Galaxies without dark matter halos?

The probability of a hypothetical event (the Big Bang) can never be greater
than the probability of the most likely theory that supports the existence
of that event.

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.

If the probability of the big bang were less than that of the big bang with
Omega=1, there would be a nonzero probability that the latter is true but
not the former, which makes no sense.

If you were willing to bet with odds based such inconsistant probabilities
I could take your money no matter what happens.

Ralph Hartley

Ralph Hartley wrote in message
...

{invisible snip performed by Ralph}

The probability of a hypothetical event (the Big Bang) can never be
greater
than the probability of the most likely theory that supports the
existence
of that event.

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.

Suppose I see a current situation (the observable universe), and I have more
than one theory to explain that observation. I assign a probability
(somehow) for each to be correct. P1 and P2. Theory 1 requires the 'event'
(big bang). Theory 2 does not. The known probability distribution of the
origin of the universe is given by P1 + P2 + P3 + ... + P unknown. For
simplicity, we normalize this sum to 1.0.

If Theory 1 requires the big bang, then the probability of the big bang in
Theory 1 is 1.0. So the 'probability' that the big bang event took place is
exactly the probability of the theory being correct: P1.

Now if the 'big bang' is also required by (mutually exclusive) Theory 3,
(and the probability within the Theory 3 for the BB is 1.0) then we have the
case where the probability of the existence of the big bang event is P1 +
P3. So you are correct -- IF there is more than one big bang theory and IF
your 'theory' provides an internal probability of 1.0.

If the probability of the big bang were less than that of the big bang
with
Omega=1, there would be a nonzero probability that the latter is true but
not the former, which makes no sense.

If you were willing to bet with odds based such inconsistant probabilities
I could take your money no matter what happens.

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."

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.'

So, you are strictly correct in correcting the statement of mine that you
took out of context. 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.

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.'

greywolf42
ubi dubium ibi libertas

Ralph Hartley wrote in message
...

{invisible snip performed by Ralph}

The probability of a hypothetical event (the Big Bang) can never be
greater
than the probability of the most likely theory that supports the
existence
of that event.

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.

Suppose I see a current situation (the observable universe), and I have more
than one theory to explain that observation. I assign a probability
(somehow) for each to be correct. P1 and P2. Theory 1 requires the 'event'
(big bang). Theory 2 does not. The known probability distribution of the
origin of the universe is given by P1 + P2 + P3 + ... + P unknown. For
simplicity, we normalize this sum to 1.0.

If Theory 1 requires the big bang, then the probability of the big bang in
Theory 1 is 1.0. So the 'probability' that the big bang event took place is
exactly the probability of the theory being correct: P1.

Now if the 'big bang' is also required by (mutually exclusive) Theory 3,
(and the probability within the Theory 3 for the BB is 1.0) then we have the
case where the probability of the existence of the big bang event is P1 +
P3. So you are correct -- IF there is more than one big bang theory and IF
your 'theory' provides an internal probability of 1.0.

If the probability of the big bang were less than that of the big bang
with
Omega=1, there would be a nonzero probability that the latter is true but
not the former, which makes no sense.

If you were willing to bet with odds based such inconsistant probabilities
I could take your money no matter what happens.

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."

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.'

So, you are strictly correct in correcting the statement of mine that you
took out of context. 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.

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.'

greywolf42
ubi dubium ibi libertas

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*.

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).

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.

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.

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?

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?

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.

When the Earth was found to be an oblate spheroid, not a sphere, that was
not evidence against the "round earth" theory. Nor can evidence for or
against different theories for how the earth formed be taken as evidence
for or against the "round earth" theory.

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.

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

Ralph Hartley

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*.

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).

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.

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.

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?

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?

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.

When the Earth was found to be an oblate spheroid, not a sphere, that was
not evidence against the "round earth" theory. Nor can evidence for or
against different theories for how the earth formed be taken as evidence
for or against the "round earth" theory.

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.

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

Ralph Hartley

Phillip Helbig---remove CLOTHES to reply
wrote in message ...
The most popular theory, probably. The most probable theory, that's
more difficult to assess.

In which case, the original comment in defence of the BB -- that the BB was
'practically a certainty' -- is unsupportable. Which was my point, before
this long tangential digression.

I think that this is a misunderstanding due to the enthusiasm of
supporters of inflation. There is practically no-one in the scientific
community who doubts that the big bang, in the original meaning of the
term (the universe was formed a finite time ago and has since been
expanding from a hotter, denser state, possibly a singularity),
occurred.

