
Does it mean that because a perfect circle doesn't exist in reality that you can't imagine it or find some abstract way to represent the concept of a perfect circle? Of course not. That's what maths is, it can talk about the concepts of perfection even if they can't be physically realised.
QUOTE (Eric England+Oct 6 2006, 05:51 PM)
A perfect circle or line, are made up of dimensionless points that are given a dimension of location. Until a dimensionless point that has no location is found, there is no chance for mathematics to establish anything other than approximate location.
Having a location does not make a point have dimension, simply that it exists. A point at the origin of a 3d space is not 3d because it exists in that space, but is a 0d object.
How many coordinates do you need to describe a point within a point? None, because there is no freedom within a point. Hence it's zero dimensional.
How many coordinates do you need to describe a point along a line? You need 1, therefore a line is one dimensional.
Etc etc. You are getting confused about describing a location on an object with describing where that object is in a larger frame of reference.
How many coordinates do you need to describe a point within a point? None, because there is no freedom within a point. Hence it's zero dimensional.
How many coordinates do you need to describe a point along a line? You need 1, therefore a line is one dimensional.
Etc etc. You are getting confused about describing a location on an object with describing where that object is in a larger frame of reference.
Eric & AlphaNumeric
I agree with your take on math as an abstract approximation.
However, of what value does zero or infinity have in that definition? None, I think. In the WHOLE system of the Universe, "infinite" can not exist, because the Universe contains EVERYTHING. Everything can be counted, while "infinite" can't.
I'm not sure about jal and Troc on this. Is this the main part of the toe thing? Where is all the "action"?
J
I agree with your take on math as an abstract approximation.
However, of what value does zero or infinity have in that definition? None, I think. In the WHOLE system of the Universe, "infinite" can not exist, because the Universe contains EVERYTHING. Everything can be counted, while "infinite" can't.
I'm not sure about jal and Troc on this. Is this the main part of the toe thing? Where is all the "action"?
J
QUOTE (inQZtive+Oct 6 2006, 06:05 PM)
Everything can be counted, while "infinite" can't.
Except for countable infinities (check Google if you don't believe me).
Except for countable infinities
(check Google if you don't believe me).
AlphaNumeric....nQZtive
I'm here.
The/your point is often confused with reality.
If you have been following my thread then you know what is my position.
jal
QUOTE
AlphaNumeric
Having a location does not make a point have dimension, simply that it exists. A point at the origin of a 3d space is not 3d because it exists in that space, but is a 0d object.
Having a location does not make a point have dimension, simply that it exists. A point at the origin of a 3d space is not 3d because it exists in that space, but is a 0d object.
I'm here.
The/your point is often confused with reality.
If you have been following my thread then you know what is my position.
jal
THE TOE THE VARIOUS CONNECTIONS AMONG PHYSICS AND MATHEMATICS FIELDS
is well possible that the supersymmetry and spontaneous supersymmetry
breaking must be relationed with NUMBER THEORY,as well as the SUPERSTRING
theory
is possible connect the continuity of space-time and the discretizations above with
a correlations of space-extended to complex number fields and time associated to the imaginary numbers in continuum real,where the rotations ellipsoidal cut the connect imaginary numbers,transcendent numbers:e,pi,generating the pure numbers-integral numbers,that that be linked the vibrations with determined and its harmonics and superharmonics,prime set.transfinite-that ordinal and cardinal.then the integral numbers are the connexions of complex numbers,more transcendents that generate coupled the space-time in supercontinuity that is:
discretizations and continuous in high dimension with arranges of quaternions,octonions,that define the vibration of the string in integral parts.
have that connexion of flat surfaces and curve surfaces are generated through of connexion of space-time continuos and discretes the in transcendent coordinate
are integers,as the ALEPH NUMBERS OF CANTOR.as well as the fractal are linked to
integral numbers.then the TOE must connect the various fields of the mathematics
with some physics fields,and those parts if connect all by the linked of those several fields.
