Conundrum: Infinite past & Clock

[Speakpigeon]

Even if time itself has been for ever, there are no inifinite timespans.
In other words: any timepoint is a finite distance frim any other timepoint.
Thus there are no inifinite timspans to ”traverse”.

Thanks for articulating this particular idea. It shows even UM's buncombe has its usefulness, you see.

Still, me, I would disagree with it. I can't find any good reason that an infinity of time in the past couldn't have come with something existing at every one moment along that time span.

Unfortunately, I also can't see anything practical that we could do with this piece of metaphysical wisdom. We already struggle to get past the Big Bang, so infinity is way beyond our reach.

Obviously, it remains true that the time span between any two points in time is finite.


____________________

I guess the inherent limitation with our mathematical concept of infinity is that it is broadly speaking algorithmic in nature. Infinity is conceived by mathematicians as the purely notional limit of an unbounded series of terms. In this sense, infinity is not thought of, conceived, as anything like an ontological reality.

The idea of an infinite future doesn't require any new notion of the infinite because we think of the future as something happening one step at a time, much like we can only think of an unbounded series of terms one step at a time, one term coming after another. And we get away with it by imagining that we could continue considering the following terms of the series, one after the other, one at a time, ad infinitum, without ever getting to infinity itself.

Now, the idea of an infinite past seems something different altogether in this respect. The concept of the past as something already done with, seems to require that in the case of an infinite past, infinity has already happened, and therefore that infinity is a full-blown ontological reality, not just a pure abstraction. At any moment in time, including now, there's been an infinity of seconds, and an infinity of millennia, that have already gone by.

This may be something of a problem to get our heads around it. Think of a simple clock. If we try to assume that such a simple clock had always existed, what time would this clock display right now? I'm sure we're all going to be stuck here, like, forever.

Still, I trust this forum packs more brain power within fewer skulls than the current U.S. administration, so despite my own personal limitations in not seeing any way out of this conundrum, I will wait to see if someone else here can come up with an imaginative solution, hopefully one not involving the impossibility of having a clock at every moment in the past.


I'll be waiting for your answers. The clock is already ticking. Don't make me wait till the end of time.
EB

 

[Juma]

Even if time itself has been for ever, there are no inifinite timespans.
In other words: any timepoint is a finite distance frim any other timepoint.
Thus there are no inifinite timspans to ”traverse”.

Thanks for articulating this particular idea. It shows even UM's buncombe has its usefulness, you see.

Still, me, I would disagree with it. I can't find any good reason that an infinity of time in the past couldn't have come with something existing at every one moment along that time span.

Unfortunately, I also can't see anything practical that we could do with this piece of metaphysical wisdom. We already struggle to get past the Big Bang, so infinity is way beyond our reach.

Obviously, it remains true that the time span between any two points in time is finite.


____________________

I guess the inherent limitation with our mathematical concept of infinity is that it is broadly speaking algorithmic in nature. Infinity is conceived by mathematicians as the purely notional limit of an unbounded series of terms. In this sense, infinity is not thought of, conceived, as anything like an ontological reality.

The idea of an infinite future doesn't require any new notion of the infinite because we think of the future as something happening one step at a time, much like we can only think of an unbounded series of terms one step at a time, one term coming after another. And we get away with it by imagining that we could continue considering the following terms of the series, one after the other, one at a time, ad infinitum, without ever getting to infinity itself.

Now, the idea of an infinite past seems something different altogether in this respect. The concept of the past as something already done with, seems to require that in the case of an infinite past, infinity has already happened, and therefore that infinity is a full-blown ontological reality, not just a pure abstraction. At any moment in time, including now, there's been an infinity of seconds, and an infinity of millennia, that have already gone by.

This may be something of a problem to get our heads around it. Think of a simple clock. If we try to assume that such a simple clock had always existed, what time would this clock display right now? I'm sure we're all going to be stuck here, like, forever.

Still, I trust this forum packs more brain power within fewer skulls than the current U.S. administration, so despite my own personal limitations in not seeing any way out of this conundrum, I will wait to see if someone else here can come up with an imaginative solution, hopefully one not involving the impossibility of having a clock at every moment in the past.


I'll be waiting for your answers. The clock is already ticking. Don't make me wait till the end of time.
EB

Thepracticsl implication is that even if time has been forever, then everything that happens, happens at its own timepoint and thus is at a finite timespan away from now.

