[Bill S]

I personally don't use the word 'eternity' to mean anything except a length of time.

It’s good to have clarity.  IMO, holding an idiosyncratic viewpoint is better than insisting that eternity is not a length of time, then treating it as though it were just that. 

If your interpretation of eternity is that it is a length of time, and mine is that it is not, we will, probably, never make a great deal of progress, though.

Jibes then.  Typo, sorry.

Shame! I thought your inner poet was emerging.  Dancing with concepts; I like it. 

[alancalverd]

If we are at a point, does that not imply that there is a before and after relative to that point?

Sure does! My diary has lots of scribbles for yesterday and a few ideas for tomorrow. Not to mention the rabbits!

[alancalverd]

In the “infinite universe” in which there is no change and no time; “something happened” ??  You've left me way behind, there.

Why is there no change and no time in an infinite universe? There is an odour of Christian theology (the omnisicent god has no need for time) here, that has no place  in serious cosmology! Stuff happens, as observed. We have no reason to believe that the universe is not infinite, and indeed it is a lot easier to explain what happens in the observable universe if we presume that there is a lot more outside it. The trick is that anything that happens locally in an infinite universe may eventually be reflected by something equivalent unhappening elsewhere, thus preserving the eternal nature of the whole whilst permitting temporal change within it.   

Apologies for the nonsequential flow of my arguments - I keep coming across bits that I should have discussed when they arose, but real life keeps intruding! Not sure where I picked up the bit about the laws of physics prior to the big bang. 

[Bill S]

Sure does! My diary has lots of scribbles for yesterday and a few ideas for tomorrow.

Unless you have an eternal diary, you have side-stepped the issue.  You were talking about the relation of eternity to time. You said it had nothing to do with before and after. Then you said: “We are at a point in an eternal, infinite universe”.  How can there be a point, with a before and after, in eternity which “.. has nothing to do with before and after”?

Why is there no change and no time in an infinite universe?

I tried to address that in #267 - #270, without resorting to theology, which, I agree, has no place in serious cosmology. I could look for some examples, but don’t have time for that at the moment.  Your response to the question above could have some relevance.

[Halc]

If we are at a point, does that not imply that there is a before and after relative to that point?

There is (potentially) a before and after to any point in a temporal space.  On the other hand, I by no means consider myself to be at only one such point. I'm at quite a number of them, none particularly special.

I personally don't use the word 'eternity' to mean anything except a length of time.

If your interpretation of eternity is that it is a length of time, and mine is that it is not, we will, probably, never make a great deal of progress, though.

Didn't say I would not accept a different definition. I just personally would not choose the word to mean that other thing.

In the “infinite universe” in which there is no change and no time;

That I do not agree with.  Infinite or not, there is very much change. At time 1 the candle is taller than at time 2, and then there's the rabbits. The count of rabbits is different at one time than at a subsequent one, and that means there is change.

[alancalverd]

How can there be a point, with a before and after, in eternity which “.. has nothing to do with before and after”?

OK, I wasn't being sufficiently pedantic. Eternity being an infinite line on the time axis, the position of a point on that line has no effect on the line itself. However many points we place on the line, it still stretches infinitely in either direction  from any point. The existence of 1, 7, and -3 has no effect on the number of possible integers which remains infinite, but their order describes a unique path within the integer line. As my father used to say, "the graveyards are full of men who were once indispensable". Sic transit gloria mundi!

[alancalverd]

Mathematical infinities are theoretical concepts that are unbounded, but not necessarily infinite.

AAAAGH! You will be telling us next that a dog is an animal but not necessarily a dog!
Mathematics tells us that there are different infinities. All are infinite but some are bigger than others. Back to the simple case:
The sequence of integers is infinite: for any integer N, I can conceive of N + 1, so there is no upper limit to the integer series.
The sequence 1, 1½, 2, 2½, 3...... obviously (a) is infinite and (b) has twice as many members as the sequence of integers
And so forth.

[Halc]

The sequence 1, 1½, 2, 2½, 3...... obviously (a) is infinite and (b) has twice as many members as the sequence of integers

If there is a value for 'how many members', then it isn't infinite.  If there isn't, you can't meaningfully speak of doubling it.  There exists a bijunction between the integers and the latter sequence you give, thus there are no more meinmbers one sequence than the other.

[alancalverd]

That's the joy of infinities, and the reason Cantor lost his marbles. You can't put a limit on either sequence but the second obviously contains more elements in a given segment. It is, if you like, a "denser" infinity.