antonio carlos motta
is well possible that the supersymmetry and spontaneous supersymmetry
breaking must be relationed with NUMBER THEORY,as well as the SUPERSTRING
theory
is possible connect the continuity of space-time and the discretizations above with
a correlations of space-extended to complex number fields and time associated to the imaginary numbers in continuum real,where the rotations ellipsoidal cut the connect imaginary numbers,transcendent numbers:e,pi,generating the pure numbers-integral numbers,that that be linked the vibrations with determined and its harmonics and superharmonics,prime set.transfinite-that ordinal and cardinal.then the integral numbers are the connexions of complex numbers,more transcendents that generate coupled the space-time in supercontinuity that is:
discretizations and continuous in high dimension with arranges of quaternions,octonions,that define the vibration of the string in integral parts.
have that connexion of flat surfaces and curve surfaces are generated through of connexion of space-time continuos and discretes the in transcendent coordinate
are integers,as the ALEPH NUMBERS OF CANTOR.as well as the fractal are linked to
integral numbers.then the TOE must connect the various fields of the mathematics
with some physics fields,and those parts if connect all by the linked of those several fields.
antonio carlos motta
THE TOE THE VARIOUS CONNECTIONS AMONG PHYSICS AND MATHEMATICS FIELDS
is well possible that the supersymmetry and spontaneous supersymmetry
breaking must be relationed with NUMBER THEORY,as well as the SUPERSTRING
theory
is possible connect the continuity of space-time and the discretizations above with
a correlations of space-extended to complex number fields and time associated to the imaginary numbers in continuum real,where the rotations ellipsoidal cut the connect imaginary numbers,transcendent numbers:e,pi,generating the pure numbers-integral numbers,that that be linked the vibrations with determined and its harmonics and superharmonics,prime set.transfinite-that ordinal and cardinal.then the integral numbers are the connexions of complex numbers,more transcendents that generate coupled the space-time in supercontinuity that is:
discretizations and continuous in high dimension with arranges of quaternions,octonions,that define the vibration of the string in integral parts.
have that connexion of flat surfaces and curve surfaces are generated through of connexion of space-time continuos and discretes the in transcendent coordinate
are integers,as the ALEPH NUMBERS OF CANTOR.as well as the fractal are linked to
integral numbers.then the TOE must connect the various fields of the mathematics
with some physics fields,and those parts if connect all by the linked of those several fields.
antonio carlos motta
have the work of the monster groups and moonshinse vertex that can produces numbers that be greater that all the atoms of universe,and produce permutations that can to be infinite.the infinite,appear in the breakdown of space and time,non-linearity,that lead us to think in the surreal numbers of conway,as well as the produtorium of space-time are renormalization of some tending to INFINITE,but that always being INTERGERS NUMBERS
is well possible that the supersymmetry and spontaneous supersymmetry
breaking must be relationed with NUMBER THEORY,as well as the SUPERSTRING
theory
is possible connect the continuity of space-time and the discretizations above with
a correlations of space-extended to complex number fields and time associated to the imaginary numbers in continuum real,where the rotations ellipsoidal cut the connect imaginary numbers,transcendent numbers:e,pi,generating the pure numbers-integral numbers,that that be linked the vibrations with determined and its harmonics and superharmonics,prime set.transfinite-that ordinal and cardinal.then the integral numbers are the connexions of complex numbers,more transcendents that generate coupled the space-time in supercontinuity that is:
discretizations and continuous in high dimension with arranges of quaternions,octonions,that define the vibration of the string in integral parts.
have that connexion of flat surfaces and curve surfaces are generated through of connexion of space-time continuos and discretes the in transcendent coordinate
are integers,as the ALEPH NUMBERS OF CANTOR.as well as the fractal are linked to
integral numbers.then the TOE must connect the various fields of the mathematics
with some physics fields,and those parts if connect all by the linked of those several fields.
antonio carlos motta
have the work of the monster groups and moonshinse vertex that can produces numbers that be greater that all the atoms of universe,and produce permutations that can to be infinite.the infinite,appear in the breakdown of space and time,non-linearity,that lead us to think in the surreal numbers of conway,as well as the produtorium of space-time are renormalization of some tending to INFINITE,but that always being INTERGERS NUMBERS
Yes, some action.
