**From:** Matt Mahoney (*matmahoney@yahoo.com*)

**Date:** Thu Mar 20 2008 - 19:16:09 MDT

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--- Mike Dougherty <msd001@gmail.com> wrote:

*> On Wed, Mar 19, 2008 at 4:10 PM, Matt Mahoney <matmahoney@yahoo.com> wrote:
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*> > The model assumes that the set of states is isomorphic to N. Any real
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*> > implementation with finite memory must have finite subjective experience.
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*> All
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*> > implementations must have finite memory because the universe has a
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*> Bekenstein
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*> > bound of about 10^122 bits.
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*>
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*> I looked up Bekenstein bound on wikipedia (it's a start)
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*>
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*> "S=A/4 where A is the two-dimensional area of the black hole's event
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*> horizon in units of the Planck area, \hbar G/c^3."
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*>
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*> Can someone explain how a two dimensional area is used to measure the
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*> amount of information that can be stored in a 3 (or more) dimensional
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*> universe? (Or if this is too basic a question, simply email me
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*> off-list with some educational URLs)
*

I had independently derived an order of magnitude estimate of the information

content of the universe a few years ago using a different approach. I

estimated the number of possible standing wave patterns in a volume of size R

as a function of the mass-energy E = mc^2 in that space, which depends on

Planck's constant h. Then I set R = Tc where T = 4.3 x 10^17 s is the age of

universe and c is the speed of light. Then I estimated the largest mass that

could be contained in a sphere of radius R before the escape velocity reached

c (the Schwartzchild radius). I came up with S ~ T^2 c^5/hG ~ 10^122 ignoring

small constants because the radius of the universe is not well defined in

expanding, curved spacetime, the exact mass of the universe isn't known, and I

don't have the physics background to compute the exact value anyway.

I only recently came across the Bekenstein bound, which gives S = 2.02 x

10^122 if you let the surface of the universe be 4*pi*(Tc)^2. Actually this

is 2.91 x 10^122 bits because thermodynamic entropy uses natural logs.

Calculating with Bousso's figure of 1.4 x 10^69 bits/m^2 gives the same

result.

It is rather interesting that the volume of a bit is about that of a proton or

neutron, but S does not depend on the properties of any particles. Either

this is a coincidence or the size or number of baryons is changing because S

increases with T^2 while the volume increases with T^3. There are about

S^(2/3) ~ 10^80 baryons in the universe, enough to make a coating one particle

thick.

It has always puzzled me why the universe didn't collapse into a black hole

shortly after the big bang if it had the same mass as today. It also puzzles

me that a black hole is not symmetric with respect to time (stuff goes in but

not out) even though Einstein's general field equations are. Shouldn't there

be another solution with the opposite sign, one where stuff goes out but not

in, like an expanding universe? In that case, dark energy is just gravity?

-- Matt Mahoney, matmahoney@yahoo.com

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