Conundrum: Infinite past & Clock

[Bomb#20]

First, I'm of Danish-Swedish descent (the bridge). Think Bergman and Kierkegaard, not Quisling.

Close enough.

Sort of from der inside Norway.

Bite your tongue, philistine! Think Grieg, not Nielsen and Berwald.

(Who the heck are Nielsen and Berwald, you ask? My point exactly.)

Most people have no background in understanding infinity and rely on naive intuitions or half-remembered hand-waving explanations from freshman year math class.

You're assuming as true here that there is such a thing as infinity as mathematicians have come to conceived of it. Maybe that's just not true. And as long as you don't have empirical evidence to present, I will hand-wave your assumption as baseless.

Oh, wait, I'm misunderstanding you! The reality is that you're only talking about the concept of infinity, not of anything like actual infinity. Sorry, I'm not used to discussing in the abstract like you guys.

No, he's talking about both the concept of infinity and also about actual infinities if there are any. If there are any then they'll match one or another of the mathematical concepts of infinity.

So, the concept? Well, self-evidently, ordinary folks won't be understanding the mathematician's newly minted concept of infinity any time soon. They will be pleased to keep understanding their own concept of it. So, you're jibe is really irrelevant.

It just happens it was me who started this particular conversation on infinity, not you. So either you address my point in my own terms or you provide the empirical evidence showing there's nothing in the real world corresponding to the elementary notion of infinity I'm using.

Keep in mind that even if it's true that there's something in the real world corresponding to your concept of infinity, that doesn't make the unsophisticated notion of infinity I'm using wrong.

The real situation is that mathematicians have developed their own concept of infinity. Good for them, but that doesn't invalidate the Common Man's notion of infinity. It just means we're talking of different things. That of the Common Man came first I'm sure. Mathematicians could have used a different word for their new concept. Don't complain now.

Don't be so quick to dismiss the mathematicians. Bear in mind that they really, no kidding, have thought this stuff through more than you have. You're right that their concepts are different from the Common Man's notion of infinity; but when you criticize them for not using a different word, what you're not taking into account is that mathematicians didn't come up with their concepts in a vacuum. They came up with their concepts by starting out from the Common Man's notion of infinity, and thinking about all the puzzles you're grappling with, and also about more puzzles they found in their study that you haven't even encountered yet, and then they refined and refined the notion of infinity until it was able to successfully deal with those puzzles. What you're not taking into account is that the Common Man's notion of infinity, the notion you're hoping for an explanation of the puzzles in terms of, will never deliver, because it is self-contradictory.

The Common Man thinks he can keep understanding his own concept of infinity, but he really can't, because he gets his notion of infinity by using intuition as his guide and extrapolating from the familiar finite, and he inevitably ends up with a confused notion that breaks down when he dives into it too far, because his intuition is based on too many unconscious assumptions that he carried over from what he knows of finite objects. The mathematicians observed that this was going on, abandoned unreliable intuition, and let themselves be guided by pure logic. Whenever they found a contradiction, they studied it and studied it until they identified an unconscious premise they had accidentally believed only because it was true of finite objects and that had led them into the inconsistency, and then they discarded that assumption. The mathematical notions of infinity that you complain about are the result of that process -- they are simply the Common Man's notion, minus enough premises to eliminate the self-contradictions.

(Mathematicians have more than one concept of infinity because you can delete premises in more than one way. When the Common Man believes premise A and B about the infinite, even though they contradict each other, you can fix the problem by deleting A, but you can also fix the problem by keeping A and deleting B. Presto: you now have two different mathematical notions of infinity. You're free to believe in one or the other; you're also free to regard them as theories to use rather than theories to believe in, and study the infinite objects of each of them.)

Here's post #1:

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.

Here's post #88.

”actual infinity” is not a point on the line. you seem to have misunderstood something.

Sorry, but if there is an actually infinite past, then there has to be a point in time which is actually in the past and an infinitely long time away from now and from any other point in time.