And, as you've noted just above, this 'belief' is not be based on scientific
notions of probability.

Whether or not inflation occurred is less certain. There is
a common misunderstanding that the big bang without inflation is somehow
full of paradoxes etc. Coles and Ellis, in the reference I cited,
devote several pages to debunking this. (For those who don't know,
Coles and Ellis are quite respected "mainstream cosmologists".)

Having not yet read Coles and Ellis, I'll take your word for it. There are
many such 'enthusiastic' popularizers, and many assumptions and conclusions
that turn out to be incorrect (myths). One is the assumption that gas and
stars move in lockstep in the motions of spiral galaxies. This may easily
be another.

I still think you misunderstand probability here.

Not in the least. You admit that it is 'difficult' to assign probability to
any theory. Hence, the theory(ies) of the Big Bang cannot be described as
'practially a certainty.'

greywolf42
ubi dubium ibi libertas

Phillip Helbig---remove CLOTHES to reply
wrote in message ...
The most popular theory, probably. The most probable theory, that's
more difficult to assess.

In which case, the original comment in defence of the BB -- that the BB was
'practically a certainty' -- is unsupportable. Which was my point, before
this long tangential digression.

I think that this is a misunderstanding due to the enthusiasm of
supporters of inflation. There is practically no-one in the scientific
community who doubts that the big bang, in the original meaning of the
term (the universe was formed a finite time ago and has since been
expanding from a hotter, denser state, possibly a singularity),
occurred.

And, as you've noted just above, this 'belief' is not be based on scientific
notions of probability.

Whether or not inflation occurred is less certain. There is
a common misunderstanding that the big bang without inflation is somehow
full of paradoxes etc. Coles and Ellis, in the reference I cited,
devote several pages to debunking this. (For those who don't know,
Coles and Ellis are quite respected "mainstream cosmologists".)

Having not yet read Coles and Ellis, I'll take your word for it. There are
many such 'enthusiastic' popularizers, and many assumptions and conclusions
that turn out to be incorrect (myths). One is the assumption that gas and
stars move in lockstep in the motions of spiral galaxies. This may easily
be another.

I still think you misunderstand probability here.

Not in the least. You admit that it is 'difficult' to assign probability to
any theory. Hence, the theory(ies) of the Big Bang cannot be described as
'practially a certainty.'

greywolf42
ubi dubium ibi libertas

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

Ralph Hartley wrote in message
...
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

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

Ralph Hartley wrote in message
...
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

greywolf42 wrote:

Ralph Hartley wrote:

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.

Modified by the evidence you have seen so far. If you pick a good prior,
the evidence will eventually win over your prejudices.

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.)

No. I'm saying that the *posteriori* probabilities are that way. I haven't
seen any Non-BB theories that aren't contradicted by evidence. None have
enough a-posteriori probability to be worth bothering with.

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
withhold dark matter where everything looks fine.

Non Big Bang theories (if there were any worth mentioning) would have to do
the same thing, so it's a wash. If you don't believe in dark matter, you
still need to explain why some galaxies behave *as* *if* they had dark
matter and some do not. I don't see how eliminating the Big Bang helps you
do that.

I'm talking about non-Bayesian statistics.

I don't see what "the non-Bayesian probability of the Big Bang" even
*means*! The Big Bang ether happened or it didn't. I can express my
knowledge as a probability (basically what odds I would consider a fair
bet), that's what Bayesian probability means. What do *you* mean by "the
probability of the big bang"?

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.

NON-Bayesian probability doesn't apply *at* *all* to unique events, so why
would I want to do such a thing?

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.

I generally believe in the "earth is pretty much round" theory, which
includes all of those.

I will bet you a dollar that, when all is said and done, it will turn out
that the earth is more or less round. I will give you 100:1 odds (i.e. my
odds for a round earth are more than 0.99).

I was not born with this belief, but having seen lots of evidence for it,
hold it fairly strongly, and would only be convinced otherwise by sailing
over the edge. Show me the edge, and I'll give you $100, but forgive me for
asking to hold your $1 in the meantime.

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 difference to the overall probability!

How? Why? And if you reject Bayesian probability what do you even *mean*.

The problem is
that you are starting with a Bayesian prior that the probability of the Big
Bang is arbitrarily close to 1.0.

No. I had to be convinced. I was.

Ralph Hartley