I would rather think, he is saying what he is saying. Math is uncertain when it comes to reality. Uncertain means approximate. Whenever it becomes certain, it isn't reflecting reality. He's not talking about influencing one other.
"A spatial point is an entity with a location in space but no extent (volume, area or length). In geometry, a point therefore captures the notion of location; no further information is captured." – Wikispeedia
There is no way a "model" point, line, or circle can be made from this description. There is no way to determine, even the one dimension of location. Until the space is determined to have a particular extent, there is no possibility for a dimensional reality whatsoever.
I would rather think, he is saying what he is saying. Math is uncertain when it comes to reality. Uncertain means approximate. Whenever it becomes certain, it isn't reflecting reality. He's not talking about influencing one other.
"A spatial point is an entity with a location in space but no extent (volume, area or length). In geometry, a point therefore captures the notion of location; no further information is captured." – Wikispeedia
There is no way a "model" point, line, or circle can be made from this description. There is no way to determine, even the one dimension of location. Until the space is determined to have a particular extent, there is no possibility for a dimensional reality whatsoever.
Having a location does not make a point have dimension, simply that it exists. A point at the origin of a 3d space is not 3d because it exists in that space, but is a 0d object.
A 3d space has not yet been determined. Only assumed and approximated.
Actually, this has been my "point" all along with the "TOE Project". Zero dimensional "principle points". One at the center of the other. The ones I'm refering to, however, do allow for freedom.
They are again, an absolute 1 & 0. The 1 & 0 that are used in mathematics are not absolute.
And yes, there is "countable infinity", but that is a misnomer. In the final analysis, all points are infinte in infinity.
QUOTE
Exactly, Einstein is saying that while you can use maths to model reality, that doesn't mean they influence one another.
I would rather think, he is saying what he is saying. Math is uncertain when it comes to reality. Uncertain means approximate. Whenever it becomes certain, it isn't reflecting reality. He's not talking about influencing one other.
"A spatial point is an entity with a location in space but no extent (volume, area or length). In geometry, a point therefore captures the notion of location; no further information is captured." – Wikispeedia
There is no way a "model" point, line, or circle can be made from this description. There is no way to determine, even the one dimension of location. Until the space is determined to have a particular extent, there is no possibility for a dimensional reality whatsoever.
QUOTE (->
| QUOTE |
| Exactly, Einstein is saying that while you can use maths to model reality, that doesn't mean they influence one another. |
I would rather think, he is saying what he is saying. Math is uncertain when it comes to reality. Uncertain means approximate. Whenever it becomes certain, it isn't reflecting reality. He's not talking about influencing one other.
"A spatial point is an entity with a location in space but no extent (volume, area or length). In geometry, a point therefore captures the notion of location; no further information is captured." – Wikispeedia
There is no way a "model" point, line, or circle can be made from this description. There is no way to determine, even the one dimension of location. Until the space is determined to have a particular extent, there is no possibility for a dimensional reality whatsoever.
Having a location does not make a point have dimension, simply that it exists. A point at the origin of a 3d space is not 3d because it exists in that space, but is a 0d object.
A 3d space has not yet been determined. Only assumed and approximated.
QUOTE
How many coordinates do you need to describe a point within a point? None, because there is no freedom within a point. Hence it's zero dimensional.
Actually, this has been my "point" all along with the "TOE Project". Zero dimensional "principle points". One at the center of the other. The ones I'm refering to, however, do allow for freedom.
