You don't seem to quite grasp why I reject "closer". — Metaphysician Undercover
2) The limit of the journey corresponds to the final destination, which if anything would be (∞,0). — Ryan O'Connor
I surely disagree. There is no "final destination." That's MU's error, why are you amplifying it? — fishfry
Perhaps I don't grasp it, or perhaps I just don't agree with it. Let's assume it's the former. Please tell me whether the following points aligns with your view:
1) One can travel along y=1/x in the positive-x direction, without bound.
2) The limit of the journey corresponds to the final destination, which if anything would be (∞,0).
3) The point (∞,0) does not exist (since ∞ is not a number) therefore there is no limit. — Ryan O'Connor
I surely disagree. There is no "final destination." That's MU's error, why are you amplifying it? — fishfry
Yes that's what I'm saying, there is no final destination — Metaphysician Undercover
In short, I believe our disagreement is simply the result of us having a different definition of limit. — Ryan O'Connor
It is correct to say that the value gets lower and lower, but it is incorrect to say that it approaches 0, because no matter how low it gets it never approaches 0. — Metaphysician Undercover
The real description is that the value of y gets lower and lower without ever approaching zero. — Metaphysician Undercover
(and perhaps you would even agree that the greatest value which y never reaches is 0) — Ryan O'Connor
There is no such value. Might it be 100? Or 1000?. y=1/x, x>1 has a greatest lower bound, 0, which it never reaches — jgill
We both agree that y gets lower and lower (and perhaps you would even agree that the greatest value which y never reaches is 0) but I call that approach and you call that not approaching. Let us agree to disagree on definitions! — Ryan O'Connor
An infinite acceleration is required to go from rest to moving. — Metaphysician Undercover
/ / ----------o
resolving the problem of how the non-dimensional truly relates to the dimensional. — Metaphysician Undercover
This function is not differentiable at zero. There is no instantaneous velocity at zero and no definite acceleration either. I agree that this is counterintuitive, and your intuition is not uncommon. But it's wrong. Clearly it's wrong. If you experienced infinite acceleration even for a moment, every atom in your body would be flattened like so many pancakes.
I actually agree with you about the intuition. If we're not moving, how do we start moving? It's a bit of a mystery actually, I'm not sure what physicists say about this. Well I guess I do know. If we're a steel ball in Newton's cradle, or we're a ball on a pool table, we start moving when we get smacked by another ball that transfers its momentum to us. But how does our velocity go instantaneously from zero to nonzero? The Newtonian physics works out, but not the intuition. — fishfry
relativity theory which denies the reality of rest, — Metaphysician Undercover
As I explained, by way of example, to assume such a "greatest value", or "lowest value" is contradiction. When we say that the natural numbers are infinite, and therefore have no highest value, it's contradiction to say that 20 is closer to the highest value than 10. Likewise, when there is no lowest value, it's contradiction to say that .01 is closer to the lowest value than .02. — Metaphysician Undercover
No it's not. When you get in your car and start driving to the store, do you experience infinite acceleration? What's that feel like, exactly? — fishfry
I actually agree with you about the intuition. If we're not moving, how do we start moving? It's a bit of a mystery actually, I'm not sure what physicists say about this. — fishfry
I'm not convinced that Diogenes appreciated that profundity of Zeno's paradoxes. — Ryan O'Connor
I addressed the issue in my post. There is only a need to conclude infinite acceleration if we assume absolute rest, — Metaphysician Undercover
I actually agree with you about the intuition. If we're not moving, how do we start moving? It's a bit of a mystery actually, I'm not sure what physicists say about this. Well I guess I do know. If we're a steel ball in Newton's cradle, or we're a ball on a pool table, we start moving when we get smacked by another ball that transfers its momentum to us. But how does our velocity go instantaneously from zero to nonzero? The Newtonian physics works out, but not the intuition. — fishfry
Yes that's what I'm saying, there is no final destination, so to even produce any representation (such as ∞,0), as if it is a final destination, is a misrepresentation amounting to contradiction. — Metaphysician Undercover
There's at rest in a given inertial frame. Which is to say, really, that any acceleration, on your theory, should involve instantaneous infinite acceleration. My hand is at rest on the table. I raise it to type. Space-time not locally crushed in the process. — tim wood
There's at rest in a given inertial frame. Which is to say, really, that any acceleration, on your theory, should involve instantaneous infinite acceleration. My hand is at rest on the table. I raise it to type. Space-time not locally crushed in the process. — tim wood
You are equating 'approaching' with 'arriving at'. — Ryan O'Connor
But if my trip never ends there are some situations where I could still give you some useful information since in some situations I could still tell you which direction I'm pointing (e.g. what I'm approaching). — Ryan O'Connor
I addressed this in my post. The position and velocity functions are not differentiable at time zero. So there's no well-defined acceleration. Nor as others pointed out does relativity bail us out. Relative to your own frame of reference, you are at zero velocity at time zero and nonzero velocity a short time afterward. You have to come to terms with that. — fishfry
I know one mathematician who thinks the world is discrete and that continuity is a fiction, and then I know another who believes the reverse. — norm
This "at rest" which you refer to isn't real, because the earth is moving. — Metaphysician Undercover
If I point out to Metaphysician Undercover that he can get in his car and drive to the store without being crushed before he drives the first inch; am I failing to appreciate the profundity of his beliefs? I think not! — fishfry
If you can apprehend this, then why can't you turn it around, and see that when infinity is at the low end, there is no such thing as "the lowest number", and it doesn't make any sense to say that someone counting lower and lower is "approaching" the lowest number? — Metaphysician Undercover
In practice the world is continuous (time passes continuously), but in theory the world is discrete (represented by distinct units, numbers). — Metaphysician Undercover
If time can be broken down into a collection of instants and if at one instant we're stationary and the next instant we're not — Ryan O'Connor
I think he's touching on something — Ryan O'Connor
A mathematical line is composed of points. But there is no "next" point after any given point. — fishfry
By the way, how do the zero-dimensional, zero-length points in the unit interval make up the one-dimensional, length 1 unit interval? That's actually another mystery... — fishfry
that a line is not composed of points, but instead points emerge from lines? — Ryan O'Connor
I would argue that objects are continuous but measurements are discrete. This allows us to use the richness of mathematics that calculus offers while avoiding the paradoxes of actual infinity. — Ryan O'Connor
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