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| A 'simple' Physics postulation... |
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| magic:
--- Quote from: TimFox on July 11, 2021, 07:38:03 pm ---It is very easy (and smug) to dismiss early work on a concept as a "kluge" in hindsight, just like the 20th-century physics innovation of the "Dirac delta function", which was useful for decades before the mathematically-rigorous definition in terms of "distribution theory". --- End quote --- No, that's backwards. The early work I called "handwavy" and the kludge is all the mental gymnastics that followed to make it "strict". Such as: --- Quote from: some mathematician somewhere ---Let's consider all infinite sequences of rationals divided by the relation of Cauchy co-convergence, that's clearly the set of numbers that are real. I mean, because we need it that way to make our theory work. --- End quote --- Makes a lot of sense :D Or, you said something about transfinite numbers, any progress on figuring out how many alephs there are before the continuum? --- Quote from: yet another mathematician ---So we have that problem that we don't really know what a "set" is, let's try some common sense axioms and everything will clear up. --- End quote --- :-DD Yes, I'm kidding somewhat. But that's because the whole thing is funny :P |
| Nominal Animal:
Thinking that there is no single moment when the object has zero velocity because moments have duration is mixing completely different scales together ignoring their associated assumptions/contexts and replacing them with another, and getting garbage as a result. As stated, the only sensible answer – both in the human scale and in the physics sense – is that yes, the trajectory does include a point where the vertical velocity component is zero. Anything else is randomly picking one set of details and completely ignoring others. (When we do do that, we try to pick a consistent set. That is the difference between an approximation and an informed guess.) If we assume the object is made from ordinary matter, it is actually a writhing mass of atoms and molecules that never "stop" unless cooled to so close to absolute zero that you cannot measure the movement anymore. How do you measure the location of such a blob? Its center of mass? In the human scale, objects pretty much perfectly follow Newtonian physics, because of the inherent assumptions about scale and precision. Mixing in Planck timescales is utterly silly, because that object itself is just a vaguely defined fuzzball of atoms and molecules; probably losing and accruing atoms and molecules on its surface constantly. If we assume it is an uniform solid, it is no longer a physics question; it is a speculative question about fictitious physics. Sci-Fi. |
| T3sl4co1l:
Another way of putting it: where is a line? Say you mark a measurement with a chalk line. What position is that line actually representing? The chalk mark is obviously fairly wide. Do it again with a pencil, or a scribe. It still has width, and subsequent uncertainty. (The scribe at least might leave a v-shaped groove that we could find the root of. But other than that, it still has width.) What if, instead, we declare that the position shall be the edge between two regions. We can use a permanent marker held tightly against a rule, which marks a sharp ink line in the same position as the ruler's edge. The position is perfectly defined because the ink doesn't spread out (heh, well assuming a nonporous material and gel-like ink/paint, but you get the idea). Of course the rule and pen tip and everything won't be perfectly smooth and repeatable and all that, and the materials are ultimately made of atoms, but the important difference is taking the edge of some region, rather than trying to eyeball the middle of it. It's the same idea over time rather than space. An instantaneous moment is a zero-time boundary between times before and after that moment. A finite moment, is some period of time around a moment. Tim |
| TimFox:
Some of these snide comments about technical language in mathematics make me think that 19th and 20th century mathematical progress is something that happened to other people. |
| aneevuser:
--- Quote from: TimFox on July 13, 2021, 01:48:00 pm ---Some of these snide comments about technical language in mathematics make me think that 19th and 20th century mathematical progress is something that happened to other people. --- End quote --- Well, 19th and 20th century mathematical progress is something that happened to mathematicians, I think it's fair to say. You won't find many "users of mathematics" (physicists, engineers, etc) who have studied formal definitions of limits, or who have heard of the IVT, or of Dedekind cuts or whatever. But I don't think it matters too much, most of the time; you don't need to be able to make an epsilon-delta argument to learn enough calculus to get a physics or engineering degree. |
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