Ok, what now?

Wait, I not well veresed with potential and actual in infinity, is pi a potential or actual infinity. — BB100

Why does dividing things by three, into thirds, create an "infinite" number of threes after the decimal point, as if we can never get to an actual third of something? — Harry Hindu

Well, no.
π = 3.14159...
1/3 = 0.333...
Sure, the righthand side has unending digits, but don't confuse the representation and the number.

When you glance at your speedometer and it reads 60 mph, indeed that is based on an approximation made over a small interval of time. So you do have a point, although a rather insignificant one. — jgill

(y)
It's all contextual.
Similarly with differential calculus; if the plot has a sharp turn or just one point (which would have no context), then it's not differentiable, which would represent something we don't really see much in the world.

Physics can differentiate the two at time t by different motion vectors, speed and direction; by momentum too for that matter. — jorndoe

The problem is that there is no such thing as motion at time t. You might say that there is motion at an extended duration of time, and infer that because of this there would be motion at any given point during that time duration; but that would be a faulty inference. It would be like saying that at any point on a line segment, there is a line, just because we have assumed a line which goes through that point. But there is no line at any point, just like there is no motion at any point in time even though we assume that motion passes through that point. The two, motion and point in time, are incompatible, just like point and line are incompatible.

What single word would you suggest be used in this context, rather than instantaneous? — jgill

How about just calling it "velocity"? We know that "velocity" implies an average over a period of time, just like "instantaneous velocity" implies an average over a period of time. The method for figuring out the average which is called "instantaneous velocity" is just more sophisticated than the old fashioned way of figuring out "average velocity", so it may give us a more accurate or precise determination of the same thing, "the velocity". Nevertheless, the two are just different formulas for giving us the same thing "velocity". So use of the word "instantaneous" is rather deceptive, it does not properly indicate what the formula gives us..

Numbers represent potentials, not actuals. Why does dividing things by three, into thirds, create an "infinite" number of threes after the decimal point, as if we can never get to an actual third of something? — Harry Hindu

I've never read much of Harry's stuff (on the suspicion that more is less) but, for the second time this weekend, I do applaud him for going against the flow, and I must say I can't understand how people would so miss the point, and would take the above rhetorical question as anything but a defense of mathematical practice against philosophical over-thinking. He was just saying, see how the fact that we can divide one by 3 despite the potentially infinite recurring decimal (Achilles can catch up) means we don't have to (in this case anyway) take infinity as a thing.

Wasn't he?

, speaking of things at time t does not mean removal of context.
Velocity or momentum or some such vectors (at t) depend thereupon.
It's not like we have something appearing and vanishing at t, whether talking averages or differential calculus.
How/can you differentiate things at t in the two mentioned scenarios...?

The problem is that there is no such thing as motion at time t — Metaphysician Undercover

True enough, if taking a photo of a moving object - which has the effect of freezing the motion. We use time = t in lots of formulae, and make accurate predictions. But in everyday affairs we experience time more as intervals, although we say things like "I'll meet you at three".

Is time flowing at time = t? I suspect it is.

I can't understand how people would so miss the point, and would take the above rhetorical question . . . — bongo fury

My point was accuracy of statement. Philosophical overthinking seems normal on this forum. :cool:

It's really difficult to see, but there is a variation of 0.111... cm. in the size of the apples.

I've never read much of Harry's stuff (on the suspicion that more is less) but, for the second time this weekend, I do applaud him for going against the flow, and I must say I can't understand how people would so miss the point, and would take the above rhetorical question as anything but a defense of mathematical practice against philosophical over-thinking. He was just saying, see how the fact that we can divide one by 3 despite the potentially infinite recurring decimal (Achilles can catch up) means we don't have to (in this case anyway) take infinity as a thing.

Wasn't he? — bongo fury

Thanks for the excellent clarification.

When we use a calculator to divide 1 by 3, we get 0.333...

Try as we might, we can never put the 1 back together again with evenly divided thirds in the calculator, because it would require you to enter an infinite amount of 3's after the decimal, yet we end up giving 's divided apple to just one person, is that person missing any of the apple?

We agree that an object has a location at a particular time.

We agree that the location does not change at an instant.

Where we disagree is that there are those amongst us who are happy to ascribe a velocity at a particular time, and those who are not.

What is hard to see is how those who do not ascribe a velocity at a particular time can do any basic mechanics.

It's the 0.9999... = 1 denialists, hard at work again.

speaking of things at time t does not mean removal of context. — jorndoe

Time t has no context. If you say "time t", "time" is said at a different time from when "t" is said, because time is passing. So time t covers a duration of time. By the time you say "now" it's in the past. Talking about "time t" is already, by that fact, a removed from context; context being real existence in passing time. It is impossible to have a time t which is not a removal from context. That's the problem here, time t is an ideal which is not consistent with temporal existence as we know it.

