Meeting a Terrific Challenge

Discussion of Larson Research Center work.

Moderator: dbundy

dbundy
Posts: 140
Joined: Mon Dec 17, 2012 9:14 pm

Re: Meeting a Terrific Challenge

Post by dbundy » Fri Jan 04, 2019 5:53 am

The LST community views the physical universe as a stage of space and time for matter and its interactions. As David Hestenes expresses it, the goal of their research program is to find the set of the fewest interactions among the set of the fewest particles of nature, This has resulted in the standard model of particle physics.

Larson's program of research is radically different. It assumes that everything in the physical universe stems from the reciprocal relation between space and time, which it assumes exists in discrete units of three dimensions. This has led us to deduce that, instead of adding time as a fourth dimension to the Pythagorean theorem equation, which is the basis for the LST community's concept of spacetime, we conceive of two separate Pythagorean equations, one for space and one for time, each with three dimensions. which are reciprocals.

The equation of space, √(12 + 12 + 12) = √3, is calculated from the LC in units of space, while the equation of time is the inverse of this, 1/√(12 + 12 + 12) = 1/√3, calculated from the LC in units of time. The respective volumes of space and time associated with each of these equations for their respective radii are inverse, and the space volume is calculated to be 27 times smaller than the time volume.

For unknown reasons, this value coincides with the value of the number of poles in the 3d space calculated from the tetraktys:

0d = 30 = 1
1d = 31 = 3
2d = 32 = 9
3d = 33 = 27

when the coefficients of the binomial expansion equation of the tetraktys (see Pascal's triangle) are taken into account, which, for three dimensions, are 1, 3, 3, and 1. Now, the question is, how do we calculate the number of poles for the inverse tetraktys, the tetraktys of time, we might say? Do we just invert the numbers:

1/0d = 1/30 = 1/1
1/1d = 1/31 = 1/3
1/2d = 1/32 = 1/9
1/3d = 1/33 = 1/27

This seems logical, but who has ever heard of inverse dimensions? Nevertheless, when we calculate the number of poles in our revised "Bott clock" we get:

0d = 34 = 81
1d = 35 = 243
2d = 36 = 729
3d = 37 = 2187

which numbers, at first glance, look nothing like the inverse dimensional numbers. However, notice that, if we take the 34 = 81 value of poles as the new unit, as indicated should be the case in our "clock," and make it the inverse of the first tetraktys, as also indicated in our "clock," we get the exact inverse of the number of poles in the first tetraktys:

1/0d = 81/81 = 1/1
1/1d = 81/243 = 1/3
1/2d = 81/729 = 1/9
1/3d = 81/2187 = 1/27

The question is now, of course, is this just a little mathematical sleight of hand on our part? Is the logic twisted to suit our objective? The reader will have to make that decision, but I find it hard to believe that we could continue to make these observations by virtue of mere coincidence.

dbundy
Posts: 140
Joined: Mon Dec 17, 2012 9:14 pm

Re: Meeting a Terrific Challenge

Post by dbundy » Mon Jan 07, 2019 3:08 pm

When we mess with the foundation of mathematics, we mess with the foundation of physics and the technology that is the foundation of Western civilization. God have mercy on my soul, because I can't stop now!

The posts on page 3 of this topic deal with the relationship between the tetraktys and the LC and its consequences. The major conclusion is that the tetraktys is as far as we can take the binomial expansion. There are no higher dimensions in physical phenomena, in spite of Clifford algebra.

Notwithstanding this apparent fact, we've seen how John Baez et. al, explain incredibly complex mathematics in an attempt to go beyond three dimensions (four counting 0). It is very interesting to see how they have mistaken the "directions" of dimensions, or at least mis-labeled them, so that it's difficult to not confuse non-specialists with their mathematical and geometrical concepts.

Nevertheless, the "Bott clock," which we have revised (see previous posts above), helps us to understand the new scalar concepts tremendously, I think, even though it still lacks the clear connection with the LC. I think I can add that too to the clock.

On page 3 of this topic I show how the number 8 of the 3d expansion follows the expansion of the LC: 23, 43. 63, ...2n3.

This connection of numbers and geometry is real easy to show, when n = 1, because the 3d expansion generates the 2x2x2 stack of 8, 1-unit cubes of the LC, which contains all the dimensional sub-spaces of the LC, and the numbers of Pascal's triangle, which are just the coefficients of the binomial expansion (1 3 3 1), at the 3d (fourth) level.

However, if there really are no higher dimensions than these three (four), then how do we modify the binomial expansion to follow the geometric expansion of the LC? The clue is found in the LC expansion, which is actually a cubic expansion, when period 8 is taken into account; that is, 8/8 = 13, 64/8 = 23, 216/8 = 33, ...2n3/23.

Fortunately, this means that n3 is a factor in the third dimension, implying that n2, n1 and n0 are also factors in their respective subspaces of the tetraktys:

20 x n0; 21 x n1; 22 x n2; 23 x n3 = 20; 21; 22; 23, which, when multiplied by their respective binomial coefficients, 1, 3, 3, and 1, produces the LC, when n = 1:

1 monopole, 3 dipoles, 3 quadrupoles, 1 octupole = 27 poles

When n = 2, we get 125 poles, and 3 gives us 343, 4 gives 729 and 5 generates 1331 (just a coincidence, I think). The interesting thing is that these products and sums also form a cubic progression, starting with n =1 ----> 33 = 27:

n = 2 ----> 53; n = 3 ----> 73; n = 4 ----> 93; n = 5 ----> 113. This is an important factor relative to the atomic spectra, but more on that later. Right now, I want to incorporate this into our Bott clock:

Image

Poles are an alternate way of thinking of magnitudes in two "direction" from a center point:

30 = (1) point:
o
31 poles = 2 end and 1 center point arranged to form a line :
<----o---->
32 poles = 6 end and 3 center points arranged to form an area:
<----o---->
<----o---->
<----o---->
33 poles = 18 end and 9 center points arranged to form a volume:
<----o----> <----o----> <----o---->
<----o----> <----o----> <----o---->
<----o----> <----o----> <----o---->

When n = 5:
<---<---o--->--->
When n = 7:
<---<---<---o--->--->--->

In the case of the clock, n = r, so that for each r = 1, 2, 3, … n, there is a dual set of tetraktii generated, each corresponding to its respective LC.

This is much easier to work with than thinking that the dimensions can be incremented higher and higher, as in the fourth dimension and beyond of Clifford algebras:

Image

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