They are again, an absolute 1 & 0. The 1 & 0 that are used in mathematics are not absolute.
And yes, there is "countable infinity", but that is a misnomer. In the final analysis, all points are infinte in infinity.
inQZtive,
I forgot about responding to your post.
The action has been mostly happening in the "philosophy" thread of the project. Not too many chiming in though.
The action has been mostly happening in the "philosophy" thread of the project. Not too many chiming in though.
Eric & AlphaNumeric
I agree with your take on math as an abstract approximation. However, of what value does zero or infinity have in that definition? None, I think. In the WHOLE system of the Universe, "infinite" can not exist, because the Universe contains EVERYTHING. Everything can be counted, while "infinite" can't.
I think you're doing AlphaNumeric a disservice, by saying you agree. I'm the only one of us who is saying "approximation".
Here's a couple of things to think about.
To know what "everything" represents, you would have to go beyond everything, to make sure you were including everything. That's easy to do when you pull out all the money in your wallet, make sure it's empty and then count the money. In my case, I don't even have to count the money. It's a different story with the universe.
It can't be so easily said, that one has arrived at "everything" and there is "nothing" beyond that.
As for infinite not existing, I do have to disagree. There is nothing to say, there isn't something greater than infinity. Infinity just doesn't depart from or arrive at, a point or a number. There is simply an absolute (non-approximate) perspective lacking, to put it in.
And one last thought. Even one point or number can not be counted yet, to arrive at everything.
All points and numbers in infinity, are infinite. We can't even get from 0 to 1. What is the smallest fraction of 1 you would begin with? It's not determinable. If it can't be determined, then it can't be multiplied by its inverse, to arrive at 1.
The same holds true for nothing and everything. Nothing being 0 and everything being 1.
So far, we rely on approximations, call them "finite", and that's the historically recognized limit of both mathematics and physics. We assume approximates to have something to play with, while knowing full well that we haven't proved anything.
GR is accurate within so much. QM is also uncertain. Plank the same, etc. etc.
The historical definition of infinity is only partially sufficient, to see the true value it has in understanding the overall nature of the universe.
Eric
Yeah, I know it's there. So are aliens, bigfoot, etc.
To me, the use of infinities, because of getting them as an answer, is not consistent. The answer (or the question) was wrong somewhere. Infinity is philosophy, not proper (logical) math.
Eric shows the philosophical side of this issue.
I think that extrapolation will get us to a very close "approximation" of "everything".
mott.carl seems to have some valid points. I think that there must be a language/translation problem though. (or he is a little crazy!)
J
Infinities "limit" theories but don't outrightly spoil them.
As AlphaNumeric said in another thread, he feels I think finite is bad and infinity is good.
Finite is good in regards to application and getting an increasingly thorough view of what the universe isn't, but bad when it comes to understanding what the universe actually is and why.
Finite has a beginning and end. Infinite does not. "Countable infinities" doesn't mean we've ever found a beginning or end to infinity.
We like finite and don't like infinity, and there's an understandable reason for this.
Finite implies that something is "really" happening. It began and will end, but for now, it's happening! Whoopie! We're having a big bang, everyone is invited, just pick up a vibrating string and play it to your heart's content until the big crunch comes along, with or without warning.
That's what we sense all around us. Beginnings and ends. We think we're perceiving "event horizons". AlphaNumeric thinks I use the term randomly, but I don't. We've never concisely located an event horizon, but we do need our "approximations". Birth and death are approximations.
Mathematics and physics intersect at the proximity of "one/something". Proximity is the closest we've come.
Infinity on the other hand, is different than the approximation of "one (all) something(s) really happening". What infinity says, is that the universe is always in the state of potential of "will happen". It offers a promise that finite can not.
The single most important thing that has ever been said in mathematics and physics, is the one thing we consistently have trouble with.
"Reality is merely an illusion, albeit a very persistent one." – Einstein
We persist in believing something is really happening (for now), instead of realizing it will happen eternally.
