I think you've stated my case for me very well, flannel. "Approximate" with respect to a representation means near, or close to what is actually the case. This does not imply truth, but the contrary, it implies a lack, or deficiency of truth. So the fact of the matter is that we just do not have an accurate, precise, or truthful representation of what acceleration actually is. And that is exactly the deficiency which I've been claiming. — Metaphysician Undercover

If you choose to reject all evidence you could see, then you will of course always have that deficiency. You seem very committed to that deficiency. Other people, luckily for the rest of us, seem more committed to finding stuff out.

Truth - the true - and rigor are always wrt some standard that is itself "strictly exact or accurate." It is you who are confused on this point, that you apparently do not understand. If, for example, I say that the gross GNP for the UK in 2022 was $3,273.92B, adults will recognize two things - maybe more than two things, but at least two - 1) that it is extremely unlikely that the GNP is exactly that amount to the penny, and 2) assuming good metrics, GAAP, and honesty in reporting, the amount in question is "strictly exact and accurate."

And then there are those who will say, "We don't know to the penny and we cannot know to the penny, therefore it is silly to think we can know what the UK GNP is for the UK in 2022." And this would be you, MU, except you would take it to an even deeper and more absurd level, involving not merely economics but arithmetic and science. And in these making it clear you have a profound misunderstanding of these things.

Perhaps you imagine your truths in carved adamantine mounted on polished-granite Doric columns in a Platonic space somewhere, and being thus inaccessible, dismiss truth as not having any world-function value, being itself Platonic. And so this is not a horse, that is not a chair, nor that a tree, but all these, and all else, just poor imitations such that no truth appertains to them. Well guess what, you're just plain wrong and wrong-headed, and the proof and evidence is all the world's work that gets done using all kinds of truths. If you disagree, then how does all the world's work get done if absent truth?

If you choose to reject all evidence you could see, then you will of course always have that deficiency. — flannel jesus

I don't see how this is relevant. I am not rejecting any visible evidence, I am describing deficiencies of mathematical logic.

And this would be you, MU, — tim wood

Completely false representation. Strawman.

Perhaps you imagine your truths in carved adamantine mounted on polished-granite Doric columns in a Platonic space somewhere, and being thus inaccessible, dismiss truth as not having any world-function value, being itself Platonic. And so this is not a horse, that is not a chair, nor that a tree, but all these, and all else, just poor imitations such that no truth appertains to them. Well guess what, you're just plain wrong and wrong-headed, and the proof and evidence is all the world's work that gets done using all kinds of truths. If you disagree, then how does all the world's work get done if absent truth? — tim wood

Sorry tim, I have no idea how this nonsense is in any way relevant. I've already explained how pragmatic principles are not necessarily truths. So your question has already been answered.

I get it. No two things are ever the same. Nothing is ever measured exactly, nor can it be. But if I want to buy a pallet of 8' 2x4s per spec., I will get them, "rigorous and exact" per specification. And will it then be true to say they are 8' 2x4s, and will they truly be 8' 2x4s? Of course they will. And you may come in and say, "Oh no, they're not the same and there is no way to tell if they're even 8' 2x4s: this one is three one-millionths of an inch longer than that one, and that one,...& etc."

And you will insist that you are correct, and I hold there are three responses to you. First, that you're wrong. By the applicable criteria, they are 8' 2x4s, period. Second, that you are in a very narrow sense correct, but uselessly so. With the lumber, for example, your argument is just a pig-in-the-parlor, the wrong animal in the wrong place at the wrong time. Third you are vacuously correct, in that if you insist on one inappropriate standard, then all are equally valid. Then you are headfirst down a rabbit-hole trying to say something, anything, intelligible and correct, but you have made that either empty or impossible.

The true - or truth - is not some Platonic ideal perfection: it is rather a measure of efficacy. And if you disagree, then in addition to being nonsensical, you obviously do not believe in God. (Nor will being a non-believer magically make you correct.)

