[Halc]

The set of integers might be “eternal” by definition 1, but it has relevance only in terms of a “finite reality”.

Not sure what you mean by 'finite reality'.  The set of integers is not a finite set.

By definition 2, there is no concept of change, therefore it is meaningless to talk of a set of anything, as this involves differentiation, which requires change.  Change requires time, and by definition 2, eternity is timeless.

There are plenty of sets that don't involve change.  Yes, integers, or the Mandlebrot set are examples.
The set of valid chess states is an example (a finite one) that involves time and change, yet is an eternal structure by definition 2.  That designation is kind of thin since chess is arguably a created thing and exists in our time as well as containing its own time.

[Bill S]

Not sure what you mean by 'finite reality'.

That in which we perceive ourselves to be existing.

The set of integers is not a finite set.

By Def. 1, that is true, but by Def. 2, it is not.

Possibly Def. 2 needs rewording so as to make it less susceptible to “invasions” from Def. 1.

There are plenty of sets that don't involve change.  Yes, integers, or the Mandlebrot set are examples.
The set of valid chess states is an example (a finite one) that involves time and change, yet is an eternal structure by definition 2.

By Def. 2, eternity is timeless.  Any differentiation between parts would involve the input of an external observer who existed in time.  To be clear, I’m not saying (at this point) that a set or sequence could not exist in eternity; only that by Def. 2 it would be meaningless.
 
How can a set, or sequence, of anything have any meaning if it is not possible to consider individual members independently?

[Halc]

Not sure what you mean by 'finite reality'.

That in which we perceive ourselves to be existing.

So your statement means "The set of integers might be “eternal” by definition 1, but it has relevance only in terms of the reality in which we perceive ourselves to be existing."
I must disagree with that.  A different reality would also find integers relevant, although not necessarily all realities.
As I said, I have an inherent bias against anthropocentric views.

The set of integers is not a finite set.

By Def. 1, that is true, but by Def. 2, it is not.

I don't see any mention in either def about a thing itself being finite or not.  Def 1 talks about time being infinite, but the set of integers is not a temporal structure.  It has no time at all, let alone finite or infinite time.

There are plenty of sets that don't involve change.  Yes, integers, or the Mandlebrot set are examples.
The set of valid chess states is an example (a finite one) that involves time and change, yet is an eternal structure by definition 2.

By Def. 2, eternity is timeless.[/quote]Depends on what you mean by timeless.  A timeless structure does not exist within time, but time can still exist within it.  The chess example and our 'cosmos' are both such examples of timeless temporal structures.  An example of a non-timeless structure is the Tower Bridge in London. It isn't eternal.

Any differentiation between parts would involve the input of an external observer who existed in time.

I don't see why an observer is necessary.  Observation is necessary for said differentiation between parts to be known by said observer, but differentiation need not necessarily be known by anything.
 

How can a set, or sequence, of anything have any meaning if it is not possible to consider individual members independently?

Well, we're observing them in this topic, so the problem is moot.  Yes, for the purpose of this topic, we are observing various things and deriving meaning from them.

[Bill S]

So your statement means "The set of integers might be “eternal” by definition 1, but it has relevance only in terms of the reality in which we perceive ourselves to be existing."
I must disagree with that.  A different reality would also find integers relevant, although not necessarily all realities.

Perhaps it would have been better if I had said something like: “That in which we, or any other entity we might choose to imagine, could conceivably visualise ourselves as existing”.  However, I am inclined to think that any such hypothetical realities that found integers relevant, would be realities that experienced time.

Recall that “timelessness” is integral to Def. 2 of eternity.

As I said, I have an inherent bias against anthropocentric views.

There is nothing essentially anthropocentric about our “finite reality”, it existed before any anthropoids of which we have knowledge appeared.  The denizens of a “reality” would be unlikely to pre-date that “reality”, which is one reason why I, too, tend to eschew anthropocentric theories. 

don't see any mention in either def about a thing itself being finite or not.

That’s because both are definitions of eternity, not of the nature of any possible “inhabitant” of eternity.

