Refuting Zeno's Paradox-Series on Infinity Part 7
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[2012-05-14 03:13:38] Thepoliticalrealist - Assume Achilles ...
Assume Achilles runs at 10 feet per minute and that the turtle mosies along at 1 foot per minute. Assume now that their contest has been going on for 3 minutes. Achilles has moved 30 feet and the turtle only 3. How has Achilles not passed the turtle? For Achilles to reach a final distance greater than that of the turtle there must have been a convergence of points and Achilles must have overtook the turtle.
[2012-04-03 15:10:46] Neverbeendead - Part 2 of my answer ...Part 2 of my answer. The math of the professor is also correct. Achilles can still move further with his speed after a minute. When two truths contradict each other the answer is always simple. Reality revealing a possible impossibility. Enjoy the study of all impossibilities. Are they as possible as the one revealed example and how do they all interact with each other?
[2012-04-03 15:09:43] Neverbeendead - Part 1 of my answer ...Part 1 of my answer The math of xeno is correct. The turtle is always ahead in this correct system of Xeno. The turtle is always half the distance ahead of its previous distance ahead. You can actually do the conversation in real time in the name of the turtle: Now i'm 0,5 ahead, now i'm 0,25 ahead and so on but you're gonna have to talk faster and faster or tape it with camera that is able to do more and more frames per second and watch it while the speed of the video slows down.
[2012-03-09 02:03:45] tman1223334444 - If you say ∞+1=∞ ...If you say ∞+1=∞ and any other form of manipulating ∞ is ∞, what value ( besides the limitless things you can find about it) does it have to math/physics if what ever you do to it is ∞?
[2012-02-27 10:49:11] digitizerSF - PLEASE...post the ...PLEASE...post the next one!! Where' is part 8? (Replace "1 minute" with epsilon and we're well on our way to dealing with basic analysis!)
[2012-02-14 07:40:42] zieben64 - I got a good idea ...I got a good idea when you said a "third turtle". here it goes Assume Zeno is right, you do not reach 1--you will arrive at a contradiction. Zeno says we can get to 1/2, good. Give the same argument for 1/2 as Zeno does for 1, that it cannot be obtained. But we already know we can obtain 1/2. This is a contradiction, so premise is false. I think yours is better though now that I think about it
[2011-12-24 13:57:44] steverock85 - I think math is ...I think math is perfect tool to relate to our reality. It can not tell us how and why about things that is not within our set to explore any more than physics. Physics is based on math as it is a tool to observe our reality. "Real" truth will always be a guess or imagination of our own mind. Maybe nothing exist and everything exist at the same time, giving us infinity set of possibilities. Maybe there is no real truth... Who knows...
[2011-12-24 13:40:52] steverock85 - But they are two ...But they are two unrelated sets in our mind. Like the division set of one is not the division set of two. The one will connect us to the two, but how do we reach one itself?
[2011-12-24 13:36:10] steverock85 - Beautiful :) Still ...Beautiful :) Still, I don't think infinity can be defeted that easily. When we observe each point in 1/2^m they are counted as 1 static point. Or you can think of it as you give yourself one static number in time to explore each half way point. If you do so, you will be doing just that in a very, very long time. But if you have infinity of time, then you will reach it, or rather, "there is an observation for each point, including the the point where akiles passes the turtle".
[2011-12-10 00:03:15] iateyourgranny - Also, you didn't ...Also, you didn't seem very nice to philosophers. You said you would explain in a way that they would understand (implied as different from other mathematicians'), but you gave the same explanation that any high school maths teacher would give.
[2011-12-10 00:01:28] iateyourgranny - What I mean is the ...What I mean is the maths is sound, yes. But I'm just not certain that it really relates to reality. As far as I've learned, calculus depends on continuity. But what will it do when nature gets discontinuous on the most basic scale? I did pose a question to my calculus professor, about if a function defined from integers onto integers can be continuous. According to the definition of continuity that he gave, it turns out it indeed can. I'll need more thinking.