Now if I specify a sequence that begins with 1 and has no finite second element, I have defined an infinity with infinitesimal density, and if I talk about a continuum with no boundary, I have defined an infinitely dense infinity. You can have as many infinities in between as you wish. The boundary between arithmetic and algebra is that you can't handle a continuum with arithmetic tools, which places a limit on Cantor's approach.

So much for mathematics. As far as astrophysics is concerned, we seem to be living in a fairly sparse infinity with a few aggregated lumps.

[Bill S]

AAAAGH! You will be telling us next that a dog is an animal but not necessarily a dog!

That depends on how you define "dog".

[Colin2B]

AAAAGH! You will be telling us next that a dog is an animal but not necessarily a dog!

That depends on how you define "dog".

In the statement you are referencing I don’t believe it is dependent.

[Bill S]

Alan was making a prediction as to what I would  “be telling us next”.  I reserve the right to decide what my next assertion might depend on. 

[Bill S]

There is (potentially) a before and after to any point in a temporal space

Of course there is.  I thought we were talking about eternity. Only if you define eternity as a length of time could there be a point with a before and after. 

It might be worth another look at #268 – 269; especially point 7.

[Halc]

I thought we were talking about eternity. Only if you define eternity as a length of time could there be a point with a before and after.

It might be worth another look at #268 – 269; especially point 7.

Very well, we seem to be discussing a definition of eternity that isn't a length of time.  Let's see what your posts have to say about it.
From 268:

2.  Eternity is not just a very long time.  It is not time, and has no direct relationship to time, other than in our finite reasoning, and in our need to form a mental picture of “for ever”.

OK, this just reiterates what it isn't: a length of time.

5.  ...  I am not advocating that we should not think about infinity/eternity; ...

This is the only other mention, and you seem to imply the word means the same thing as 'infinity'.  OK, perhaps that's why all the posts about infinity, despite it seeming to be irrelevant to the question I thought I was being asked.

From 269, which has only one mention of eternity:

7. Multiplying or dividing infinity makes no practical sense because the result would have to be infinite.
...
A corollary of this is that there can be no change in infinity/eternity, because this would lead to a situation in which there would be eternity before the change, and eternity after the change.

Again, you seem to just use it as a synonym for 'infinity'.

So why not just use the word 'infinity' when you mean that?  The word is already there, and it seems confusing to occasionally substitute 'eternity' for it when you mean the same thing.

[Bill S]

It seems that Alan is not the only one who is not “being sufficiently pedantic”.

I do try to cover the possible alternative interpretations that my fellow not-pickers might identify, but that doesn’t always work.

So why not just use the word 'infinity' when you mean that?

Because colloquially there is a distinction which, seemingly, I am not alone in recognising.

The relation of eternity to time mirrors that of infinity to number.

[Bill S]

On the other hand, perhaps I am being over pedantic.

2.  Eternity is not just a very long time.  It is not time, and has no direct relationship to time, other than in our finite reasoning, and in our need to form a mental picture of “for ever”.

OK, this just reiterates what it isn't: a length of time.

 

Let’s find the reiteration. 

“Eternity is not just a very long time”.  This says specifically that eternity is not the incredibly long time that it is often presented as.

Someone might suggest that it is, nevertheless, time in some guise.  “It is not time”, eliminates this option.

“…and has no direct relationship to time,”  This anticipates another possible “diversion”.

“…other than in our finite reasoning, and in our need to form a mental picture of “for ever”.  This acknowledges the underlying need for a term that links infinity to time in our 3+1D world.

[Halc]

So why not just use the word 'infinity' when you mean that?

Because colloquially there is a distinction which, seemingly, I am not alone in recognising.

You didn't seem to give a distinction. You pointed to two posts both of which only used the word as 'infinity/eternity', indicating you mean the same thing by the words, not distinct concepts.

OK, this just reiterates what it isn't: a length of time.

  Let’s find the reiteration.

I mean you've said it more than once.

[Bill S]

"What I tell you three times is true."  Lewis Carroll

[Colin2B]

"What I tell you three times is true."  Lewis Carroll

Yes, but The Bellman believed in Snarks.
Most of this thread seems to be about building Snarks, not much real physics.

[alancalverd]

And all the time, the Snark was a Boojum.
Which I pointed out earlier.
Though in a parallel universe.

"The time has come," the Walrus said, "To talk of many things: Of shoes--and ships--and sealing-wax-- Of cabbages--and kings-- And why the sea is boiling hot-- And whether pigs have wings."

which pretty well sums up this forum! Vivat!