What your watch will show depends on its construction but would show the time since it was started.
If it is a thought-watch that has been there all the time then its display will have started over inifinitely times.

The mistake made here is to see the watch as a mile-measurer. As an accumulator.
When a real clock is ”full” it simply restarts. ..10,11,0,1...

 

[bilby]

If the past is infinite, then at any point in time, an infinite time has elapsed.

The only thing that has to have existed for all of that time is time itself, although other things may also have existed for some or all of it.

 

[Lion IRC]

With a past-eternal, perpetual motion clock it should (eventually) become quite easy to predict what time the clock dial would read at any future instant.
(Think Groundhog Day movie)

 

[untermensche]

I can't find any good reason that an infinity of time in the past couldn't have come with something existing at every one moment along that time span.

How could an infinity "have come"?

An infinity is not an amount.

No matter how much time we say occurred before some moment in time it will always be a finite amount of time.

It is impossible to ever say, no matter how far back you go, that ah ha, now an infinity has occurred.

Claiming an infinity has occurred or has been completed somehow is not understanding what infinity is.

 

[bilby]

I can't find any good reason that an infinity of time in the past couldn't have come with something existing at every one moment along that time span.

How could an infinity "have come"?

An infinity is not an amount.

No matter how much time we say occurred before some moment in time it will always be a finite amount of time.

Nope. If it is infinite it will always be infinite. Only if it is finite will it always be finite.

You are assuming your conclusion. Again.

It is impossible to ever say, no matter how far back you go, that ah ha, now an infinity has occurred.

Unless the past is infinite, in which case you can always say that, at any time, no matter how far back you go.

Claiming an infinity has occurred or has been completed somehow is not understanding what infinity is.

Claiming an infinity has occurred is perfectly reasonable. If the past is unbounded in one direction, then an infinity of past time has completed, and that has always been the case.

Your error is to try to work out what happens in relationship to the beginning of time. But by definition an infinite past had no beginning; and to consider a beginning is to define the past as finite, which is begging the question.

 

[Speakpigeon]

Thepracticsl implication is that even if time has been forever, then everything that happens, happens at its own timepoint and thus is at a finite timespan away from now.

What your watch will show depends on its construction but would show the time since it was started.

It would have started an infinitely long time ago.

If it is a thought-watch that has been there all the time then its display will have started over inifinitely times.

It would be a real clock.

The mistake made here is to see the watch as a mile-measurer. As an accumulator.
When a real clock is ”full” it simply restarts. ..10,11,0,1...

Okay, not bad.

Still, once you accept that the clock indeed displays something, why would you say that the clock should display "11110000" rather than "00001111" for example? Can you answer that question?


So, let's say a clock with a finite counter would be no good at all for that very reason. So, please assume a clock with an infinite counter. We can imagine the clock being just a row of simple pebbles, and one pebble is added at the end of the row every second for example. I guess we also have to assume that space is also infinite, at least in one direction.
EB

 

[Speakpigeon]

If the past is infinite, then at any point in time, an infinite time has elapsed.

The only thing that has to have existed for all of that time is time itself, although other things may also have existed for some or all of it.

Yes, that may be so, but given the assumption, I'm trying to see what we can prove, or at least what we can argue properly.
EB

 

[Speakpigeon]

With a past-eternal, perpetual motion clock it should (eventually) become quite easy to predict what time the clock dial would read at any future instant.
(Think Groundhog Day movie)

Sorry, you will have to explain a bit because I'm not a cinema goer and I've too sketchy an idea as to what the film you're talking about would show.
EB

 

[Juma]

It would have started an infinitely long time ago.

Stop here.
You already agreed that any actual timepoint is at a finite distance from now. The start of the clock must then be at a finite distance from now.

Or was your intent to mean that the clock has been going forever?

 

[Juma]

It would have started an infinitely long time ago.



It would be a real clock.

The mistake made here is to see the watch as a mile-measurer. As an accumulator.
When a real clock is ”full” it simply restarts. ..10,11,0,1...

Okay, not bad.

Still, once you accept that the clock indeed displays something, why would you say that the clock should display "11110000" rather than "00001111" for example? Can you answer that question?
[\Quote]
Of course. It shows 11110000 because it previously showed 11101111. Its a statemachine. It goes from state to state. An equally god example is a clock that goes from 0 to 1 and then to 0 etc.