Def 1 talks about time being infinite, but the set of integers is not a temporal structure.  It has no time at all, let alone finite or infinite time.

Which is precisely why I reason that infinity/eternity under Def 1 is a convenient usage that is an approximation, at best, and should not be confused with Def 2.

Several more things to address in that post, but out of time again.

[Halc]

I am inclined to think that any such hypothetical realities that found integers relevant, would be realities that experienced time.

I probably agree, but 8 is less than 13 whether or not there is a reality in which the integers are found relevant.  That relation of 'less than' is not a perception-dependent relation.  So this reality where there is an experience of time is irrelevant to the nature of the integers, which are themselves timeless.  I can't prove that integers are not dependent on perception, but to assert otherwise is to assert idealism: reality supervening on perception instead of the other way around.

As I said, I have an inherent bias against anthropocentric views.

There is nothing essentially anthropocentric about our “finite reality”, it existed before any anthropoids of which we have knowledge appeared.

That, on the other hand, is a realist position.  My problem with a realist position is that it doesn't explain why it's there instead of nothing.  I've been trying to explain how I resolve this problem.

Yes, I agree, but would word it as: Certain things (Earth for instance) were created before and existed in this solar system before there were humans (or any life for that matter) to perceive it.
I would not say 'reality' existed before me because parts of what you'd probably consider reality are in our future, not past, so it isn't all on one side of us like that.
I'm also not a realist, so I don't say things 'exist' at all.  For instance, I say the Earth existed 'in this solar system' above, which makes it a relation instead of an ontological property. The relativist position is most of what solves the something-not-nothing issue.

[CPT ArkAngel]

Why is there something rather than nothing is a question asking for a cause. How could there be a cause to the existence of the Universe? How could there be a cause to the intrinsic and fundamental structure of the Universe? How could there be a beginning in the first place? There is no beginning and no cause. Energy is conserved... There is no proof of the contrary. Only when energy will not be conserved in a controlled experiment we could start to discuss about it.

[Bill S]

Let’s look at two definitions of eternity.

1. Infinite or unending time.

2. A state to which time has no application; timelessness.

At first glance, these appear contradictory, but, “common usage by educated people” demonstrates that both are useful definitions, in different contexts.  Would you agree with that?

Of course.  Didn't say otherwise.  But those are different meanings, and if ambiguous, it should be made clear which is meant in a statement.

In spite of this, we still have examples of using one definition to “explain” factors in the other.

A timeless structure does not exist within time,

Agreed. (Def. 2)

but time can still exist within it.

Only by Def. 1.   

   An example of a non-timeless structure is the Tower Bridge in London. It isn't eternal.

Agreed, but consider that if “a non-timeless structure….isn't eternal”, it follows that an eternal structure is timeless.  A problem with trying to embed a non-timeless structure in a timeless structure is that it conflates the two definitions.

The chess example and our 'cosmos' are both such examples of timeless temporal structures.

Only if you mix Defs 1 and 2. 
By “our 'cosmos'”, do you mean our Universe? I have aimed for clarity in my usage of these terms, and if you are using “cosmos” sensu Gribbin, then I agree it is timeless, but remain unconvinced that it is “temporal”.

[Halc]

Let’s look at two definitions of eternity.

1. Infinite or unending time.

2. A state to which time has no application; timelessness.

At first glance, these appear contradictory, but, “common usage by educated people” demonstrates that both are useful definitions, in different contexts.
...

A timeless structure does not exist within time,

Agreed. (Def. 2)

but time can still exist within it.

Only by Def. 1.

Def 1 talks about infinite time. Finite time within a structure is not eternity by def 1. Time as we know it (that which is measured in seconds) seems to be finite in some models, and not others. Some of the examples I gave are definitely finite, and some are not, and some have no time at all.

An example of a non-timeless structure is the Tower Bridge in London. It isn't eternal.

Agreed, but consider that if “a non-timeless structure….isn't eternal”, it follows that an eternal structure is timeless.

