Note that in our pocket universe in the cosmic landscape populated by eternal chaotic inflation

r = 10^28 cm

The number of BITS of our universe as a COMPUTER SIMULATION is

~ 10^56/10^-66 ~ 10^122 BITS

On Apr 23, 2006, at 9:56 PM, Jack Sarfatti wrote:

Kaku says very simply on p. 562 of "Introduction to Superstrings and M Theory"

"Let us define the derivative operator as

d = dx^aPa (A.3.3)"

Now here I take h = c = 1

Pa = i&a

"Notice that because the derivatives commute

[Pa,Pb] = 0 (A.3.4)

so therefore

d^2 = 0 (A.3.5)

What could be simpler formally without jillions of excess formulae? Clearly the factor of i does not matter.

Then on p 549

"then the only commutator that changes" relative to the Poincare group

[Pa,Pb] = 1/r^2Mab

for DeSitter group O(4,1)'a Lie algebra

Then on p. 550

"r is called the de Sitter radius"

I define the dark energy density /\zpf ~ 1/r^2

"Notice that if r goes to infinity, we have the Poincare group. Thus, r corresponds to the radius of a five-dimensional universe such that if r goes to infinity" (i.e. the dark energy density /\zpf = 1/r^2 goes to zero in the UNBROKEN supersymmetry limit) "it becomes indistinguishable from the flat four-dimensional space of Poincare. Letting the radius go to infinity is called the Wigner-Inonu contraction and will be used extensively in super gravity theories. After the contraction, the de Sitter group becomes the Poincare group." p. 550 Kaku

From this I infer that

1. The physical observation of dark energy Omega ~ 0.73 means we live in 5D DeSitter space approximately on the large scale of cosmology.

2. Therefore the local basis invariant

d^2 = (1/2)[Pa,Pb]dx^a/\dx^b = /\zpfMabdx^a/\dx^b =/= 0 when /\zpf > 0

where {Mab} = Lie algebra of Lorentz group O(3,1).

Now this seems obvious physically. So we need to see if the excess mathematical baggage Waldyr provides in rebuttal is really physically relevant? Perhaps, but his point is not obvious to my mind.

"As far as the laws of mathematics refer to reality, they are not certain, as far as they are certain, they do not refer to reality." Einstein