I don't see how this is relevant. I am not rejecting any visible evidence — Metaphysician Undercover

You sure are, and you seem proud of it. That's your right, of course. Science doesn't speak to you, and you don't speak to it. I would say it's unfortunate that you would just remove all scientific knowledge from being a viable part of your own knowledge, but you seem happy enough with the decision.

I am increasingly thinking of 'truth' as a misleading and undefinable concept. For one thing, just because some statement are true, that does not provide a reason for postulating that there is a meaningful abstract noun 'truth'. 'True' is (at most) a predicate, an adjective modifying the proposition being discussed - making it a noun is simple reification. Defining 'truth' only creates a 'thing' that we can argue about. We can instead ask 'What does it mean for a proposition to be true?'. Secondly, in science, 'truth' was replaced by 'certainty' by Descartes, which was later replaced by 'confidence', reflecting the lack of total certainty of anything other than that, updating Descartes, 'there is thinking, therefore there is thinking'. Describing something as 8 ft long means that we expect, with 95% confidence, that the length of the 2x4 is between 8 - delta and 8 + delta feet long, where delta is situation specific, and can be either explicit or specified.

Interesting discussion of how we characterise objects in 'Women, Fire and Dangerous Things' by Lakoff. A tree is recognised as a tree because it is similar to objects that have been previously characterised as trees.

I get it. No two things are ever the same. Nothing is ever measured exactly, nor can it be. But if I want to buy a pallet of 8' 2x4s per spec., I will get them, "rigorous and exact" per specification. And will it then be true to say they are 8' 2x4s, and will they truly be 8' 2x4s? Of course they will. And you may come in and say, "Oh no, they're not the same and there is no way to tell if they're even 8' 2x4s: this one is three one-millionths of an inch longer than that one, and that one,...& etc." — tim wood

Measurement of static objects is not the same as measurements of motions, so your example is not analogous, as the problem I was discussing, the issue of acceleration, does not occur. As for the 2x4s being "the same", they are clearly not the same in any rigorous application of the law of identity. They are similar, as things of "the same type" are similar.

And you will insist that you are correct, and I hold there are three responses to you. First, that you're wrong. By the applicable criteria, they are 8' 2x4s, period. Second, that you are in a very narrow sense correct, but uselessly so. With the lumber, for example, your argument is just a pig-in-the-parlor, the wrong animal in the wrong place at the wrong time. Third you are vacuously correct, in that if you insist on one inappropriate standard, then all are equally valid. Then you are headfirst down a rabbit-hole trying to say something, anything, intelligible and correct, but you have made that either empty or impossible. — tim wood

Here you contradict yourself. You say I am "vacuously" correct, and you say I am "uselessly" correct, Also you say I am "wrong". Your claim that I am wrong is not justified though. That "they are 8' 2x4s, period" means that they are all the same type, just like we are all human beings. It does not mean that they are all the same. Do you not understand the difference between being of the same type, and being the same thing?

And, the fact that you judge my correctness as unimportant or insignificant, is irrelevant to the fact that I am correct. You, like flannel jesus, simply refuse to respect the evidence which demonstrates that this problem in specific circumstances, has a significant effect on certainty. And as points out, certainty is very important to us.

You sure are, and you seem proud of it. That's your right, of course. Science doesn't speak to you, and you don't speak to it. I would say it's unfortunate that you would just remove all scientific knowledge from being a viable part of your own knowledge, but you seem happy enough with the decision. — flannel jesus

Hey, you gave me the example, as "evidence", and I showed complete respect for that evidence. The I showed you the problem, which you dismissed as a matter of approximation. That approximation becomes a significant problem under specific circumstances. So it's not me who is rejecting the evidence, it is you who is rejecting the evidence. You gave me the example, I showed you the problem within your example.

If you are interested in continuing, and examining the implications of this problem we could. Tim, above, seems to think that identifying such problems is useless, "vacuous", but as I said earlier, this very problem produces the Fourier uncertainty which forms the base of "the uncertainty principle". So denying that there is a problem, is really a denial of the evidence, and claiming that the problem is insignificant is a refusal to accept the evidence.

