As I read these, there's a failure to distinguish between what we might call a map co-ordinate and a dimension/duration. — tim wood

The problem is that there is no specific real thing, in physics, which corresponds with "duration". Duration is simply a relation between one activity and another, and as a relation it is a feature of the coordinate system employed. That is why there is serious ontological discussion as to whether time is real or not, and the general consensus is that the principles employed in physics assume that time is not real.

In physics, time is defined by its measurement: time is what a clock reads. — Wikipedia

Notice, a clock does not read time, people read time with the use of a clock. So it's just like any other measurement. If I measure between the house and the car, the reading, 50 meters for example, is part of the map. Likewise with time and also "duration". In physics duration is part of the map, as a measurement.

Since the measurement of time is just a number of 'units' produced by relating one activity to another, physicists have no idea of what is actually being measured. The 'units' are completely artificial. The tendency is to claim that there is nothing real, and time is an illusion. This effectively avoids the issue. But any physicist (more correctly metaphysician), who wants to understand the reality of what is being measured, is confronted with the question of what constitutes a real unit of time.

The problem with the declaration that points in time are unreal is that the photoelectric effect demonstrates that there must be very real points in time. The way that electrons react to electromagnetic radiation indicates that there must be a point in time when an electron is emitted. The emission occurs as a "quantum" of energy at a determinate point in time, rather than as a continuous flow of energy.

The fact that we have not been able to understand or properly identify these real points in time manifests as the misunderstanding of the wave function collapse. The collapse must be in some sense real because it is observable, but since the conventional employment of points in time is done through arbitrariness rather than correspondence, as points are apprehended as unreal, the result is many worlds, according to many possible points. On the other hand, complete denial of the reality of points in time produces a continuous wave function with no possibility for any real points of collapse.

So what are you saying, the principle of maximum entropy allows you to derive something other than a 50/50 distribution, by adding in a measurement of energy? I thought you said that the principle of maximum entropy would produce a 50/50 distribution as the least biased.

What does "beta" stand for in the energy measurement?

At its core, the maximum entropy principle can be viewed as a natural generalization of assigning equal probability to equally likely events. — Alexandre Harvey-Tremblay

I'm having a hard time grasping your explanation of the maximum entropy principle. Isn't it the case that "equal probability" and "equally likely" are synonymous? How could anyone ever assign a probability other than equal probability to events which they apprehended as equally likely? And if they assigned unequal probability this would signify that the events are not considered to be equally likely. So I can't see that you are telling me anything.

Since we're talking about it, I also once saw Sonia Sotomayor at a very fancy restaurant in DC; Arlo Guthrie sitting on a bench in Harvard Square Cambridge; Richard Dryfus in the Baskin Robins in Central Square Cambridge where I was working; Michael Dukakis riding on the Green Line subway in Boston, which was no big deal because he rode the T to work every day when he was governor; and Godfrey Cambridge in NYC. — T Clark

Sure you did T.C., just like i saw drug references in Merry Poppins.

Just generally, the Wittgenstein you talk about bears little resemblance to the one with which I am familiar. — Banno

Par for any commentary on Wittgenstein. Each and every one of us is familiar with a different Wittgenstein. Add to that the premise that multiple interpretations are most often caused by ambiguity from the author, and the logical inference is that Wittgenstein is very likely highly ambiguous. Therefore the direction of discussion in a focused commentary on Wittgenstein ought to be the question of how to distinguish intention behind ambiguity, and, the relevance of the intentional use of ambiguity in philosophy. And here we find issues like what type of rhetoric ought the intentional use of ambiguity be classified as, is this a form of "sophistry", "deception", etc..

I remember Royal Crown Cola, — T Clark

Good old Arsey Cola, with a name like that, no wonder they didn't go far. Or did they? I think they merged with Dr Pepper or something like that. Now they're boosting the caffeine level, an energy drink is much better suited for the name "arsey". If I was 15 again, I'd buy it for the name.

To elucidate with an example: suppose you have a constraint that a coin can either yield heads or tails. The methodology I employ, based on the principle of maximum entropy, would produce a 50%/50% probability measure as the least biased. Now, if you were to claim that the correct probability is in fact 40%/60%, you'd need a solid empirical basis for such a claim. If the only constraint is that the coin can yield either outcome, claiming a 40%/60% distribution introduces a bias not supported by the given constraint via the principle. The set of all possible distribution includes all possible values of X/Y including those that are not 50/50. The principle claims the 50/50 measure has the least bias. This is a trivial example, but for more complex systems, the solution to the Lagrange equation provides the expression of this measure. — Alexandre Harvey-Tremblay

Can you demonstrate how application of the maximum entropy principle arrives at the 50/50 probability rather than 40/60, or something else? Here, you just say the method "would produce a 50%/50% probability measure as the least biased", and you say a 40/60 distribution would require support from empirical evidence. So the implication is that empirical evidence is what backs up the 50/50 claim. So how is this not just a case of applying statistics gathered from empirical evidence to produce probabilities? And isn't this just the normal way of producing probabilities, from statistics gathered from empirical evidence? I don't see how "maximum entropy" enters the scenario.

The "uncertainty" you're discussing is not about subjective interpretations but about the inherent probabilistic nature due to the variability of microscopic states. — Alexandre Harvey-Tremblay

How can you claim to know this though? Even if a multitude of subjects agree on the description, the description, as a description, is inherently subjective (of the subject). So the appearance of the "probabilistic nature" may still be the product of a faulty description. The description might make it appear like there is an inherent probabilistic nature, when there really is not. Even if all the people agree on the constraints, the probabilistic nature might still be due to uncertainty within the description.