Then, maybe, there's no actually infinite past, just no beginning, no first moment in time. Who would know?
EB

So in post #1 you say an infinity of seconds that have already happened, and are now done with, make that infinity a full-blown ontological reality. But in post #88 you say no beginning, no first moment in time, i.e., no second that's the first second and that doesn't have another second before it, i.e., the total number of seconds already done with is not any finite number, i.e., it's infinite, would not qualify as an actually infinite past. You say there would have to be not only an infinity of seconds, but also some particular second infinitely long away from now. So, does an actual infinite past require a specific infinitely ancient point in time, or doesn't it? Well, according to the Common Man's notion of infinity, both. It's that internal contradiction that invalidates the Common Man's notion of infinity. It's not the mathematicians nefariously stealing the word for their own purposes that did it to you.

 

[DBT]

Why is not every point in time in an infinite past a specific point?

 

[Bomb#20]

Why is not every point in time in an infinite past a specific point?

Who says it might not be? The usual concept of an infinite past includes infinitely many points, each of which is a specific point, a specific finite number of seconds in the past. There's a point 1 second in the past, a point 2 seconds in the past, a point a googol seconds in the past, a point a googol plus 1 seconds in the past, no point infinity seconds in the past, and so forth.

 

[Speakpigeon]

Bite your tongue, philistine! Think Grieg, not Nielsen and Berwald.

(Who the heck are Nielsen and Berwald, you ask? My point exactly.)

I have to concede your point as to Grieg, Nielsen and Berwald, but you don't have to be a philistine to completely ignore who these guys might be. This is a small planet, so they say, but it's already too big for how much time I will have to spend on it.

And now it's time for lunch! See?
EB

 

[Speakpigeon]

Most people have no background in understanding infinity and rely on naive intuitions or half-remembered hand-waving explanations from freshman year math class.

You're assuming as true here that there is such a thing as infinity as mathematicians have come to conceived of it. Maybe that's just not true. And as long as you don't have empirical evidence to present, I will hand-wave your assumption as baseless.

Oh, wait, I'm misunderstanding you! The reality is that you're only talking about the concept of infinity, not of anything like actual infinity. Sorry, I'm not used to discussing in the abstract like you guys.

No, he's talking about both the concept of infinity and also about actual infinities if there are any.

Thanks for confirming what I thought.

If there are any then they'll match one or another of the mathematical concepts of infinity.

Hopefully.

Could be also that reality is just infinite in the ordinary sense...

Or could you explain for all of us to understand how the layman's notion of infinity would be a non-starter?
EB

 

[Speakpigeon]

Keep in mind that even if it's true that there's something in the real world corresponding to your concept of infinity, that doesn't make the unsophisticated notion of infinity I'm using wrong.

The real situation is that mathematicians have developed their own concept of infinity. Good for them, but that doesn't invalidate the Common Man's notion of infinity. It just means we're talking of different things. That of the Common Man came first I'm sure. Mathematicians could have used a different word for their new concept. Don't complain now.

Don't be so quick to dismiss the mathematicians.

I haven't. I certainly didn't dismiss any mathematicians' concept of the actual infinite. I wouldn't dismiss something I don't know and probably wouldn't understand.

Bear in mind that they really, no kidding, have thought this stuff through more than you have. You're right that their concepts are different from the Common Man's notion of infinity; but when you criticize them for not using a different word, what you're not taking into account is that mathematicians didn't come up with their concepts in a vacuum. They came up with their concepts by starting out from the Common Man's notion of infinity, and thinking about all the puzzles you're grappling with, and also about more puzzles they found in their study that you haven't even encountered yet, and then they refined and refined the notion of infinity until it was able to successfully deal with those puzzles. What you're not taking into account is that the Common Man's notion of infinity, the notion you're hoping for an explanation of the puzzles in terms of, will never deliver, because it is self-contradictory.

