Surprisingly for Xeno there are not an infinite number of points in the metric of distance but that does not apply to time, which is a concept based on distance not a “real” issue. If they are not related by an exact relation then one must converge even if the other doesn’t if they are related by an exact relation then they converge at infinity. The answer is to get your head round how time and space are related and forgo the useless conclusion of distance having infinite points.
Na I just mean unless you can explain it you wont really of understood it. Mission accomplished.
Learn calculus is my suggestion and look at Maclauren-Taylor series which attempt to solve insoluble calculus by using infinite series to approximate it. Aristotle did that, clever huh.
I always found such exhaustive solutions to be unsatisfying, but they do work up to a point.
I’ve talked about this many times, and find that the question is one of comprehension, its not easy to resolve unless you can explain why its easy to resolve.
God no, I’ll stick with my ignorance on that one. Aristotle had too much time on his hands.
Why do we need to resort to maths however, to explain why something does eventually close the distance between itself and some other point in space…? If you’re a maths-head, then sure, knock yourself out. But it remains that my more common-sense explanation works jus’ fine.
I mean sorry, is it wrong…? C’mon Mr. C., throw me a frickin’ bone here. I’m presuming you’re understanding what I’ve been trying to say.
Maybe I should have added ‘metaphorically’ a lot of times in the last few posts.
Maybe you should start doing some genuine philosophy. Find your own terra incognita in the domain of knowledge and start mining for new, precious metals.
We don’t but maths is about absolutes and converge is another way of saying their is an absolute and general solution often as not. Divergent maths is a pain in the ass as its non linear, and can’t be put in a box, converges at infinity means its assymptotic and their is no solution in this case. Mathemeticians like solutions that can be shown beyond reasonable doubt and since it reflects the science perfectly it tends to just support the evidence, eventually the ball stops bouncing and the arrow thunks into the turtles ass whether the maths is wrong or not it is subservient to science not the other way around.
Oh and since it started off as a mathematical problem that ignored reality, it ended quite convincingly as one that reflected reality, everyone’s happy, well except people who cannot understand the simplicity that the more you cut something up even ad infinitum the closer to a solution it comes hence integral calculus, the more bars in a graph under the curve the close to reality is the bouncing balls solution, at infinite bars, or time points the solution converges exactly to a relation that mimics radioactive decay.
We use maths also because when you understand the solution its impossible to refute it without claiming reality is wrong, it converges with reality.
Anyway, thanks for your help Caldrid, I suspect however, with muggins here, you’re throwing good money after bad. I kinda get what you’re saying but, I lack the sense of visualisation when it comes to maths. With my version I can see in my mind’s eye quite happily the virtual lines of perfect (and un-interfered-with) trajectory springing from any moving part of our bodies, or any moving object, extending off into infinity, fanning out in space as new lines are ‘drawn’ with each change in the direction of movement as the limb orbits around its joint etc. But with equations… Nope, I just see numbers and squiggles.
This thread is. But no it is a gradually diminshing sine wave that ceases at t=x or converges. A balls bounce is a periodic decay modled precisely by the half life decay constant. This could be loosely determined as a decay constant where as time is further and further halfed or split into smaller and smaller parts, then x converges to a solution and t is relative to it.
In theory and in a zero atmosphere scenario with a decay constant set to the exponential terms like the half life, the ball should stop bouncing when it’s halflife t(s) is doubled.
t_1=the time it takes for the ball to make its first bounce.
superfluos maths gibberis in function notation to make it look like I know what I am talking about.
Since the exponent is negative then the decay is a negative for time and positive for distance.
As you can see the limits are between 0 and infinity, but the equation has both a general and exact solution of 1/decay constant or the half life, you can manipulate it therefore to establish any of the terms precisely as an exact relation.
Maybe I should have added ‘metaphorically’ a lot of times in the last few posts.