Because of this, I don't think you can call this a "least biased" position at all. All you are doing is replacing individualistic biases with systemic or conventional biases. The real issue with quantum uncertainties is our inability to describe what is observed. Sure there are conventions for making such descriptions, but even your words, "microscopic states", betrays this problem of description, because these are not states at all, but activities. So there is a problem already inherent within this convention of portraying activity as states. And, the "variability of microscopic states" is just a product of the fact that these so-called states are not states at all, but activity, and we're attempting to describe this activity as states.

It's not that multiple observers would perceive different uncertainties; rather, given the same empirical data and constraints, the method produces a consistent and unique probability distribution that reflects the maximum entropy (least biased) given what we know. — Alexandre Harvey-Tremblay

So the phrase "given what we know" reveals the issue. If all we know is the statistics, then all you are doing is producing probabilities based on statistics. How is this any different from any other way of producing a probability distribution?

Entropy maximization is a principle used in statistical mechanics to derive probability distributions that are least biased given certain constraints. The idea is rooted in the maximization of the Boltzmann entropy while adhering to constraints that reflect empirical observations. In the context of statistical mechanics, this leads to the derivation of the Gibbs measure, which provides a probability measure for predicting outcomes of energy measurements. — Alexandre Harvey-Tremblay

OK, so tell me if I understand correctly.

A "probability distribution" is a set of possible outcomes. What you seem to be saying is that there is the possibility of producing numerous different probability distributions from the same set of constraints. Therefore you need some principle as to which probability distribution ought to be selected. I'd say you do not have the required constraints if you wanted to proceed further, and make a probability distribution of probability distributions, and that would produce an infinite regress of uncertainty anyway, so you employ the entropy maximization principle.

This principle stipulates that you choose the probability distribution which best represents the uncertainty relative to the constraints which are representative of the situation; the uncertainty being the reason why there is a multitude of possible probability distributions in the first place. So the "empirical observations" you refer to, have uncertainty inherent within them. The probability distribution which best represents this uncertainty is the best probability distribution to choose.

If this is the case, what tool do you use to identify the uncertainty? If the uncertainty is inherent within the observations, and the observations are a feature of the subject observing, wouldn't any determination of uncertainty be purely subjective, and this would lead to infinite arbitrary possibilities for uncertainty determinations? For example, if I describe a situation to you (make observations), you could say there is uncertainty in such and such aspects. Someone else would say there is uncertainty in different aspects, And someone else would say something different, etc.. This is simply the nature of descriptive language, which is what is used for empirical observations.

If there is infinite possibility with how you represent uncertainty relative to the constraints, isn't it possible to shape your outcome (selection of probability distribution) in any way that you want by using this principle? So in reality it is the most biased, instead of the claim that it is least biased.

That sky is beautiful! I just love to see a deep blue sky like that. The blueness almost hurts my eyes because it seems somehow unreal. But it gives me comfort to know there's still some ozone left.

Is there math without symbols? Well, yes, if one has the patience to express mathematical ideas through common language. What of the visual aspect of the subject? Well, there have been blind mathematicians who have been quite accomplished. I knew one: Larry Baggett, at the University of Colorado. So one could replace symbols with ordinary language, which seems to imply math is a substrata we contemplate by one or the other. — jgill

Common language uses symbols, but of a different type from mathematics. The mathematical symbol is principally a visual object, while the symbol of common language is principally an aural object. There is a big difference in meaningful purpose, or usefulness between these two types of symbols. The aural symbol serves to aid us in communication and assists in providing for our immediate needs. It's temporal existence is fleeting though. The visual symbol persists through time and serves as a memory aid. As an extension of memory (external memory) it enhances computational capacity.

We have developed ways to unify the two. Mathematical symbols have aural names, and aural words have letters which allow them to be written in the visual form. I believe that it is this ingenuity, which provided for the combining of these two, which led to the explosion of human development in the latest era of human development, beginning with cave painting, perhaps. The private memory aid of visual symbols became combined with the communicative power of common aural symbols, when the visual symbols were talked about, thereby producing a unification of distinct human memories which increased computational capacity exponentially.

By that I meant that calculus is exact in what it does. Same formulas same inputs yield the same answers. — tim wood

Right, 2+2 always equals 4. There's is no doubt about that. But how this relates to the physical world is another issue altogether. I'm interested in the latter, not the former, because the former is very boring to me. And your suggestion, "it works", is equally boring.

By leveraging entropy maximization techniques, my formulation recovers the core elements of quantum mechanics and offers an equivalent yet comprehensive perspective on the theory. — Alexandre Harvey-Tremblay

It seems like entropy maximization is central to your position. Can you explain what this is?

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

The flaws I spent the last week and a half explaining. And it isn't the system, which I say is hypocritical, but it's people like you who recognize the faulty assumptions (arbitrary points in time for example) inherent within the system, then insist that there are no deficiencies to the system, who I say are hypocritical.

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

This is very unsound logic. A system which uses numerous different axioms must be either all right or all wrong? That doesn't even make sense. And you say "it is exact", but also to "an arbitrary degree of precision". Making exactness arbitrary leaves "exact" as completely meaningless. So you are saying absolutely nothing here. And your "metaphor" is even worse, being in no apparent way, analogous.

Yet, I have usually read on the internet that spring and autumn seasons will be "shorter" due to climate change — javi2541997

In my area, summerlike weather often extends later into the fall, then suddenly there is a switch to winter-like weather. The same thing can happen in the spring, winter-like weather persists, then as if someone throws a switch, the heat of summer appears. So the traditional spring and fall weather seem to get obliterated. This all seems to be a part of a pattern of greater extremes in the weather, and the swinging from one extreme to the other, too dry, then suddenly too wet, too hot then too cold.

