I strongly disagree with this. Zenos paradox is very much a philosophical puzzle and is appropriately placed in my opinion. If Zeno truly is right and he does make a decent argument then it would have serious philosophical ramifications. Well this may be a high idea it is most certainly a philosophical one as well.
The notion of "infinite" has always fascinated me. In fact, sometimes i get the sense that infinite, automatically brings in the world of the paradoxical by its very nature. Think about it, of course it would not make sense to our finite understanding to say that there is an infinite amount of space between two finite points. This is because the nature of the realm through which we attempt to express "infinite"(The conscious thinking mind/intellect) is itself finite, in other words it does not have the capacity to deal with such concepts and fully grasp them, thus the conscious thinking mind is vulnerable to rejecting concepts that don't "play by its rules" as it were. To reject the notion of the infinite in any case on the basis of logical reasoning which is a tool of the finite conscious thinking mind/intellect. Whilst it can not fully grasp such concepts it can choose to either accept or reject such a notions. To use reason and logic to approach the infinite almost feels, to me, like using the wrong tool for the Job. I think the infinite is more suited to intuitive reasoning what do you think?
From how I pictured this in my head, it would seem like you would not move at all because you're spending all your damn time dividing.
Sorry for the wall of text. Got a little carried away. Was really bored at work. Stick with me on this one. To say that there is an infinite amount of points between two points in space is not saying that there is an infinite amount of distance. In fact it is a finite distance because anything that can be measured and has end points is finite. The idea is that between two points there is an infinite amount of subdivisions that can exist. Basically I can always make smaller and smaller points or subdivisions because you can think of smaller and smaller numbers infinitely. So basically we take an infinite amount of points, which composing a certain finite amount of space and empirically represent that amount of space by agreeing up certain base sizes or units such as feet meter whatever to use as reference points. This is why Zeno fails in my opinion. He's representing motion and time in an inaccurate way. Just because there is an infinite amount of subdivision doesn't mean it doesn't compose a finite a amount of distance. Think of it this way you can divide 2 by x and get a number for basically any value of x greater than zero all the way to infinity but no one would say the magnitude of 2 is infinite. That's basically what Zeno did. He said I have some distance and I can go halfway, and then halfway again forever dividing the distance left to travel, let's say d=10 by 2^x. Similarly as to before this equation has an infinite amount of possible values because you can always think of a smaller and smaller number. The problem with zenos representation is that it treats motion as if it were just attempting to half the distance. But that's not how motion work, we move however fast we are and we'll move a certain distance after x amount of time based on our speed and acceleration. Given the right amount of time and speed we can go always go a certain distance. The reason being that infinite subdivisions doesn't mean the space is itself infinite and therefore easily traversable. That's just my .02 though, I'm no mathematician, just a math nerd as you could probably tell. Honestly though Zeno has a pretty decent argument. Definitely a hard theory to beat.
To say that there is an infinite amount of points between two points in space is not saying that there is an infinite amount of distance. The idea is that between two points there is an infinite amount of subdivisions that can exist. I believe, in saying that an infinite amount of points are contained within the bounds of two points finitely separated, is to say, or at least to implicitly suggest an infinite amount of distance. Or, if not, let me ask you, nativetongues, is every subdivison, contained within one single subdivision, spatially extended? And, if so, and one single subdivision, in a series of them, can be divided infinitely, and each infinite subdivision contained within that single subdivision's bound is extended in space, then, what is the extended distance separating each subdivision within an infinity of them?
All I'm gonna say in response to this is all infinities are not the same. If you don't believe me ask a mathematician or read a book on it. So even though theoretically a distance of 2 feet and a distance of 5 feet will both contain an infinite amount of points, you would intuitively not say they are equivalent distances. That is because we take an infinite amount of points and compare it to other sets of infinite points until we find two that visually are identical or some ratio of the two. It's a way of measuring something which is theoretically infinite, but in reality is very obviously finite. So I will say that, unless you are someone who subscribes to the skeptical whirlpool or immaterialism, it's very obvious that a distance represents a finite amount of space, because there is a beginning and an end. Infinity can never be represented numerically because it has no end, it is merely a never ending direction.
I think even in terms of distance this may be true. Let us say that theoretically if a person would start to walk that distance, but at the same time let us say that he shrinks at such a rate that as he moves forward he has covered relatively no ground at all, the distance between the ends of his room remain the same but because he keeps getting smaller the relative distance he has to walk keeps getting longer and longer infinitely...
He's not trolling. This is a pretty serious philosophical puzzle. I know it seems a little silly, but there is a lot to ponder about this question. How can one measure an infinite amount of points? It's definitely a mindfuck and something that is worth exploring. Just google zenos paradox.
This is like the third or fourth version of this thread I've seen. Who knows how many I missed I didn't realize this "paradox" was so popular hey man. ba-a-a-ack off. I can be a sheep all I want!
I never said it was easy. Just that it can have real implications to philosophy. Sorry if I'm coming across as a prick. Just letting you know it's a very real philosophical question. I learned about it a decent amount last year in my philosophy class.
Well it's very tempting to argue this, it really does nothing to disprove Zeno. Zeno would merely argue that you are using empirical evidence to argue a rational idea. He would just say that motion as you perceive it is very possibly a figment of your imagination, or that we are all immaterial things and motion is a projection of our conscious or some shit like that. Sounds a little ridiculous ,and I don't subscribe to his belief, but it is very hard to disprove without empirical evidence. Zenos paradox is just that a paradox. There's no way of really solving it in a rational manner at least with our current understanding of infinity. Basically we all know Zeno is wrong, it's just impossible to prove rationally, which is why Zeno is so frustrating.
It's more of a mind fuck if every step you take is half as far as the step before you'll never get there. The way it was phrased in the OP is not a mind fuck. That's just small fractions.
No offense taken. I tried to comprehend what you are trying to comprehend. I got all the way down to an atom and split that in two. I think that causes an atomic explosion so thats as far I got. Can we split the nucleus of an atom in two?
We can't physically split. But an atom is most definitely composed of smaller parts, and those of even smaller parts, possibly going on for inifnity. Honestly I'm not quantum chemist but it's something I'm fascinated with and would love to study/ work on some day. Just think of it this way. I can always conceive of a smaller distance even if I can't physically represent or understand what that difference is. I can always add more zeros to a low decimal going on forever. Thus you can create infinite subdivisions of anything finite. 2/x can be any number, except 0 and will approach infinity as x approaches zero, at least from the positive side, which isn't an issue because we're not creating negative subdivisions, which wouldn't make sense.
So, if me sitting on this couch is 0. And 10 feet to the door is infinity, once I walk past the door I go infinity and beyond, therefore passing infinity. I don't know who zeno is but it sounds like he is trying to make up excuses.
You can smoke half a joint, and then half of that, and so on, forever. On paper. In your head of course, those tiny tiny hits won't get you too high, so don't expect everlasting pot.