That approximation becomes a significant problem under specific circumstances. — Metaphysician Undercover

No, it really doesn't. If you know the location of something at 1s, and the location of the same thing at 2s, you made the logical leap of assuming that means it had a constant speed over that duration, rather than the much more carefully thought out concept that you have the AVERAGE speed over that duration. You're making careless logical leaps and then acting as if you've disproven physics.

It doesn't matter what problem you think there is with the example, if the measurements are real measurements that real people really obtained. These are, in fact, the sort of realistic measurements one could make to verify how the speed of a falling ball changes over time.

I'd only be interested in examining the implications with you on the condition that you accept the measurements as real raw data.

If you think it's impossible for that to be valid raw data, then feel free to show me what the raw data of a ball falling really looks like.

No, that's what Ive been arguing, we really do not know the true physical properties of objects. I — Metaphysician Undercover

This is not the Correspondence Theory of Truth - you have introduced the metaphysical concept of truth into the mix. If you and I are traveling in a car together and the digital display shows that the car is going 60 mph and I utter the statement "The car is going 60 mph according to the speedometer". then that is a true statement. And if you are in the back seat looking over my shoulder and say "The speedometer shows that the car is going 60 mph". then we have a mutual shared understanding and agree.

Whether the speedometer is accurate or not is irrelevant to whether the statement is true or false.

No, it really doesn't. If you know the location of something at 1s, and the location of the same thing at 2s, you made the logical leap of assuming that means it had a constant speed over that duration, rather than the much more carefully thought out concept that you have the AVERAGE speed over that duration. You're making careless logical leaps and then acting as if you've disproven physics. — flannel jesus

As you said already, that "AVERAGE speed" is just an approximation. It does not accurately represent the motion of the thing over that period of time, because during that period of time the thing was accelerating. That is exactly what I am arguing, we do not have an accurate representation of acceleration. To represent a thing's average speed in the time between 1s and 2s, is not a good representation of acceleration.

It doesn't matter what problem you think there is with the example, if the measurements are real measurements that real people really obtained. These are, in fact, the sort of realistic measurements one could make to verify how the speed of a falling ball changes over time — flannel jesus

Sure, they are "real measurements, but the fact remains, that representing a thing's average speed over a period of time, does not provide a good representation of acceleration.

I'd only be interested in examining the implications with you on the condition that you accept the measurements as real raw data. — flannel jesus

I accept that these measurements can be made. But as I said, the problem is with the mathematical way of calculating. So the real question is, are you ready to accept the flaws which I have pointed out. It seems to me, like you just want to try to explain them away, by choosing different words. First you used "approximate", then when I showed you the problem with approximation, you then switched to "average".. It really makes no difference which words you choose, because the problem is very real, and you cannot make it go away by using different words to describe it.

This is not the Correspondence Theory of Truth - you have introduced the metaphysical concept of truth into the mix. If you and I are traveling in a car together and the digital display shows that the car is going 60 mph and I utter the statement "The car is going 60 mph according to the speedometer". then that is a true statement. And if you are in the back seat looking over my shoulder and say "The speedometer shows that the car is going 60 mph". then we have a mutual shared understanding and agree.

Whether the speedometer is accurate or not is irrelevant to whether the statement is true or false. — EricH

I disagree. If the speedometer is faulty, then the car is not going 60mph according to the speedometer. The speedometer is incapable of determining the speed of the car, therefore the reading does not accord with the speed and there is no such thing as 'the speed of the car "according to the speedometer". Your use of words is just trickery Eric. Face the fact, when the speedometer is broken there is no such thing as the speed of the car according to the speedometer.

OK I'll modify the statement to meet your exacting standards. Instead of this:.

"The car is going 60 mph according to the speedometer" — EricH

we'll say this

"The digital readout on the speedometer shows 60 mph"

:yawn:

So the real question is, are you ready to accept the flaws which I have pointed out. — Metaphysician Undercover

You haven't pointed out any logical flaws. You've made careless logical leaps that I've pointed out, and you haven't accepted the logical flaws in what you said .

Do you accept that leaping to "constant speed" was a careless logical flaw?