It serves well to demonstrate that averages are not very good representations. When they state the average temperature for a day, you'll even hear some forecasters refer to this as the "normal temperature". Obviously though, the average is not the normal, as the normal is a fluctuation from one side of the average to the other.

Then, with respect to the extremes, the engineers will produce a once in ten year event model, and a once in a hundred year event model, to show the potential for flooding, extreme drought, heat or cold, but these ought to be considered as mere conjectures. We really do not know how wildly, and how often, the pendulum may swing from one extreme to the other.

Conclusion: Google seems to warn us about cosy autumn and hot spring weather! — javi2541997

Better conclusion: Google doesn't know how to count.

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

Sure, call it a "limit" instead of a point if you want, that doesn't change what it refers to, and that is a point of division, which separates one period of time from another. And as I said, the problem is not specifically that such limits or points are unreal, the problem is that the concept is applied as if they are real. So you can argue all you want, that there is no real problem because we all know that such limits are not real, but then the problem is the hypocrisy with which the concept is applied, as if the limit is real.

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

No, this is not what I'm arguing. I am pointing out the flaws and deficiencies and indicating that I believe a better system is possible. Whether or not exact measurement is possible is completely irrelevant, What is relevant is whether it is possible to improve the current technique. 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. Don't you agree, that pointing to the flaws and deficiencies of a technique, and indicating that these ought to be rectified, is a very good thing to do, even if those who currently use the technique tend to feel insult, offence, and so they strongly defend the technique which they use?

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 am not criticizing you, or any idea you've had, I am criticizing the technique you are demonstrating. I am explaining that your technique for modeling acceleration through the application of averages, is inadequate for representing the most significant and important aspect of the concept of "acceleration", and this is the point in time at which acceleration begins.

Now it seems to me that we disagree as to whether this truly is the most significant and important aspect of "acceleration". Your model places this point as outside the representation, a limit which is approached, as tim states above. So you are inclined to say it's not my problem, that point in time is outside of "acceleration" as I model acceleration. It's not a part of "acceleration" so your criticism is irrelevant. I insist that it is an integral part of your model of "acceleration", significant, important, and necessary to your representation, so this is a requirement. The application of the limit is the primary premise.

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

Well, if you had been more attentive to what I wrote, you would have seen that this is the question I was asking about, when the mention of "acceleration" first came up, and we could have gotten right to the problem, without us wasting each other's time for the last nine days or so.

I see now, that my posts were addressed to EricH, as Eric is the one who brought up acceleration in the midst of our discussion concerning the possibility of medium-free waves. Perhaps you missed those posts, so I'll reproduce them now.

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

You see, I have always been asking about that time period, and the whole interim has simply been a diversion. Do you see why it appears to me like you are simply avoiding the issue? You say "slow down", but we are discussing the opposite, acceleration. So unless you can show how your actions of attempting to decelerate the discussion are relevant, then I can only see your digressions as intentional diversions.

But it seems that according to meteorologists, autumn will be a short season. It will not be long, just two months. — javi2541997

No, no, no, you're counting wrong. How many fingers do you have javi? October, November, December, that makes three months. Autumn is a quarter of the year, always has, and always will be. The problem is with the leap years, they always screw everything up. On top of that, the rate of spin of the earth is not even considered to be constant.

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

I mean "a good representation" of what actually happened, as i said, the goal is truth, in the sense of correspondence.

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

I gave the goal, truth. That's why Eric got sidetracked and started talking about correspondence theory of truth.

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

No, I'm telling you it's inadequate. I specifically requested those points in time to demonstrate to you, the inadequacy of your technique. Of course you would not suggest those points, because that time period, the time when acceleration starts, cannot be adequately represented by your technique. And this is a very real problem for high energy physics. I'm starting to think, that just like I was fully acquainted with your measuring technique, of using averages, you were actually fully aware of the problem I am talking about. And, like tim, you simply want to ignore it, and deny that it is a problem.

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. My averaging method serves my purpose, and I do not care if it doesn't serve yours. So keep your problem to yourself, and don't try to make your problem my problem.' But I'm not saying it's your problem or mine, I'm saying it's a problem with the technique. It's the technique's problem.

Infinite divisibility a convenient fiction in calculus... — tim wood

I see, I need to say no more on this issue, you've stated my case for me.

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

This is a misrepresentation. He is not talking about a short interval of time, he is talking about a point in time. I mean, you can say that you do not believe that there is such a thing as points in time, therefore this assumption is wrong, but the problem is that we always use, and refer to, points in time when making any temporal measurements, as the start and end points of the measured period. The start point divides time into prior and posterior, such that there is no duration within that point.

And so far I do not think I have written anything you do not know perfectly well, or disagree with. — tim wood

As stated I disagree with your representation of Zeno's arrow paradox. He is very clearly talking about points in time, not infinitesimal intervals of time. And, your statement, that there is no such thing as a point in time, does not negate the fact that we use points in time for all of our measurements of time. So, you might insist that points in time are not real, they are "a convenient fiction", but as the premise for temporal measurements, you are then insisting that all temporal measurements are unsound conclusions.

Suppose objects are moving relative to each other. And, we can describe the spatial relations between objects. Would you not agree that any specific spatial relations would only exist at "a point" in time? The objects are moving, so any interval of time would not provide determinate relations. So the reason for the assumption of points in time is to provide for "truth" in spatial relations of moving objects. Without these points there is no such truth. Now, not only are temporal measurements unsound, but spatial measurements as well.

