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
In physics, time is defined by its measurement: time is what a clock reads. — Wikipedia
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
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
Just generally, the Wittgenstein you talk about bears little resemblance to the one with which I am familiar. — Banno
I remember Royal Crown Cola, — T Clark
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
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
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
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
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
By that I meant that calculus is exact in what it does. Same formulas same inputs yield the same answers. — tim wood
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
And at the risk of trying your patience, what exactly are those flaws and deficiencies which justify your calling the "system" hypocritical? The reason I ask is that in sum you appear to be criticizing a tool, a tool which given appropriate inputs delivers results to an arbitrary degree of precision. — tim wood
Seen the correct way, calculus, e.g., is neither flawed nor deficient, and certainly in no way hypocritical. Instead it is exact. In a sense then it is either all right or all wrong, and because all that it does is just what it does, then it must be all right. Further, since it gives answers to an arbitrary degree of precision, it is therefore in itself altogether correct. — tim wood
Yet, I have usually read on the internet that spring and autumn seasons will be "shorter" due to climate change — javi2541997
Conclusion: Google seems to warn us about cosy autumn and hot spring weather! — javi2541997
And you and I, and I suspect you and most people, attach an altogether different significance to what you call the "deficiencies." And yes, people often ignorantly refer to "points" in time. But calculus usually refers to the value of a variable as some input approaches a limit - no infinities, although they're approached, and no "points in time." And if Zeno wants to think in terms of points in time, what is that to us beyond an historical oddity - however reasonable it may have seemed to him at the time? And to be sure, "point in time" is easy to say, but were there actually such a thing, a durationless interval, then atomic motion would stop and everything on the instant collapse. — tim wood
I think we're at an impasse. i think you hold that nothing can be measured exactly, of things subject to measurement, and thus all knowledge of such things is deficient and flawed. I — tim wood
If you ask me to figure out a way to get an answer, I can tell you, and THEN we can go into if the technique is adequate or not. Until then, your own problem with your own technique is something for you to work on with yourself, and it's not a criticism of me or any idea I've had. — flannel jesus
I'm completely happy to look at that time period too, you just never asked me a question about it. Instead of asking, you started telling me what I would do. You're doing things in the wrong order and being too hasty, making careless assumptions again. Slow down. — flannel jesus
That something is "accelerating" requires a multitude of measurements of velocity, and each measurement of velocity requires multiple determinations of spatial-temporal location. — Metaphysician Undercover
The concept of "acceleration" involves a fundamental philosophical problem. Acceleration is the rate of increase of velocity. So if an object goes from being at rest, to moving, there is a brief period of time where its "acceleration" is necessarily infinite. This is a fundamental measurement problem, and another form of the same problem is at the heart of the uncertainty principle of quantum physics, as the uncertainty relation between time and energy in the Fourier transform.
This problem was exposed by Aristotle as the incompatibility between the concept of "being" (static) and the concept of "becoming" (active). The way that modern physics deals with this problem, through the application of calculus does not resolve the problem. It simply veils the problem by allowing the unintelligible issue, infinity, to be present within the mathematical representation.
Now, the very same philosophical problem which Newton and his contemporaries had to deal with in the relationship between bodies, becomes paramount in modern physics in its relationships of energy. The issue though, is that Newton and his contemporaries were dealing with relatively long durations of time, so the methods of calculus were adequate for covering up this problem which only increases as the period of time is shortened. Now physicists are dealing with extremely short durations of time, so the uncertainty becomes very relevant and significant. That's what the time/energy uncertainty indicates, the shorter the time period, the more uncertain any determination of energy will be.