If you are using def 2, yes, where 'timeless' means 'not contained in time' and not 'doesn't contain time'.

A problem with trying to embed a non-timeless structure in a timeless structure is that it conflates the two definitions.

So what? I can glue my inaccurate time piece to the wall so it runs fast and is also fast to the wall.  Is that offensive that the same word means two different things in relation to the same object?
Perhaps better to converse in a language that forbids multiple meanings to any one word.  The dictionary wouldn't be much larger, but there would be a lot more, shorter entries in it.

The chess example and our 'cosmos' are both such examples of timeless temporal structures.

Only if you mix Defs 1 and 2.[/quote]Mix is OK.  Both are eternal by def 2.  Only the cosmos may be eternal by def 1.  The chess example is not, so there's no dual usage of a word going on there.  Temporal and eternal mean different things.

By “our 'cosmos'”, do you mean our Universe?

No. Using your definition. Our universe is likely 'caused' by something more fundamental. Cosmos, by your definition, is not. The structure is larger than our 'universe' which is a word I tend to use to describe our particular bubble of space-time.  I think you limited that definition even further by saying it's all we can observe, but then it's not eternal (1) since we only observe finite time.

I have aimed for clarity in my usage of these terms, and if you are using “cosmos” sensu Gribbin, then I agree it is timeless, but remain unconvinced that it is “temporal”.

It contains my running fast clock, so that makes it temporal.  Does that word mean something different to you?  Dictionary says 'relating to time'.

[Bill S]

Why is there something rather than nothing is a question asking for a cause.

This is why I would rather ask; “How could there be…” rather than: “Why is there…”

How could there be a cause to the existence of the Universe? How could there be a cause to the intrinsic and fundamental structure of the Universe?

It depends on your definition of “Universe”.  Using Gribbin’s distinction; I would say your questions, if applied to “cosmos”, would invite the answer: “there couldn’t be a cause”.  Applied to “Universe”: there probably could be a cause, but I have no idea what it might be. 

There is no beginning and no cause.

On a cosmic scale I agree. 

Energy is conserved... There is no proof of the contrary. Only when energy will not be conserved in a controlled experiment we could start to discuss about it.

Point taken; but I suspect that conservation of energy in an expanding universe might raise complications that are best avoided at this stage.

[Bill S]

Time as we know it (that which is measured in seconds) seems to be finite in some models, and not others.

The point that seems easily to be overlooked/ignored is that time cannot be infinite in any model that asserts that infinity is not a number. Def. 1 sidesteps the “not a number” issue, for convenience.  I have no quarrel with this.

If you are using def 2, yes, where 'timeless' means 'not contained in time' and not 'doesn't contain time'.

(2. A state to which time has no application; timelessness.)  If time is not applicable under Def. 2; then 'timeless' means 'not contained in time' and  'doesn't contain time'.

So what? I can glue my inaccurate time piece to the wall so it runs fast and is also fast to the wall.  Is that offensive that the same word means two different things in relation to the same object?

Of course it’s not; nor is that example, in any way, helpful in the consideration of any differences there might be between “infinity” by Defs 1 and 2.

I would like to address the final point in #127 separately, partly because I think it is too important to become lost among other points, and also because I need to give it some thought – possibly, pick some stones out of the path, first. 

[CPT ArkAngel]

The Universe means everything. If I'm correct, that's the usual meaning of Universe with a capital 'U'. The Big Bang is not the beginning, it is just a phase.

Gravitational waves were postulated to conserved energy. And there we have them...

If you start with an infinite Universe, you won't find any satisfying solution because infinity cannot be rationalized. Yet, we have a constant speed of light in the vacuum, we have other constants and discreet particles. Let's start with a finite Universe, then we may add things to it only when no other solution is reasonable. In a finite and quantized Universe, there is a maximum to entropy...

Let's test a Big Bounce hypothesis where the Big Bang is just a phase transition.

Just before the Big Bang, all matter is condensed in an object having the lowest possible entropy. This could be a Schwarzchild black hole but it includes all space and time (no external space). This implies a prior Big Crunch which has condensed all matter in the previous cycle. This means there was an excess of attraction vs repulsion.

