The idea of an infinite past

[untermensche]

You claim a second can be divided infinitely.

Then what is the duration of an infinite division?

No hand waving. Just a length of time.

 

[Elixir]

unter never explained how time would "flow smoothly" without being infinitely divisible.

I'm wondering how many starting points any particular point in time can have?

Heh. He has also declined to tackle the question of prior states. He can't point to any state that did not result from a prior state, so by his own metric, a finite past is absurd.

 

[untermensche]

It is an empty empty claim when somebody claims to know about all prior states.

But what can be known for certain is infinity is not a quantity in any way.

There is nothing in the real world that you can try to apply infinity to that doesn't reduce to absurdity.

An infinite slice of time. An infinitely small movement.

Absurdities that have no value that can be attached.

 

[Elixir]

It is an empty empty claim when somebody claims to know about all prior states.

Yeah, especially when the person lays claims to knowing that there's a finite number of them.

Actually, there are many states (not infinite, but more than you can count) known to have arisen from prior states.
And NONE that are known to arisen without a prior state.

More of your "that's absurd" irrational dismissal, cloaked as "empty empty claim". It's a rational statement, you can't deal with it - ergo "Absurd... empty claim".
SHOW that it's an empty claim, dude. Otherwise, that itself really IS an empty claim.

 

[untermensche]

It is an empty empty claim when somebody claims to know about all prior states.

Yeah, especially when the person lays claims to knowing that there's a finite number of them.

Saying you can't apply the magic concept of infinity to reality is a claim about the imaginary conception of infinity.

It is not something that can be applied to reality.

It is something humans pulled from their asses.

It is not a real world concept.

It is a purely mathematical concept.

To try to apply it to reality is like saying the sun suffers from social anxiety disorder. Total absurdity.

 

[Juma]

If time is infinitely divisible how much time is contained in each infinite division?

Good question.

First, this makes me think of another: How much time in one infinitely divisible second of time?

Obviously, there's just 1 second of time in one second of time.

But then, one second of time is a quantity, so one second of time, a quantity, contains an infinity of divisions, which means that infinity is indeed a quantity.

And to answer your question, one second of time divided by infinity result in an epsilon, an infinitesimal, an infinitely small, quantity of time.

In case you're so ignorant you don't know about infinitesimals, here is some crash course made for you by Wiki:

Infinitely small
https://en.wikipedia.org/wiki/Infinitesimal

In mathematics, infinitesimals are things so small that there is no way to measure them. The insight with exploiting infinitesimals was that entities could still retain certain specific properties, such as angle or slope, even though these entities were quantitatively small. The word infinitesimal comes from a 17th-century Modern Latin coinage infinitesimus, which originally referred to the "infinite-th" item in a sequence. Infinitesimals are a basic ingredient in the procedures of infinitesimal calculus as developed by Leibniz, including the law of continuity and the transcendental law of homogeneity. In common speech, an infinitesimal object is an object that is smaller than any feasible measurement, but not zero in size—or, so small that it cannot be distinguished from zero by any available means. Hence, when used as an adjective, "infinitesimal" means "extremely small". To give it a meaning, it usually must be compared to another infinitesimal object in the same context (as in a derivative). Infinitely many infinitesimals are summed to produce an integral.

I underscored that which shows that infinities are considered quantities.

Please pay attention in particular to the last sentence: Infinitely many infinitesimals are summed to produce an integral.

This sentence shows that the idea of calculus is that an infinity of infinitesimals sums up as a finite quantity. Ergo infinity is considered a quantity. No doubt a special kind of quantity, but a quantity nonetheless.
EB

I would say that infinitesimals are a mind tool used in specific contexts. For integration it is useful because it focus on the possibility of finding a scale at which the function to be integrated can be approximated as constant. That only works if there are some limitations on the function: that there is a limit on its derivata, that doesnt change infinitely fast.