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

OK, so if you believe that mathematics attempts at representations of the world, and you also apprehend that calculus is based in "a convenient fiction, then it ought to be a no-brainer for you to see the deficiencies of calculus which I am pointing to. Simply put, it fails to do what mathematics "attempts" to do, in your words, give us a representation of the world. It just gives us a convenient fiction.

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

The camera takes two shots, one at -.1s, and one at +.1 seconds. You produce the average, the speed for that time period, but this is obviously not a good representation. In reality the thing is moving in half that time period, and not moving in the other half. Furthermore, in the half that it is moving, it's average speed must be twice as fast as what your average says for that time period. I think that's a very significant, and in some applications, potentially a very important difference. If we add to this, the fact that by the special theory of relativity simultaneity is relative, there is the potential for even more significant inaccuracy, and uncertainty.

Is calculus used to solve problems? — tim wood

Yes

And just what are the problems of Zeno's paradoxes? — tim wood

Try Wikipedia.

Achilleus gets where he's going, and faster than the tortoise. The arrow flies through the air and so forth. — tim wood

Not according to the logic applied to the premises. That's why the term "paradox" is used.

As to the arguments themselves. they all involve some faulty assumption. — tim wood

Yes, they are faulty assumptions about the continuity of space and time, which are still held. You are on the right track here. Do you see that these same faulty assumptions are still held today? Next, can you apprehend that improved mathematical axioms will not resolve the the problems created by these faulty assumptions. No matter how good the logic, false premises will always leave the conclusions unsound.

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.

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

As I said, I think calculus is very useful in very many situations. However, its usefulness has limitations. and when it is employed beyond these limitations it is misleading. This I believe is the case in modern high energy physics, it is employed beyond its limits. And, I believe It is misleading because people like you will argue that the problem which has not been resolved, the problem I referred to in the exchanges between Newton, Leibniz, and Berkeley, has actually been resolved.

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.

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'm not ready to give up. However, I'm already fully aware of the process you are laying out, and completely understand and respect its usefulness. Therefore I am bored and ready to move on. I can tell you however, that there is a point in time when we can know for sure that the acceleration is going up wildly, and that is at the 'zero point' in time, when motion starts.

So I will ask you now, are you fully aware and respectful of the problem that I am talking about? If so, then lets move directly to that specific problem and address it directly. In your example, there is a 'zero point' in time, the time when motion is supposed to have begun. 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?

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

The problem though is that we have no way to measure the rate of gravitational acceleration at the precise moment that a thing starts to fall, and it actually may be completely different from your calculated rate.

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

No, I started the conversation, as a discussion about the problem of measuring acceleration in general, that's why I referred a number of times to the effects of this problem on quantum mechanics, as the uncertainty principle. It was Eric I believe, who started talking about gravity as a specific example of acceleration, and then you. But that was brought up as an example of acceleration. It appears like you just do not want to look at the problem I mentioned.

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

My spell check did not like "apparati". Anyway, I apprehend a slight mistake here. "The purpose of the measuring apparatus is to measure velocity" is true by coherency theory of truth, not by CToT. This is the categorical separation I referred to, and to mix them up is known as a category mistake. To state the "purpose of x is..." is to make a statement which is true or false by a stated definition, not by correspondence.

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

I might agree to this, but you are just drawing us further away from the possibility of any truth by CToT. If acceleration is not considered to be the cause of change in velocity, being the intermediary between the prior motion and the posterior motion, and instead is just a calculated change in motion, then there is nothing real in the world which "acceleration" refers to. We can see the same issue with "energy", we can say that the word refers to something real in the world, or we can say that it's just something calculated according to a formula. You seem to be choosing the latter, which denies the possibility of correspondence truth in this subject.

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

This is not truth by correspondence theory, it is true by coherence theory. The velocity determined is correct by the method of calculation, but this does not necessarily correspond to anything real.

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.

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.

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?

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?

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.

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.

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 said APPROXIMATE speed. — flannel jesus

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.

And here, thinks that this sort of approximation process provides for a "rigorous foundation". Rigorous: "strictly exact or accurate". I apprehend an implied contradiction between "approximate" and "rigorous".

Can you give an example of a statement involving the mathematical measurement of some physical property of an object that you would consider to be a true statement - per the correspondence theory of truth? — EricH

No, that's what Ive been arguing, we really do not know the true physical properties of objects. I think that's what the experimentation with Bell's theorem, discussed earlier in this thread, indicated.

This seems like you're still overthinking it. You're focusing so much on abstract mathematics and not enough on concrete measurements. Galileo didn't discover acceleration due to gravity via abstract mathematics, he measured it. If you can't imagine measurements, then let me do the imagining for you. I don't believe it's particular challenging. — flannel jesus

I think that this is a misrepresentation, and this is why were having difficulty coming to agreement here. We cannot directly measure acceleration, nor can we even directly measure velocity. Determinations of these require a multitude of measurements, with an application of mathematical principles, such as averaging. Because this process of averaging is a requirement for any determination of acceleration, these determinations are not properly called "measurements" but are better represented as logical conclusions, i.e. conclusions derived from the application of logical principles to some premises. The premises might be called measurements.

So, we start out by asking, how fast was it falling approximately at 1s? We look at our high speed footage and we measure is position at 0.9s and 1.1s. We find the positions are 3.97 and 5.93 respectively (measured in meters from the starting point). 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

According to what I expalined above, you have taken two measurements, the position at .9s and the position at 1.1s, applied some logic, and concluded the object was moving at 9.8m/s in the duration. Of course, if the object was actually accelerating during this time period, this is not a true representation. If the object was accelerating, its velocity was different at .9s from what it was at 1.1s. But your method concludes that the object was going at the same speed for the entire .2s period, and this is contradictory to the premise that the object is accelerating. So it's very clear to me that this method of averaging does not give a true representation, regardless of assertions that it does.