So, let's say a clock with a finite counter would be no good at all for that very reason. So, please assume a clock with an infinite counter. We can imagine the clock being just a row of simple pebbles, and one pebble is added at the end of the row every second for example. I guess we also have to assume that space is also infinite, at least in one direction.
EB

Then you already have an infinite supply of peebles and are just moving them from one heap to another...

 

[untermensche]

Nope. If it is infinite it will always be infinite.

Infinite is not an amount.

No matter how many years you go back you will not have infinity.

It is impossible to have infinity. It is not an amount.

 

[Speakpigeon]

It would have started an infinitely long time ago.

Stop here.
You already agreed that any actual timepoint is at a finite distance from now. The start of the clock must then be at a finite distance from now.

No. Not if it started an infinitely long time ago.

Or take it as the clock never having to start, which ever you prefer.

Or was your intent to mean that the clock has been going forever?

Of course, yes.
EB

 

[Speakpigeon]

It would have started an infinitely long time ago.



It would be a real clock.

The mistake made here is to see the watch as a mile-measurer. As an accumulator.
When a real clock is ”full” it simply restarts. ..10,11,0,1...

Okay, not bad.

Still, once you accept that the clock indeed displays something, why would you say that the clock should display "11110000" rather than "00001111" for example? Can you answer that question?

Of course. It shows 11110000 because it previously showed 11101111. Its a statemachine. It goes from state to state. An equally god example is a clock that goes from 0 to 1 and then to 0 etc.

???

And how would it be possible to establish that the previous state was indeed "11101111"? Why not "00001110"?

Or "01011100", "10111100" etc.

You just can't assume that.

So, let's say a clock with a finite counter would be no good at all for that very reason. So, please assume a clock with an infinite counter. We can imagine the clock being just a row of simple pebbles, and one pebble is added at the end of the row every second for example. I guess we also have to assume that space is also infinite, at least in one direction.
EB

Then you already have an infinite supply of peebles

Sorry, I forgot about that. Yes, you'd have to have an infinite supply of pebbles.

and are just moving them from one heap to another...

I guess you mean moving one pebble after another from the supply heap to the clock's line of pebbles.

_____________________

We could even imagine two lines of pebbles, both infinite but in only one direction, and going in exactly opposite directions from each other. They would also be separated by just the space necessary for one pebble. All the counter has to do is to shift one pebble from the supply line to the counter line. Easy do.

Or better still, there is just one infinite line of pebbles, each one marked "0" on one side and "1" on the other. All the pebbles in one direction show a "1" (the past). All the pebbles in the other direction (the future) show a "0". Every second, the one pebble among those showing "0" which is also next to one showing "1" is flipped over to show "1" too. And so on.

Well, I guess that's all there is to say then.

It works. Thanks!
EB

 

[beero1000]

Even if time itself has been for ever, there are no inifinite timespans.
In other words: any timepoint is a finite distance frim any other timepoint.
Thus there are no inifinite timspans to ”traverse”.

Thanks for articulating this particular idea. It shows even UM's buncombe has its usefulness, you see.

Still, me, I would disagree with it. I can't find any good reason that an infinity of time in the past couldn't have come with something existing at every one moment along that time span.

Unfortunately, I also can't see anything practical that we could do with this piece of metaphysical wisdom. We already struggle to get past the Big Bang, so infinity is way beyond our reach.

Obviously, it remains true that the time span between any two points in time is finite.

There would still be no infinite timespans because the length of a span of time is defined to be the difference between two times. Distance has exactly the same 'difficulty', the universe could be infinite in extent, but in order to speak sensibly about distance, we must talk about the distance between two points, which is always finite. The notion of an infinite universe (in extent or in time) is the notion of unboundedness - that there are points farther apart than any number we can name.

____________________

I guess the inherent limitation with our mathematical concept of infinity is that it is broadly speaking algorithmic in nature. Infinity is conceived by mathematicians as the purely notional limit of an unbounded series of terms. In this sense, infinity is not thought of, conceived, as anything like an ontological reality.

Not really. That idea is outdated by 100+ years, and persists because the first (and usually only) time most people see infinity in math classes is usually in the context of precalculus or calculus, where it is used as a shorthand for a version of the epsilon-delta limit definitions, which don't formally require the infinite at all. Mathematicians actually see being 'infinite' as a property of objects, where the infinite numbers are sizes (or orders) like any other. It would be like saying the concept of 3 is algorithmic because it is the algorithmic notion of the counting process 1, 2, 3. Technically, you could view it that way, but that's a little stilted, and not how most people think of the property '3'.