When the Universe reaches the bottom (the lowest entropy), the attractive force (whatever produces this force) passes by a symmetrical point where it becomes null and then this produces an excess of the repulsive force for a brief moment, something like a Planck time. Gravity disappears when the energy budget is 50-50, repulsion-attraction. But in fact, it never gets to this budget because it is a symmetrical point where attraction just disappears. It implies that there are asymmetries left to account for the structure. These asymmetries may be fundamental or related to a multiverse.

A finite Universe implies intrinsic asymmetries. Only an infinite Universe may have a complete symmetry. If you want a cause to our existence, it is the fact that there are irreducible physical asymmetries. The annihilation of an electron-positron pair doesn't result in nothing but two photons. This means there is no complete symmetry between them, though there are symmetries to be filled with the rest of the Universe.

Returning to the Big Bang, this results in a delay between repulsion and attraction.  The phase of repulsion is in advance of the attractive phase. This is dark energy.  Now the Universe has a much greater asymmetry in the form of a delay in the phase of the waves. Repulsion results in an increase in the degrees of freedom and the entropy. Attraction results in a decrease in the degrees of freedom. All forces should be mediated by particles. The known candidate for this effect is the photon which produces a delay of gravity in its direction of motion. Gravity moves at the speed of light. This adds to the original delay, though it is small, it means Dark Energy increases. But, as the Universe is finite, it will reach a maximum entropy and go through another phase transition when a symmetry of the repulsion force will be filled in. Dark matter has an important role to account for the ratio of gravitational mass vs repulsive mass. It could potentially have only an attractive component.

GR does not include the phase transitions or the Big Bang...

[Bill S]

Thanks CPT Archangel. That’s a great explanation for the evolution of the Universe.  There are so many things in it that merit attention, it probably needs a thread of its own.  I look forward to returning to it. 

[Halc]

Time as we know it (that which is measured in seconds) seems to be finite in some models, and not others.

The point that seems easily to be overlooked/ignored is that time cannot be infinite in any model that asserts that infinity is not a number.

I know of no models that defy the rules of mathematics and assert any such thing.

If you are using def 2, yes, where 'timeless' means 'not contained in time' and not 'doesn't contain time'.

(2. A state to which time has no application; timelessness.)  If time is not applicable under Def. 2; then 'timeless' means 'not contained in time' and  'doesn't contain time'.

Def 2 is a 2nd definition of eternal (or eternity), and that does not preclude things that contain time, as our universe obviously does.  I consider it to be eternal but not timeless.

So what? I can glue my inaccurate time piece to the wall so it runs fast and is also fast to the wall.  Is that offensive that the same word means two different things in relation to the same object?

Of course it’s not; nor is that example, in any way, helpful in the consideration of any differences there might be between “infinity” by Defs 1 and 2.

I wasn't commenting on the differences.  I was responding to your comment about conflating the two definitions of eternity.  'Infinity' is not mentioned in Def 2.

[Bill S]

I know of no models that defy the rules of mathematics and assert any such thing.

Nor I, but we still find, in the same post, things like: “Eternity is not a length of time.” and “Just think of it as infinite time”  While this can be explained away, that does require changing definitions. 

We seem to have agreed that one-word-one-definition is neither attainable, nor desirable, but some agreement about definition, in any specific context, is essential. 

I think we have agreed that infinity is not a number, and eternity not a length of time.  If so, perhaps we should have a go at defining a sequence. 

My suggestion for a starting point is: “A sequence is a statement of a particular order in which related entities follow one other”.

[alancalverd]

That presumes a relationship.

"He put his hat on, walked out of the door, and was shot by a sniper."  Obvious sequence (it could not have happened in any other order) but no essential relationship between the events. Interestingly, it could be the start of a novel in which the detective looks for a connection, but this sort of thing happens in real life with none.

So a sequence is a temporal or spatial order. Not to be confused with a series, where there is a logical connection such that the next member is predictable from those we already know.

