Ph3N0M Posted April 18, 2013 Report Share Posted April 18, 2013 Exactly what paradox are you talking about, that has been debunked? You can't call something a paradox if the real reason of trouble is that there was simply no real definition of the thing causing confusion(in this case, the number of elements of an infinite set, before cardinality was discovered and debunked the confusion). No need to call me Jesus. Was just offering friendly advice on what to read if you are fascinated by these things. Link to comment Share on other sites More sharing options...
Sackboy Posted April 18, 2013 Report Share Posted April 18, 2013 I am good at math that is not school sh*t , the concepts are clear to me but problem solving annoys me a lot . I somehow can't do it , the education system sucks . I love the concepts of mathematics and have even delved into some very deep concepts but the school stuff is too boring for me . None the less Zenos paradox is one of the most interesting paradoxes , paradoxes related to infinity fry my brain , like this one http://en.m.wikipedia.org/wiki/Galileo%27s_paradox Here , what's your explaination for zenos paradox ? Link to comment Share on other sites More sharing options...
Ph3N0M Posted April 18, 2013 Report Share Posted April 18, 2013 I wasn't talking about Zeno's paradox. Was talking specifically about the current ongoing discussion about how come the "number" of squares is equal to the "number" of numbers, while at the same time, being "lesser" than it. The different infinities that I mentioned has nothing to do with Zeno's paradox, and that's why I asked when you said that "I have read about different infinities as well , its a paradox that has been debunked now". Anyway, regarding Zeno's paradox: Zeno said that to cover a distance of 1, you must first cover 1/2, then 1/4, and so on, which implies that you simply can't cover it(in fact, can't even start covering the distance). His main problem was regarding summing up an infinite number of terms, which is now made precise with the epsilon-delta arguments of analysis. We now know what the sum of an infinite number of terms means, and when it exists. In this case, (1/2 + 1/4 + ...) of Zeno is the limit of the sequence of partial sums(that is partial steps to cover the distance), which is 1(can be proved rigorously). So, that expression IS actually equal to 1. Link to comment Share on other sites More sharing options...
Sackboy Posted April 19, 2013 Report Share Posted April 19, 2013 But the paradox is that it will have an infinite number of steps , and can a process with infinite number of steps ever complete ? Because the last step will never occur. Link to comment Share on other sites More sharing options...
Nemo Posted April 19, 2013 Report Share Posted April 19, 2013 why are we (or zeno) assuming that the steps taken are necessarily half ? or is it that this is something he cooked up to set up the premise of the paradox in the first place ? like instead of going by a set pattern and discovering a paradox he established a paradox and then worked backwards towards legitimising it. Link to comment Share on other sites More sharing options...
The Wolfy among us Posted April 19, 2013 Report Share Posted April 19, 2013 This is actually a cloud. And that's not a paradox. Link to comment Share on other sites More sharing options...
Ph3N0M Posted April 19, 2013 Report Share Posted April 19, 2013 But the paradox is that it will have an infinite number of steps , and can a process with infinite number of steps ever complete ? Because the last step will never occur. See. When you are walking a distance of 1, it is true that at some point your position(your legs may be in the air at that time, as they may be making their next step at that time) will be at 1/2, sometime later at 3/4 and so on. But your individual steps have a finite nonzero length, which ensure that you'll reach 1 after a finite number of steps. If you were a machine that could take arbitrarily small steps, and it were forced to make a first step of 1/2, second of 1/4, third of 1/8, etc., then it would surely never reach 1. It would always be very near 1, but never at 1. The final position of that machine after nth step would be (1/2 + 1/4 +1/8 + ... 1/2^n), which will be always less than 1. It doesn't happen because covering arbitrarily small steps is not possible in reality. In reality, the process stops when your position reaches 1 and it takes a total time of (1/2 + 1/4 + 1/8 + ...) = 1 seconds, assuming that you cover the first 1/2 distance in 1/2 seconds, another 1/4 in 1/4 seconds and so on. why are we (or zeno) assuming that the steps taken are necessarily half ? or is it that this is something he cooked up to set up the premise of the paradox in the first place ? like instead of going by a set pattern and discovering a paradox he established a paradox and then worked backwards towards legitimising it. That's the catch. He is not assuming that the steps taken are half. He is just saying that at some point you will be at half(without knowledge of what the length of the individual steps are). He is saying that since you'll need a non-zero time to cover each half-distance how come you complete the process in a finite time? His confusion is there because he is not versed with the possibility of an infinite series, converging to a number. Link to comment Share on other sites More sharing options...
