By Small Means, Great Things are Brought to Pass
Doug
6 Comments
I tried to point out to John Baez, via Peter Woit’s blog, that by not recognizing that the “dimensions” of mathematics do not correspond to physical dimensions, the LST community is tripping up on a small, but very significant, stumbling block.
They equate the four levels of the tetraktys with four different, ad hoc, number systems, based on the ad hoc use of imaginary numbers: At the first level, 0 imaginary numbers are associated with the familiar real number system, but adding 1 imaginary number to the reals enables man to generate the marvelous complex numbers, the second level which provides the foundation of all the science and technology running the world today.
Recently, another number system has been widely incorporated in computer simulations and robotics that was invented in the Nineteenth Century, by Sir Hamilton, which is called the quaternions. Quaternions have found wide application lately, even though their true nature is misunderstood in most cases. This number system, residing at the third level of the tetraktys, incorporates three imaginary numbers.
Finally, at the fourth level, the octonions incorporate no less than seven imaginary numbers and are the subject of Baez’s Scientific American article, which Woit blogged about, because it ties octonions to string theory, and Woit’s purpose in life is to debunk string theory hype, whereever and whenever it appears.
However, Woit had to admit that Baez and his co-author were not actually hyping string theory: They were hyping octonions, declaring that, “if string theory is right, the octonions are not a useless curiosity: on the contrary, they provide the deep reason why the universe must have 10 dimensions: in 10 dimensions, matter and force particles are embodied in the same type of numbers—the octonions.”
This is a reference to the supersymmetry of string theory. It turns out that the only way to describe the elements of the theory without inducing anomalies, is to use the 8 “dimensions” of octonions plus the two extra dimensions of strings and time - a total of ten “dimensions.”
Of course, I tried to point out that the universe doesn’t have ten dimensions, it only has the three observed dimensions of space and the one observed dimension of time - the four dimensions of motion, if you will, and their inverses, but just as the members of the LST community can’t understand that motion doesn’t have to be one-dimensional, they also can’t seem to understand that each physical dimension has two “directions,” and that they should look into the mathematics of ten “directions,” instead of ten “dimensions.”
Unfortunately, however, in our era of political correctness, such views are squelched and Woit refused to allow my comment on his blog to be published. Oh, well. It’s their loss. We will continue to apply our meager brain power to the truth and keep plugging along to see what we can accomplish without their Cadillac brains and resources.
In the next post, I will begin to explain the integration of the geometry of Larson’s Cube, the mathematics of the tetraktys and the numbers of the new number line, which will enable us to desribe the preons of our version of the standard model in terms of more than the initial color combinations we have been using. Now we can put real numbers to the entities in the model, numbers that are related to the energy levels of the atomic spectra.
Proving once again that many times, by small and simple means, great things are brought to pass.
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Reader Comments (6)
Wow a new Entry!
I can see that you have been recently into inversive geometry relationships and I applaud that.
My russian friends would like to read your thoughts about the concept of Separateness of SUDRs, TUDRs, etc.... Apparently photons, atoms, etc... are separated by some amounts of time and space because if they were not they would superimpose on each other. It would be nice if you could elaborate more in that direction, e.g.: what is the difference between the time/space of a photon (or atom) and the time/space between photons (or atoms)...
That's such a good question. When space is defined normally, it is considered as a separation of locations satisfying a set of geometric postulates. In the case of flat space, the postulates of its geometry are Euclidean. In the case of curved space, the postulates are non-Euclidean, but in the RST, the assumption is flat space and observations now confirm that the geometry of the universe is flat.
Non-Euclidean geometry is shown to be consistent, but that is because Euclid's fifth postulate opens the door to considering alternate interpretations of parallel lines that only appear to be parallel.
We can get past that distraction by redefining space as follows: space is the reciprocal of time in the equation of motion. The separation of objects is a history of their past motion.
In the universe of nothing but motion, we define motion in the beginning as a scalar increase of space and time in three dimensions. This condition is the perfectness of nothing (nothing is perfect.)
To introduce something into nothing, we postulate a reversal in the expansion at some "point" in the space/time expansion. This gives rise to the SUDRs (when the reversals are space reversals) and TUDRs (when the reversals are time reversals), because a local reversal of a universal expansion is a contraction, but a contraction is constrained to one unit by geometry and mathematics.
The time aspect of SUDRs progresses normally, while the oscillation of the space aspect confines its progression, and vice-versa for the space aspect of the TUDRs. It then follows that the SUDRs and TUDRs can be either in the future or the past of the space or time aspect of one another and contact becomes possible, when the former condition holds for a given set.
Consequently, the combination of SUDRs and TUDRs in the form of S|T units propagates in BOTH space and time, each making its respective contribution via its non-oscillating aspect. These first combinations are photons propagating at the speed of light relative to any S|T combo not able to propagate in both space and time.
The question is, how does an S|T combo, which is now an oscillating progression of space and time, stop progressing in one or the other of its two reciprocal aspects? Before answering that question, we can note that a cessation of progression, in either space or time, constitutes the establishment of a system of reference with respect to that object.
For example, if the spatial progression of one S|T unit ceased at some "point" in time, and then another right after that, their separation in space would depend on what the duration of time was between the two events.
There would exist a line of space between them. Subsequently, if the spatial progression of a third unit ceased, it would also be separated by some interval of space, depending on the interval of time between its cessation event and the previous ones.
However, it is impossible to say in which direction it would lie, relative to the spatial locations of the two previous units. Nevertheless, regardless of the direction, a line drawn between the locations of the three units would form a plane, provided it was not on the line of the two previous locations.
From this observation we can conclude that any motion (or direction) not in the same dimension of an existing motion (or direction), must be motion in another dimension. This avoids the pitfall of the fifth postulate.
Now, once these S|T units are occupying non-progressing, spatial, locations, any vectorial motion will change their relative positions in this new system of spatial reference, but their separation in time continues.
As to how the scalar progression of the S|T units ceases in the spatial aspect and not the time aspect, or vice-versa, one has to consider how these units combine. One thought is that if the S|T unit is an oscillating ball (the smaller SUDRs are wholly contained by a larger TUDR, in the material sector, or vice-versa in the cosmic sector, then the proportion, or ratio, of total space motion to total time motion can potentially reach a point that the uniform space progression of the TUDR starts to be cancelled, slowing and eventually stopping the space progression of the combo, relative to the unimpeded progression of single S|T units (photons).
But development along this line is in progress. I'm about to start writing up some exciting findings, though. Stay tuned.
And do you think that the Doppler effect can still arise in this context?
Doug wrote:
"Now, once these S|T units are occupying non-progressing, spatial, locations, any vectorial motion will change their relative positions in this new system of spatial reference, but their separation in time continues."
LOL. That's an interesting question. As the separation in time continues, you might think that there would be a Doppler effect, if time itself were oscillating. But the change in wave length would represent a change in space, not time, so the reasoning starts to get circular, since the scalar expansion of space is cancelled by the scalar space oscillations.
Off the top of my head, I would think then that the answer is no, but who knows...
Good question.
Look at what I just stumbled!
Looks like 4 years ago I was already pondering whether the Universe is digital or analog ;)
http://forum.rs2theory.org/comment/728#comment-728
Yes, I see. The same question that arises in physics, arises in mathematics and geometry: are there really magnitudes that aren't numbers?
I don't think so. The ratios of irrational numbers are demonstrably numbers, so we are still left with the fundamental truth that where two facts exist, one above the other, there will ALWAYS be another, greater than them both, until you reach the greatest of all.