I'm sure these people are doing their job and it's a difficult one I couldn't do myself. Still, I also inevitably ignore the details of their work and it remains unclear to me that it would show somehow that the Common Man's notion of infinity would be self-contradictory. If I take the dictionary definition of the infinite as a good indication of what the ordinary notion of infinity is, I don't understand why it would be self-contradictory. So, here it is:

infinity
2. endless time, space, or quantity

It seems too basic to give room for self-contradictoriness.

So, could you explain, in plain English, if at all possible?

The Common Man thinks he can keep understanding his own concept of infinity, but he really can't, because he gets his notion of infinity by using intuition as his guide and extrapolating from the familiar finite, and he inevitably ends up with a confused notion that breaks down when he dives into it too far, because his intuition is based on too many unconscious assumptions that he carried over from what he knows of finite objects.

Well, and that's where I become sceptical of your claim about it being self-contradictory. I don't see how the Common Man would be "diving into it too far" just by conceiving of infinity as something without an end or boundary. I'm suspecting here that you are confusing what mathematicians themselves did initially, i.e. "diving into it too far", with what the Common Man does, which is usually not diving into it very much. Possibly some philosophers, theologians, intellectuals of one sort or another tried it and encountered paradoxes, but those would hardly be the Common Man.

The mathematicians observed that this was going on, abandoned unreliable intuition, and let themselves be guided by pure logic. Whenever they found a contradiction, they studied it and studied it until they identified an unconscious premise they had accidentally believed only because it was true of finite objects and that had led them into the inconsistency, and then they discarded that assumption. The mathematical notions of infinity that you complain about are the result of that process -- they are simply the Common Man's notion, minus enough premises to eliminate the self-contradictions.

(Mathematicians have more than one concept of infinity because you can delete premises in more than one way. When the Common Man believes premise A and B about the infinite, even though they contradict each other, you can fix the problem by deleting A, but you can also fix the problem by keeping A and deleting B. Presto: you now have two different mathematical notions of infinity. You're free to believe in one or the other; you're also free to regard them as theories to use rather than theories to believe in, and study the infinite objects of each of them.)

So, can you give an example of contradictory premises that the Common Man would believe?

Ooops, here is one, apparently...

Here's post #1:

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.

Here's post #88.

”actual infinity” is not a point on the line. you seem to have misunderstood something.

Sorry, but if there is an actually infinite past, then there has to be a point in time which is actually in the past and an infinitely long time away from now and from any other point in time.

Then, maybe, there's no actually infinite past, just no beginning, no first moment in time. Who would know?
EB

So in post #1 you say an infinity of seconds that have already happened, and are now done with, make that infinity a full-blown ontological reality. But in post #88 you say no beginning, no first moment in time, i.e., no second that's the first second and that doesn't have another second before it, i.e., the total number of seconds already done with is not any finite number, i.e., it's infinite, would not qualify as an actually infinite past. You say there would have to be not only an infinity of seconds, but also some particular second infinitely long away from now. So, does an actual infinite past require a specific infinitely ancient point in time, or doesn't it? Well, according to the Common Man's notion of infinity, both. It's that internal contradiction that invalidates the Common Man's notion of infinity. It's not the mathematicians nefariously stealing the word for their own purposes that did it to you.

I seem to understand what I said pretty good myself. I don't see there's any problem here. So, excluding the case of a finite past, what I said is that either we think of the past as an actual infinity and then "there has to be a point in time which is actually in the past and an infinitely long time away from now and from any other point in time". Or we think of the past in the same way as we think of the future and then there isn't any actual infinity (in the past). Where's the contradiction?

To be honest, I also suspect that most people think of the past as finite, so they wouldn't have a chance to get to this dilemma. One contradiction would come from diving too far into the concept of an almighty God, who presumably would have to be not only infinite, but an actual infinity. But notice that the usual belief here is that the world was created and therefore that our own past would still be finite. In any case, I don't see anybody conceiving of God as existing in time. Rather, time would have started with the creation of our world, and would therefore be finite, and then no contradiction.

