The man with 1,000 Klein Bottles UNDER his house – Numberphile
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The man with 1,000 Klein Bottles UNDER his house – Numberphile


Move that aside, move this over here Put this in a box here Toss this over here, get rid of that Throw this out of the way [glass noises] It was 1995 A friend of mine, doing scientific glass-blowing Calls me up and says, “Hey, can you help program my glass oven?” I said, “Sure” So we work on this Macintosh that produces glass This oven so that the temperature was up/down and everything He says, “Well, how’d you want to get paid?” And I say, “Don’t pay me, let’s build something. Let’s make a Klein bottle!” So he says, “Oh yeah!” And so we work together And we sort of weld the stuff and we’re building this out of… Out of glass and we finally finish it And I say, “This is a glass Klein bottle!” And so I say “I’ll go over to the math department, in Berkeley” “And I’ll show my friend, Ken Rivet this Klein bottle” “He’s a topologist, he’ll actually appreciate it!” I say, “Ken, look what I made!” And this guy… He’s a professor of math He looks at it, and he says… “That’s a glass Klein bottle!” “I’ve always wanted one!” “How much money do you want?” And so I say, “Pfft” “I don’t know, a hundred bucks” He reaches into his pocket and starts counting out twetny-dollar bills! I’m stunned So suddenly, this five-watt lightbulb goes off in my head You know, if I make a bunch of these… I can probably sell ’em! The problem is making a bunch of them… You know, it takes me two or three days to make one So I call around… Glass companies, glass shops… “How much would it cost to make like…” [shrugs] “A bunch of ’em?” I want the price to be low enough, that I can sell ’em Turns out… Making one or two isn’t going to do it Making ten or twenty isn’t going to do it I’d have to have, like, a THOUSAND made Come on over. Check this out Under my house is a… is, my little forklift robot To go pick Klein bottles from stock Tilt the thing. If you look carefully at it… *Let’s see if I can actually show this…* Oh this is just home but this is only incidental This is not Klein bottles, this is how to run a warehouse, really This is the lift mechanism for, from a car window. From an old Pontiac car So I went to the junkyard, got a window tilt… Everything’s made from junk The up/down, that’s an old electric drill that I got for 5 dollars The wheels, you know, they’re little motors drive the wheels around *Let’s tilt this up, lift it* So here’s my… Here’s a box of.. oh, hey! And yes, there are Klein bottles in here [Brady laughs] And indeed… indeed This is a box of throwaway Klein bottles, things, you know… Things that have flaws on them, but I don’t care about that The main thing is, there are lots and lots of bottles It’s the footprint of my house! I mean it’s… *Let’s see, it’s… hey, go back, go back, go back* Let’s…drop this off From here on out, you’re going to have to look at a tv camera Because you have to appreciate that there’s lots of bottles and… Heading over to, where I store bottles under my house Let’s see, there are lots and lots of baby Klein bottles In boxes under my house And lots and lots of… Medium sized Klein bottles, under my house The reason for having so many bottles… Isn’t, “Oh I gotta have, you know, in case somebody orders a lot!” It’s so that, in manufacturing a lot of them… I can keep the cost low enough, that I can sell them Turns out that, small production runs are REAL expensive So if I can just have ONE production run Save enough bottles for the next *ten years* So notice now, there’s a… Both Brady and Cliff Both are being seen by the rear camera of my little forklift robot *Hang on* *Behind you, behind you is a cat* *Okay* *Hang on a sec* *Sure* [Brady straining] *No keep going on, cat’s gone, don’t worry about it* *That’s alright, I’ve got the shot now if you come around towards me* [machine whirring] Goodbye!! 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I’m trying! [Brady straining] [laughter]

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