Accordingly, using the current mathematical conventions, such calculations of acceleration will never be done "beyond all reasonable doubt", because the current convention is to allow the unintelligible (infinite) to be a part of the mathematical representation.. — Metaphysician Undercover
But it seems that according to meteorologists, autumn will be a short season. It will not be long, just two months. — javi2541997
A good representation of what? You keep saying things like "inadequate" or "not a good representation". Some measurements are adequate for some purposes and inadequate for other purposes. You can't just raw say it's inadequate, it can only be inadequate in relation to some goal. — flannel jesus
Now it's not like you gave me a specific goal and I said "all we need to do is measure the location at these points in time". — flannel jesus
In fact measuring them at those points in time was YOUR suggestion, not mine. Don't tell me it's inadequate - tell yourself. — flannel jesus
Infinite divisibility a convenient fiction in calculus... — tim wood
He supposes (reasonably for him we may suppose) there is an interval of time so short that within it the arrow is not moving. — tim wood
And so far I do not think I have written anything you do not know perfectly well, or disagree with. — tim wood
But that aided by keeping in mind that all the rules, laws, theories, and mathematics just attempts at representations of the world itself (-as-it-is-in-itself) expressed in terms of what people can understand. — tim wood
Why would it fail to give a good representation? The only problem with our high speed camera data for this moment in time is that it has limited resolution, so we wouldn't necessarily be able to see how it starts moving at that moment in time (I've been rounding previous measurements of distance to 2 decimal places to sort of mimick the problem of camera resolution). — flannel jesus
Is calculus used to solve problems? — tim wood
And just what are the problems of Zeno's paradoxes? — tim wood
Achilleus gets where he's going, and faster than the tortoise. The arrow flies through the air and so forth. — tim wood
As to the arguments themselves. they all involve some faulty assumption. — tim wood
I was not any good at calculus, but I think calculus is what you are talking about. So question to you, MU: do you buy calculus? Or is that flawed and misleading? — tim wood
you're asking the right questions, except instead of saying "let's look at the data and check if the acceleration is going up and down wildly" you're just saying "oh well we can't know for sure so I give up, there's nothing left to discover."
Don't give up so quick, we have a lot of data from the camera. I mean, if you WANT to remain ignorant of the pattern of how things fall by gravity, then by all means give up here. But the rest of the world is operating on many centuries worth of physics past the point that you give up. — flannel jesus
I didn't give this bit the attention it deserves. You said "the fact that the assumption of "constant acceleration" is adequate and useful at low rates of acceleration" - that's wonderful! If you agree that it's useful and adequate enough at low rates of acceleration, then you've accepted the only thing I really wanted you to. Gravity accelerates things at 9m/s/s, on planet earth, at least for the low rates of acceleration that we measured. — flannel jesus
You go on to talk about other instances of acceleration that aren't directly caused by gravity, which I think it's fair to say is beside the point. The conversation is about how gravity accelerates things, not about how your leg muscles accelerate your own body. — flannel jesus
Precisely. And the purpose of the 10 million different measuring apparatuses (apparati?) is to measure velocity. So QED we are measuring velocity. And so the statement is true per CToT. We are not dealing with your metaphysical notions of truth or falsity here. And of course it is not 10 million. Duh. — EricH
Acceleration does not cause anything. No wonder you are confused. Acceleration is a change in the velocity of an object. An object can undergo acceleration by being acted on by a force (F = ma) or by being affected by the curvature of spacetime. — EricH
No matter how finely we chop up time - or how many different ways we chop up time - we get the same results. So this is a true statement:
The velocity of our object is increasing by 9.8 m/s every second within the limits of accuracy of our measuring devices.
Again, we are using CToT, not your metaphysical notions of truth. — EricH
So far in my analysis, I've just looked at a couple slices in time and calculated the average velocity for that slice. — flannel jesus
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
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
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
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
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
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
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
I took it slow and just built up a couple facts. — flannel jesus
Inadequate compared to what? — flannel jesus
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
Everyone else who has been involved in this discussions understands that the ball is accelerating continuously in the scenario under consideration. — wonderer1
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
MU apparently disqualifies naming. We cannot name anything because we do not know what it is. — tim wood
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
we'll say this
"The digital readout on the speedometer shows 60 mph" — EricH
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
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
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
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
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
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 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
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
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
If you choose to reject all evidence you could see, then you will of course always have that deficiency. — flannel jesus
And this would be you, MU, — tim wood
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
I said APPROXIMATE speed. — flannel jesus
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
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
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
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
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
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
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
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'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
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
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
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
Ultimately you're a waste of time, and I would like you to stop it! — tim wood
What's all this talk about faith? You think people came up with the 9.8 number on faith? — flannel jesus
I am skeptical there's any hidden meaning in the song. — T Clark
I think it's incredibly feasible to agree to the truth of something without fully understanding it. — flannel jesus
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
So, the solutions offered as such by mathematics are not solutions? What do you imagine mathematics and solutions to be? — tim wood
"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
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
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
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
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
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
These are incompatible. Reconcile them! — tim wood
Show your math. — wonderer1
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
Why don't you try answering his question? — tim wood
I believe them. — T Clark
Assume all of that is done to your satisfaction beyond all reasonable doubt. — EricH
Plus he was in "Merry Poppins" and some other movies. — T Clark
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
Also, is there a distinction when you put the word in quotes? — EricH
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
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
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
Really, I am just looking for a good argument that says "positing inaccessible differences is sort of nonsensical." — Count Timothy von Icarus
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