The idea of an infinite future doesn't require any new notion of the infinite because we think of the future as something happening one step at a time, much like we can only think of an unbounded series of terms one step at a time, one term coming after another. And we get away with it by imagining that we could continue considering the following terms of the series, one after the other, one at a time, ad infinitum, without ever getting to infinity itself.

Now, the idea of an infinite past seems something different altogether in this respect. The concept of the past as something already done with, seems to require that in the case of an infinite past, infinity has already happened, and therefore that infinity is a full-blown ontological reality, not just a pure abstraction. At any moment in time, including now, there's been an infinity of seconds, and an infinity of millennia, that have already gone by.

Back to the first comment: gone by from when? From any point I choose to measure, only a finite amount of time has passed until now. Sure, I can keep choosing times earlier and earlier, and I will get more and more of the past, but at no point will I see an infinite amount of time go by between two points in time. It's the same as distance. If the universe is infinite in extent, I still wouldn't say that 'an infinity of meters have been traveled'. From where? By what?

This may be something of a problem to get our heads around it. Think of a simple clock. If we try to assume that such a simple clock had always existed, what time would this clock display right now? I'm sure we're all going to be stuck here, like, forever.

Still, I trust this forum packs more brain power within fewer skulls than the current U.S. administration, so despite my own personal limitations in not seeing any way out of this conundrum, I will wait to see if someone else here can come up with an imaginative solution, hopefully one not involving the impossibility of having a clock at every moment in the past.

I'll be waiting for your answers. The clock is already ticking. Don't make me wait till the end of time.
EB

It would display an hour later than whatever it was displaying an hour ago, etc. If I have a simple clock (one that always existed or not), what time would it display right now? The question is clearly relative to what the clock displayed at some other point in time, no matter how long the clock has existed.

 

[Speakpigeon]

Even if time itself has been for ever, there are no inifinite timespans.
In other words: any timepoint is a finite distance frim any other timepoint.
Thus there are no inifinite timspans to ”traverse”.

Thanks for articulating this particular idea. It shows even UM's buncombe has its usefulness, you see.

Still, me, I would disagree with it. I can't find any good reason that an infinity of time in the past couldn't have come with something existing at every one moment along that time span.

Unfortunately, I also can't see anything practical that we could do with this piece of metaphysical wisdom. We already struggle to get past the Big Bang, so infinity is way beyond our reach.

Obviously, it remains true that the time span between any two points in time is finite.

There would still be no infinite timespans because the length of a span of time is defined to be the difference between two times. Distance has exactly the same 'difficulty', the universe could be infinite in extent, but in order to speak sensibly about distance, we must talk about the distance between two points, which is always finite. The notion of an infinite universe (in extent or in time) is the notion of unboundedness - that there are points farther apart than any number we can name.

Sure.

Hence the difficulty in deciding what time a clock that would have always been there would display.

____________________

I guess the inherent limitation with our mathematical concept of infinity is that it is broadly speaking algorithmic in nature. Infinity is conceived by mathematicians as the purely notional limit of an unbounded series of terms. In this sense, infinity is not thought of, conceived, as anything like an ontological reality.

Not really. That idea is outdated by 100+ years, and persists because the first (and usually only) time most people see infinity in math classes is usually in the context of precalculus or calculus, where it is used as a shorthand for a version of the epsilon-delta limit definitions, which don't formally require the infinite at all. Mathematicians actually see being 'infinite' as a property of objects, where the infinite numbers are sizes (or orders) like any other.

I'm pleased to hear that.

It would be like saying the concept of 3 is algorithmic because it is the algorithmic notion of the counting process 1, 2, 3. Technically, you could view it that way, but that's a little stilted, and not how most people think of the property '3'.

Sure, concerning how most people conceive of ordinary numbers, I agree. But you would have to produce a better argument to convince me that most people don't think of an infinite future the way I described it.

The idea of an infinite future doesn't require any new notion of the infinite because we think of the future as something happening one step at a time, much like we can only think of an unbounded series of terms one step at a time, one term coming after another. And we get away with it by imagining that we could continue considering the following terms of the series, one after the other, one at a time, ad infinitum, without ever getting to infinity itself.

