Tim Attwood <tim### [at] comcastnet> wrote:
> >  Schwarzchild radius is not dependent on density, only on the amount of
> > mass.

> That's only true for black holes. For normal matter it varies by density,

  "The Schwarzschild radius (sometimes historically referred to as the
gravitational radius) is a characteristic radius associated with every
mass. It is the radius for a given mass where, if that mass could be
compressed to fit within that radius, no known force or degeneracy
pressure could stop it from continuing to collapse into a
gravitational singularity."

  "The Schwarzschild radius is proportional to the mass, with a
proportionality constant involving the gravitational constant and the
speed of light."

http://en.wikipedia.org/wiki/Schwarzschild_radius

  No mention of density anywhere, only of mass. The Schwarzschild radius
of a mass can be calculated directly as the mass multiplied by a
*constant* (which is 2*G/c^2). Volume doesn't appear anywhere in the formula.

> if the mass of the universe is infinite it falls inside
> it's Schwarzschild radius, since rs = 2Gm/c^2 ... and infinity divided by
> a large number is still infinity.

  Which is a rather definite proof that there's a finite amount of mass
in the universe.

> >  I call this the shakespeare-monkey fallacy.

> It's not a fallacy, it's a paradox, there's a difference. It's not possible
> to predict random events, but it's still possible to know that they will
> occur. For example if you use a simple coin toss, and toss the coin
> forever, the distribution will be 50/50, so you can say with 100%
> confidence that sometime in the future there will be another "heads",
> yet at the same time you don't know at all if the next toss will be
> a "heads".

  It's a fallacy. An infinite amount of data, even if all values have the
same "chance" of appearing in the data, does not automatically mean that
every possible pattern appears.

  The proof is rather simple: For example, the ordered set of natural
numbers is an infinite set where each value has an equal "chance" of
appearing, yet eg. the pattern "2 1" never appears.

  Note that nowhere did I imply randomness. And even if randomness is
implied, the question is still non-trivial. If what you want is an
evenly-spaced random natural number generator, you'll have to define
what "random" means. That's not a trivial definition.

  Even if you pop random natural numbers (by whichever definition of
"random" you may want to use), it's still possible that a certain pattern
never appears. Given that there's an infinite amount of finite patterns,
it may take an infinite amount of time to pop a certain one. The probability
of that pattern appearing may asymptotically approach 1, but it's still
possible that it never appears.

> General relativity didn't predict most of these observations

  That depends on your definition of "predict".

  If by "predict" you mean "Einstein never mentioned it in his papers"
then it's true.

  However, if "predict" means "the result can be derived from the theory"
(which is usually the meaning of that word in science), then most cosmological
phenomena (except quantum level phenomena) can be derived from GR.
  For example the expansion of the universe can be derived from GR in
this way.

-- 
                                                          - Warp

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