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  • Here is a perfectly legal $20 banknote from the United States of America,

  • and the gamble is, you extend your fingers like this in a V-shape

  • and you try to catch it when I drop the banknote like this -- yeah? -- in mid-flight.

  • And if you can catch it when I drop it you get the bank note,

  • and if you don't you don't get the banknote.

  • I'm going to drop it at some ...

  • [Brady, off camera] *argh*

  • [Professor] ... unannounced time. [Brady] Ok.

  • [Brady] *argh*

  • [Prof] You shouldn't guess. *laughs*

  • [Brady] *argh*

  • [Prof] One more time.

  • [Brady] *ohhh*

  • Now most people, at least the vast majority of people, can't get it.

  • And that's because there is something called the reaction time in most humans.

  • In other words, you see something or you feel something, and then it's processed in the brain.

  • And the brain sends back a command to the body saying, "Do something," and that's the reaction time.

  • And that reaction time in most people is of the order of 0.2 seconds.

  • It varies from person to person, but approximately 0.2 seconds.

  • We learn in high school and elsewhere that when you drop any object

  • you know this, this, or this,

  • the stuff falls in free fall

  • over distance which is equal to half g t squared,

  • where t is the time of the fall

  • and g is the gravitational acceleration.

  • g is about 10 meters per second per second.

  • It's 9.8 but that's close enough.

  • t, reaction time that we have to catch this, is 0.2.

  • So if you square that that's 0.04,

  • halve that is 0.02, times 10,

  • that is equal to 0.2, that's in meters.

  • That is equal to 20 centimeters approximately.

  • So in the human reaction time, I mean the average reaction time,

  • this object falls by 20 centimeters.

  • This is according to my ruler 15.5 centimeters.

  • So it's significantly, but not by much, shorter than 20 centimeters,

  • so it falls more than its own length.

  • So when you start from, even from the bottom,

  • you can't catch it.

  • Because by the time the signal is sent to the brain,

  • and brain sends back the signal to do something,

  • it's already fallen more than its body length.

  • So it is quite amazing that the United States of America made a banknote

  • which is slightly shorter than 20 centimeters

  • which matches exactly 0.2 seconds human reaction time.

  • [Brady] This isn't going to work on everyone, humans are different.

  • [Professor ] Humans are different.

  • For example I know that although my esteemed assistant,

  • and in fact the cameraman, the man behind Numberphile,

  • couldn't catch it in the previous experiments.

  • Actually when we do it honestly he sometimes can, because his reaction time is actually pretty good.

  • [Brady] With my right hand.

  • [Prof] With your right hand, yes.

  • And also I'm cheating. You see if you wanted to make sure that people have the minimum chance,

  • you ask him to extend those two fingers. These two fingers don't move so fast.

  • Those two are probably the fastest pair so try doing it with ... If you can hold your camera?

  • [Brady] In my right hand? [Prof] And with your right hand. [Brady] Hang on a second... [Prof] Ok lets do this.

  • [Brady] Hang on a second. Ok.

  • [Prof] Here. Now Brady Haran, he's really quick.

  • [Brady] Ohh!

  • [Prof] *chuckles* Well $20 dollars is at stake. You shouldn't be guessing.

  • [Brady] Ohh! I was catching them before!

  • [Prof] I know, you were catching them before, but now

  • [Prof] *chuckling* No, no, you were guessing. [Brady] I guessed.

  • [Prof] You guessed. [both] *laughing*

  • [Prof] Ok, you have the $20.

  • [Prof heard speaking on a different video]

  • But this time each paper clips is linked to the rubber band but not between themselves.

  • Let's finish with something that is a work in progress.

  • So far we have been linking paper clips together.

  • And sometimes we refer to this as addition.

Here is a perfectly legal $20 banknote from the United States of America,

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A2 初級

マネーキャッチ - Numberphile (Money Catching - Numberphile)

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    林宜悉 に公開 2021 年 01 月 14 日
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