Well, look what you have shown me. Between .9s and and 1.1s the object was moving at a constant speed. Then it accelerated between 1.1s and 1.9s. Then between 1.9s and 2.2s it moved at a constant speed again. — Metaphysician Undercover

I won't accept your criticism that I said it's an average speed while you're out here making completely absurd conclusions like it's a constant speed. Let's get that out of the way first.

we'll say this

"The digital readout on the speedometer shows 60 mph" — EricH

This says nothing about the problem we're discussing.

You haven't pointed out any logical flaws. You've made careless logical leaps that I've pointed out, and you haven't accepted the logical flaws in what you said .

Do you accept that leaping to "constant speed" was a careless logical flaw? — flannel jesus

Sure. "constant speed" was a bad use of terms, But "approximate", and "average" do not imply that the speed was anything other than constant. You have provided no representation of the movement of the object during that time period. This is the problem, you have no indication of what the object was actually doing during that time period, no representation of 'the movement of the object'. You have provided two different positions at two different times, and the object was said to be moving as it past each position, that's all Now you insist that "constant} is not a proper representation of the object's speed during that time, but you have provided no representation of a non-constant motion.

That is what I say is the problem, there is no representation of a non-constant speed. Newtonian mechanics takes constant speed (uniform motion) for granted, in his first law. A change to constant speed requires an application of force. But because uniform motion is taken for granted, the application of force cannot be properly understood. It is just represented as a change to uniform motion.

So. let's proceed as you suggest, and consider that "constant speed", or "uniform motion" is a careless logical principle. It does not actually represent anything real in the universe. It's just an ideal, and real motions are always changing all the time, so that this ideal is not a proper representation of any real motion.

Now look what you gave me.

So we find out that in that 0.2s time frame, it travelled about 1.96m, which means it was going about 9.8m/s. — flannel jesus

You provide two different positions and the thing was moving as it passed each position, and you've provided a time of passing, that's all Now you insist that "constant speed" is inappropriate for the duration. That's fine, as explained above, constant speed is just an ideal, and motion is really changing all the time. But all you have is "it was going about 9.8m/s" during that time period:. This indicates one speed during that entire time period, and we agree that "constant speed" is an inadequate representation. Do you not also agree with me, that "going about 9.8m/s" is a completely inadequate representation of what is actually going on in that time period?

Sure. "constant speed" was a bad use of terms — Metaphysician Undercover

I really respect you for saying this, wonderful.

But "approximate", and "average" do not imply that the speed was anything other than constant. — Metaphysician Undercover

That's right, they don't imply that, that's part of why they work. They don't imply much at all. They're just simple truths given the data, no extra implication.

Now you insist that "constant} is not a proper representation of the object's speed during that time, but you have provided no representation of a non-constant motion. — Metaphysician Undercover

I didn't say it's not constant either, you're still making logical leaps. Slow down.

But all you have is "it was going about 9.8m/s" during that time period:. This indicates one speed during that entire time period, and we agree that "constant speed" is an inadequate representation. Do you not also agree with me, that "going about 9.8m/s" is a completely inadequate representation of what is actually going on in that time period? — Metaphysician Undercover

Inadequate compared to what? Google "how to calculate average speed". The first result gives me "It is calculated by dividing the total distance something travels by the total amount of time it spends traveling." In fact many Google results give me that. That's what I was trying to calculate. I don't see why it's inadequate, it achieved the exact goal that I wanted it for. I now have the average speed for the .2 seconds timeframe around the 1 second mark, the 2 seconds mark, etc. That's what I wanted, that's what I got. It's perfectly adequate for achieving the goal I was hoping to achieve.

Sure. "constant speed" was a bad use of terms, But "approximate", and "average" do not imply that the speed was anything other than constant. You have provided no representation of the movement of the object during that time period. — Metaphysician Undercover

Everyone else who has been involved in this discussions understands that the ball is accelerating continuously in the scenario under consideration. Your lack of comprehension is not caused by the other people in the discussion.

This says nothing about the problem we're discussing. — Metaphysician Undercover

One step at a time. Do you acknowledge that "The readout on my speedometer shows 60 mph" is a true statement per the CToT?

