Re: Galaxies without dark matter halos?

[Mod. note: as with other postings in the thread, s.p.r. crossposting
removed.]

Ralph Hartley <[EMAIL PROTECTED]> wrote in message
news:[EMAIL PROTECTED]
> greywolf42 wrote:
> > Ralph Hartley:
>
> >>The probability of a hypothetical event can never be *less* than the
> >>probability of the most likely theory that *requires* the existence of
> >>that event. In fact it can't be less than the sum of the probabilities
of
> >>*all* such (mutually exclusive) theories.

> ...

> > With that out of the way, let's look at the statement from Phillip to
which
> > I was responding, and which you removed:  "First, you are confusing the
big
> > bang with inflation. The big bang is practically a certainty.  Whether
or
> > not inflation occurs is still open."
>
> His statement correctly describes our current state of knowledge. Perhaps
> it sells Infation a bit short, but I agree that the evidence for Inflation
> is only *good*, while that for the Big Bang is *overwhelming*.

I'm not surprised you think so -- if you attempt to use Bayesian statistics
in the manner below.

> > The most probable theory of the big bang (at least measured by current
> > popularity) certainly includes inflation.  Yet the inflation theory is
not
> > 'mutually exclusive' of all the other big bang theories.  Without
inflation,
> > the probability (as I understand it) of the big bang being 'correct' is
far
> > lower than the probability 'with inflation.'
>
> Huh??? The (Bayesian) probability of the big bang is very close to 1.
> Depending on how you rate the evidence for inflation the relative
> probabilities with and without inflation will vary, but still sum to near
> 1 (they are mutually exclusive by construction).

The Bayesian probability is whatever you set the prior.  Since you have
defined your 'prior' as including only variants of the Big Bang.  (You
didn't mention any non-Big Bang theories that you addressed -- thus setting
the prior for all big-bang variants to 1.0.)

And remember 'reality' may not be describe by any of our current theories.
So Bayesian methods are right out.

> In the last few years, evidence has tended to favor inflation, so it has
> gained probability (at the expense of non-inflation big bangs). If new
> evidence against inflation were found, or a better non-infationary Big
Bang
> theory were formulated, the probability of a non inflationary big bang
> would go up.

However, it is not a zero-sum game with variants on the Big Bang the only
possible theories of the cosmos.

> Of course, there are possible observations that would throw doubt on *all*
> big bang theories, but I haven't seen any, and it would have to be pretty
> good.

Well, we've seen galaxies that have no hint of dark matter.  This would
require yet another ad hoc revision to the model -- allowing one to randomly
distribute 'dark matter' wherever one finds a discrepant observation -- and
withold dark matter where everything looks fine.

> > So let me reword my statement to keep the point and
> > context, both:
> >
> > The probability of a hypothetical event (the Big Bang) can not be
> > significantly greater than the probability of the most likely theory
> > that supports the existence of that event.
>
> I don't see what this has that my "out of context" quote didn't. It still
> is not true.
>
> Counter example:
>
> Suppose theory A and theory B are mutually exclusive, each have
probability
> 0.5, and both require event E (that is, they support E with weight 1).
>
> Then P(E) = P(A)+P(B) = 1 > 1/2 = max{P(A),P(B)}
>
> If this doesn't prove your statement false, what part of "can not" am I
> not understanding?

I'm talking about non-Bayesian statistics.  See my next sentence.

> > In other words, the existence of the Big Bang can in no way be
characterized
> > as 'practically a certainty', if the basis for the most likely event is
> > 'still open.'
>
> I can't make sense of this at all. What do you mean by "the basis for the
> most likely event", and why does it still being open imply that the Big
> Bang is not a practical certainty?

Well, it appears that we agree that the 'basis for the most likely event is
still open.'

Hence -- since it is 'open' -- we have no way to set the probability.
Therefore, since one cannot define a real (non-Bayesian) probability for the
(qualitatively) 'most likely' BB theory -- we cannot define a real
(non-Bayesian) probability of "near certainty" (arbitrarily close to 1.0 in
a NON-bayesian sense) to the existence of the Big Bang explosion.

>  From your post I am *guessing* that by "the basis for the most likely
> event" you mean "Whether or not inflation occurs" since that is what is
> "still open". If so, it certainly doesn't follow.

Close enough.  Inflation is certainly considered to be included in the 'most
likely' (or rather most popular) theory of the BB, at present.  (It wasn't
in the past, and it might not be in the future.)

> When the Earth was found to be an oblate spheroid, not a sphere, that was
> not evidence against the "round earth" theory.

It was evidence against a 'round Earth' -- IF the 'round Earth' theory
postulated a spherical Earth.  If the oblate spheriod was found by
observation (not theory), then the original theory was modified to
accomodate the slight difference.  In short, there is more than one 'round
Earth' theory.  The observation merely selected among them.  That you would
continue to call the theory by the same name would simply be sloppy.  Humans
(including scientists) often are sloppy.

> Nor can evidence for or
> against different theories for how the earth formed be taken as evidence
> for or against the "round earth" theory.

It depends on which 'round Earth' theory you are championing.  There are
many.  (Expanding Earth, plate tectonics, immoble Earth, shrinking
crust....)  Some 'Earth formation' theories even include a non-round Earth.

> Similarly, the Big Bang describes the rough shape of the universe. Neither
> arguments about its exact shape (e.g. the value of Omega), nor about its
> origin (inflation or not) make any difference.

Of course they make a differenct to the overall probability!  The problem is
that you are starting with a Bayesian prior that the probability of the Big
Bang is arbitrarily close to 1.0.  But the question is, what *IS* the
probability of the Big Bang?  One is not allowed to use a Bayesian
assumption of what you're trying to show.

> The strength of the evidence for the Big Bang is at least comparable to
> the evidence for a round earth in Magellan's time.

I disagree completely.

greywolf42
ubi dubium ibi libertas