So using infinitesimals is a way of transforming the problem of calculating the area of a varying function, which we do not know how how to do, into a scale where we are calculating the area of rectangles, something we do know how to do.

The weird thing is that when we are in the scale of infinitesimals the length of the interval have no relation to the length of the ”macroscopic” original integration interval. There is no factor K such that K * dx = b-a (where [a,b] is the integration interval)

But then how can we calc integrals? How do we relate the infinitesimal areas to the total one?

By only care about the cases where it can be shown that the function is so ”slowly” changing that it can, for small dx, can be approximated with a constant. In that case we can show that the entire integral have a asymptotic limit value when we make dx smaller and smaller and we conclude that if we make the transition of to infinitesimals the area shouldnt suddenly jump.

But that doesnt change the fact that there is no relation between the size of infinitesimals and normal quantities.

In that meaning infenitesimals are not quantities.

 

[Speakpigeon]

I would say that infinitesimals are a mind tool used in specific contexts. For integration it is useful because it focus on the possibility of finding a scale at which the function to be integrated can be approximated as constant. That only works if there are some limitations on the function: that there is a limit on its derivata, that doesnt change infinitely fast.

So using infinitesimals is a way of transforming the problem of calculating the area of a varying function, which we do not know how how to do, into a scale where we are calculating the area of rectangles, something we do know how to do.

The weird thing is that when we are in the scale of infinitesimals the length of the interval have no relation to the length of the ”macroscopic” original integration interval. There is no factor K such that K * dx = b-a (where [a,b] is the integration interval)

But then how can we calc integrals? How do we relate the infinitesimal areas to the total one?

By only care about the cases where it can be shown that the function is so ”slowly” changing that it can, for small dx, can be approximated with a constant. In that case we can show that the entire integral have a asymptotic limit value when we make dx smaller and smaller and we conclude that if we make the transition of to infinitesimals the area shouldnt suddenly jump.

But that doesnt change the fact that there is no relation between the size of infinitesimals and normal quantities.

Yes, I was aware of this while doing my post. That's why I talked of "the idea" (of calculus is that an infinity of infinitesimals sums up as a finite quantity).

I didn't claim that we would know that an infinity of infinitesimals generally sums up as a finite quantity. Here we need to distinguish the practical problem of finding a result for particular cases of curves or functions, and the conceptual perspective on infinitesimals. What matters for this discussion is whether we can conceive of infinitesimals as quantities. So what matters here is that infinitesimals be conceived of by most practitioners as summing up to a finite quantity even if only in one case. Obviously, they are special quantities but we can conceive of them without encountering any contradiction. If we did, mathematicians would have stopped using them the way they do.

In that meaning infenitesimals are not quantities.

You've only shown in your post here that there are cases, many cases I would agree, where we don't know how to sum up infinitesimals to get a finite result. Sometimes, it will be because the result is in fact infinite. In other cases, it will be because we haven't found a way to relate the kind of infinitesimals we're dealing with to a finite result even though it's probably finite. This doesn't matter for this discussion. All we need is at least one case where we have a clear conception that infinitesimals add up to a finite result. If that's the case, then we can effectively conceive of an infinity of infinitesimals as equal, and therefore comparable, to a finite quantity, and therefore something to be regarded as a quantity itself, if a special kind of quantity.

Obviously, infinitesimals are not finite quantities. Broadly, we think of them the way we think conventionally of the infinite as the number of terms in a series without an upper bound. Infinitesimals are the notional result of an infinite number of divisions of a finite quantity, assuming you could keep dividing without ever stopping. That's all conceptual but the point is that we can conceive of that without contradiction. And if we can do that at least in one case, then it's good enough.
EB

 

[Speakpigeon]

You claim a second can be divided infinitely.

No I don't.
EB

Note 1 - Please learn your English. If you can't bring yourself to read what's written, then there's no point to this discussion.

