That the car was "going at a constant speed" is just an assumption, so it may not be the truth of the matter. — 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
But I am going to ask you to write something - anything - that is true. — tim wood
Are you gong to argue that the car is not moving at any speed during its traverse of the distance A to B? — tim wood
This is the point. When we use math to figure out things like instantaneous velocity, the volume of a supposed infinitely small tube, etc., — Metaphysician Undercover
it is implied that we know things about reality which we do not. This is a falsely supported certitude. — Metaphysician Undercover
If the property which we assign to the thing, "speed", in this example, has faults within its conception (contradictions for example), — Metaphysician Undercover
Are tangent and instantaneous rate of change not the same thing? — Ryan O'Connor
If you reject the notion of instantaneous rate of change, how can you not reject the notion of tangents? — Ryan O'Connor
I'm talking about mathematics. I understand that 0.333... converges to 1/3, but it is only (a useful) convention which states that convergence and equality are the same. If you're saying that it's proved somewhere that the two terms are equivalent then let's leave it at that. — Ryan O'Connor
The Stern-Brocot string for any rational number has finite characters. I don't accept the claim that that LL = LLLRrepeated since LL corresponds to a position in the tree and LLLRrepeated corresponds to a path along the tree. However, let's not waste any more time on 1/3. — Ryan O'Connor
As with your speedometer argument, your addition of a shutter only complicates the issue without providing any further explanatory power. We add a shutter to cameras only to limit the amount of light that the film is exposed to. Without a shutter we can (at least in principle) still take photographs. Remove the shutter and the instant the first photon hits the film we have a photograph. — Ryan O'Connor
And if no further photons hit the film we have an image with absolutely no blurriness. — Ryan O'Connor
This image captures no motion. It is not a video by any definition. I was anticipating you challenging the practicality of such a photograph, which is why I went quantum, but perhaps that's not necessary. — Ryan O'Connor
I understand how videos and flipbooks work, and yes we use stills to create them, but the magic ingredient which you are ignoring is time (specifically non-zero intervals of time). We hold each frame for 1/24 seconds before advancing to the next frame. — Ryan O'Connor
(I believe) Zeno's paradox was already informally solved by Aristotle. I'm just defending his view. And loosely speaking the view is simply that we start with videos, not stills. With videos we not only can capture motion but we can also pause the video to extract a still. With only stills, motion is not possible, as per Zeno. Zeno's paradox is important and seen as unresolved because the notion of stills being fundamental is deeply rooted in our beliefs. — Ryan O'Connor
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
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
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
My view is that actual infinity should not be permitted in math any more so that than it is permitted in physics, but that's just my view and it's contrary to contemporary math so I'm willing to leave it at that. — Ryan O'Connor
We measure the car at 60mph and maybe that's accurate to within a small margin of error. — tim wood
My impression is that you're a finitist, so I presume that you believe our universe had a beginning of time. If particles are fundamental, they must have existed at that initial moment, right? Were they concentrated at a point? I take it that you think a measurement involves the interaction of particles, so at the initial instant wouldn't they all be measuring each other? If so, how would they ever move, given the quantum Zeno effect? — Ryan O'Connor
Consider this: "QFT treats particles as excited states (also called quanta) of their underlying quantum fields, which are more fundamental than the particles." source — Ryan O'Connor
I think you're splitting hairs here. By rule I assume you mean the 'computer program' and by process I assume you mean 'the execution of the computer program'. If so, then we are in agreement, we can study the rule (i.e. the computer program). — Ryan O'Connor
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
I said "faults", and I used "contradiction" as an example of a fault. That there is a "margin of error" is another indication of fault. When a small margin of error is ignored or neglected, as if it doesn't exist, one can fall for a paradox like Zeno's, where that small margin of error is infinitely magnified to produce the appearance of contradiction. — Metaphysician Undercover
I'm not proposing we ban Infinity altogether. I'm proposing that we restrict ourselves to only use Infinity in a potential sense. — Ryan O'Connor
My view is that actual infinity should not be permitted in math any more so that than it is permitted in physics, but that's just my view and it's contrary to contemporary math so I'm willing to leave it at that. — Ryan O'Connor
[/quote]switched to a quantum sensor. With an SLR camera I agree that every photo has some degree of blurriness, but with quantum sensors that's not necessarily the case. There is no law which states that we can't know the position of a particle with perfect precision.
Also, I don't think particles are points, but instead excited states of quantum fields. — Ryan O'Connor
Forget about cameras, sensors, and speedometers - it all boils down to the question of whether a line can be constructed by assembling points. — Ryan O'Connor
Your earlier post indicated that you agree that this is a mystery (given the orthodox views)? Why not consider alternate views? — Ryan O'Connor
I'm not proposing we ban Infinity altogether. I'm proposing that we restrict ourselves to only use Infinity in a potential sense. — Ryan O'Connor
If you place iron filings over a magnetic field the filings will take a form in line with the field. While it's true that we only see the filings, it is untrue to say that the field is just a model. It's real. The same goes for quantum fields. — Ryan O'Connor
No. If we terminate the potentially infinite process we still get something useful (e.g. the rational approximation of pi on your calculator is a useful button). — Ryan O'Connor
But nonetheless banishing infinity from mathematics is a move of an ostrich — Gregory
But he/it doesn't, so the issue of passing particular points is no different from passing any point, and yet all those other points are never mentioned. Why is that, do you suppose? Achilleus - or the Arrow - seems to have no problem whatever passing those. Zeno's then, just an entanglement with words. — tim wood
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.