Zeno's Paradox, Phil the Philosopher ep:1
Nothing is real. The universe is a lie. Buy gold! Buy!
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Phil the Philosopher, An omnipotent paradox. Ep:2
, evenn though it came to a conclusion, there is surely a lot of loopholes in my theory as well. i didnt really explain calculus, i only told you about one in a hundred ways of finding a solution to this, we need to extreminate one logic and shift them around...using the help of logic, a rule that could break other rules, you could say that i cheated while using an infinite variable. in Quantum mechanics, the electrons could move from point A to point B without covering the space between them they could even exist in many location inn the same time, would zeno's paradox work on them? and we all have subatomic particles in our bodies that are capable of doing that, so does that mean we all teleport? hmm, looks like i just formed another paradox, anyway, speaking of reality and logic always entertain me, have a think about it
Goodness! You sure know what you are talking about. Glad to know toonator has members not foreign to fundamental calculus and physics.
All these paradoxes can be put in and equivalent form; A fast and slow objects moving along a line. If the slow object starts with a head advantage, the fast object can’t beat it in the race.. because when the fast object reached the starting position of the slow object, the slow object would have already moved. This scenario can be repeated infinitely.. that is the fast object needs infinite steps to catch up let alone win .. ie never wins. This is a real problem, and has been considered so by so many eminent mathematicians over the years.. in fact at one time, some thought that mathematics was doomed as a result of Zeno’s work.
The paradoxes contributed to the advance of, and was finally solved by the science of infinitesimals or calculus. At the heart of the problem is that the space and/or time dimensions are continuous or infinitely divisible.. because if not, there would be no paradoxes.. so one in fact can take the paradoxes to be a proof that not all the variables of physics are continuous.
Since space can’t be discrete, because it would mean things disappearing completely then popping up again at a different place, so time must be discrete. We should be ok with this, as we always measure time by oscillating or rotating things.. since there is a maximum speed which is that of light for any moving object, and a minimum distance/diameter, the period of rotation can’t be smaller than a certain value.. that is finite/discrete. This can solve all of Zeno’s paradoxes. ‘’Time enters mechanics as a measure of interval, relative to the clock completing the measurement. Conversely, although it is generally not realized, in all cases a time value indicates an interval of time, rather than a precise static instant in time at which the relative position of a body in relative motion or a specific physical magnitude would theoretically be precisely determined’’.
The calculus solution to Zeno’s paradoxes relies on the science of infinitesimals and that infinite sums can lead to a finite value. But when we look carefully, we see that the variables used in the proof are assumed to go to the limit in a controlled manner not random or independent.. like saying put y=ax then take the limit as x goes to zero. It is true that y goes to zero like x, and it is an equivalent process, but the fact that there is a ‘ratio’ between the two which is a, is ‘discretization in disguise’. That is the variables are not quite free to approach their values independently. So in my opinion even the calculus proof relies on the admission that some of the variables are discrete.
Not to forget also that QM is the champion of discreteness in the variables of physics. In this respect one notes that if time is discrete, then all other physics quantities that involved time must be discrete too. That is velocity, force, momentum, energy etc are all discrete.
But... Is this a theory or a true thing that has not been discovered? X'D
Plus, the arrow is only a symbol of motion. Whether it's an arrow or an atom or even a runner described by Zeno, measurements are finite that can be divided infinetly. I believe the term for such a thing is called a 'supertask'.
! However, I would disagree that an atom is the smallest measurment. Atoms do, at times, float freely. They don't just jump like pixels on a screen, they drift at their own speed; meaning, an atom can travel half the width of an atom, or even a fourth, or eighth, etc. Hence the paradox at play.
a paradox is something that brushes reality, but doesn't at the same time. It sits in between what's right, and wrong.
speaking of this paradox, i can see what you mean, but as the fractions get smaller and smaller, the time it takes to get half way is also smaller (because of length and velocity), therefore if we have 1/32 of the length, we'd also get 1/32 of the speed it takes to cross. So, this happens in real life and it happens all the time, but it happens so fast that we cannot measure it. The points would've never touched in the first place anyways either, because some of the air atoms between A and B would sometimes stay in the way between both atoms (right now, you are kind of floating in a way by standing or sitting). So, basically, this paradox works until the length reaches the length of an atom, because that's where the arrow stops.
Very commendable points! I love these inspired thoughts.
Stuff moves because way-point gets smaller as you go in, like this: 1/2 is the first way-point, the second one is 1/4, 1/2 of 1/2, and so on. Since they keep getting smaller, though, it would go like this: 1/2, 1/4, 1/8, 1/16, 1/32, etc. But since they keep getting smaller, it's never going to add up to more than one. Plus, we go past the halfway point to go to anything, so that just cancels the whole paradox out.
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