Zeno's paradox when seen from the perspective of pure mathematics is easily dealt with using the limit concept, but giving it an anthropomorphic twist makes it absurd. And the idea of a first non-zero coordinate shows a very limited knowledge of mathematics.
Would you agree a wise intellectual warrior should first know his enemy before striking? — jgill
its demonstratable that space is infinitely packed. — Gregory
Quantum physicists descriptions of reality are not necessarily accurate. They have to fit true philosophy. — Gregory
If we allow that the real line is made of points (which are just real numbers) then the answer is that there is no first nonzero positive real number. That is the answer, so your claim that "we cannot answer this question" is false. — fishfry
Now who's claiming a line is made of points? You are the one doing that! — fishfry
that doesn't entitle you to mischaracterize the math of the real numbers. There is no smallest positive real number. — fishfry
In your model of a continuum, whatever it is, is there a smallest real number? — fishfry
There is no problem. Mathematical analysis took care of that years ago. — jgill
You're throwing ideas out there that are philosophical and calling them science. — Gregory
What we know is what our senses say, yet you say our senses and the paradigms they are in are close to having ZERO accuracy. Why trust your use of measuring equipment then? We have no real understanding of what stuff looks like at the quantum level. — Gregory
But your solution to Zeno's paradox is that the quantum world doesn't exist unless we measure it. Which, well, is more paradoxical than what Zeno proved......And you are saying that there is nothing there at all unless we measure it. What kind of nonsense. — Gregory
You should try posting an unpopular opinion in the politics-related threads around here. Namecalling is all they've got. — fishfry
I pointed out that video is actually a sequence of stills... — fishfry
even a still captures motion because it records photons over a nonzero interval of time. — fishfry
So we're talking past each other. Perhaps we can find agreement at least in that. — fishfry
it's not the job of math to solve Zeno's paradoxes; and even if it is, it's not an interest of mine. I wish you the best with your efforts in that direction but I can't help. — fishfry
dt is a differential form. — fishfry
I'm not trying to solve the nature of the continuum here. — fishfry
This is why I called you an idealist. — Gregory
There is no true ontology in that field of research and if you think your body is primarily empty space I'd have to say you have a cognitive distortion — Gregory
Aristotle's "solution" was that the whole exists prior to parts. To which I ask:
1) do the parts of the whole exist
2) how many are there of these parts. — Gregory
I've noticed that when I hit the button and enter Ryan, your handle doesn't come up. Do you know why that is? Moderators, any clues? — fishfry
Why is this my problem, or math's problem? — fishfry
It is a lot more satisfying to do this than to argue indirectly, IMO. — jgill
I can offer a couple of reading suggestions based on these two comments. — aletheist
The greatest error of modernity is saying that the world is information and is not as it appears to us. The world we see transcends any interpretation of QM and psychological studies on mind-matter interaction. What you see is what there is. There is more there, but not less. Any other position is insanity. Zeno's paradox will never have a complete solution, but it is a sign of a healthy position to be comfortable with a paradox — Gregory
But what good is that? (in reference to talking about a potentially infinite process) — Metaphysician Undercover
This is probably the crux. "Math does not have to be practical". — Metaphysician Undercover
Your ontology is weak. You say a table is one, yet it has 4 legs and a top piece. What number of parts do these have? This process is infinite and it takes a delicate balance to understand all it's intricacies. Motion passes through infinity and the finite, but you want to reduce the question to Aristotle's lame argument,: namely that parts are only potentially there. Bringing in QM isn't going to help your case mr. idealist. The world is real. "Ignore the world and the world will come to you" — Gregory
even pi can only be understood as part of a finite number — Gregory
We already discussed the difference between the rule ("program" in this case) which sets out, or dictates the process, and the process itself. If the process is interrupted, it ends, and is therefore not infinite. The rule ("program") is never infinite, nor is it potentially infinite, it's a finite, written statement of instruction, like "pi", and "sqrt (2)" are finite statements, even though they may be apprehended as implying a potentially infinite process. — Metaphysician Undercover
I don't see how you can say this. Pi says that there is a relationship between a circle's circumference and diameter. This information is totally useless if you do not proceed with a truncated version of the seemingly infinite process, such as 3.14. "The solution to the problem is pi" doesn't do anything practical, for anyone, if you cannot put a number to pi. — Metaphysician Undercover
That leaves the question, when there is no interval of time, is it meaningful to speak of time or anything that requires time. — tim wood
If it makes sense to speak of a time as a "time" when there is no motion, then that same notion applied to a car implies that it's spending most of its time, even while in motion, not in motion. — tim wood
I've looked into constructivism a bit, which is enjoying a modern resurgence due to the influence of computer science and computerized mathematical proof assistants. But you would reject even that. — fishfry
But why am I supposed to be burdened for finding a mathematical viewpoint other than the standard one accepted by almost all the world's mathematicians except for those pesky constructivists and rare finitists and ultrafinitists? Why is this my problem, or math's problem? — fishfry
I suppose I owe you that. I'm going to find it depressing and frustrating but I'll take a run at it sometime. — fishfry
Why isn't Aristotle's solution just circular because it makes the results of a mathematical construction prior to the construction itself? — magritte
If I give up points as bounds, then how would I have anything but an endless line? — magritte
There is an issue of truth here. There is something there causing the form, and the concept of "field" attempts to account for whatever it is. If the concepts employed are inadequate, then it's not true to say that this is what is there. — Metaphysician Undercover
If the process is terminated then it is untrue to say that it is potentially infinite. — Metaphysician Undercover
And if we know that in every instance when such a process is useful, it is actually terminated, then we also know that it is false to say that a potentially infinite process is useful, because it is only by terminating that process, thereby making it other than potentially infinite, that it is made useful. — Metaphysician Undercover
