Precisely. And the purpose of the 10 million different measuring apparatuses (apparati?) is to measure velocity. So QED we are measuring velocity. And so the statement is true per CToT. We are not dealing with your metaphysical notions of truth or falsity here. And of course it is not 10 million. Duh.So the accuracy of the measuring apparatus is always suited to the purpose it is designed for, and it is judged by its usefulness not for truth or falsity. — Metaphysician Undercover
First of all it is clear that you are OK that we can measure average velocity.I agree that for many practical purposes the use of averages is completely acceptable. — Metaphysician Undercover
Acceleration does not cause anything. No wonder you are confused. Acceleration is a change in the velocity of an object. An object can undergo acceleration by being acted on by a force (F = ma) or by being affected by the curvature of spacetime.But the acceleration itself, which is the cause of the body's motion has already occurred by the time the body is moving. — Metaphysician Undercover
So, the high speed cameral has limitations, and when we get to situations with things accelerating at an extremely rapid rate, in an extremely short period of time, as in the case of high energy physics, the high speed camera is inadequate. And, the fact that the assumption of "constant acceleration" is adequate and useful at low rates of acceleration where a small error is insignificant, is not proof that it would be adequate for high rates of acceleration where the small error would be greatly amplified. — Metaphysician Undercover
I was not any good at calculus, but I think calculus is what you are talking about. So question to you, MU: do you buy calculus? Or is that flawed and misleading? — tim wood
you're asking the right questions, except instead of saying "let's look at the data and check if the acceleration is going up and down wildly" you're just saying "oh well we can't know for sure so I give up, there's nothing left to discover."
Don't give up so quick, we have a lot of data from the camera. I mean, if you WANT to remain ignorant of the pattern of how things fall by gravity, then by all means give up here. But the rest of the world is operating on many centuries worth of physics past the point that you give up. — flannel jesus
I didn't give this bit the attention it deserves. You said "the fact that the assumption of "constant acceleration" is adequate and useful at low rates of acceleration" - that's wonderful! If you agree that it's useful and adequate enough at low rates of acceleration, then you've accepted the only thing I really wanted you to. Gravity accelerates things at 9m/s/s, on planet earth, at least for the low rates of acceleration that we measured. — flannel jesus
You go on to talk about other instances of acceleration that aren't directly caused by gravity, which I think it's fair to say is beside the point. The conversation is about how gravity accelerates things, not about how your leg muscles accelerate your own body. — flannel jesus
Precisely. And the purpose of the 10 million different measuring apparatuses (apparati?) is to measure velocity. So QED we are measuring velocity. And so the statement is true per CToT. We are not dealing with your metaphysical notions of truth or falsity here. And of course it is not 10 million. Duh. — EricH
Acceleration does not cause anything. No wonder you are confused. Acceleration is a change in the velocity of an object. An object can undergo acceleration by being acted on by a force (F = ma) or by being affected by the curvature of spacetime. — EricH
No matter how finely we chop up time - or how many different ways we chop up time - we get the same results. So this is a true statement:
The velocity of our object is increasing by 9.8 m/s every second within the limits of accuracy of our measuring devices.
Again, we are using CToT, not your metaphysical notions of truth. — EricH
So let's bring this zero point into your numerical expressions, and produce a "slice in time" which is the period between -.1s and +.1s. Do you agree that the averaging technique will not give a good representation of this time period? If you agree, then how do you propose that we deal with this period of time? — Metaphysician Undercover
This is why calculus is misleading, it has produced a very acceptable work-around for the problems first exposed as Zeno's paradoxes, which is very useful in a wide range of practises. However, since it does not actually resolve the problems of Zeno's paradoxes, these problems reappear, as the uncertainty principle for example, when we reach the limits of its applicability. If one insists that the problems have been resolved, then the true nature of the uncertainty principle will not be understood. — Metaphysician Undercover
Why would it fail to give a good representation? The only problem with our high speed camera data for this moment in time is that it has limited resolution, so we wouldn't necessarily be able to see how it starts moving at that moment in time (I've been rounding previous measurements of distance to 2 decimal places to sort of mimick the problem of camera resolution). — flannel jesus
Is calculus used to solve problems? — tim wood
And just what are the problems of Zeno's paradoxes? — tim wood
Achilleus gets where he's going, and faster than the tortoise. The arrow flies through the air and so forth. — tim wood
As to the arguments themselves. they all involve some faulty assumption. — tim wood
You produce the average, the speed for that time period, but this is obviously not a good representation. — Metaphysician Undercover
So the issue is that space and time are understood as infinitely divisible continuums, or one continuum, and so division of them, or it, may be completely arbitrary. This does not correspond with reality, hence Zeno's paradoxes. The proposed solution was "infinitesimals", but these were arbitrary, and therefore still not consistent with reality. Calculus bring "infinite" right into the mathematics, and this is a form of indefiniteness, hence uncertainty. — Metaphysician Undercover
A good representation of what? You keep saying things like "inadequate" or "not a good representation". Some measurements are adequate for some purposes and inadequate for other purposes. You can't just raw say it's inadequate, it can only be inadequate in relation to some goal. — flannel jesus
Now it's not like you gave me a specific goal and I said "all we need to do is measure the location at these points in time". — flannel jesus
In fact measuring them at those points in time was YOUR suggestion, not mine. Don't tell me it's inadequate - tell yourself. — flannel jesus
Infinite divisibility a convenient fiction in calculus... — tim wood
