Archive for July, 2012

We live in a universe that is macroscopically four dimensional, for which the evidence is much clearer than the claimed discovery of the Higgs boson.  Since the 1980s crystals have been observed with rotational symmetries of orders 5, 8, 10, 12 which cannot occur for three dimensional spaces.  The existence of a fourth macroscopic spatial dimensions is a fundamental feature of the universe which the current Standard Model is not equipped to handle.  In fact it is not difficult to see from clear evidence that the universe is not only four dimensional but it is compact, and indeed spherical.

So in a four dimensional spherical universe the natural physics would be a classical physics.  I have been working toward a ‘Standard Model’ type theory as a U(1) x SU(2) x SU(3) gauge theory on the 4-sphere as a temporary measure towards a correct physics. It is unclear to me whether the explanation of the accepted particle theory where objects that exist for time lengths in the order 10^{-8} seconds should have sense in fixed masses.  In any case, the issue of what constitutes mass in a four-sphere universe is honestly an open question.  One expects the Einsteinian answer — that mass is equivalent to the extrinsic geometry of a three dimensional universe in a four-dimensional spherical ambient space — to have sense extending from subatomic to cosmic scales.   Quantum observations can arise from a classical physics on a 4-sphere and parsimony dictates that such a theory is likely to be the correct physical theory for the actual universe we inhabit.


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The iris dataset consists of 150 datapoints, each a 4-tuple, with sets of 50 labeled by ‘Iris-sertosa’, ‘Iris-versicolor’ and ‘Iris-virginica’.  The protein twists datasets consist of millions of datapoints with 4-tuples labeled by amino triples of the form ‘LYS-MET-PHE’.  The 4-tuples correspond to the axis-angle decomposition of twists in SO(3).A fairly simple test shows that a multiclass svm performs well in classifying the iris dataset.  With mlpy package installed, the python code for the test is this:

from cvxopt import normal, matrix
import numpy as np
import matplotlib.pyplot as plt
import mlpy
import _svm

labels = { 'Iris-setosa': 0, 'Iris-versicolor': 1, 'Iris-virginica':2} 
counts = { 'Iris-setosa': 0, 'Iris-versicolor': 0, 'Iris-virginica':0}
tcounts = { 'Iris-setosa': 0, 'Iris-versicolor': 0, 'Iris-virginica':0}
file = open( 'iris.data', 'r')
count_max = 25

x = np.zeros((count_max,4))
y = np.zeros(count_max)

xtest = np.zeros((50-count_max,4))
ytest = np.zeros(50-count_max)

for line in file:
    v = line.split(',')
    triple = v[4]
    if labels.has_key(triple) and counts[triple] < count_max:
        x[counts[triple],:] = [ float(v[0]), float(v[1]), float(v[2]), float(v[3])]
        y[counts[triple]] = labels[triple] 
        counts[triple] += 1
    elif labels.has_key(triple):
        xtest[tcounts[triple],:] = [ float(v[0]), float(v[1]), float(v[2]), float(v[3])]
        ytest[tcounts[triple]] = labels[triple] 
        tcounts[triple] += 1

da = mlpy.LibLinear( solver_type = 'mcsvm_cs')
print "Before svm learning"
da.learn(x, y)
print "After svm learning"

ynew = da.pred(xtest)

N = len(ynew)
c = 0
for i in range(N):
    if ynew[i] == ytest[i]:
        c += 1

print float(c)/float(N)

The protein shape determination problem is in a sense the inverse problem, but it is worthwhile to attempt to predict the class label of amino triple given a point in the twist space of SO(3).  The basic idea here is to cut up the configuration space using the classifier and then for a given amino triple predict by chosing from a subspace of SO(3).  The same method using a multiclass svm produces perfect classification on test sets for single amino-labeled points on SO(3).

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Evidence for four macroscopic spatial dimensions is extremely clear: observed crystal symmetries of orders 5, 8, 10 and 12.  With a proper explanation of the redshift as an artifact and the uniform lower bound on the CBR, compactness of the universe is also an easy deduction.  In a sense this evidence is elementary, not relying on sophisticated theories of particles and forces.  Once the shape is fixed, quantization of energy has an explanation in the shape of the universe, as for spheres, every geodesic is closed with the same length.

The Einsteinian picture sharpens and we can connect matter and energy as being responsible and being equivalent to the extrinsic curvatures in the physical universe.  So what is the most natural physics for a four dimensional spherical universe?  That the establishment of the Standard Model was a great intellectual achievement is without doubt, but it is still worthwhile to ask whether it even makes sense to have a particle classification when most of the objects that are studied in the smashing experiments in colliders have half-lives in the order of 10^-8 seconds.

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The question of what constitutes absolute reality is eternal, and if we fully realize that the religions and ideologies, histories written by particularly politically dominant interests, are often not simply misguiding but totally and cynically fabricated in others, we must admit the necessity of intuitive connecting of dots and making associations to make some conclusions about what describes the nature of reality that can be agreed on with some confidence in its truth.

Given that we now know that the universe has four macroscopic spatial dimensions but that we have not fully updated our realities fully to this fact, we have the gigantic task of producing a coherent reality that in principle fits all clearly verified phenomena, we have to use some reasoned short-cuts.  Intuitive connections provide such shortcuts which may have some unknown probabilities of error but they allow us to work in realistic timescales to address problems which might otherwise be deemed intractible.  For example, the problem of producing a science that can unify physics and simultaneously give us the foundations of an objective metaphysics, allow us to fit in the metaphysical puzzles that we are aware of into some reasonable framework seems impossible and over-ambitious but could possibly be achieved if we judiciously use intuitive connections as a working tool.

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Gone fishing

I been sleeping until the crack of noon

Midnight howlin’ at the moon

Goin’ out when I want to, comin’ home when I please

Don’t have to ask permission if I want to go out fishing

Never have to ask for the key

                                     I sat upon the shore
Fishing, with the arid plain behind me
Shall I at least set my lands in order?
London Bridge is falling down falling down falling down
Poi s'ascose nel foco che gli affina
Quando fiam ceu chelidon - O swallow swallow
Le Prince d'Aquitaine a la tour abolie                        430
These fragments I have shored against my ruins
Why then Ile fit you. Hieronymo's mad againe.
Datta. Dayadhvam. Damyata.

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