We are given the "sense" that something is happening, which is good enough for me.
What is being built at Cern, is a bigger and more powerful "sensing machine". It will not prove a thing, about what the universe really is and why. It may, however, give us a better understanding of what the universe isn't.
I forgot about responding to your post.
QUOTE
I'm not sure about jal and Troc on this. Is this the main part of the toe thing? Where is all the "action"?
The action has been mostly happening in the "philosophy" thread of the project. Not too many chiming in though.
QUOTE (->
| QUOTE |
| I'm not sure about jal and Troc on this. Is this the main part of the toe thing? Where is all the "action"? |
The action has been mostly happening in the "philosophy" thread of the project. Not too many chiming in though.
Eric & AlphaNumeric
I agree with your take on math as an abstract approximation. However, of what value does zero or infinity have in that definition? None, I think. In the WHOLE system of the Universe, "infinite" can not exist, because the Universe contains EVERYTHING. Everything can be counted, while "infinite" can't.
I think you're doing AlphaNumeric a disservice, by saying you agree. I'm the only one of us who is saying "approximation".
Here's a couple of things to think about.
To know what "everything" represents, you would have to go beyond everything, to make sure you were including everything. That's easy to do when you pull out all the money in your wallet, make sure it's empty and then count the money. In my case, I don't even have to count the money. It's a different story with the universe.
It can't be so easily said, that one has arrived at "everything" and there is "nothing" beyond that.
As for infinite not existing, I do have to disagree. There is nothing to say, there isn't something greater than infinity. Infinity just doesn't depart from or arrive at, a point or a number. There is simply an absolute (non-approximate) perspective lacking, to put it in.
And one last thought. Even one point or number can not be counted yet, to arrive at everything.
All points and numbers in infinity, are infinite. We can't even get from 0 to 1. What is the smallest fraction of 1 you would begin with? It's not determinable. If it can't be determined, then it can't be multiplied by its inverse, to arrive at 1.
The same holds true for nothing and everything. Nothing being 0 and everything being 1.
So far, we rely on approximations, call them "finite", and that's the historically recognized limit of both mathematics and physics. We assume approximates to have something to play with, while knowing full well that we haven't proved anything.
GR is accurate within so much. QM is also uncertain. Plank the same, etc. etc.
The historical definition of infinity is only partially sufficient, to see the true value it has in understanding the overall nature of the universe.
Eric
QUOTE
AlphaNumeric Posted on Oct 6 2006, 05:08 PM
QUOTE (inQZtive @ Oct 6 2006, 06:05 PM)
Everything can be counted, while "infinite" can't.
Except for countable infinities (check Google if you don't believe me).
QUOTE (inQZtive @ Oct 6 2006, 06:05 PM)
Everything can be counted, while "infinite" can't.
Except for countable infinities (check Google if you don't believe me).
Yeah, I know it's there. So are aliens, bigfoot, etc.
To me, the use of infinities, because of getting them as an answer, is not consistent. The answer (or the question) was wrong somewhere. Infinity is philosophy, not proper (logical) math.
Eric shows the philosophical side of this issue.
I think that extrapolation will get us to a very close "approximation" of "everything".
mott.carl seems to have some valid points. I think that there must be a language/translation problem though. (or he is a little crazy!)
J
QUOTE (inQZtive+Oct 9 2006, 07:18 PM)
The answer (or the question) was wrong somewhere. Infinity is philosophy, not proper (logical) math.
While you make think infinities in maths are the result of mistakes or some illogical route, you're wrong. The work of Cantor put infinity (or rather, the many different kinds of infinity) on solid foundations of logic. You're not alone in finding it strange, many of Cantors contemparies had trouble accepting his work initially but plenty of that area has been explored since and it's all logically consistent.
As for Mott.carl, he always just spouts a huge paragraph of science or maths buzzwords about just about everything which never ends up meaning very much.