It's not like we have something appearing and vanishing at t, whether talking averages or differential calculus.
How/can you differentiate things at t in the two mentioned scenarios...? — jorndoe

The problem is that "time t" is not real, it's an ideal. And Banno wants to understand these things without assuming Platonism, so we must reject such ideals, as not reality. So asking about how we might differentiate things at t is nonsense because "t" doesn't refer to anything real.

It's the 0.9999... = 1 denialists, hard at work again. — Banno

Now you've jinxed it. :D

We agree that an object has a location at a particular time.

We agree that the location does not change at an instant. — Banno

Actually we haven't gotten to these questions yet. As is evident in the prior post, I think "a particular time" is an ideal, which on it's own is without any real validity. What validates it is a reference to something.

What is hard to see is how those who do not ascribe a velocity at a particular time can do any basic mechanics. — Banno

I do a lot of basics mechanics. Complex mathematics is not required for basic mechanics. In fact, mathematics is generally not required for mechanics at all. Fancy that.

Time t has no context — Metaphysician Undercover

Sure it does, especially how we're talking about it here, other times, events, occurrences, you name it.
Actually, I'm not sure it's coherent to go all out context-free here.

The problem is that "time t" is not real — Metaphysician Undercover

Excellent.
I'm going to quote you on that next time I'm late for a meeting with my boss.

:joke:

Indeed. But look to who is on which "side".

How do you work out the velocity at t2 if the velocity at t1 is always zero? :rofl:

A 1kg mass is released from a height of 300m. What velocity will it reach after 1 second?

Obviously, since at 1second, the mass cannot move, its velocity will be zero.

Strawman. Do you put out fallacious arguments on purpose? Just curious.

SO - tell me the answer, and how you arrived at it.

I say 9.8 m/s.

But then, of course, I'm assuming an acceleration of 9.8m/s/s. And that's gotta be wrong, since an object can't accelerate without moving.

SO come on, help us re-write the physics texts.

- tell me the answer, and how you arrived at it. — Banno

I don't remember the acceleration of gravity. I do remember that there's an infinite converging progression involved in answering your question.

What do you conceptually commit yourself to if you embrace an answer that can't be witnessed experimentally? The evidence is entirely intellectual.

SO come on, help us re-write the physics texts. — Banno

More strawman. Why?

What do you conceptually commit yourself to if you embrace an answer that can't be witnessed experimentally? — frank

WTF?

Covered this already.

Sometimes on this forum all one can do is laugh and walk away.

How do you work out the velocity at t2 if the velocity at t1 is always zero? :rofl: — Banno

Just like "t1" is an ideal, so is "t2". I thought you rejected Platonism? Do you believe in Einsteinian relativity?

Sometimes indeterminate forms come up, like 0 / 0.
In arithmetics, it doesn't really mean much.
In some cases, in calculus, it can.
Best not conflate, the angle matters, context matters.

If we only want to speak of intervals, non-zero durations, then what about the starts and ends thereof?
Are we going to toss it all out...? :o

Anyway, successful tested-and-tried application speaks for itself.

If we only want to speak of intervals, non-zero durations, then what about the starts and ends thereof?
Are we going to toss it all out...? — jorndoe

That's another aspect of the very same problem. I'm not suggesting that we toss any of these things out, only that we recognize that in practise all such determinations are less than ideal. Then we might be inspired to look for solutions to the problems which result from using such deficient principles, instead of just assuming that the mathematicians have already discovered the ideals.

Based on my metaphysics "1" does exist. Because everything exists within the mind of God. Everything, conceptual, actual, potential, possible, probable etc. exists in the mind of God. Nothing exists outside of consciousness, which is God's mind.

Maths aren't things we find? Fractals and the Mandelbrot set seem to disagree with this. We cannot "do" infinity by definition. Finite beings cannot create infinities. Only infinite beings can create infinities. Which is one of my arguments for God, ironically.

1) Infinities exist.
2) Finite entities cannot create infinities by definition, because finite beings are limited, infinities are unlimited.
3) Infinities are caused by infinite beings.
4) Infinite beings exist. Ergo,
5) God exists.

What you have proved here is that since I play with infinities, I am an infinite being.

Thanks!

No, I didn't prove that at all. That's totally a non-sequitur. So, just because I use language doesn't mean I created English does it? Obviously not. You can talk about infinities all you want to. But you cannot produce one. For you to produce something that would go on forever, you yourself would have to live forever to do it. That's the whole point.