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.