Or am I missing something?
EB

________________________

Edit: Yes, I missed something, I thought I was, and it's the fact that you seem to have misread my post No. 88. You seem to be conflating the two members of the either/or alternative I'm considering.

So, yes, either there is an actual infinity of the past and then "an actual infinite past require a specific infinitely ancient point in time", or the past was merely infinite and there would not have been any actual infinitely ancient point in time. For example if the past was conceived somewhat like the future is. Time, for example, could exist one second at a time, so to speak, so even an infinite past wouldn't make any actual infinity because it wouldn't in effect exist at all, which is by the way grammatically literally the case. Or something else.
EB

 

[Juma]

I'd be so fascinated if you could just exhibit one dictionary definition. An actual dictionary definition.

In English, please.

https://en.m.wikipedia.org/wiki/Measure_(mathematics)

There you go.

Hmm. Wonder why speakpidgeon ignores this...

 

[Speakpigeon]

I'd be so fascinated if you could just exhibit one dictionary definition. An actual dictionary definition.

In English, please.

https://en.m.wikipedia.org/wiki/Measure_(mathematics)

There you go.

Measure (mathematics)
https://en.m.wikipedia.org/wiki/Measure_(mathematics)

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume.

Cute.



So now, you should be able to answer the question I already submitted to beero1000:

I can assign a number between 0 and 1 to every moment in time, eternal past and infinite future. If you specifically wanted an 'actual infinity' of points infinitely far in the past/future, you could even include 0 being the time infinitely far into the past and 1 to be the time of an instant infinitely far in the future.

You keep thinking in terms of "assigning" values or numbers to moments in time. I already agreed you can do that but it's not a "measure".

Why couldn't my clock work like that?

You would have to explain how it would work, if only in principle.

There's no unique correspondance between [0,1] and time. There's even an infinite number of possible time functions of [0,1]. We don't even need to think in terms of continuous functions. So, how would you go about selecting which correspondance would do?

So, how would such a clock work in principle? Me, I don't know.

But that's definitely an interesting angle.
EB

So, can you explain how to assign a number to each moment in time in "a systematic way"?

Go on, break new ground!
EB

 

[Speakpigeon]

The name of the game here is that people start threads with an OP and other people try to respond to what the OP actually says. So, just look here what the OP says:

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

Now, you try to respond to that and everyone will make up their own mind as to whether you're making sense.

Easy: the answer is that the clock is one hour more than what it was an hour ago modulus the period of the clock.

The clock can be anything (within its period) as long it it is conformant with its earlier values.

why is that a problem?

Excellent! You engineer should be able to provide a reasonably short algorithm doing the job, i.e. an algorithm stopping at some point in time and giving a definite answer to my question.

Can I suggest the broad principle?

Assumption: A simple clock has always existed;
Question: What value X would the clock display at time N?

N:= 0 (Starting time, i.e. now) ;
P:= 100 (clock period);
{A} X(N):= X(N-1) + 1
IF X(N) instantiated THEN

DISPLAY X(N) mod P​

ELSE

N:= N - 1;
GOTO {A}​

ENDIF
STOP

Or something else?
EB

Note - Sorry, instruction {A} should read as a recursive function but I can't quite remember how you write this in Pascal. It was a very long time ago!

 

[Juma]

Measure (mathematics)
https://en.m.wikipedia.org/wiki/Measure_(mathematics)

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size. In this sense, a measure is a generalization of the concepts of length, area, and volume.

Cute.



So now, you should be able to answer the question I already submitted to beero1000:

I can assign a number between 0 and 1 to every moment in time, eternal past and infinite future. If you specifically wanted an 'actual infinity' of points infinitely far in the past/future, you could even include 0 being the time infinitely far into the past and 1 to be the time of an instant infinitely far in the future.