Note 2 - Maybe it's not only your English. Maybe you just don't understand very basic notions most people understand, such as the difference between being able to conceive of something and claiming this something exists. I suspect that's your problem. You seem to think you're very smart but obviously you're not if you can't understand very simple things like this.

 

[Speakpigeon]

I'll repeat the specific claim made here in this thread about the possibility of an infinite past, for those who think they can prove otherwise:

I think that the notion of possibility is that of no contradiction with what we know of reality. I can't see how a more restrictive notion of possibility could be cogent. On this understanding, I believe an infinite past would be possible. Certainly, nobody here brought up any contradiction with known facts.

And I will add that it would be possible in the same way to divide one second of time infinitely.
EB

 

[fromderinside]

I know someone would admit to being in the counting room.

No untermenche? That's not possible either? Shame.

 

[untermensche]

In that meaning infenitesimals are not quantities.

I do not need any long winded explanations to understand that.

Infinitesimals are phantoms, fantasies. They could never be something real.

People that claim reality can be divided infinitely are lost children who have read too many comic books.

They have a hard time understanding when things are pure fantasy.

 

[untermensche]

The concept of infinity is in conflict with the idea of completion.

All the time in the past has completed at every given moment.

The concept of infinity is in conflict with all the time in the past.

 

[Juma]

In that meaning infenitesimals are not quantities.

I do not need any long winded explanations to understand that.

Infinitesimals are phantoms, fantasies. They could never be something real.

People that claim reality can be divided infinitely are lost children who have read too many comic books.

They have a hard time understanding when things are pure fantasy.

That is true: Reality cannot be divided at all.

 

[untermensche]

A brick cannot be divided?

They are indestructable?

 

[Speakpigeon]

I do not need any long winded explanations to understand that.

Infinitesimals Bricks are phantoms, fantasies. They could never be something real.

People that claim reality bricks can be divided infinitely are lost children who have read too many comic books.

They have a hard time understanding when things are pure fantasy.

And you have to take my word for it.
EB-Bot

 

[Kharakov]

The duration of a moment is 0. How many moments are in any length of time? An infinite amount.

How much can untermensche not understand this? An infinite amount.

 

[DBT]

The concept of infinity is in conflict with the idea of completion.

All the time in the past has completed at every given moment.

The concept of infinity is in conflict with all the time in the past.

No, it is not. You basically have a choice between no beginning to time, an inexplicable first cause (from what?), or something from absolute nothing.

None of these options seem rational. Existence itself appears absurd. That there is something rather than nothing is unimaginable, yet here we are struggling with the mystery of existence.

We don't have enough information to say that eternity of time is impossible.

 

[Phil Scott]

I do not need any long winded explanations to understand that.

Infinitesimals Bricks are phantoms, fantasies. They could never be something real.

People that claim reality bricks can be divided infinitely are lost children who have read too many comic books.

They have a hard time understanding when things are pure fantasy.

And you have to take my word for it.
EB-Bot

If a brick could be divided, then there could be a divided brick. But that's absurd.

QED. QFT. KTHX. STFU.

 

[Speakpigeon]

You basically have a choice between no beginning to time, an inexplicable first cause (from what?), or something from absolute nothing.

None of these options seem rational.

They're perfectly rational. They are arrived at through a rational process of analysis. The problem is we are stuck there. We can't choose between them and we can't seem to be able to go any further in the analysis.

Existence itself appears absurd.

Existence may be absurd as possibly meaningless but it's not illogical.

That there is something rather than nothing is unimaginable, yet here we are struggling with the mystery of existence.

We don't have enough information to say that eternity of time is impossible.

And I'd be surprised that we could ever have enough information.
EB

 

[Speakpigeon]

The duration of a moment is 0. How many moments are in any length of time? An infinite amount.

It took me a long moment to understand the deep truth in that.

How much can untermensche not understand this? An infinite amount.

I guess it shall take me an infinity of time to understand.
EB