[2011-11-29 10:49:13] SSCCMath142 - Thank you for ...Thank you for removing your earlier comment. Zeno's paradox is not about modern physics' take on this problem at the atomic level. It is about refuting Zeno's arguments, which required a clear definition of infinity and infinitesimal. Calculus successfully deals with situations approaching 0 * infinity. I really doubt any professional philosophers are still seriously arguing about this paradox. I only "attacked," as you say, the amateur "philosophers" who haven't yet learned the math.
[2011-11-28 06:42:03] iateyourgranny - no need to attack ...no need to attack philosophers for questioning the relevance of your precious mathematics in the real world, professor
[2011-11-28 06:39:07] iateyourgranny - Let's use this ...Let's use this infinitesimal calculus that you speak of then. For each dx that tends to 0, the time taken tends to 0. Then the total time taken to reach the turtle is 0 * infinity. Besides, modern physics has shown that as you take a smaller and smaller interval for the position of Achilles, the uncertainty in his velocity gets higher and higher, until he might just as well be slower than the turtle. So I think the problem is in the supposed ability to break down distance infinitesimally.
[2011-10-05 18:26:09] Hrejwaltz - now go crazy.... ...now go crazy.... watch?v=I1Xs0G__KJM
[2011-10-05 18:23:41] Hrejwaltz - watch?v=Eb-Fi8GI6PE ...watch?v=Eb-Fi8GI6PE&feature=related here it is... 1D infinite, but very finite in 3D A simple Mobius Strip.... the concept is the same for each new dimension... 2D infinite is finite over 4D... [someone recall Space-Time fabric? it is the basics of this idea] 3D infinite is finite over 5D and so on...
[2011-10-05 18:19:13] Hrejwaltz - That was the error. ...That was the error... Since we understand that, yes, no matter how much two of us walking different distances, we walked the same amount, the infinite.... as Galileo's paradox... between 0 and 1 is the exactly same amount of between 0 and 2 or 0 and infinite... The apparent amount is the illusion, not the movement... Older cultures knew that... "interpretations are illusions" they say, but the fact is just one. btw, each infinite could be contained and finite in higher dimensions.. not new wave.
[2011-10-05 18:12:39] Hrejwaltz - then we have the ...then we have the 6D.... it would, following this explanation, be a cube... made by the planes of range of possibility.... and so on Zeno's paradox, prior to confirm that the runner would not pass the turtle, proves that each and every single movement is not a single and ordinary fact, but we surpassing probabilities... or, as i like to think, MAKING DECISIONS... He may not had this in mind, but he proved that every movement is impossible, and called everything beyond that impossible or ILUSION.
[2011-10-05 18:07:54] Hrejwaltz - Lets take a single ...Lets take a single atom... considering the movement in 3D, the "world"... it has 360 degrees of movement in each of the 3 planes it is allowed to move... x, y, z Is a huge possibility of movement, but limited and countable... So, 5D could be the RANGE of possibility... a plane made by timelines
[2011-10-05 18:03:40] Hrejwaltz - that makes 4D the ...that makes 4D the passing of time, as described by einsten.... a collection of points, infinite in their own, making a LINE... timeline... then you have possibilities... one thing could move to left or right, making 2 different possibilities in the next time frame... respecting the Zeno's motion law... A could not reach C without pass thought B if B is in the path from A to C... [Half path] if defines a limited range of possibility... a plane of possibility made by timelines...
