I was sitting the other day bored out of my mind and i came up with “proof” that logic does not comport with reality…
Consider this…
I’m sitting in my chair… i want to goto the bathroom… I’m about 20 feet away from the bathroom… to get there i have to walk half the distence first… then I would be 10 feet away… again… i have to walk half the distence first… so on and so forth…
I always have to walk HALF the remaining distence prior to reaching my destination… and if u do the math… I would never actually be able to reach the bathroom… i could get really close… but i would never be able to reach it… and i REALLY have to go!
This problem is known as Xeno’s Paradox, and can be easily solved by using grade 12 calculus.
This is a bit of a paraphrase, but:
Motion is usually thought of as a distance travelled over time4. Xeno’s Paradox ignores the changes in time and therefore the changes in speed of the moving object. The arrow in the first example would be pretty fast, so even in a small amount of time it would go pretty far. In the example, however, the time is reduced to almost nothing and since anything multiplied by almost nothing equals almost nothing, the distance, of course, becomes very small. In real-life, however, time keeps increasing5. Because of this, time multiplied by a speed gives a number and motion occurs.
So long as it is true that we must cover HALF the remaining distence prior to reaching the destination it is utterly impossible…
this conclusion rests on 2 premisses
that no value other then 0, can ever reach zero by being devided by 2
that one must always walk HALF the remaning distence prior to reaching the destination. (the value of the distence MUST be devided by 2 prior to reaching zero)
Conclusion: You cannot reach a destination unless you are already there.
This is a simple deduction… for this to be false one of the premisses must be false… but which one?
It’s not a simple deduction. You’ve hidden your assumptions in some informal handwaving. Let’s make your argument more formal.
If one is a distance x from a point and one is traveling toward the point, one must take a step of x/2 towards the point.
If one repeats this stepping process a finite number of times, say n times, one is a distance x/2^n away from the destination.
But x/2^n is not zero for any finite n, unless x is zero.
All you can infer from this is that one may not reach the destination in a finite number of the sort of steps described in the argument. It does not follow that one may not reach the destination at all using those sorts of steps, for one might reach the destination in an infinite number of steps. Furthermore that infinite number of steps might even be accomplished in a finite time! If we use calculus to conceptualize the notion of taking an infinite number of steps, we can demonstrate that this is exactly the case. Hence the paradox is solved.
both time and space are both infinitely divisible so that really doesn’t solve the paradox of motion… not only is half the distance never covered, half the time is never spent…
what solves it is the fact that humans do not move infinitessimally…
why are people saying space and time are infinitely divisible? I dont have my notes with me, but there are limits related to the smallest distance that can be moved by certain particles, and the smallest amount of time that a particle can act in.
This is completely irrelevant to the argument I made. I hope you weren’t trying to criticize my argument…
On the contrary, even quantum physics still works from the perspective of continuum mechanics. The popular notion of quantum mechanics “quantizing” or discretizing everything is misbegotten. If you take an intro quantum mechanics course you’ll see that concepts like continuity and continuous differentiability are very important to the physical interpretation of quantum mechanics. But these are ideas formed on the basis of the real/complex numbers, which form a continuum. In general, physics and mathematical analysis (that is, rigorous calculus) are so closely intertwined that I doubt we will ever see a physics formulated on the basis of quantized space.
In any case, with a little development my argument is essentially the resolution of the paradox. (I have a B.S. in math and physics so don’t dismiss what I say without a little thought – I’ll recommend some reading materials if you like).
no, I was responding to the original post, not your argument…
you missed the point of my objection… if you are counting the infinite series as a whole, you are still counting by one unit at a time… one infinite unit plus one infinite unit… still counting by ones…
If that proposition is correct, then it couldn’t be a question. The phenomena you describe in the proposition are nonsensical unless they bare a logical relationship, which is a rational function of the mind- nothing to do with the experience or the things experienced.
Whether or not there are “pre-existing structures of the mind” is determined merely by the formation of the thought process in posing the question. You are demonstrating the actuality of the predetermined structures of the mind in the logically active proposition.
Hmm…
I wonder what Locke would say to that. I know what Hume would say. But he’s boring.
Modern neuroscience does not support that idea. It points to the existence of mental “software” or what might be called “pre-existing structures of the mind.” Where do you find evidence of no pre-existing structures?
Modern Neuroscience isn’t even close to being logically sound, it is laden with presumption and error (and I’m not just talking about the inductive fallacy of the scientific method). My argument there are no pre-existing structures of the mind derives from the sheer absence of proof of such structures - people behave (and therefore one presumes, think) in so many different ways that even if there are pre-existing structures they clearly aren’t important or fade with time…
a) pee in your pants
b)scream really loudly so that people will hear you and take you to the loo
( although they will most probably send you to a mental institution if they hear why you can’t reach the bathroom so I do not think this option should be very popular for people in your situation.)
c)start thinking logically and just walk 10 feet and then 10 feet again.
d)start thinking even more logically and walk 20 feet non-stop.
I can see your argument says that you will never reach the loo. but that is only because you are stubborn and you half the distance every time. So logically you will not reach it. This is because you tell yourself that you will walk half the distance of every previous distance walked. What is the calculator’s end result? Please tell me, but i know it is probably 0.00450078 or something like that. The reality is that you half the distance every time. The logic is that you will thus have a tough time reaching the bathroom. This is just my opinion. But I have to admit i am not particularly mathematically gifted so if you can you should try to convince me that my viewpoint is bogus.
Well if you dismiss Neuroscience all in one go, then there is no point in talking about that.
While there is a lot of variation, there is not infinite variation in behavior. There are patterns. We can make fairly accurate predictions about what people will tend to do in a given situation. It isn’t perfect, but it isn’t useless.
I just think you are forgetting that there are two different realities here.
You are working with only one.
In your reality you create a series of distances ( numbers ) that are each half of what the previous distance ( number ) was.
In the reality of anyone else walking to a bathroom they do not do this. They are not prevented from reaching bathroom because when they reach that last 0.000450047 metres or whatever they defy the series that is created and just walk that small way further by breaking the so-called series. Like that other person said, the trouble with deviding a number by 2 until eternity is that you will never reach naught. only deviding naught by 2 will give you naught. So you will never reach naught metres. But no one restricts themselves by halving like that.
LOL 