Problems with actual infinities

[Walt Zingmatilder]

1: Infinite universe where the present was made previously.
Everything in the present comes from the past.
If we need to borrow from something we could have a problem actually getting it if the past is infinite. Supposing I am owed a fiver and that fiver cannot be given until that fiver is paid etc all the way into infinity.....when would you get your fiver?
2:
Infinite points on a finite line.
The problem here of course is resolving a point with no dimension? Points with no dimension may be mathematically ealing,  but are they physically real?

3.An infinity created by perfectly aligned facing mirrors

Even if we could achieve this the infinity would be empty unless
An image was created by something introduced between the mirrors.

To return to the borrowed fiver analogy. The only way you are going to get the fiver is if someone puts one in in finite time.

[jeremyp]

Sorry. I have no idea what you are talking about.

Can we just concentrate on point 1 for now and can you explain it in a coherent way please.

[Stranger]

1: Infinite universe where the present was made previously.
Everything in the present comes from the past.
If we need to borrow from something we could have a problem actually getting it if the past is infinite. Supposing I am owed a fiver and that fiver cannot be given until that fiver is paid etc all the way into infinity.....when would you get your fiver?
2:
Infinite points on a finite line.
The problem here of course is resolving a point with no dimension? Points with no dimension may be mathematically ealing,  but are they physically real?

Applying human intuition to this sort of thing seems to be your problem. There is no logical problem with real infinities. We know they are logically self-consistent from mathematics. Whether they actually exist is another question but not one you're going to resolve with this sort of rather simplistic 'argument'.

The "we'd never get here of the past was infinite" is confused thinking for two reasons. Firstly, in confuses a past with no start with a start in the infinite past. Secondly, time flowing appears to be an artefact of perception, rather than something fundamental. Time is a dimension of space-time. There is no 'present' to be made. The 'present' is a relative concept.

[Walt Zingmatilder]

Applying human intuition to this sort of thing seems to be your problem. There is no logical problem with real infinities. We know they are logically self-consistent from mathematics. Whether they actually exist is another question but not one you're going to resolve with this sort of rather simplistic 'argument'.

The "we'd never get here of the past was infinite" is confused thinking for two reasons. Firstly, in confuses a past with no start with a start in the infinite past. Secondly, time flowing appears to be an artefact of perception, rather than something fundamental. Time is a dimension of space-time. There is no 'present' to be made. The 'present' is a relative concept.

Not sure there is any confusion with a past with no start and an actual start in an infinite past. Time flowing? Do we perceive that?or do we perceive time? Aren’t you confusing the two?

[Stranger]

Time flowing? Do we perceive that?or do we perceive time? Aren’t you confusing the two?

We perceive the flow of time. The idea is not present in physics. There is no 'present' and there can't possibly be a universal 'present' in relativity.

[Walt Zingmatilder]

We perceive the flow of time. The idea is not present in physics. There is no 'present' and there can't possibly be a universal 'present' in relativity.

Not sure what you are trying to say here. Is time a dimension or is it an illusion Stranger?can we perceive it or not? It seems to me how we perceive it is secondary. Perhaps how we perceive it is a good analogy to represent time’s dimensionality

[Nearly Sane]

...
2:
Infinite points on a finite line.
The problem here of course is resolving a point with no dimension? Points with no dimension may be mathematically ealing,  but are they physically real?
...

Small, possibly infinitesimal, point. Points on a line do not need to have no dimension to be infinite.

[Walt Zingmatilder]

Small, possibly infinitesimal, point. Points on a line do not need to have no dimension to be infinite.

Your contention, your burden.

[Nearly Sane]

Your contention, your burden.

Technically of course you made the initial claim that they needed to have no dimemsion which you didn't back up but leaving your hypocrisy aside, size as a dimension does not have a known or logical limit of smallness, therefore there any size that can be thought of can be halved, quarterd, eighthed etc etc.

[Walt Zingmatilder]

Technically of course you made the initial claim that they needed to have no dimemsion which you didn't back up but leaving your hypocrisy aside, size as a dimension does not have a known or logical limit of smallness, therefore there any size that can be thought of can be halved, quarterd, eighthed etc etc.

I think I merely asked whether a dimensionless point was a physical rather than merely a mathematical entity rather than a claim. Are you showing here that we can consider them to be physically real?

[Nearly Sane]

I think I merely asked whether a dimensionless point was a physical rather than merely a mathematical entity rather than a claim. Are you showing here that we can consider them to be physically real?

No, you asserted that points on a line needed to be dimensionless for them to be infinite.

And since I'm not talking about dimensionless points (whatever they may be) I'm not saying anything about them.

Your OP is a mess of undefined, illigical burblings.

[Walt Zingmatilder]

No, you asserted that pounts on a line needed to be dimensionless for them to be infinite.

And since I'm not talking about dimensionless pounts (whatever they may be) I'm not saying anything about them.

Your OP is a mess of undefined, illigical burblings.

If you then have an infinite set of things of finite length and put them together then surely the combined length is infinite. Seems Ligical to me ha ha.

[Nearly Sane]

If you then have an infinite set of things of finite length and put them together then surely the combined length is infinite. Seems Ligical to me ha ha.

No.

[Walt Zingmatilder]

No.

Is that your final answer?

[Stranger]

Not sure what you are trying to say here. Is time a dimension or is it an illusion Stranger?

It's a direction through space-time that depends on the frame of reference.

[jeremyp]

If you then have an infinite set of things of finite length and put them together then surely the combined length is infinite. Seems Ligical to me ha ha.

Zero is a finite length, so you can have an infinite set of things of finite length adding up to a finite length as long as only a finite number of the things in the set have a non zero length.

[Walt Zingmatilder]

Zero is a finite length, so you can have an infinite set of things of finite length adding up to a finite length as long as only a finite number of the things in the set have a non zero length.

Yes I sort of see that. Are there physically things with zero length? I'm thinking if we have a length of metal rod. Could we actually have a metal object of zero length?

[jeremyp]

Yes I sort of see that.

In fact, at least in the abstract, if you have a whole set of objects, each of which is half the length of the previous one, you can have an infinite number of objects all of a finite length that add up to a finite length.

Are there physically things with zero length?

A photon has zero length according to special relativity. Or, from its point of view, the entire Universe has zero length.

I'm thinking if we have a length of metal rod. Could we actually have a metal object of zero length?

No, because, to be a metal you need at least some atoms.