BigBango wrote:Abstract thinking is not "fantasy", it is "logic", mathematics, the notion of time and other mental tools we have with which we can use to try to understand the nature of reality. Science, on the other hand, takes our abstract theories and uses them to collect "real" data about the nature of reality. It just turns out that reality, as known through exhausting testing, does not always conform to what our abstract thinking has predicted.
It seems you have this backwards. The truths of science constantly change as they are based on experiential whims; on the 'uncertain' nature of 'experiential' evidence. Whereas the truths of logic/math are constant/unchangeable, and are
not reliant upon said subjective views.
Logic/math are 'a priori' (pre-experiential) truth. Science is an 'a posteriori' (post experiential) truth. Therefore,
Logic always trumps Science. Although I have great respect for science, it pales in comparison to the certainty/truth of logic (and math).
BigBango wrote:Xeno's paradox about motion is only a paradox that exists in the world of abstract mathematics where there are an infinite number of points along any segment of a line and we assume things in reality move from one point to another in that abstract space. But what we find is that in the real world things move through a discrete quantized space unlike the real number line.
Zeno's Paradox -- Zeno's paradoxes states that I can't walk over to you because I first have to get halfway there, and once I do, I still have to cover half the remaining distance, and once I get there I have to cover half of that remaining distance, ad infinitum. There are an infinite number of halfway points, and so according to (flawed) logic, I'll never be able to get there. But it's easy to prove this false by simply doing it, which we can all do. So we seemingly have a paradox, a contradiction, something that seems true but which, clearly, is not.
Since true paradoxes don't actually exist (as they are not logically possible), where is the flaw in this seemingly paradox?
Zeno's paradox, as written, conveniently disregards the dimension of 'time' to falsely denounce the possibility of 'motion'. Like a good magician, Zeno has his audience focus on the infinite number of 'distance' segments (and not on the infinitely decreasing 'time'), which leads our minds to (falsely) conclude that it would therefore take
for-ev-ver (an infinite amount of 'time') to cross over an infinite number of halfway points. But, this is not the case. For each and every halfway point, time is reduced in half (it takes half as much time to arrive at each halfway point).
For example: I can walk 1 yard per second. So if I were to walk to the halfway point (50 yards) across a football field, it would take me 50 seconds. And then 25 seconds later, I'll find myself at the next halfway point. And then 12.5 seconds later, at the next halfway point. And after 100 seconds have transpired,
I find myself magically standing in the end zone.
It is 'time' that propels me through space (and across the football field).
Zeno's paradox only proves, that without time, motion is impossible. But we already knew that. We already knew that motion can't occur without the pre-existence of time. Motion occurred (I traveled from 0 yard line to 100 yard line), therefore Time must exist. Now we have proof! Thanks Zeno