While you make think infinities in maths are the result of mistakes or some illogical route, you're wrong. The work of Cantor put infinity (or rather, the many different kinds of infinity) on solid foundations of logic. You're not alone in finding it strange, many of Cantors contemparies had trouble accepting his work initially but plenty of that area has been explored since and it's all logically consistent.
As for Mott.carl, he always just spouts a huge paragraph of science or maths buzzwords about just about everything which never ends up meaning very much.
AlphaNumeric,
I do realize that infinity is used in higher maths (which I am still learning). Because of that, I can't say too much! Just my "gut"
I've read several times (in different places) that "infinities" pop up and spoil theories, causing the need for "adjustments", which seems lame.
J
I do realize that infinity is used in higher maths (which I am still learning). Because of that, I can't say too much! Just my "gut"
I've read several times (in different places) that "infinities" pop up and spoil theories, causing the need for "adjustments", which seems lame.
J
What you're referring to are infra-red and ultra-violet divergences in some quantum field theories. There are techniques to deal with them and return a sensible answer. I know it sounds odd and perhaps a bit of a fiddle, but it's not really (well, too much). The method is known as renormalisation and it's applied consistently throughout a theory and it turns experimentally verified accurate results.
For a vague (and perhaps totally unrealistic) example consider
f(x) = (1/x) + 5 + x
f(0) is undefined due to the 1/x term
f(x) as x-> infinity is also unbounded due to the x term
However, there's a term in f(x) which doesn't have any dependence on x, the constant 5 term. Renormalisation basically gets rid of the terms involving the x variable and just leaves you with the bits which are constant.
For a vague (and perhaps totally unrealistic) example consider
f(x) = (1/x) + 5 + x
f(0) is undefined due to the 1/x term
f(x) as x-> infinity is also unbounded due to the x term
However, there's a term in f(x) which doesn't have any dependence on x, the constant 5 term. Renormalisation basically gets rid of the terms involving the x variable and just leaves you with the bits which are constant.
AlphaNumeric,
Thanks for your replies, and assistance.
I was checking some notes, and remembered another one.
The charge of the field at the center of an electron?
Does the mathematical example you gave apply there too?
J.
Thanks for your replies, and assistance.
I was checking some notes, and remembered another one.
The charge of the field at the center of an electron?
Does the mathematical example you gave apply there too?
J.
No, renormalisation is about computing the value of Feynman integrals you get in things like quantum electrodynamics. While you can derive the Coloumb force from QED, you don't deal with the 1/r^2 charge force directly.
For the simplest equations you'd do for two electrons bouncing off one another there's no problem, you can evaluate them directly and unless you want very accurate predictions, that's enough.
For more complex situations (pair production within reactions!) then you get divergences. They typically arise because you're summing over all possible paths and motions of the particles involved and at some point you've consider the two electrons very very close to one another and the 1/r^2 force you mention is going to not like that in most cases. The integrals you'd be doing are going to have expansions similar to Taylor expansions (but with some negative powers too) and it's that which you're interested in, not the 1/r^2 thing specifically.
I'm probably being so vague that I'm not being much help. I've only just begun to do renormalisation properly myself (though I did first learn about it last year) so it's a bit garbled in my head and then having to explain it without maths over the net makes my explainations even worse
For the simplest equations you'd do for two electrons bouncing off one another there's no problem, you can evaluate them directly and unless you want very accurate predictions, that's enough.
For more complex situations (pair production within reactions!) then you get divergences. They typically arise because you're summing over all possible paths and motions of the particles involved and at some point you've consider the two electrons very very close to one another and the 1/r^2 force you mention is going to not like that in most cases. The integrals you'd be doing are going to have expansions similar to Taylor expansions (but with some negative powers too) and it's that which you're interested in, not the 1/r^2 thing specifically.
