You may have gotten the impression that I find Noyes, Rhodes, Bastin et al a load of nonsense but this is definitely NOT the case. There are several glaring mathematical errors (illogical, unclear or wrong) but these aside, the material is well worth the study from a physics point of view. It explains (a priori) a gently inflating universe and phases of universe evolution such as baryogenesis, confinement and structural constants in the general case. My brother and I believe it is a new and valid approach to quantum physics and indeed any structure based in finite discrimination.

]]>There is a major flaw in Noyes’/Bastin’s papers. Any run of Program Universe as they have defined it does NOT produce Tables which represent such a Combinatorial Hierarchy (3,7,127). At 256 bits it produces on average a basis for the DCSS of dimension 254 (rather than anywhere near 127) and is approximately Gaussianly Distributed with Standard Deviation around 3. This particular structure (3,7,127) has a probability lying over 42 standard deviations below the average. Thus extremely unlikely.

A quick answer to your questions. The limit they propose of n x n matrices is absurd. Yes, there does exist a binary matrix of 256 by 256 having 256 x 256 elements. It is not n x n, but n x 2^n AVAILABLE matrices which grows much, much faster that 2^n – 1. I don’t understand how these people can make this fairly simple error in counting! So we have a Universe Table of 256 bit strings. We construct a 256 x 256 bit binary array with determinant 1 or -1. There is no limit to the hierarchy as Noyes,Bastin, Rhodes suggest. Any Table comes with a Closed Portion(topologically closed meaning in this case that it contains all its elements including zero) on the left and an Unclosed Portion to the right. This number may be anything between 2 and n but averages around a half the length.

His (Noyes’) probability arguments make no sense to me. Basis sizes multiply, they don’t add, so to calculate the Fine Structure Constant he ADDS 3 + 7 + 137 and then says one of these in 137 will be a fermion/photon interaction. The dimensions should be MULTIPLIED (being a Direct Product of Finite Cyclic Groups) so 1/(3x7x127) should be his probability! This argument is just plain wrong as a probability calculation. How can a mainstream qualified working physicist make such an elementary probability calculation error???

Yes we can always find j independent strings such that 2^j -1 <= n x 2^n.

It is almost self-evident: We simply take each bit position in the string and form a unit in the string Ie: {1,10,100,1000,1000,…2^(n-1)}. These may be combined under exor to form any of the 2^n – 1 possible non-zero bit strings. So we can take any j of these and they are a Linearly Independent basis set under Exor. Thus any Universe Table will have a basis of a random size j where j ranges from 2 to n in a reversed Poisson Distribution. (Actually it looks more like a reversed Black Body Spectral Intensity/Wave Length curve having a sharp cutoff at high probability on the right).

Most of my work has been focused on finding a good mathematical model to extrapolate to large bit lengths. My computer starts to complain miserably about not being able to assign gigabytes of Heap-Space over 32 bits then goes into a sulk for days. We are dealing with literally astronomical numbers; we are dealing with Power Sets of possible Tables thus at 32 bits we have 2^2^32 = 2^4294967296 possible tables. Obviously individual tables can't be counted or classified by experiment and I limit my experiments to about 24 bits at most but generally I stick around 16 bits.

My Average Basis Size Working Extrapolation is B(i+1) = (Ni + B(i))/2), N(2) = 1.5 (ie: 50/50 1 or 2)

A significant (from a Quantum Physics view) Basis Size is 240 = 2^4x3x5 which lies within 5 sd of the average 254. Standard Gauge Theory is based on group O(1) x SU(2) x SU(3). The Basis Size factors create a composite Cyclic Group Structure of Z(2)xZ(2)xZ(2)xZ(2)xZ(3)xZ(5). These cyclic groups form the Central Groups (commutative,anticommutative) of SU(2) and SU(3). O(1) is the Unit Circle Group of planar rotations and is implicit in every SU(n) group.

This (240) is the only number near 254 which factorizes in a way consistent with the Standard Model Gauge Theory.

Is this post too long? :}

In summary:

The Combinatorial Hierarchy does not terminate at level 4; it just becomes less and less probable that effects will be noticeable without a galaxy sized counting instrument coupled to a planet sized computer!

The correspondence between Feynman Diagrams and Program Universe is truly (I think) the hugest thing in physics. In one way or another I have been working on Finite Discrimination for over 40 years and I am grateful to Rhodes, Anson, Noyes, Bastin etc for their inspiration despite some of the glaring errors. Noyes' knowledge of physics is terrific but his mathematical methods are quite suspect. You can see though how a tabular Label/Content interaction scheme would behave like a discrete quantum field permeating space.

Counting is Fundamental!

Les Green – ZOS

]]>Laci also points out to me that the turul bird illustrating the first in the sequence is a symbol of Hungarian right-wing nationalism. I hope that nobody could think I would promote such a cause! This particular turul sits at the western end of the Elizabeth bridge; the thousands of motorists who cross the bridge clearly pay no attention to it, so I hope you don’t either.

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