So we get all our results together, and quickly notice that every time a second passes, the cube seems to be traveling 9.8m/s faster than it was traveling the previous second.

Why are these sorts of measurements, and this sort of experiment, unimaginable to you? Are they still unimaginable to you now? — flannel jesus

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. And so on. How is this imaginable to you? It implies that the force (gravity) acted to accelerate the object over a period of time, then it quit acting on the object for a period of time (between .9s and 1,1s) when its velocity remained constant, then it acted again, then the force quit acting again, etc.. How is this imaginable to you? Why would the force stop and start acting in complete coincidence with the timing of your measurements, when the timing of your measurements is completely arbitrary?

But you are dismissive of the map because it is not the territory, and that is an unseemly and unaccountable (on rational terms) error for someone like yourself. — tim wood

No, I am dismissive of the map because it is misleading, as I clearly explain above, in this post. And, a misleading map gets people lost.

As with the 2+2=4, you say that the 2+2 does not represent the same thing as 4, and of course it exactly represents the same thing as 4. — tim wood

I disagree that "2+2" represents the exact same thing as "4", and you're very naive to believe this. I've explained why, elsewhere. If it did represent the exact same thing, equations would be completely useless. The left side of the "=" would necessarily represent the exact same thing as the right side, and the equation would do absolutely nothing for us. But of course, that's not how we use equations in practise, the left side always represents something different from the right side, and in working out why the two distinct things are equivalent we solve a problem.

And I refute this thus: When they are doing something, are they doing that thing, or are they doing something else? If you had read a little more closely, you would have seen that Socrates did indeed find people who knew what they were doing, but not wise, because they, knowing something, thought that they knew more that they did, thus knowing something, but not wise. That is, the Oracle had told Socrates that he was the wisest, and Socrates had to discover that wisdom and knowledge are not the same thing. — tim wood

Sorry, I do not follow your claimed refutation.

Now, whether you think they're actually capable of being done to your satisfaction is entirely different question from your ability to imagine a scenario where they were done to your satisfaction. — flannel jesus

I thought I explained this . The current state of "mathematics", the axioms and rules which are the current conventions, make it impossible that this could be done to my satisfaction. So I cannot imagine this scenario. You are asking me to imagine something which I am saying is impossible for me to imagine. For me to imagine this being done to my satisfaction would be to imagine it being done with something other than "mathematics".

This is very analogous to the issue with the aether in an inverse way. The nature, characteristics and properties, of "the aether" are dictated by definition, because we have no sense perception, empirical data of it. So, for the M-M experiment it was stipulated that the aether was a separate substance from the massive bodies, therefore the bodies would make a disturbance in the aether, a sort of wake. The experiments showed no such disturbance, therefore there is no "aether", as defined.

But what the experiment really indicates is that the dictated properties of the aether are incorrect. And of course this is consistent with empirical evidence, because we see that light and electromagnetism passing right through many bodies, therefore the aether must also exist within the bodies, and not be a separate substance.

So in the case of "mathematics", above, the word refers to something very real, supported by much empirical data, and usage of axioms and rules. So we have a very real thing being referred to, which we can look at, and see the properties of. This reality dictates the definition of the thing, mathematics. I'll call it a tool. Now, I look at this tool, and say that it is simply incapable of doing the job to my satisfaction. The tool referred to by "mathematics" cannot do the job I want done, and so I need a different tool. Therefore, either we can alter this tool to make it useful to my task, or we can come up with a new tool to do the task.

In the case of "aether", the situation is inverted. We cannot see, or otherwise perceive what we are looking for. We know from logic that it is there, whether it best be represented as "aether" or as "field", or whatever term. Now if we adhere to the defining terms of aether, which stipulate that aether is a substance separate from the substance of bodies, then we can know that there is no aether. But this conclusion does not help is to solve the problem. We still need to identify the medium, and learn its properties. That there is no "aether" in this case does not mean there is no medium, it just means the defining features of the medium were wrong. Likewise, when I say "mathematics" is incapable of resolving a specific problem, I do not mean that the problem is irresolvable. I mean that the defining feature of mathematics make it so that mathematics cannot resolve the problem. Therefore we need to either change the defining features of mathematics (as in the case of aether), which in this case means actually changing the tool, or, we need to come up with another tool (with a different name), like in the case of "aether", we'd give the medium a different name. .

I'm also genuinely quite amazed at the conspiratorial nature of your approach to acceleration due to gravity. Do you really not think there's sufficient evidence for it? Are the physicists of the last hundreds of years incompetent or just lying? How did we manage to make it to the moon, or send rovers to Mars, if we don't even grasp the very basics of gravity? I can't tell how sincere you are about all this. — flannel jesus

I believe that what you call "acceleration due to gravity" is not well understood by human beings. And, I explained that the fact that people have the capacity to predict motions of bodies does not imply that the true nature of those motions is well understood. So questions like "how did we manage to..." have little if any bearing on this issue. The capacity to do things does not imply that the doer understands what is being done; that is what Socrates demonstrated. In fact, Socrates demonstrated the very opposite, in no cases of people doing things, did the people adequately understand what they were doing.

But we know you, MU - and these others don't although they're learning - that you do not agree even that 2+2=4. — tim wood

This is an intentional misrepresentation. I do believe 2+2=4, and I've told you this before. What I've argued against, and strongly do not believe is that "2+2" represents the very same thing as "4". So what I do not believe is that "=" means "is the same as" which is what is argued by many here at TPF.