You keep thinking in terms of "assigning" values or numbers to moments in time. I already agreed you can do that but it's not a "measure".

Why couldn't my clock work like that?

You would have to explain how it would work, if only in principle.

There's no unique correspondance between [0,1] and time. There's even an infinite number of possible time functions of [0,1]. We don't even need to think in terms of continuous functions. So, how would you go about selecting which correspondance would do?

So, how would such a clock work in principle? Me, I don't know.

But that's definitely an interesting angle.
EB

So, can you explain how to assign a number to each moment in time in "a systematic way"?

Go on, break new ground!
EB

Since you are unclear I give some different answers:
1) use seconds relative assimation of kennedy
2) the distance to a neutrino flying through kennedy when he was shot
3) count the oscillations of a cesium atom under specific cirumstances TBD with 0 when kennedy was shot.
4) the positions of the hands on a miracously infinitely running clock.

- - - Updated - - -

Easy: the answer is that the clock is one hour more than what it was an hour ago modulus the period of the clock.

The clock can be anything (within its period) as long it it is conformant with its earlier values.

why is that a problem?

Excellent! You engineer should be able to provide a reasonably short algorithm doing the job, i.e. an algorithm stopping at some point in time and giving a definite answer to my question.

Can I suggest the broad principle?

Assumption: A simple clock has always existed;
Question: What value X would the clock display at time N?

N:= 0 (Starting time, i.e. now) ;
P:= 100 (clock period);
{A} X(N):= X(N-1) + 1
IF X(N) instantiated THEN

DISPLAY X(N) mod P​

ELSE

N:= N - 1;
GOTO {A}​

ENDIF
STOP

Or something else?
EB

Note - Sorry, instruction {A} should read as a recursive function but I can't quite remember how you write this in Pascal. It was a very long time ago!

Who had said that we could somehow predict what the clock should show without ever seen it before?

 

[bilby]

If the past is infinite, you cannot ever measure anything 'relative to the beginning', because by definition, there is no 'beginning' to use as a reference.

There's nothing to stop you from arbitrarily selecting any time as 'zero' in a given reference frame, and measuring time in both directions from that datum. Assuming that both past and future are infinite, you cannot by definition use that reference point to establish a finite measure of the distance from it to the 'beginning' or 'end' of time, because those things are by definition nonexistent.

Humans are inclined to assume that all things have a 'beginning' and an 'end'. We are also inclined to assume that an object in motion requires the continuous application of force in order to remain in motion. Our intuition is often mistaken, and that infinite time (in past, or future, or both) is counterintuitive is very weak evidence indeed for its nonexistence.

 

[Bomb#20]

What you're not taking into account is that the Common Man's notion of infinity, the notion you're hoping for an explanation of the puzzles in terms of, will never deliver, because it is self-contradictory.

I'm sure these people are doing their job and it's a difficult one I couldn't do myself. Still, I also inevitably ignore the details of their work and it remains unclear to me that it would show somehow that the Common Man's notion of infinity would be self-contradictory. If I take the dictionary definition of the infinite as a good indication of what the ordinary notion of infinity is, I don't understand why it would be self-contradictory. So, here it is:

infinity
2. endless time, space, or quantity

It seems too basic to give room for self-contradictoriness.

So, could you explain, in plain English, if at all possible?

That's not the self-contradictory part. That's the part all the mathematicians keep, in all their various infinity concepts. That's why they still call their concepts "infinity". The problem is the subconscious baggage that the Common Man carries forward from the finite.

The Common Man thinks he can keep understanding his own concept of infinity, but he really can't, because he gets his notion of infinity by using intuition as his guide and extrapolating from the familiar finite, and he inevitably ends up with a confused notion that breaks down when he dives into it too far, because his intuition is based on too many unconscious assumptions that he carried over from what he knows of finite objects.