We measure the car at 60mph and maybe that's accurate to within a small margin of error. But at no point during its 60 mph run is its speed zero. — tim wood
It seems to me that with any line I look at I'm looking at an infinite number of points. Not potential points, but actual points - that is, to the degree that one, or any, point is actual. — tim wood
Just out of curiosity though, how do you develop a theory of the real numbers without infinite sets? Even the constructivists allow infinite sets, just not noncomputable ones......The problem with finitism is that you can't get a decent theory of the real numbers off the ground. — fishfry
If I see a coherent one presented I'll engage with it. In the past I've engaged extensively with constructivists on this site and learned a lot about the contemporary incarnations of that viewpoint. I've also studied the hyperreals of nonstandard analysis. So in fact I'm very open to alternative versions of math, but I don't see that you've presented one. — fishfry
What is real and fundamental in quantum physics is the points where particles appear. — Metaphysician Undercover
The so-called "underlying quantum fields" are models produced from observations of particles, and are meant to model the interactions of particles. — Metaphysician Undercover
So if we turn to study that rule, should we not put our efforts into avoiding this rule, making it so that the rule never comes up, because it's like a trap which the computer will fall into? Therefore instead of pretending to be having success at carrying out infinite processes, which is self-deception, we should be looking at ways to make sure that such rules are banished. — Metaphysician Undercover
Not all contemporary math. — jgill
You're approach is typology but you haven't said anything about the system works. (Topology says how you get results)
An object is bounded by points and a finite surface area. This is how continua is defined. The infinity is in the paths within these bounds, because parts, motions, and paths are uncountably infinite with it — Gregory
The arrow moves through any point with forward velocity so it's never ever at rest — Gregory
You are making a claim about reality (i.e. it's made of events of information). Aristotle slumped into this when he said parts are potential. What exists is the whole composed of all it parts, which are bounded by points (finite) and limit in space (finite). A material body doesn't have math in it. We use imperfect mathematical formulations to understand to described in the field of physics. You can't draw philosophical conclusions from physics is the conclusion. You fell for the Parmedian world view by trying to figure out the logic of his disciple — Gregory
The Zeno effect and the anti-Zeno effect refer to how observation changes eternal states. The ancient Arrow paradox is just used to illustrated the effect and the effect does not resolve the Arrow paradox because its not specifically related to it — Gregory
I'm agreeing that IN REALITY there may not be such a thing. But in math, there most definitely is. — fishfry
You can't maintain your credibility while arguing against freshman calculus. here's the proof "somewhere," a somewhere I already linked to earlier. — fishfry
You know you keep making claims totally contrary to photographic technology.....There are no single-photon detectors outside of physics labs. But again, I don't know why you're belaboring this point. If you don't think that 1/3 = .333... AND you agree that you are making a mathematical point, then there is no conversation to be had. — fishfry
I don't think we're having the same conversation anymore. — fishfry
What is real and fundamental in quantum physics is the points where particles appear. — Metaphysician Undercover
You can study that rule, but you cannot study the process dictated by that rule, because it does not exist. — Metaphysician Undercover
The tangent line IS defined as the limit of the secant (for a function from the reals to the reals). — fishfry
Are you talking about Mathematics or some kind of notion of reality that goes beyond math? — fishfry
I don't understand why you like one infinite representation rather than another, but you are riding a hobby horse and making no rhetorical points with me at all. You're wrong on the math and confused on the metaphysics. — fishfry
Why are you saying this? I assume you must know it's wrong, no mechanical device is capable of exposing a light-sensitive medium for a true instant. Are you speaking metaphorically? If you set your hypothetical camera to an instantaneous shutter speed no photons could get in and the image would be blank. — fishfry
video is nothing more than a series of stills, whether analog or digital frames. — fishfry
We're not going to solve Zeno's paradoxes here. — fishfry
the square root operation is closed over real numbers — TheMadFool
The op is asking a philosophical question about the existence of certain mathematical objects, not whether those mathematical objects have mathematical existence. — Metaphysician Undercover
Discrete curves? — Gregory
Insofar as the car is moving and never while it is moving not moving, then any method of description that stops it is simply not reflecting reality, but maybe if anything, something other than reality. — tim wood
Photographs are not instantaneous. The shutter stays open for a period of time, usually a fraction of a second.......any measurement is taken over time. There's no difference between photo and video. Video after all is just a collection of still images, either analog or digital frames. And a single photo is taken over a period of time, namely the shutter speed. — fishfry
The person who puts one's efforts into pointing at the problems in existing systems need not be the one who produces the repair........You demonstrated that you do not grasp the need for the point to be prior to the line, therefore your claim that it would result in a weaker mathematics is based in misunderstanding. — Metaphysician Undercover
What quantum physics demonstrates to us is that points have real existence, and continuities are constructed. — Metaphysician Undercover
I don't see how you get from points to continua. — Metaphysician Undercover
Now let's say that in '2+2', the '+' represents a process. — Metaphysician Undercover
Continua is infinitely pointed. So it has instants all over it. — Gregory
How I see it, we need to say "the infinite" is on one side and "the finite" is on the other and motion is movement between them — Gregory
Idn. I've been recently working on this question from the angle of non-Euclidean geometry. I'm trying to understand what space even is — Gregory
A car traveling 60 mph down the road. Is anyone here going to suggest that at any time, however defined, that car is not moving, or, that there some time, some moment, when it is by no test whatsoever distinguishable from a parked car? The moving car is a reality. — tim wood