Is the Mandelbrot Set Real?

John K Clark (
Thu, 7 Aug 1997 21:01:47 -0700 (PDT)


On Thu, 07 Aug 1997 "Eliezer S. Yudkowsky" <> Wrote:

>Who says this is constant? Virtual particles are popping in and out
>of existence all the time.

Good point.

>Even supposing the Bekenstein Bound - what about all the digits of

If the Bekenstein Bound is correct the maximum amount of information that
can be stored inside a sphere is related to its radius and its mass. If the
Universe shrinks to a mathematical point in the Big Crunch then gravity will
increase the energy in the universe, and thus its mass (remember E = MC^2),
without limit, and this mass will increase faster than its radius will
decrease. This means that at the Big Crunch the total information in the
universe will diverge to infinity even if it's finite right now.

Some say the second law of thermodynamics, which states that entropy always
increases, is pessimistic, but that would only be true if the total amount of
information was constant. We'd be in bad shape if Entropy did not increase,
it would mean the heat death of the Universe, but as long as entropy ALWAYS
increases infinite life is possible.

On Wed, 06 Aug 1997 Hara Ra <> Wrote:

>for example the word 'googol' describes a Real number but not a
>Preal one.

Why, because there is not a googol of anything? If Tipler is correct a beam of
light could circumnavigate the universe a googol times, in fact an infinite
number of times between now and the Big Crunch, light moves at the same speed
but the trip keeps getting shorter without limit.

>Ok, to get really gritty - the maximum amount of bits storable if
>you converted the entire universe into data storage using
>nanotechnology. 1 bit per proton.

No reason in theory one proton couldn't store far more than one bit.

John K Clark

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