Mathematics, as used in the sciences at least, is the language used to try to describe with some rigor, precision, accuracy, and consistency what is happening in nature, and when done well, called a solution — tim wood

OK, we have here: "mathematics...is the language used to try to describe.. and when done well, called a solution". Notice your use of "try", and "a solution" only occurs when "done well". And, as I've described using English, one of very many languages used to describe what is happening in nature, there are aspects of nature (such as acceleration) which cannot be described by the current grammar of this language called "mathematics". So, as I've pointed out, when people use mathematics to try to describe these aspects of nature, their attempts fail, therefore this ought not be called "a solution".

Btw, as you well know there are at least several mathematicians who post here, and a characteristic of their work is the effort to demonstrate and make clear their own arguments and points about their topic, to educate and contribute to a general clarity and understanding. You on the other hand pontificate without substance, demonstration, evidence, clarity, or proof. And while you claim to understand that this is a philosophy site, you consistently refuse any substantive reply to the question, "How do you know?" — tim wood

Some mathematicians really demonstrate that they do not know what is being done with mathematics. They insist on silly principles such as the one mentioned above, that "=" means "is the same as". This indicates that they really have a very deep misunderstanding of what an equation is and what is being done by mathematicians with the use of equations. This is exactly what Socrates demonstrated many years ago, that when people are doing things, they really cannot accurately describe what they are doing, and this means that they do not know what they are doing.

Ultimately you're a waste of time, and I would like you to stop it! — tim wood

Why do you keep asking me questions if you want me to stop posting? Your use of language demonstrates a base irrationality.

What's all this talk about faith? You think people came up with the 9.8 number on faith? — flannel jesus

No, I don't think it was produced from faith. But if you told me the thing was going 9.8 metres per second after a second, and I had absolutely no understanding of how you came up with that number, but still I believed you, wouldn't this belief be based in nothing other than faith?

I am skeptical there's any hidden meaning in the song. — T Clark

I am skeptical there is any song without hidden meaning. I perceive hidden meaning in every song --- or maybe that's just me. But if I perceive it, and you do not, then doesn't that mean that it's hidden from you? Therefore it is hidden meaning. Agree?

Of course asking the author does no good, because if there is meaning which is intentionally hidden, the author couldn't tell you because then it would not be hidden.

I think it's incredibly feasible to agree to the truth of something without fully understanding it. — flannel jesus

Sure, but the condition was understanding, not "fully" understanding. And, I really do not understand what "fully understand" would mean, because sometimes when I think that I understood something it turns out that I really did not. So "fully understand" would be a difficult concept to understand..

The same is true for the example given before about acceleration. You may not understand or even philosophically agree with certain aspects of acceleration mathematically, but without that understanding you can still acknowledge observations that say, "after dropping the bowling ball, it was going at about 9.8m/s downward after 1 second , and it was going about 19.6m/s downward after 2 seconds , and it was going about 29.4m/s downward after 3 seconds". — flannel jesus

No, that's the point, I would not agree to this. I would want to see the measuring technique, the justification for this claim, that "it was going at about 9.8m/s downward after 1 second", etc.. What I said, is that some others might accept this, as a matter of faith in some principles they hold, but I am not inclined to accept things on faith. And the point is that I do not believe that accepting somethin completely on faith is really a judgement of truth. I would say that faith provides a type of understanding, but not all types of understanding necessitate truth. I would argue that "truth" implies a special type of understanding

So if you told me that it was going " 9.8m/s downward after 1 second", and I said yeah, sure, I believe you, I would not consider that I've judged what you have said to be true, unless I have some understanding as to why you said that. If I believe that I understand why you said that, then I would say that I accept it as truth. If I have no understanding whatsoever, of why you said that, yet I still accept it, then I accept it for some reason other than believing that it is true. Many statements are accepted for reasons other than the belief that they are true.

So, the solutions offered as such by mathematics are not solutions? What do you imagine mathematics and solutions to be? — tim wood

Mathematics may provide some solutions sometimes, but in respect to the problem being discussed, the problem of acceleration, mathematics does not provide a solution. What it does is provide a "work around",. It veils the problem so that it disappears in some situations, so long as the temporal duration is not too long or too short, but then it simply reappears in other situations. As I said, the problem now reappears as the uncertainty principle, so the mathematics has clearly not resolved the problem.

"In metaphysics and philosophy of language, the correspondence theory of truth states that the truth or falsity of a statement is determined only by how it relates to the world and whether it accurately describes (i.e., corresponds with) that world."

Now you are introducing the notion of understanding into the mix - and it's not clear to me what you mean here. If by the word "understanding" you mean that a statement is grammatically and syntactically correct and expresses a thought/notion that could potentially be real? Then that is trivially correct. — EricH

Let's consider the definition you provided, truth concerns how a statement relates to the world. Do you not agree, that in order to establish a relationship between a statement and the world, there are certain requirements such as 1) understanding the meaning of the statement, 2) understanding the world which the relationship is to be established with. Without these two types of understanding how could there possibly be a relationship between the statement (a bunch of letters), and a thing which is called "the world"?

