StevenA
1st July 2008 - 09:24 AM
A stationary object in a constant velocity space should be describable in terms of a closed orbit(al) or standing wave - though motion occurs within this pathway, the pathway itself could be seen to describe a complex cycle of the object.
For a stationary observer in this space, this would mean that they would detect a specific frequency or wavelength equal to the distance of this loop and the specific form of the loop beyond that observation point would be unimportant (the observer is defined to be stationary in this space and has no ability to detect something beyond their point of origin).
This creates a space of loops of different lengths that intersect the observational origin and distinct objects are defined by distinct fundamental wavelengths.
If an object possesses greater/finer detail than a single wavelength, this can be represented by harmonics, or wavelengths that are even divisions of the fundamental wavelength, which in spacial terms conveys smaller ratios of volumes (a wavelength at a higher frequency has its cycle embedded on a smaller scale of space). So, for example, if an observer were detecting a molecule composed of 3 atoms A, B and C, with atomic bonds serially connected, this could be seen similar to a diagram:
A-B-C
And in terms of the atomic bonds/interactions, by two wavelengths with a ratio of 1:2.
Imagine two loops intersecting at an observation point, with one containing the 2 elements, A and C and the other containing only the element B, then these two loops presenting each element within them sequecially to an observer and we have two sequences:
CODE
ACACACAC...
BBBBBBBB...
And looking vertically we can see at each time that B is alternately associated with A and then C over time, but A and C do not interact together at the same time.
Because A and C exist within the same wavelength, but at different phases of it, they are always separated by time or space in this example and that can be true for different wavelengths as well, if they share a common divisor, such as two objects with wavelengths 2 and 4 could have elements in different phases of these wavelengths that are always separated in time or space, such as:
CODE
ABABABABABAB...
CDEFCDEFCDEF...
Again, looking at these two sequences in vertical strips, we get snapsnots of which elements can interact at an observation point at any moment in time and we find that A alternately interacts with C and E (and never B, D or F) and that B alternately interacts with D or F (and never with A, C or E) and that also all of C, D, E and F are independent of each other as well.
But the properties of such a space are amazingly complex (in fact they appear directly correlated to many of the "hard" problems in science).
Here's a 2-D "map" of some of the properties of interactions between objects of various wavelengths (this "map" shows whether or not two objects of some size/wavelength can appear stationarily connected within this space), and all that's being done is determining whether or not two numbers share a common divisor (for example, wavelengths of 2 and 5 would nto appear stationarily correlated in this space, because they share no common divisor, but two objects with wavelengths 4 and 12 could appear to possess stationary physical features with different aspect ratios):
http://mathworld.wolfram.com/RelativelyPrime.htmlIn those plots, the X axis would represent one wavelength and the Y axis the other.
Just to demonstrate some of the interesting complexity that can arise from this, consider a problem of two objects incrementally growing in size within this space, but never appearing to interact within this space, but in constant motion relative to each other. In this case if we wanted to find an optimal "pathway" for the growth in wavelengths over time that made the objects appear to be as similar in size as possible, yet remain distinct and non-interacting, we'd be looking for sequences of ratios X:Y, for which X!=Y, but with X as close as possible to Y.
For example, if we began with one object of wavelength 2 and another with a wavelength of 3, then these would be relatively prime and provide no preferential interactions between any of the phases (observations from either of these objects to the other would appear identically blurred from all phases of observation).
But in the case of wavelengths of 2 and 3, if we attempted to increase the size of either (by 1), they would have to interact as if we increase the wavelength of 2 to 3, we'd have a new ratio of 3:3 and we'd see these two objects merge together into a single object, or if we increased the wavelength 3 to 4, we'd have a ratio of 2:4 and these would appear as 2 independent objects with 1:2 aspect ratios.
If we begin with ratios of 2 to 7, we could increase 2 to 3 and move to 3/7, then either 3/8 or 4/7 etc., but this series ends up terminating shortly. (You can look at this similar to the GCD plot on the Wolfram link being a maze and trying to find a pathway closest to the 45 deg line of symmetry in it)
Though if we begin with a ratio of 2:11, it appears a pathway can be traced through this to possibly arbitrarily large wavelengths (there's likely a way of showing that at least some pathway should exist to arbitrarily large numbers, even if it's not optimal in the sense of finding ratios closest to 1)
But here's the beginning of a pathway I traced out for a few thousand elements that appears optimal (assuming it doesn't ultimately "dead end") - 2/11,3/11,4/11,5/11,6/11,7/11,7/12,7/13,8/13,9/13,10/13,11/13,11/14,11/15,11/16,11/17,12/17,13/17,13/18,...
To compress this, I can simply denote the endpoints of each subsequence in this as:
2/11->7/11->7/13->11/13->11/17->13/17->13/19->17/19->17/23->19/23->...
Is there some nice pattern to all this? The intent of this thread was to just show how a constant velocity space with a stationary observer attempting to perceive stationary patterns within this space appears to give rise to quite a complex realm of objects and interactions, just from the manner of observation within this space - these "first person" features or equivalent rules of interaction would be superimposed upon whatever objects actually existed external to observer. (I keep thinking of the fish in water analogy)
The properties of interactions between objects within this space are determined by the manner in which the phases of oscillations are interleaved at the point of observation.
You're still as deluded and moronic as ever. Euler and I continue to mop the floor with you and your crank buddies like Precursor. You think material we teach is 'complicated'. You're forced to post nonsense like this rather than put your physics/maths where your mouth is in threads like the one Euler started. Euler and I have done a few of those questions for you and Precursor. You've done none. Why is that? 
)