He supposes (reasonably for him we may suppose) there is an interval of time so short that within it the arrow is not moving. — tim wood
And so far I do not think I have written anything you do not know perfectly well, or disagree with. — tim wood
But that aided by keeping in mind that all the rules, laws, theories, and mathematics just attempts at representations of the world itself (-as-it-is-in-itself) expressed in terms of what people can understand. — tim wood
And you and I, and I suspect you and most people, attach an altogether different significance to what you call the "deficiencies." And yes, people often ignorantly refer to "points" in time. But calculus usually refers to the value of a variable as some input approaches a limit - no infinities, although they're approached, and no "points in time." And if Zeno wants to think in terms of points in time, what is that to us beyond an historical oddity - however reasonable it may have seemed to him at the time? And to be sure, "point in time" is easy to say, but were there actually such a thing, a durationless interval, then atomic motion would stop and everything on the instant collapse.It just gives us a convenient fiction. — Metaphysician Undercover
No, I'm telling you it's inadequate. I specifically requested those points in time to demonstrate to you, the inadequacy of your technique. — Metaphysician Undercover
So now you intentionally avoid that specified time period saying, 'that's not my problem, it's your problem, because I have no interest in that time period. — Metaphysician Undercover
And you and I, and I suspect you and most people, attach an altogether different significance to what you call the "deficiencies." And yes, people often ignorantly refer to "points" in time. But calculus usually refers to the value of a variable as some input approaches a limit - no infinities, although they're approached, and no "points in time." And if Zeno wants to think in terms of points in time, what is that to us beyond an historical oddity - however reasonable it may have seemed to him at the time? And to be sure, "point in time" is easy to say, but were there actually such a thing, a durationless interval, then atomic motion would stop and everything on the instant collapse. — tim wood
I think we're at an impasse. i think you hold that nothing can be measured exactly, of things subject to measurement, and thus all knowledge of such things is deficient and flawed. I — tim wood
If you ask me to figure out a way to get an answer, I can tell you, and THEN we can go into if the technique is adequate or not. Until then, your own problem with your own technique is something for you to work on with yourself, and it's not a criticism of me or any idea I've had. — flannel jesus
I'm completely happy to look at that time period too, you just never asked me a question about it. Instead of asking, you started telling me what I would do. You're doing things in the wrong order and being too hasty, making careless assumptions again. Slow down. — flannel jesus
That something is "accelerating" requires a multitude of measurements of velocity, and each measurement of velocity requires multiple determinations of spatial-temporal location. — Metaphysician Undercover
The concept of "acceleration" involves a fundamental philosophical problem. Acceleration is the rate of increase of velocity. So if an object goes from being at rest, to moving, there is a brief period of time where its "acceleration" is necessarily infinite. This is a fundamental measurement problem, and another form of the same problem is at the heart of the uncertainty principle of quantum physics, as the uncertainty relation between time and energy in the Fourier transform.
This problem was exposed by Aristotle as the incompatibility between the concept of "being" (static) and the concept of "becoming" (active). The way that modern physics deals with this problem, through the application of calculus does not resolve the problem. It simply veils the problem by allowing the unintelligible issue, infinity, to be present within the mathematical representation.
Now, the very same philosophical problem which Newton and his contemporaries had to deal with in the relationship between bodies, becomes paramount in modern physics in its relationships of energy. The issue though, is that Newton and his contemporaries were dealing with relatively long durations of time, so the methods of calculus were adequate for covering up this problem which only increases as the period of time is shortened. Now physicists are dealing with extremely short durations of time, so the uncertainty becomes very relevant and significant. That's what the time/energy uncertainty indicates, the shorter the time period, the more uncertain any determination of energy will be.
Accordingly, using the current mathematical conventions, such calculations of acceleration will never be done "beyond all reasonable doubt", because the current convention is to allow the unintelligible (infinite) to be a part of the mathematical representation.. — Metaphysician Undercover
And at the risk of trying your patience, what exactly are those flaws and deficiencies which justify your calling the "system" hypocritical? The reason I ask is that in sum you appear to be criticizing a tool, a tool which given appropriate inputs delivers results to an arbitrary degree of precision.I am pointing out the flaws and deficiencies and indicating that I believe a better system is possible. — Metaphysician Undercover
And at the risk of trying your patience, what exactly are those flaws and deficiencies which justify your calling the "system" hypocritical? The reason I ask is that in sum you appear to be criticizing a tool, a tool which given appropriate inputs delivers results to an arbitrary degree of precision. — tim wood
Seen the correct way, calculus, e.g., is neither flawed nor deficient, and certainly in no way hypocritical. Instead it is exact. In a sense then it is either all right or all wrong, and because all that it does is just what it does, then it must be all right. Further, since it gives answers to an arbitrary degree of precision, it is therefore in itself altogether correct. — tim wood
By that I meant that calculus is exact in what it does. Same formulas same inputs yield the same answers. — tim wood
And yes, people often ignorantly refer to "points" in time. But calculus usually refers to the value of a variable as some input approaches a limit - no infinities, although they're approached, and no "points in time". — tim wood
So, unless you can demonstrate that it is impossible to find a better system than the use of limits, then my activity of pointing to the flaws in this system and suggesting that we find a way to change this system, is very reasonable activity — Metaphysician Undercover
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