But if by "understanding" you mean something more than our shared understanding of the plain language meaning of words, then this raises all sorts of questions - what do you mean by "understanding"? Can we ever fully understand anything at all? Warning! Warning! Infinite regress ahead! — EricH

I do not know what you mean by "shared understanding". To me, "understanding" is something personal. I might understand you, and you might understanding me, but this does not mean that we have a shared understanding, because each of us has a different understanding.

here's what my OED has for "understanding", and I think we could pretty much choose any of these. 1 a) the ability to understand or think, intelligence. b) the power of apprehension; the power of abstract thought. 2) an individual's perception or judgement of a situation etc. 3) an agreement; a thing agreed upon, esp. informally. Note that "understand" is defined first as perceive the meaning of (words, a person, a language, etc.) and second, perceive the significance, explanation or cause of.

It's starting to appear as if you don't know how to apply math to the situation. (Not that there is anything wrong with that.) — wonderer1

I really do not believe that there is a way to successfully apply math to the situation. That's the point, it's a philosophical problem which math cannot resolve. math has its limits, and there are many problems which it cannot resolve.

In 1966, Abraham Robinson introduced Non-standard Analysis, which provided a rigorous foundation for working with infinitely small quantities. This provided another way of putting calculus on a mathematically rigorous foundation, the way it was done before the (ε, δ)-definition of limit had been fully developed. — tim wood

I already told you the problem with the "rigorous" solutions. They are not real solutions because they allow "infinite" which is fundamentally unintelligible, as indefinite, into the mathematical representations. So any mathematical model employed, using these axioms which are designed to produce a "rigorous foundation" will have indefiniteness, which is a form of unintelligibility, built into it.

This is the problem with "formalism" (https://en.wikipedia.org/wiki/Formalism_(philosophy_of_mathematics)) in general. In its attempt to exclude the problems involved with applying the ideal (mathematical principles) to the material (physical) world, complete with accidents which appear as indefiniteness, formalism allows the indefiniteness (unintelligibility) to inhere within the formal (logical) structure itself. The result is that the source of unintelligibility (which inevitably arises in application), is impossible to isolate and identify.

If you do not understand this, then so be it. I will not try to explain, because I've done so numerous times on this forum, and I've come to respect that those who do not understand this are in that position because they deny the issue, and refuse to accept it as a real problem. They perceive that mathematics is very useful, and cannot apprehend the possibility that it could have problems. So it's generally a misunderstanding which is supported by a closed mind, and I am incapable of influencing people like you to open your minds.

And it is equally clear that, short as the article is, you did not understand any of the rest of it either. "Berkeley did not dispute the results of calculus; he acknowledged the results were true. The thrust of his criticism was that Calculus was not more logically rigorous than religion. Berkeley concluded that the certainty of mathematics is no greater than the certainty of religion." Berkeley was writing as a Christian apologist. — tim wood

Yes, what I tried to explain is that the type of "truth" that Berkeley is talking about here is a faith based truth. It is "truth" in the sense of coherence theory. If there is coherency within the logical system it produces truth. This is why I as well, do not dispute the usefulness of things like relativity theory, and calculus. The problem is with the "false", in the sense of correspondence theory, principles which the "free-thinkers" in Berkeley's words, employed. The "free-thinkers" we can understand as the pure mathematicians who dream up mathematical axioms. The problem is that there is no requirement that any mathematical axioms be "true" in the sense of correspondence. And if the axioms prove to be useful they are accepted, and used, regardless of truthfulness (correspondence). Now we all know that the soundness of any logical argument relies on the soundness of the premises (mathematical axioms in this case), so if you prefer, we can replace "truth" with "sound", and analyze how sound the supposed "rigorous" logic is.

In this case the subject was "fluxions" (https://en.wikipedia.org/wiki/Fluxion). According to the Wikipedia entry, this concept was central to the disagreement between Newton and Leibniz. If you have not studied this, principal disagreement between Newton and Leibniz concerned the relative importance of Newton's "momentum", as mass times velocity, and Leibniz' "vis viva" (https://en.wikipedia.org/wiki/Vis_viva) as mass times velocity squared. As it turned out, each is important in its own way, but Leibniz' principle needed be adapted by a coefficient of a half.

Any claim of yours, then, of any problem with the maths in question here, whether mathematical, philosophical, or metaphysical, is ignorant, stupid, self-serving, and that you used it to evade a fair question on your inconsistent usages of "truth," I call vicious. — tim wood

Uh huh. As I explained, I avoid your questions because I apprehend them as rhetorical. Your questions are presented not for the purpose of finding a point of mutual agreement, from which we can proceed in a rational inquiry, but they are designed for the purpose of opening up a point of attack. And when I refuse to answer, you are reduced to ad hominem, like above, demonstrating that you are overwhelmed by emotional weakness.

These are incompatible. Reconcile them! — tim wood

I do not see the incompatibility. To represent reality in the way of correspondence (truth), requires necessarily that one has some understanding of the reality being represented. Therefore "truth" in the sense of correspondence, implies understanding.

Show your math. — wonderer1

What math? It's a philosophical problem, one which mathematics has not resolved. Look, there's a point in time, when a body at rest becomes a body accelerating. The body changes from being at rest, to being in motion at some point in time. Since the rate of increase of velocity (acceleration) is expressed as over a period of time, at this point in time, when the body changes from being at rest to being in motion, the rate of increase must be infinite because it's a number expressed over zero, x/0.

Regardless of philosophical issues, we can in fact experimentally verify, to some reasonable degree of precision, that bowling balls and pool balls both accelerate toward the ground when dropped. If you have philosophical problems with the concept of acceleration, you should separate that from your ability to look at that evidence and see what does, in fact, happen — flannel jesus

Yes of course, such objects accelerate. They must, in order to get from zero velocity to having some velocity. The problem is that we as human beings, do not have a very accurate understanding of acceleration. Our mathematical representation of it is very problematic. Read the following: https://en.wikipedia.org/wiki/The_Analyst

Notice that the article says that Berkeley's criticism of Newton was resolved with the concept of "limits". But this really doesn't solve the problem of acceleration because it places zero as a boundary, limit, which is never obtained. So the principle utilized is that there is no point in time when the object changes from being at rest to being in motion, because an infinite amount of time would pass before the boundary is crossed. So the crossing of that boundary, between rest and motion is never actually obtained by the mathematical representation.