No, that's what I've been arguing, we really do not know the true physical properties of objects. — Metaphysician Undercover

Well, this has to be defined, and is meaningless until defined. But let's grant it as an hypothesis. Further, that no two separate things are or ever can be the same in any way. That means we need a unique identifier for every single thing (and for every single moment because everything is always changing). And of course that is not how the world works, at all.

So it becomes a matter of abstracting and recognizing similarities and differences, and naming them. Once named (and those names used appropriately) the names become truth-bearers. That is a chair, this is a tree, that is a 2x4. And so with speed, acceleration, and every quantity and quality - all of Aristotle's accidents.

MU apparently disqualifies naming. We cannot name anything because we do not know what it is. Thus names are inaccurate, misleading, or just plain wrong. And there is a layer-cake of problems with this view. First, to say that something is cold, or hard, or accelerating is arguably subjective in itself, thus meaningless in terms of the world as the world is in-itself-as-itself. But at the same time altogether true as the judgment of a competent judge. Second, as a statement about an abstract concept or quality, it must be true (appropriately stated by a competent judge & etc.). Third, if MU is right, nothing can be said about anything - and MU, if he had any intellectual integrity, would content himself with just pointing, and otherwise remain silent. But he speaks, thus implying that he knows what he avers cannot be known - and since he knows it cannot be known, he says with his mouth what his mind knows to be untrue. Aristotle has a name for that: lying.

Or more charitably, an inappropriate and disruptive display at the wrong time in the wrong place, and the persistence in which simply identifies the pig in the parlor.

Inadequate compared to what? — flannel jesus

It's inadequate as a representation of what is actually going on. So it is inadequate in comparison to what a true representation of what is actually going on would provide. "Average" is simply not an accurate or rigorous representation of what is the case. When it is used as a representation of what is the case, it is a sort of estimation. In your own words, it is "approximate".

Consider that to "average" is to take many times, and express it as one time, that one time being the average of the many. So for example, if the sun rises between 6;00 and 6:30 for twenty days in a row, and you take the average, it would be 6:15. The you would say that the average over all those days is 6:15. But obviously, averaging is a completely inaccurate way of trying to represent what is actually going on. Now, in your .2 duration of time, there are numerous different points of time, each of which has the thing moving at a different speed from the others, and you come up with one speed which, 9.8m/s, which is supposed to apply to all those points of time. Just like in the example of the different sunrise time, giving the same value to numerous different times, as the average of those times, is obviously extremely inaccurate.

I don't see why it's inadequate, it achieved the exact goal that I wanted it for. I now have the average speed for the .2 seconds timeframe around the 1 second mark, the 2 seconds mark, etc. That's what I wanted, that's what I got. It's perfectly adequate for achieving the goal I was hoping to achieve. — flannel jesus

It may be what you wanted, but it's useless as a means to resolving the problem I'm trying to bring to your attention. You now have a period of time, .2 seconds duration, with an average speed of 9.8 m/s during that period of time. How do you think that a determination of an average speed is at all useful toward representing acceleration?

Remember what you said to me "constant" is "a careless logical flaw". Therefore we cannot assume that the acceleration during this time period is in any way constant, because that would be a careless logical flaw. So how do you think that determining an average speed over a period of time would be at all useful toward making an accurate representation of the acceleration which occurred during that time frame?

Everyone else who has been involved in this discussions understands that the ball is accelerating continuously in the scenario under consideration. — wonderer1

This use of "continuously" is more accurately stated as "constantly", and that is what flannel has described as "a careless logical flaw".

One step at a time. Do you acknowledge that "The readout on my speedometer shows 60 mph" is a true statement per the CToT? — EricH

Sure, if that's what's there on the screen, then I agree, that's a true representation. The issue is one of interpretation though. Your claim was that this readout means that according to the speedometer the car is going 60mph. But that is not what that readout actually means, it's a faulty interpretation of what the readout means.

MU apparently disqualifies naming. We cannot name anything because we do not know what it is. — tim wood

Tim, we do not need to know what a thing is in order to name it. Just point to a thing, and assign a word, or words to it. Then the thing has a name even though there might be no one who knows what it is.