"He put on his body armour, opened the hatch, and was met by a hail of fire from the enemy." Implicit context turns a sequence into a series!

[Halc]

I know of no models that defy the rules of mathematics and assert any such thing.

Nor I, but we still find, in the same post, things like: “Eternity is not a length of time.” and “Just think of it as infinite time”  While this can be explained away, that does require changing definitions. 

I think we have agreed that infinity is not a number, and eternity not a length of time.  If so, perhaps we should have a go at defining a sequence.

I would have said that by def 1, it is a length of time, but not one that can be represented by a number.  It is an unbounded length of time.  The difference between how we see it seems unimportant to what is being asked in this thread.

My suggestion for a starting point is: “A sequence is a statement of a particular order in which related entities follow one other”.

That 'statement' is pretty much the same thing as a reference frame or a coordinate system, either of which accomplishes the same thing.

[CPT ArkAngel]

Alan,

Your definition of a sequence is good, but I don't think you are right by saying that the sequence "He put his hat on, walked out of the door, and was shot by a sniper." is non causal. Your brain separates artificially the causal relations after the fact from your own perspective and knowledge. Unless you believe in freewill, the universe determines the sequence and everything is causal. For example, if he didn't put his hat on, maybe the sniper wouldn't have recognized him and never killed him. Even though the hat may not have played a crucial role, it is still a part of the causality chain and the Universe produces only one outcome. But some events are more important than others. Everything in your past light cone, including your own body, determines what you're doing.  Why the sniper shot him? why the sniper is a sniper? What happened when he was young to become a sniper? How were his parents, his family, his environment and his parents parents and so on? In the end, you can safely conclude that the Big Bang is the origin... I prefer to say it is the way the Universe is. It is also true in the Many-Worlds interpretation, even though I think it is wrong.

[Bill S]

I think we have agreed that infinity is not a number, and eternity not a length of time.

I would have said that by def 1, it is a length of time, but not one that can be represented by a number.

When he cried "Steer to starboard, but keep her head larboard!"
   What on earth was the helmsman to do?”

A length of time that cannot be represented by a number. Material for the imagination!  The only length of time I can think of that cannot be represented by a number is “infinite” time; which is a contradiction in terms.

The difference between how we see it seems unimportant to what is being asked in this thread.

Possibly because the connection is still to be made.

That 'statement' is pretty much the same thing as a reference frame or a coordinate system, either of which accomplishes the same thing.

A great response, if you want to keep the door open for agreeing, or disagreeing with the proposed definition, later.

[Bill S]

"He put his hat on, walked out of the door, and was shot by a sniper."  Obvious sequence (it could not have happened in any other order)

What about: "He, walked out of the door, put his hat on and was shot by a sniper."?  If the shot is not fatal, there are other possibilities as well; or am I missing something?

Nit-pickers of the world unite,
The details are exciting;
We could argue through the night,
And reach the morning fighting.

Good distinction between “series” and “sequence”; thanks Alan.

[alancalverd]

Arkangel: the sequence hat/door/shot is not implicitly or explicitly causal. That's the problem of forensic science - we an establish a sequence of events, but the law demands to know whether he was shot because he was wearing an enemy hat (an act of war) or any hat (an act of insanity) or the hat was irrelevant to the shooting (terrorism).  He might not have been shot if he hadn't opened the door, but if the shooter really wanted to kill him, he would have kicked the door in or fired through the window anyway. 

There's a very neat mathematical introduction to forensics. What is 2 + 2? What is 3 + 1? What is 6 - 2? That's everyday maths. What is 4? That's forensic maths.

Bill: I never said the shot was fatal! Beware of "obvious" implications. It makes no difference to the sequence of events so far, only to subsequent events, of which we currently know nothing. Here's what actually happened:

He put on his hat, walked out of the door, and was shot by a sniper. The shot grazed his left arm but, after the commercial break, 007 replied, firing his automatic from the hip, and blew the sniper's head off.....Unoriginal screenplay by Alan Calverd.....