[2011-10-05 18:00:27] Hrejwaltz - in order to make ...in order to make that understandable, we treat the collection of 3D infinites, points, each one infinite in size... now lets assume that you have the position of EVERYTHING in the 3D universe... You are now omniscient of one single step of EVERYTHING.... and then something moves, one single atom moves, it makes you no longer know everything [one false makes the sentence "ALL TRUE" a false statement] but if you could calculate again and know again, you will have 2 different infinite collections
[2011-10-05 17:56:34] Hrejwaltz - And again... The ...And again... The cardinality of infinites is very similar to the dimensions theory... if you have the infinite cellection of points you have 1D, a endless line If you have the infinite collection of lines you have 2D, a plane made by lines If you have the infinite collection of planes you have 3D, a cube made by planes then a shift occur, since you cant have infinite cube collection since they would occupy the same position in the universe bcz you already have the 3D infinite full
[2011-10-05 17:34:01] Hrejwaltz - At start you have ...At start you have infinite possibility and infinitesimal action... As steps goes by, the infinitesimal action grow and the odds of the runner DO NOT pass the turtle decreases... making the possibility of the runner to pass more likely, more possible and mainly.... more easy to occur in fewer steps When it gets as easy as it can, it doesn't matter if you can add or not because the distance of the facts are as close as it can to a single step....
[2011-10-05 17:32:53] Hrejwaltz - Between T0 and ...Between T0 and T1min you have infinite time steps... the only true question is what the hell happens when you have a shift of infinite cardinality.... I mean... the only thing this paradox shows is that each new step, whatever if it is step on distance or in time, it gets closer to the reach point of running out the possibility of the runner DO NOT pass the turtle... It is the same paradox that confines possibility and impossibility...
[2011-09-20 19:29:09] srfriggen - From what I learned ...From what I learned in my calc II class a long time ago was that, 1. After this argument Zeno declared that time did not exist! And 2, Zeno's misunderstanding came from the lack of knowledge of a continuum.
[2011-08-26 21:29:39] FrozoneNetworks - Excellent ...Excellent presentation. I certainly learnt a lot from originally knowing nothing about it.
[2011-07-23 19:36:58] okzoia - I am a philosophy ...I am a philosophy student and your proof convinced me. I'm certainly no mathematician, but your presentation was crystal clear, and it seems to square our common sense experience (that things move unproblematically) with reason. Rick
[2011-06-23 02:54:09] astronomer747 - The fallacy that ... The fallacy that Zeno makes is in assuming that the whole interval is a composition of an infinite number of points. Aristotle argued that the whole line is conceptually prior to any divisions we could make of it. Of course, the process of repeatedly dividing the distance between two points could be continued indefinitely, but infinity in this case is merely a limit concept.
[2011-06-18 17:42:11] bedwarri0r333 - wheres the rest?wheres the rest?
[2011-05-09 04:37:52] jakejakeboom - I love your videos! ...I love your videos! After watching them, I convinced myself to take an AP calc course next year. Hopefully i won't regret it...
[2011-05-04 18:51:44] zadeh79 - Planck's constants ...Planck's constants suggest a minimum possible length of time (and space). Because according to this, in the physical world, there is no interval of time less than 10^-43 seconds, the minimum transition of achilles or the turtoise, through each 'stage', must be equal to no less than their (Velocity X 10-43 sec). In other words, there is a minimum distance which must be traveled, so there is in fact, a finite number of stages.
[2011-05-04 18:26:17] zadeh79 - That explanation ...That explanation solves it, and not many people get it right.
[2011-03-02 16:24:22] SSCCMath142 - Ausgezeichnet! ...Ausgezeichnet! Let me know how it goes. (Jon--author of the video)
[2011-03-02 16:14:29] lintusama - I really love the ...I really love the way you explain these thinks. I come from Germany and I understand it! Tomorrow I'll try to present these things with infinity in my math lesson. With your help it will be very easy! Thank you so much!
[2011-01-30 01:52:20] LocustFurii - Great series! I was ...Great series! I was wondering if you could do an episode on Marko Rodin's Vortex Based Mathematics. Just google it if you haven't heard of it and goto the "Intro & Summary" page. His math formula using shows how all integers can reductively be added together to get back to 1-9 and from that is able to create a model of infinity. In fact his model seems to introduce a few different ways of creating infinite numbers. I thought you might find it interesting and I'd like to see a video response.