Third, if MU is right, nothing can be said about anything - and MU, if he had any intellectual integrity, would content himself with just pointing, and otherwise remain silent. — tim wood

Of course this is wrong too. After naming the thing we can say whatever we want about it, compare it to other things that have also been named, and so on. None of this requires knowing what the thing is. We do all sorts of talking about things without knowing what they are, that's how we learn. If we had to know everything before we could say anything, how could one every get to that state of being able to say anything?

After naming the thing we can say whatever we want about it, compare it to other things that have also been named, and so on. — Metaphysician Undercover

Indeed we can and do. And there is a truth function to all of this. If (as a competent judge) someone says the car is traveling at 60 mph, then it is. How fast is it traveling exactly? No one knows or will ever know. Thus to cavil and argue that the car is not traveling at 60 mph, and therefore it is wrong, or cannot be truly said that that it is, is to engage in disruptive absurdities. After all, near the equator the car would be moving at about 25,000 mph. Add in planetary, system, and galactic motion, and who knows.

It's inadequate as a representation of what is actually going on. — Metaphysician Undercover

It's not a "representation of what's going on". It's a measurement of its position at two points in time, and a calculation of it's average velocity between those two points in time. Of course it's inadequate for a job it's not meant for, and a job it's not doing. You're inadequate for swimming deep underwater without equipment for hours at a time. Everything is inadequate for something, that goes without saying.

How do you think that a determination of an average speed is at all useful toward representing acceleration? — Metaphysician Undercover

If you determine an average speed around one second and an average speed around another second, you can ascertain how much it accelerated or decelerated between those seconds, which is what I did.

If at second one it was going X m/s, on average given the surrounding .2s, and at second two it was going Y m/s, on average given the surrounding .2s, then between 1s and 2s it must have accelerated or decelerated a certain amount. And we could even verify that by looking at some .2s intervals between 1s and 2s. We have the data from the high speed camera, we can just look you know. 1.1s - 1.3s, what was the average velocity? 1.3-1.5, 1.5-1.7, 1.7-1.9. We can just do the same process and look.

You're trying to go too fast. You can go slow. We have the data from a high speed camera, we can take our time analysing it. You don't need to have a "perfect representation of everything immediately", which is what you seem to want. Just take it slow.

I took it slow and just built up a couple facts. Those couple facts were, around the 1s mark it was going about 9.8m/s, around the 2s mark it was going about 19.6m/s, etc. I'm not building a perfect representation here, I'm just looking at some facts.

It's a measurement of its position at two points in time, and a calculation of it's average velocity between those two points in time. Of course it's inadequate for a job it's not meant for, and a job it's not doing. — flannel jesus

A calculation of average velocity is inadequate for producing a measurement of acceleration, and this is the "job" we are discussing and "the job it is meant for" in your example. Do you not agree?

If you determine an average speed around one second and an average speed around another second, you can ascertain how much it accelerated or decelerated between those seconds, which is what I did. — flannel jesus

That requires the assumption of "constant" acceleration which is a careless logical flaw, in your own words. And in reality, in real physical circumstances the evidence shows that acceleration is never constant in that way because of conflicting forces, like air resistance. The claim that acceleration in a vacuum is constant is completely unproven because of this faulty way of calculating it, which already assumes that it is (begs the question).

If at second one it was going X m/s, on average given the surrounding .2s, and at second two it was going Y m/s, on average given the surrounding .2s, then between 1s and 2s it must have accelerated or decelerated a certain amount. And we could even verify that by looking at some .2s intervals between 1s and 2s. We have the data from the high speed camera, we can just look you know. 1.1s - 1.3s, what was the average velocity? 1.3-1.5, 1.5-1.7, 1.7-1.9. We can just do the same process and look. — flannel jesus

Now you are taking a number of averages, each one having the problem I described, and making a further average, so you now amplify the problem

I agree that for many practical purposes the use of averages is completely acceptable. But this is not what we are discussing. We are discussing whether this use of averages provides a truthful representation, and if not, then what problems arise from trying to use it where it is inadequate.