Sackboy Posted April 19, 2013 Report Share Posted April 19, 2013 Watch the video , man , tumhe lagta hai its very easy to explain but this has baffled mathematicians is 2500 years ago . Its not that easy to explain. Link to comment Share on other sites More sharing options...
Sackboy Posted April 19, 2013 Report Share Posted April 19, 2013 Dr. James Grime is a PhD in Mathematics and is working in Cambridge University right now , is he also not well versed in it too ? Link to comment Share on other sites More sharing options...
Ph3N0M Posted April 19, 2013 Report Share Posted April 19, 2013 I'll watch the video later. But I can assure you that the paradox is more philosophical than mathematical in nature. Link to comment Share on other sites More sharing options...
Sackboy Posted April 19, 2013 Report Share Posted April 19, 2013 I know , there is a very simple solution to this , I studied infinite GPs in 11th too but the fact is it cannot be explained . Link to comment Share on other sites More sharing options...
dranjithk Posted April 19, 2013 Report Share Posted April 19, 2013 http://gizmodo.com/5995005/nasa-just-found-the-two-most-perfect-planets-for-life-yet And that last paragraph in the article is stunning! Link to comment Share on other sites More sharing options...
egg man Posted April 21, 2013 Report Share Posted April 21, 2013 The paradox is solved mathematically. The question he basically posed his, there are infinite number of steps to finish the process. Or in other words, there's no last step. Then how can a process be complete without a last step. But we know the process is compete. That's a paradox. I think it ventures into physics and at certain point the step of two hands cover a distance of plank's constant mathematically. Since it's not possible physically, we can ignore steps from there. I might be entirely wrong though. Would love to hear a physicist's take on it. _________________________________ Typed with one finger on a sheet of glass Link to comment Share on other sites More sharing options...
Sackboy Posted April 21, 2013 Report Share Posted April 21, 2013 He asked for a physicist's reply in the video too , I am curious too , can we keep dividing the space time continuum like that. Link to comment Share on other sites More sharing options...
Aloy Posted December 12, 2013 Report Share Posted December 12, 2013 Giving a healthy bump to this dead thread. A must watch video if you love science aka PHYSICS.Try to to answer the outcome of the experiment.Its solution is in the spoiler. Link to comment Share on other sites More sharing options...
Aloy Posted January 3, 2014 Report Share Posted January 3, 2014 Hey,I am working on a Van De graaff generator right now for fun.I'm using PVC insulation tape as the belt and at one side i have plastic tube/glass tube and on the other side rubber band wrapped around the motor shaft.The motor runs fine,quite fast.But the device itself isn't able to create a single spark.Initially i wanted to use a rubber belt but that thing isn't available in my area.Any suggestions please?Look at this video if you don't get what i'm trying to make.Thanks in advance. Link to comment Share on other sites More sharing options...
WMWM Posted January 8, 2014 Report Share Posted January 8, 2014 Link to comment Share on other sites More sharing options...
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Somebody Posted February 7, 2014 Report Share Posted February 7, 2014 youtube.com/watch?feature=player_embedded&v=dYw4meRWGd4 wow.. that video was surprisingly intense. I stood on the ledge of a plan (for skydiving) at 10k feet and thought it was , and was trying not to pass out from that fall. This guy jumped from 26 miles up and was spinning violently and was able to hold himself together obviously he was trained and all that, but still... Link to comment Share on other sites More sharing options...
WMWM Posted February 8, 2014 Report Share Posted February 8, 2014 Link to comment Share on other sites More sharing options...
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