I'm probably being so vague that I'm not being much help. I've only just begun to do renormalisation properly myself (though I did first learn about it last year) so it's a bit garbled in my head and then having to explain it without maths over the net makes my explainations even worse
QUOTE
I've read several times (in different places) that "infinities" pop up and spoil theories, causing the need for "adjustments", which seems lame.
Infinities "limit" theories but don't outrightly spoil them.
As AlphaNumeric said in another thread, he feels I think finite is bad and infinity is good.
Finite is good in regards to application and getting an increasingly thorough view of what the universe isn't, but bad when it comes to understanding what the universe actually is and why.
Finite has a beginning and end. Infinite does not. "Countable infinities" doesn't mean we've ever found a beginning or end to infinity.
We like finite and don't like infinity, and there's an understandable reason for this.
Finite implies that something is "really" happening. It began and will end, but for now, it's happening! Whoopie! We're having a big bang, everyone is invited, just pick up a vibrating string and play it to your heart's content until the big crunch comes along, with or without warning.
That's what we sense all around us. Beginnings and ends. We think we're perceiving "event horizons". AlphaNumeric thinks I use the term randomly, but I don't. We've never concisely located an event horizon, but we do need our "approximations". Birth and death are approximations.
Mathematics and physics intersect at the proximity of "one/something". Proximity is the closest we've come.
Infinity on the other hand, is different than the approximation of "one (all) something(s) really happening". What infinity says, is that the universe is always in the state of potential of "will happen". It offers a promise that finite can not.
The single most important thing that has ever been said in mathematics and physics, is the one thing we consistently have trouble with.
"Reality is merely an illusion, albeit a very persistent one." – Einstein
We persist in believing something is really happening (for now), instead of realizing it will happen eternally.
We are given the "sense" that something is happening, which is good enough for me.
What is being built at Cern, is a bigger and more powerful "sensing machine". It will not prove a thing, about what the universe really is and why. It may, however, give us a better understanding of what the universe isn't.
Just thought I'd add that "will happen" is not just some philosophical idea, that doesn't apply directly to the physical universe.
It has never been shown that anything has ever happened or is happening. It sure seems like it, but appearances can be deceiving.
It has never been shown there was a big bang. Matter is not yet a substance. Energy is not yet a value beyond zero. A single "anything" has not been isolated. Space is not yet empty. Freedom to move has not been established. It can't be shown that anything touches anything else. Have we even found an actual "surface" to anything? Is the speed of light really finite? Is the arrow of time all there is to time?
AlphaNumeric, you know the particulars better than I do. Are these things true or not? Maybe I'm missing something, but this is how it seems to me.
Is seeing infinity as "problematic", ultimately necessary? Or can understanding it for what it really represents, one of the gatways to understanding what the universe really is and why?
If "finite" becomes an "illusion" because of it, will this be bad or will it be good?
It has never been shown that anything has ever happened or is happening. It sure seems like it, but appearances can be deceiving.
It has never been shown there was a big bang. Matter is not yet a substance. Energy is not yet a value beyond zero. A single "anything" has not been isolated. Space is not yet empty. Freedom to move has not been established. It can't be shown that anything touches anything else. Have we even found an actual "surface" to anything? Is the speed of light really finite? Is the arrow of time all there is to time?
AlphaNumeric, you know the particulars better than I do. Are these things true or not? Maybe I'm missing something, but this is how it seems to me.
Is seeing infinity as "problematic", ultimately necessary? Or can understanding it for what it really represents, one of the gatways to understanding what the universe really is and why?
If "finite" becomes an "illusion" because of it, will this be bad or will it be good?
This is what I said to jal in another thread, which was his, and he asked for it to be brought over here.
So AlphaNumeric chimes in...
So AlphaNumeric chimes in...
Utter mathematical gibberish. You've obviously never studied mathematics, particularly analysis, in any formal way beyond school level. 1 & 0 AREN'T ASSUMED in maths, they are derived from the basic axioms of maths.
Then he says this...