Well, and that's where I become sceptical of your claim about it being self-contradictory. I don't see how the Common Man would be "diving into it too far" just by conceiving of infinity as something without an end or boundary.

But he's not just conceiving of infinity as something without an end or boundary. He thinks that's what he's doing; but he's kidding himself. The extra baggage keeps showing up. You did it yourself in earlier posts; and you did it again right here in post #126. You wrote "there has to be a point in time which is actually in the past and an infinitely long time away from now and from any other point in time". That is extra baggage. You did not get that from "endless time, space, or quantity". You did not get that from "something without an end or boundary". (And worse, the way you talk about that extra point when you use it in your other arguments, it is itself an end and a boundary.)

So why does the Common Man assume endless time implies a point an infinitely long time away from now? Because everything in his experience with finite quantities has ingrained that prejudice in him. If you're at the front of a mile-long runway, it has a point a mile away from you. When you sign a 30-year mortgage, there's a time 30 years from now when you'll have to pay it off. The Eiffel Tower is 130 years old and that means there was a time when it was new, 130 years ago. So of course the Common Man takes it for granted that an infinitely old universe means the time-line has an "infinity years ago" point on it. It's an innocent mistake -- he was just pattern matching, the foundation of all human thought. But he did not get that from "without an end or boundary". He got it from his familiarity with finite quantities. When he carried that prejudice along with him into his thinking about infinite time, that was "diving into it too far". If he'd just stopped at "without an end or boundary", he'd have been fine.

I seem to understand what I said pretty good myself. I don't see there's any problem here. So, excluding the case of a finite past, what I said is that either we think of the past as an actual infinity and then "there has to be a point in time which is actually in the past and an infinitely long time away from now and from any other point in time". Or we think of the past in the same way as we think of the future and then there isn't any actual infinity (in the past). Where's the contradiction?

To be honest, I also suspect that most people think of the past as finite, so they wouldn't have a chance to get to this dilemma. One contradiction would come from diving too far into the concept of an almighty God, who presumably would have to be not only infinite, but an actual infinity. But notice that the usual belief here is that the world was created and therefore that our own past would still be finite. In any case, I don't see anybody conceiving of God as existing in time. Rather, time would have started with the creation of our world, and would therefore be finite, and then no contradiction.

Or am I missing something?
EB

________________________

Edit: Yes, I missed something, I thought I was, and it's the fact that you seem to have misread my post No. 88. You seem to be conflating the two members of the either/or alternative I'm considering.

So, yes, either there is an actual infinity of the past and then "an actual infinite past require a specific infinitely ancient point in time", or the past was merely infinite and there would not have been any actual infinitely ancient point in time. For example if the past was conceived somewhat like the future is. Time, for example, could exist one second at a time, so to speak, so even an infinite past wouldn't make any actual infinity because it wouldn't in effect exist at all, which is by the way grammatically literally the case. Or something else.
EB

Yes, I got all that. The problem is, that's not what you said in post #1. In post #1 you said:

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.

Nothing in there about an infinitely long ago point. Just infinitely many different times. Yet you (quite reasonably) concluded that that infinity is a full-blown ontological reality, not a pure abstraction, because every time in that infinite sequence of times has already happened. It's already done with, and that was enough to let you infer that it's an actual infinity, rather than a future-like potentiality that never actually becomes a completed infinity.

That's the contradiction -- your notion of infinity implies you need an infinity-ago time point in order to have an actual infinity, even though you've demonstrated that you didn't need one to make that inference.

 

[beero1000]

Seems like Bomb#20's got this.

 

[Kharakov]

That's the contradiction -- your notion of infinity implies you need an infinity-ago time point in order to have an actual infinity, even though you've demonstrated that you didn't need one to make that inference.

I think EB got caught in the unterweb... trying to tenub the untenable. Tenub is number 2 in uberbin.