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.

You're trying to go too fast. You can go slow. We have the data from a high speed camera, we can take our time analysing it. You don't need to have a "perfect representation of everything immediately", which is what you seem to want. Just take it slow. — flannel jesus

Listen jesus, I am a natural living body, and I accelerate in an extremely unpredictable way. That's a feature of living bodies. Now, you can tell me to slow down, take it slow, but if I'm already accelerated, then it too late to prevent that acceleration which has already occurred.

This is very indicative of your attitude toward the problem of acceleration. You seem to believe that we can take measurements of the body in motion, and make averages of that motion, and say that this constitutes a measurement of the cause of that motion (acceleration). But the acceleration itself, which is the cause of the body's motion has already occurred by the time the body is moving.

So you refuse to even get close to the problem I originally brought up. The highest rate of acceleration occurs at the point in time when the body changes from being at rest to being in motion, the point when it starts to move. Do you agree, that this point in time, when motion starts, marks the highest rate of acceleration? But you cannot show this with your averaging method.

I took it slow and just built up a couple facts. — flannel jesus

Your supposed "facts" are averages, and averages are a form of estimation, which is inadequate for a rigorous, accurate, or precise measurement. So when you assume that an average is a fact, you need to account for the fact of what an average is. An average is a generalization produced from a number of instances of occurrence, which does not say anything true about any particular instance. "Truth" concerning generalizations is categorically different from "truth" concerning particular things or events.

That requires the assumption of "constant" acceleration — Metaphysician Undercover

Says who? I didn't say that. This isn't careless from me, this is careless from you.

So far in my analysis, I've just looked at a couple slices in time and calculated the average velocity for that slice. We don't have to jump ahead, we have some average velocities. We can look at them, make some intuitive ideas about what they might mean and then look at more data and see if our intuitions continue to hold. That's a pretty natural progression. We don't have to jump to conclusions, we can instead jump to intuitions and then question our intuitions by looking at more data.

It seems like you have a philosophical problem with measuring things and coming to any conclusion at all based on those measurements. That's not a problem for me. Perhaps this is why science doesn't speak to you, and you don't speak to science.

Science is a little messy. Measurements are a little messy. I don't have a problem with that. That's just the reality we have to deal with. If you struggle with that, perhaps that's why your idea of physics is centuries behind everyone else.

Sure, if that's what's there on the screen, then I agree, that's a true representation. The issue is one of interpretation though. Your claim was that this readout means that according to the speedometer the car is going 60mph. But that is not what that readout actually means, it's a faulty interpretation of what the readout means. — Metaphysician Undercover

Agree that my speedometer could be broken and be a faulty representation. But now my car has 10 million speedometers (it's a very large car) and they all show 60 mph. Is it possible that all 10 million are broken? Well you can't rule it out, but it is reasonable to say that all 10 million can't be broken in exactly the same way.

So is it possible that there is a design flaw in the speedometers and the value is wrong? Well duh, of course it's possible. However I can look out the window of my large car (my car has windows) and I can verify using my eyes that indeed the car is moving. And I open a window and use my handheld velocity checker to verify the 60 mph. I can stick my hand outside the window and feel the wind. I can temporarily unbuckle my seat belt, stick my head out the window and see the tires moving.

So it is clear that the car is moving. Or is it? Uh-oh, maybe I missed something . . .

Is it possible that the car is standing still and somehow we have arranged it so that it appears that the scenery and the road are moving while the car is standing still? Sitting inside my car I can't rule it out - it's theoretically possible. But there are 10 million people outside the car observing the car move and they are verifying (all using different mechanisms to measure velocity) that my car is going 60 mph.

Is it possible that the outside observers are in fact moving and the car is standing still? They stick their fingers in the air and they feel no movement in the air.

Is it theoretically possible that somehow you have arranged this experiment so that the observers are moving at 60 mph but they do not feel any air moving? Possible, but then when they entered the experimental apparatus they would have felt some acceleration through their inner ears when they started moving (our inner ears can detect acceleration). OK - maybe when the observers entered our experimental apparatus the were standing still and we accelerated up to 60 mph very slowly so the acceleration did not register in their inner ears. Or maybe we secretly drugged them before they entered the experimental apparatus and disabled their inner ears.

