What do you make of 1/3 = .333...? Can't you distinguish between a number and one of its representations that you don't happen to like? After all 1/3 is just a shorthand for the grade school division algorithm for 3 divided into 1. — fishfry
Yeah yeah. One of Zeno's complaints. If you look at the arrow at a particular instant it's not moving. How does it know what to do next in terms of direction and speed? Not a bad question actually, one that I won't be able to answer here. — fishfry
Suppose there were such a thing as an instant of time, modeled by a real number on the number line. Dimensionless and with zero length. So the arrow is there at a particular instant, frozen in time, motionless. Where does its momentum live? How does it know where to go next? Does it have, say, "metadata," a data structure attached to it that says, "Go due east at 5mph?" You can see that this is problematic. — fishfry
It still has nothing to do with what I originally said, which is that you don't need calculus to determine the instantaneous velocity of a moving object. And I'll concede that by instantaneous I only mean "occurring over a really short time interval." I have to say I'm not nearly as invested in this point as the number of words written so far, I should probably stop. — fishfry
An object moves with constant velocity. Does it have a velocity at a given instant? — fishfry
I'm not looking for people to buy in, I'm looking for truth. If others are looking for the same thing, they might like to join me. — Metaphysician Undercover
So we ought to conclude that "objects" and "processes" are distinct categories. — Metaphysician Undercover
I don't think you solved Zeno's paradox because you're putting the infinite quantity into philosophically blurry box and focusing just on finite results. — Gregory
[in reference me me asking why everything must be sharp] That's just how math 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
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
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
Time for you to develop a new axiomatic system, then, that leads to "Truth". — jgill
Pi is a finite number because it's inbetween 3 and 4. But if the length of a circumference is multiplied by pi than you have a length with space corresponding to each number, so the circle has infinite space within a definite finite limit (like being inbetween 3 and 4). Aristotle never understood this stuff — Gregory
The fact that your philosophy would result in a weaker mathematics is a red flag that you're on the wrong track. — Ryan O'Connor
I made this video on my proposed resolution to Zeno's Paradox. What do you think? — Ryan O'Connor
When I say that processes are valid objects of mathematics, I simply mean that they can be studied in themselves, just as one might write a book entitled 'The Art of Dog Walking'. — Ryan O'Connor
What does it mean to add one unchanging quantitative value signified by '2', to another? Mathematics does not answer this inquiry, — Metaphysician Undercover
Furthermore, the nature of spatial expansion demonstrates that there must points where expansion is centered. — Metaphysician Undercover
You must be aware that Aristotle rejected points (infinitesimals) and instants — 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. Which if at all justifiable, has to be justified within its own usages. Blending, confusing, or crashing different descriptions together just results in nonsense.At every instant in time the car's motion is indistinguishable from that of a parked car. — Ryan O'Connor
You take a snapshot of a moving car. You look at the photo and ask, "How fast was it going?" — jgill
Eternal circular motion is fine. — Gregory
In fact your earlier point is correct, any measurement is taken over time. — 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
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
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.