Oops! At the very least, one page and one assumption short of absolute. Has anybody at Cambridge told you the limitation of mathematics or are they only spouting its glories?
How about physics? It's no different. There are no absolutes. Period. It's all assumuptions or approximations.
Then this...
Oops! At the very least, one page and one assumption short of absolute. Has anybody at Cambridge told you the limitation of mathematics or are they only spouting its glories?
How about physics? It's no different. There are no absolutes. Period. It's all assumuptions or approximations.
Then this...
As I also explained to you before, there's plenty of maths dealing with infinity. Once you've given a precise definition to the notion of 'countable infinities' you can precisely show the existence of an infinitely number of fundamentally different infinities.
Less rude and now, a little more accurate. Both of us know you can't count to infinity nor locate the zero to begin from, without making an assumption. So all you have is what you said, "an infinity of infinities".
Infinity in both mathematics and physics, is "problematic". Until it becomes "solved", it's all assumed approximations. They are very useful, but not absolute.
The reason a TOE hasn't been found or as Hawking descibes it, "
QUOTE
Your 1 & 0 have to be assumed (approximated). Pick either one of them and try to get to the other. It's impossible (infinity). So now, assume both of them and give 1 a +/–, with 0 stuck in the middle. Now use any combination of "finite" numbers to calculate anything you'd like.
All of your calculations will be based on an assumption and infinity still remains problematic.
Mathematics has yet to establish an absolute 1 or 0.
All of your calculations will be based on an assumption and infinity still remains problematic.
Mathematics has yet to establish an absolute 1 or 0.
So AlphaNumeric chimes in...
QUOTE (->
| QUOTE |
| Your 1 & 0 have to be assumed (approximated). Pick either one of them and try to get to the other. It's impossible (infinity). So now, assume both of them and give 1 a +/–, with 0 stuck in the middle. Now use any combination of "finite" numbers to calculate anything you'd like. All of your calculations will be based on an assumption and infinity still remains problematic. Mathematics has yet to establish an absolute 1 or 0. |
So AlphaNumeric chimes in...
Utter mathematical gibberish. You've obviously never studied mathematics, particularly analysis, in any formal way beyond school level. 1 & 0 AREN'T ASSUMED in maths, they are derived from the basic axioms of maths.
Then he says this...
QUOTE
Stop spouting crap of a pseudo-philisophical nature about all these holes in maths in such a basic level, you're wrong. It takes 365 pages to derive the existence of the number 1 !!! It takes that long because they ASSUME PRACTICALLY NOTHING and do every single step of logic required to make sure there's no room for error.
Oops! At the very least, one page and one assumption short of absolute. Has anybody at Cambridge told you the limitation of mathematics or are they only spouting its glories?
How about physics? It's no different. There are no absolutes. Period. It's all assumuptions or approximations.
Then this...
QUOTE (->
| QUOTE |
| Stop spouting crap of a pseudo-philisophical nature about all these holes in maths in such a basic level, you're wrong. It takes 365 pages to derive the existence of the number 1 !!! It takes that long because they ASSUME PRACTICALLY NOTHING and do every single step of logic required to make sure there's no room for error. |
Oops! At the very least, one page and one assumption short of absolute. Has anybody at Cambridge told you the limitation of mathematics or are they only spouting its glories?
How about physics? It's no different. There are no absolutes. Period. It's all assumuptions or approximations.
Then this...
As I also explained to you before, there's plenty of maths dealing with infinity. Once you've given a precise definition to the notion of 'countable infinities' you can precisely show the existence of an infinitely number of fundamentally different infinities.
Less rude and now, a little more accurate. Both of us know you can't count to infinity nor locate the zero to begin from, without making an assumption. So all you have is what you said, "an infinity of infinities".
Infinity in both mathematics and physics, is "problematic". Until it becomes "solved", it's all assumed approximations. They are very useful, but not absolute.
The reason a TOE hasn't been found or as Hawking descibes it, "