 

[Speakpigeon]

So, can you explain how to assign a number to each moment in time in "a systematic way"?
EB

Since you are unclear I give some different answers:
1) use seconds relative assimation of kennedy
2) the distance to a neutrino flying through kennedy when he was shot
3) count the oscillations of a cesium atom under specific cirumstances TBD with 0 when kennedy was shot.
4) the positions of the hands on a miracously infinitely running clock.

Thanks for your contribution.
EB

 

[Speakpigeon]

You engineer should be able to provide a reasonably short algorithm doing the job, i.e. an algorithm stopping at some point in time and giving a definite answer to my question.

Who had said that we could somehow predict what the clock should show without ever seen it before?

Good answer.
EB

 

[Speakpigeon]

If the past is infinite, you cannot ever measure anything 'relative to the beginning', because by definition, there is no 'beginning' to use as a reference.

Good.

There's nothing to stop you from arbitrarily selecting any time as 'zero' in a given reference frame, and measuring time in both directions from that datum.

How would you go about measuring now time already elapsed?

Assuming that both past and future are infinite, you cannot by definition use that reference point to establish a finite measure of the distance from it to the 'beginning' or 'end' of time, because those things are by definition nonexistent.

Sure, but if the universe, or more broadly "reality", exists, it must be, presumably, in a definite state at any point in time. If there was a beginning, and assuming reality was in a definite state at that moment, we can conceive of a simple mechanism by which it could have a definite state forever after, i.e. the state at time T directly causing the state at time T + ε, starting from the beginning. Or something like that.

So, what if reality has always existed? If no beginning, there's obviously no answer and that's it. But even if reality is assumed as having always existed, we can apparently assume an actual beginning in time, only one that would be infinitely away from any other point in time. What then? We could assume the same mechanism as before, since we have assumed a beginning, to ensure a definite state at every moment in time. Yet, it seems this mechanism now doesn't deliver a definite state except for the putative beginning, and this is precisely because every other moment in time would have been infinitely away from the definite beginning.

Still, I think there is a solution to that conundrum but it's not been proposed so far, although elements of it have been.

Humans are inclined to assume that all things have a 'beginning' and an 'end'. We are also inclined to assume that an object in motion requires the continuous application of force in order to remain in motion. Our intuition is often mistaken, and that infinite time (in past, or future, or both) is counterintuitive is very weak evidence indeed for its nonexistence.

Yep, I'm agnostic here. I haven't been there all the time myself.
EB

 

[Speakpigeon]

I'm sure these people are doing their job and it's a difficult one I couldn't do myself. Still, I also inevitably ignore the details of their work and it remains unclear to me that it would show somehow that the Common Man's notion of infinity would be self-contradictory. If I take the dictionary definition of the infinite as a good indication of what the ordinary notion of infinity is, I don't understand why it would be self-contradictory. So, here it is:

infinity
2. endless time, space, or quantity

It seems too basic to give room for self-contradictoriness.

So, could you explain, in plain English, if at all possible?

That's not the self-contradictory part.

Ah, excellent.

Let's remember you said that. No contradiction in the dictionary definition of infinity. This is such a relief!

That's the part all the mathematicians keep, in all their various infinity concepts. That's why they still call their concepts "infinity".

Alright, they're all but forgiven, at least for that.
EB

 

[Speakpigeon]

The problem is the subconscious baggage that the Common Man carries forward from the finite.

The Common Man thinks he can keep understanding his own concept of infinity, but he really can't, because he gets his notion of infinity by using intuition as his guide and extrapolating from the familiar finite, and he inevitably ends up with a confused notion that breaks down when he dives into it too far, because his intuition is based on too many unconscious assumptions that he carried over from what he knows of finite objects.

Well, and that's where I become sceptical of your claim about it being self-contradictory. I don't see how the Common Man would be "diving into it too far" just by conceiving of infinity as something without an end or boundary.

But he's not just conceiving of infinity as something without an end or boundary. He thinks that's what he's doing; but he's kidding himself. The extra baggage keeps showing up.