Now, the idea of an infinite past seems something different altogether in this respect. The concept of the past as something already done with, seems to require that in the case of an infinite past, infinity has already happened, and therefore that infinity is a full-blown ontological reality, not just a pure abstraction. At any moment in time, including now, there's been an infinity of seconds, and an infinity of millennia, that have already gone by.

Back to the first comment: gone by from when? From any point I choose to measure, only a finite amount of time has passed until now. Sure, I can keep choosing times earlier and earlier, and I will get more and more of the past, but at no point will I see an infinite amount of time go by between two points in time. It's the same as distance. If the universe is infinite in extent, I still wouldn't say that 'an infinity of meters have been traveled'. From where? By what?

No. You're just thinking in terms of using any finite system of measure. Sure, in practice, we can only measure time, and distances, between two given points. But I'm trying to figure out how we would do it if we were not ourselves finite beings.

I'm sure you could try, too.

It's also ironic that you should be now going back to the kind of algorithmic process that you just criticised me for describing as basic in maths, and that you were pleased to say that mathematicians had long moved beyond.

If "mathematicians actually see being 'infinite' as a property of objects", then there should be no difficulty whatsoever for you to consider, obviously in the abstract, the problem of what kind of clock could conceivably have counted time for the whole duration of an infinite past.

This may be something of a problem to get our heads around it. Think of a simple clock. If we try to assume that such a simple clock had always existed, what time would this clock display right now? I'm sure we're all going to be stuck here, like, forever.

Still, I trust this forum packs more brain power within fewer skulls than the current U.S. administration, so despite my own personal limitations in not seeing any way out of this conundrum, I will wait to see if someone else here can come up with an imaginative solution, hopefully one not involving the impossibility of having a clock at every moment in the past.

I'll be waiting for your answers. The clock is already ticking. Don't make me wait till the end of time.
EB

It would display an hour later than whatever it was displaying an hour ago, etc. If I have a simple clock (one that always existed or not), what time would it display right now? The question is clearly relative to what the clock displayed at some other point in time, no matter how long the clock has existed.

Not good enough for me, I'm afraid.

Still, I now have the answer.

Just take a look at my previous post and tell me what's wrong with my clock.
EB

 

[Lion IRC]

With a past-eternal, perpetual motion clock it should (eventually) become quite easy to predict what time the clock dial would read at any future instant.
(Think Groundhog Day movie)

Sorry, you will have to explain a bit because I'm not a cinema goer and I've too sketchy an idea as to what the film you're talking about would show.
EB

Groundhog Day meme comes partly from a movie where dude (Bill Murray) wakes up to the same day over and over again and gradually learns that he can game the system and each repeated day he does things a little bit better and better to further his aims.

Similar movie themes;
50 First Dates (Adam Sandler, Drew Barrynore)
Sliding Doors (Gwenyth Paltrow)
Pretty much all your time travel genre stuff - Back To The Future etc.

An eternal observer looking at a perpetual motion, past-eternal clock would eventually be able to (omnisciently) predict the clocks behaviour.

 

[Juma]

Of course. It shows 11110000 because it previously showed 11101111. Its a statemachine. It goes from state to state. An equally god example is a clock that goes from 0 to 1 and then to 0 etc.

???

And how would it be possible to establish that the previous state was indeed "11101111"? Why not "00001110"?

Or "01011100", "10111100" etc.

You just can't assume that.

because it seemed logical to assume a clock that increased its value by one for each tick..,
but you can assume any rule you want, it doesnt really matter.

 

[Speakpigeon]

Of course. It shows 11110000 because it previously showed 11101111. Its a statemachine. It goes from state to state. An equally god example is a clock that goes from 0 to 1 and then to 0 etc.

???

And how would it be possible to establish that the previous state was indeed "11101111"? Why not "00001110"?

Or "01011100", "10111100" etc.

You just can't assume that.

because it seemed logical to assume a clock that increased its value by one for each tick..,
but you can assume any rule you want, it doesnt really matter.

Sorry, you don't seem to understand, at all.

I guess there's nothing I can do here. I don't know which of your English or your wit isn't up to the job.

I leave it to you to decide whether you try again or not.
EB

 

[bilby]

Nope. If it is infinite it will always be infinite.

Infinite is not an amount.

No matter how many years you go back you will not have infinity.

It is impossible to have infinity. It is not an amount.

Thank you for that insightful, helpful, and above all unexpected input.

Your opinion is noted, and shall be given the consideration it merits.