Game of Cat and Mouse - Numberphile
1,433,511
Published 2019-05-28
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All Comments (21)
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Catch a more in-depth interview with Ben on our Numberphile Podcast: https://youtu.be/-tGni9ObJWk
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the mouse just needs to swim at the speed of light because if he does so the cat would go 4x the speed of light and you cant do that or the universe police will show up.
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You can't run, you can't hide, but you can swim in circle between two event horizons and make a dash to escape.
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Wow Tom and Jerry is a lot more complex than I remember
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"That would be a tense moment for the mouse" Yeah i'd also fear death if a gigantic chestnut-shell balloon hybrid came storming toward me
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The mouse has a better character arc than most hollywood action heroes
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9:36 - "the mouse can't dash from the center. So the obvious question is, where can it dash from?" I was expecting the ad for dashlane to appear
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At first I thought the "press paws" meant my hands. No, it was a pun, and it took me nearly half the video to realise that.
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2:25 - Initial theory before watching any further: -Starting from the center, the mouse has to cover distance r going directly away from the cat. -The cat has to cover half the circumference of the circle, or (2πr)/2, or πr. -As the cat is going 4x as fast, and 4>π, the cat will get there before the mouse, and at that point the mouse will have a greater distance to go. Conclusion: The mouse is doomed. [resumes video] 12:25 - Took me exactly 10 minutes to realize I was wrong about the mouse being doomed.
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Honestly this guy, as a Numberphile regular, is highly underrated. One of the best if not the best.
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I know this worst mouse ever is just a distraction to stop us using Parker Squares! You can’t fool me!
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4m/s "That's a quick cat" Has this guy ever seen an actual cat?
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To answer brady's question, the mouse can escape with any ratio less than pi + 1. the formula for the smaller circle is 1 - (pi/x) and the larger circle is just (1/x) (1/x) = 1 - (pi/x) (1 + pi)/x = 1 x = pi + 1
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Mouse uses circling tactic within sweet spot and gets 180 degrees from the cat. Mouse dashes to the edge of the pond, with the cat close by, but not directly upon it. Mouse shakes himself dry on the edge of the ... oops!
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"Worst mouse ever" Me: hold my pencil
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The mouse can actually escape if the cat is less than approximately 4.6033 times faster than the mouse. Hint: Once the mouse leaves the "safe zone" it doesn't have to dash radially.
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I loved the moment of realization when he hinted at how we can combine the two strategies to solve the problem. He presented this problem and solution very well. This is truly what maths is all about! P.S.: The number between 4.1 and 4.2 at 16:00 is in fact (pi + 1). It's a fun, easy exercise to work this out.
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When doing the circle method, what if the mouse sometimes run on a secant of the circle instead? With this method, the cat should still run in the same direction as the circle method, but the mouse got a chance to reach another point of the circle a bit faster than the circle method (secant line is shorter than arc length).
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As the mouse goes to that narrow sweet spot in an effort to increase the angle between himself and the cat, he could save a large measure of effort by heading toward the center until the angle was great enough, then swim toward the sweet spot again, arriving at just the right time to dash for the escape. This was a fantastic presentation and I learned quite a bit from it. Thank you!