So is it possible that those observers are unaware that they are the ones who are moving 60 mph and the car is standing still? We can't logically rule it out (we can always add another absurd hypothetical into the mix).

However, per the CToT there is a true statement here:

"Within the accuracy of our measuring apparatus the car is moving 60 mph relative to it's outside environment".

I call attention to this most recent thread OP that likely you-all have noticed:
"Explaining Bell violations from a statistical / stochastic quantum interpretation."

Long and impressive. And imo much value in sections 4 and 5.

Fascinating stuff - I don't have the time/energy to fully delve into it.

BTW, here's the link: https://thephilosophyforum.com/discussion/14659/page/p1

[edit]. I also recommend the latest Scientific American special issue "Mind Bending Physics". Good article on Bell (among other things).

So far in my analysis, I've just looked at a couple slices in time and calculated the average velocity for that slice. — flannel jesus

You are calculating the acceleration. That is the subject being discussed. The average velocity from a slice in time cannot be used in your calculation without the assumption that the acceleration in that slice is constant. Suppose that within that slice of time, the velocity varied greatly, perhaps even up and down. Then your average is completely useless as an indication of the real acceleration which is occurring. Therefore the technique is unreliable from the outset. It is only useful under the assumption of constancy.

You are the one going to fast, trying to sneak past the problem with using averages. There is no need to go any further than this, you need to look at the problem of averaging, and accept it. As you yourself explicitly stated, we cannot assume that the motion represented by the average is in any sense constant. That would be a serious logical flaw. Therefore any further extrapolations will not be able to prove anything about the acceleration within any of those slices in time, because it will be hidden by the averaging process. Do you agree with this?

So, do you agree that it is very possible that the rate of change to the speed of the thing (acceleration/deceleration) is extremely unstable within the small parts of those "slices in time"? Furthermore, since any such averaging requires a duration in time, and any duration can be broken down into shorter time periods, this problem inheres within the nature of that technique. The problem is intrinsic to the technique and is unavoidable. So it is impossible that the technique can give us a reliable representation of acceleration. And in our world of high energy practices, the most important and significant accelerations occur in very short slices of time, and this is where that technique of averaging becomes extremely inadequate.

It seems like you have a philosophical problem with measuring things and coming to any conclusion at all based on those measurements. That's not a problem for me. Perhaps this is why science doesn't speak to you, and you don't speak to science.

Science is a little messy. Measurements are a little messy. I don't have a problem with that. That's just the reality we have to deal with. If you struggle with that, perhaps that's why your idea of physics is centuries behind everyone else. — flannel jesus

I work in a field where the better the measurement is, the better the job is. So I've learned that it is always a good idea to keep looking for, and finding, new ways to clean up the bad habits of messy measurements.

Well you can't rule it out, but it is reasonable to say that all 10 million can't be broken in exactly the same way. — EricH

Unless each speedometer measures the velocity in a different way, it's very likely that they would all be inaccurate in the same way. For instance, if the car had the wrong size tires on. But for the sake of argument, let's say that each speedometer used a different technique to show the speed. Do you agree that if they each worked as intended, it's highly unlikely that they would ever all show the exact same thing, unless perhaps that might occur if the car was parked, and there was no wind, and the earth stopped spinning? !0 million different ways to measure the speed would take some serious innovations.

And I don't see the relevance of your long winded post.

However, per the CToT there is a true statement here:

"Within the accuracy of our measuring apparatus the car is moving 60 mph relative to it's outside environment". — EricH

I don't see why I'm supposed to agree to this. All measurements are fundamentally subjective, and so measuring apparatuses apply principles which are somewhat arbitrary, therefore statements about "the accuracy of our measuring apparatus" are not truth-apt. As I mentioned already, measurement principles are pragmatic, they are designed for specific purposes. 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.

Furthermore, since any such averaging requires a duration in time, and any duration can be broken down into shorter time periods, this problem inheres within the nature of that technique. — 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?

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.