Zeno's Paradox - Numberphile

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1. you said that at infinity the sum of that particular sequence will exactly be equal to 2. The problem is infinity is just a sense...just a "notation" if you may, to express stuff that's really, really big. what i mean is 's' may be 2.00000000..(a billion zeros)...001 but never exactly equal to 2 because i can make it smaller with an extra zero before the 1. that's mathematics. now according to quantum mechanics we cannot divide space infinitely but upto a limit. the plancks distance. if you divide the space further ...the laws of physics dont work. further division might not even be possible. it although might be possible to know what would happen if we are able to combine the equations of quantum mechanics with those of relativity (we also don't if that could be done either). too many variables after all, eh?
2. if we take speed into account in this can be solved
3. From a philosophical and mathematical perspective, it's certainly a paradox. But from a physical standpoint, it is not simply because abstract notions of infinities don't exist in the same way they do in math and philosophy. There is a well-defined, finite boundary in which the clapping process "ends" that corresponds to the distance at which the repulsive force between the electrons in the atoms in each hand dominate over the amount of force being applied to the clap.
   One of the reasons why mathematical and philosophical paradoxes are so frequent is because they do not exactly operate in accordance with the natural world in which our brains and intuition develop. They are not so much paradoxes as they are reminders that math and philosophy are imperfect and incomplete.
4. Toi Tois
5. google "planck length"
6. Actually, your hands never touch:)
7. The assumption that you can travel exactly half a distance is false.
8. It's not infinite because eventually you will run out of atom to pass through.
9. Always knew I was a paradox.
10. The tortoys is fast
11. Press 2
    Have fun
12. This channel breaks my brain and I love it.
13. s= 1+1/2+1/4+1/8... So this is the original and below is half the original
    s1/2=1/2+1/4+1/8+1/16...
    
    s-s(1/2)=1-1/2+1/2-1/4+1/4...onto infinity it can be simplified by subtracting each pair
    s(1/2)=1
    s=2
    now if you think of each half taking the same time that means you are slowing down by a factor of a half and once you reach infinity your speed or distance traveled per second should equal 0meters/sec. what happens in the real world is we travel the 2 meters in a specific chunk of time like 2 seconds so in 2 seconds you will complete this intinite series. vsauce has a great video all about that topic.
14. Sums noob here. Can someone explain to me why he can shift the position of those values in the second sum at 4:20 ? Is it because that corresponding values in the two sums can be shifted to match each other positionally? How does this not mess with the result?
15. So... what happened to the plan of following up on this question with a physicist?!
16. What if you imagine a 3,4,5 right triangle? Like this one:
    - The distance across the hypotenuse (5cm) represents the distance that achilles needs to run.
    - The distance of side length (4cm) represents how far the tortoise needs to run
    - The distance of of the base length (3cm) represents the horizontal distance apart
    
    And so, Achilles and the Tortoise need to meet at the corner of the triangle at the same time. Achilles needs to run 5 inches in the same time that the tortoise needs to run 4 inches.
    
    So lets decide a number of seconds that it will take for the tortoise and the Achilles to meet on the corner - lets say 4 seconds total... but you can choose any number.
    
    This means that if the Tortoise travels 1m/s, than he will arrive at the corner in 4 seconds; but Achilles, since he needs to travel a distance of 5 meters in the same amount of time, needs to travel at 1.25m/s in order to arrive at the corner at the same exact time as the tortoise does. That is to say: 4*1.25 = 5 and 4*1 = 4.
    
    Accordingly, if we create a subjective concept of speed, one for achilles, and one for the tortoise, we can say that 1.25cm/s = 1Achillesmeter/s, and that 1cm/s = 1Tortoisemeter/s.
    
    If Achilles walks a distance of 4 Achillesmeters/4s, while the tortoise walks a distance 4 Tortoisemeters/4s, and they start exactly 3cm apart in the horizontal direction - they will meet happily at the corner at exactly the same time. This is because 5cm=4Achillesmeters and 4cm=4Tortoisemeters. So basically, all we needed to do is change the concept of a unit with respect the constant speed that both achilles and the tortoise are traveling and the paradox is resolved.
    
    Let me know if theres any problems with this solution.
17. just like a container ship uses markers along the sea to guide it into harbor, the cutting in half infinitely thing works the same way. the marks will line up on the horizon and appear to be one point (clap) and guide you away... wonder what the stars are for...
18. it's not paradox, the way you assuming the trojan never catch up with the tortoise is that time is compressed for each comparison. till the end the time interval is so small almost feels time stopped, if time stopped, of course trojan never pass the tortoise. it's like playing a video, but the speed of the video getting slower and slower to the extend it's so slow it almost feels paused. but in real life time flows constantly (not consider general relativity here). so this never happen. it's not a paradox, it's pseudo paradox,
19. i love how he says toytoise.
20. is there any part of the paradox that says the distance is infinite? no. so you are saying that because in mathematics you can express something as an infinite number of steps that means that something is infinite in the real world? can we really assume this?