You still have to provide examples of that. I explained in my previous post what I think the Common Man does, which is broadly the dictionary definition of infinity and a universe or reality created, ergo with a beginning in time, therefore without an infinite past. Not much room for contradictions there.

You did it yourself in earlier posts; and you did it again right here in post #126. You wrote "there has to be a point in time which is actually in the past and an infinitely long time away from now and from any other point in time". That is extra baggage. You did not get that from "endless time, space, or quantity". You did not get that from "something without an end or boundary". (And worse, the way you talk about that extra point when you use it in your other arguments, it is itself an end and a boundary.)

I still don't see the contradiction. I was explicitly considering the case of an actual infinity. My consideration was explicitly based on the assumption of an actual infinity, i.e. something explicitly different from the Common Man's notion of infinity, as expressed by the dictionary definition as "endless". Again, I have been very clear I was considering two distinct concept of infinity. Sure, if you conflate the two, you get a contradiction, but then it's yours, not mine.

So I don't see where's the contradiction and you still haven't shown there is one.

So why does the Common Man assume endless time implies a point an infinitely long time away from now?

Nobody does that.

I certainly don't know of anybody who did that. And I myself didn't.

I'm sure one dude now and then may be doing it, perhaps some philosopher before Aristotle, but you would still have to exhibit the evidence of that.

Because everything in his experience with finite quantities has ingrained that prejudice in him. If you're at the front of a mile-long runway, it has a point a mile away from you. When you sign a 30-year mortgage, there's a time 30 years from now when you'll have to pay it off. The Eiffel Tower is 130 years old and that means there was a time when it was new, 130 years ago. So of course the Common Man takes it for granted that an infinitely old universe means the time-line has an "infinity years ago" point on it. It's an innocent mistake -- he was just pattern matching, the foundation of all human thought. But he did not get that from "without an end or boundary". He got it from his familiarity with finite quantities. When he carried that prejudice along with him into his thinking about infinite time, that was "diving into it too far". If he'd just stopped at "without an end or boundary", he'd have been fine.

Sorry, I don't think anybody makes that mistake except a few drunks and mentally disturbed individuals. I will wait till you exhibit the evidence that's what people do. The dictionary definition is my evidence that it's not what people do.

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.

Nothing in there about an infinitely long ago point. Just infinitely many different times. Yet you (quite reasonably) concluded that that infinity is a full-blown ontological reality, not a pure abstraction, because every time in that infinite sequence of times has already happened. It's already done with, and that was enough to let you infer that it's an actual infinity, rather than a future-like potentiality that never actually becomes a completed infinity.

I'm with you so far.

That's the contradiction -- your notion of infinity implies you need an infinity-ago time point in order to have an actual infinity, even though you've demonstrated that you didn't need one to make that inference.

No.

Again, and I already said that, I have been considering two distinct possibilities: One, the ordinary notion of an infinite past, with no beginning, as per the dictionary definition; and Two, an actually infinite past, with an actual beginning in the past infinitely away from any other point in time, this second concept obviously departing from the ordinary notion of an endless infinity. So, clearly, I'm not making an inference from infinite, endless, past to an actual beginning. Yes, that would be a contradiction, and I didn't make it. You just conflated the two alternative concepts I have been considering.

Further, I'm only one guy and hardly the Common Man. So, I will still be waiting for any evidence that the Common Man is routinely making those contradictions you've been talking about.
EB

 

[Speakpigeon]

That's the contradiction -- your notion of infinity implies you need an infinity-ago time point in order to have an actual infinity, even though you've demonstrated that you didn't need one to make that inference.

I think EB got caught in the unterweb... trying to tenub the untenable. Tenub is number 2 in uberbin.

Man of little faith!
EB

- - - Updated - - -

Seems like Bomb#20's got this.

Yes, thanks to keep me updated on what you think.
EB