It is this same proposition, which makes calculus logically rigorous, which also leads to the uncertainty principle, by allowing this "infinite" into the mathematical representation, and having boundaries within the modeling which cannot be crossed. You determine the momentum (motion) or you determine the position (rest), whichever one you choose to make an accurate representation of, the other approaches the boundary (infinite uncertainty).

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Why don't you try answering his question? — tim wood

I could not answer EricH's question because the presumptions which the question was based on were false. He said "I think you would agree that that is a true statement". I could not agree that it was a true statement, for the reasons I gave. He cited a measurement, and I explained that there is a measurement problem which did not allow me to agree that his measurement was "true". Then EricH tried to say that such a complex measurement was just an observation, which it clearly is not. That makes two false presumptions. What kind of inquiry is that, asking a loaded question with two false presumptions. That's like asking me 'did you stop beating wife, again?'.

Now flannel jesus gave me a better example of "an observation". Flannel said that heavy balls when dropped, accelerate toward the ground. I agree that they "must accelerate", because they go from being held to being in motion. But this is not an observation, it's more like a conclusion of logic. I do not notice the ball accelerating when I drop it, but I conclude that it must accelerate, because it goes from zero to having some velocity.

Now EricH's question concerned the relationship between "truth" and "understanding". EricH asked if I could agree to the truth of something without any understanding of what I was agreeing to the truth of. I'm sure many people could agree to the truth of something without any understanding of it, if this agreeing is done on faith, like the way that some religious people agree to the truth of God for example. But I am not prone to such agreements, I want to understand first, before I agree.

Regardless, this is irrelevant to the point I was making. I said "truth" implies understanding. But for someone to say "I agree that this is true", and for it to actually be true, are two different things. So "I agree that X is true" does not imply understanding in the way that truth itself implies understanding.

I believe them. — T Clark

And "Merry poppins"? Are you aware of the history of LSD and its relationship with sugar?

Assume all of that is done to your satisfaction beyond all reasonable doubt. — EricH

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..

Plus he was in "Merry Poppins" and some other movies. — T Clark

I didn't watch "Merry Poppins" until i was grown up, but I'm pretty sure it's all about popping acid. The "spoonful of sugar" gives it away.

What was the idea behind making kids entertainment which was laced with recreational drug references? It seemed to be very common in the sixties. Another good example: puff the magic drag in. Did those guys sit around thinking how can we talk about getting high while disguising the fact that we're talking about getting high? The kids will never figure it out.

E.g., if I say that I observed an object in a vacuum chamber accelerating towards the center of the earth at 9.8 m/sec**2, I think you would agree that that is a true statement (it corresponds with reality). — EricH

No I don't agree with that at all, far from it in fact. Why would I just take it for granted that this is a true statement? I would have to see your justification, your measurement technique, and how you come up with "sec**2". What does "sec**2" even mean?

Furthermore, I disagree that this is "just an observation", it is actually a very complex calculation. That something is "accelerating" requires a multitude of measurements of velocity, and each measurement of velocity requires multiple determinations of spatial-temporal location.

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Also, is there a distinction when you put the word in quotes? — EricH

I put the word in quotes, because I was talking about the meaning of that word, which I put in quotes.

Sorry, I didn't mean "the set of discernment which are not subjective." I meant, "the set of all discernments (which are necessarily made by subjects) is a set, an abstract entity," and abstract entities are generally not considered to be subjective. — Count Timothy von Icarus

I wouldn't say that. Only through Platonism do abstract objects lose their subjectivity. but whether or not Platonism provides us with a representation of the true nature of abstractions, is another question.

For example, we could have the set of all experiences where people experience red. The experiences are subjective, the set is an abstract object. — Count Timothy von Icarus

I would say that is more like a fictional, or fantasy "set". To have such a set would require that all experiences be judged as to whether or not the experience was of "red". Then there would be a whole lot of undecisive experiences, is this red or is this pink, for example. Some people would say that such and such experiences are members of the set, while others would say no. So there is really no such thing as this type of fictional, or fantasy set.

Right, but the converse is generally not accepted. "If no observer notices something as a difference, then by the very fact that no difference has been noticed as a difference, the difference has, necessarily, made no differences to any observer... and so is not a difference." — Count Timothy von Icarus

No, that does not follow, because it's contradictory. You are stating that it is a difference, therefore it makes a difference to you, in your example. That's the problem, this so-called difference is imaginary and in your imagination it makes a difference or else you'd have no example. You are an observer, and it has made a difference to you, in your imagination. Whether or not it makes a difference through the means of sensation, or through the means of imagination, is not relevant.

Really, I am just looking for a good argument that says "positing inaccessible differences is sort of nonsensical." — Count Timothy von Icarus

It is nonsensical, because the very act of positing such differences is an act which designates them as accessible. To designate specific differences as inaccessible is contradictory, because designating tham as inaccessible is to provide access to them.

Both views lead to coherent accounts, just with different numbers of things in the world.

Unless someone can show how either view leads to contradiction, then the choice is arbitrary, not empirical. — Banno

If both views are coherent, but each suggests a different number of empirical objects in the world, then there is no reason to choose one or the other, accept according to empirical evidence, therefore the choice must be empirical.