I went to Cliff's house a few years back to buy one of his bottles as a gift for my dad. He was just as effusive, welcoming, and excited for one visitor he'd never met as he was in the video.
I thought I was just swinging by to pick up the bottle and pay the check, but I ended up staying for about 45 minutes (because he just kept going!), chatting about the crawlspace, the robot, and life in general. He talked about eschewing a big career so that he and his wife could focus on making life great for their kids. And it certainly seemed to have paid off for both kids and dad: I've never met anyone who seemed to be having so damned much fun just existing. It was refreshing to see that it's totally possible to be driven almost entirely by intrinsic factors and still exist in the real world. He left an impression as being an all-around fantastic human being. The bottle was pretty cool, too.
He was wild about them, and given how creative and dedicated this fellow seemed, I'm sure they're geniuses. I didn't meet them, though, so I can't really say much more than that.
My immediate thought was "here is the real Doc Brown (from BTTF)". Well, the hair is obvious, but it's really the enthusiasm and "come Marty, let me show you this robot I built to make breakfast!" vibe. It's what gives "mad science" a good name, in purest form.
We unconditionally guarantee your Acme Klein Bottle to be free of any defects in workmanship or workwomanship for a period of ONE YEAR following purchase. If you aren't satisfied with your Acme Klein Bottle -- for any reason -- just return it for a refund or replacement. You pick up shipping charges.
We guarantee safe arrival. If your Klein Bottle arrives broken, call or send email and we will immediately send a replacement.
We slightly guarantee your Klein Bottle for THREE MONTHS against any cracks or breakage, whether due to earthquakes, clumsy undergrads, or greasy fingers. Just mail us a fragment and $10, and we will send a replacement.
We warrant each Acme Klein Bottle for a period of FIVE YEARS to be absolutely free of any magnetic monopoles. If you discover one, contact us immediately and we will refund your purchase price right after you receive the Nobel Prize.
Furthermore, we guarantee for TEN YEARS that any polyhedron spanning your unbroken Acme Klein Bottle will have about as many edges as the sum of its vertices plus faces.
We further warrant for ONE MILLION YEARS that within a Euclidean plane, the square of a right triangle's hypotenuse will equal the sum of the squares of the two remaining legs.
>We further warrant for ONE MILLION YEARS that within a Euclidean plane, the square of a right triangle's hypotenuse will equal the sum of the squares of the two remaining legs. //
Can't you break this with Lorentz contraction; it seems that would be equivalent to non-Euclidean geometry but legally within the terms. It's all about frames of reference I imagine. Though my inclination is that it might hinge on the meaning of "within" used.
The voice in that book seems different from the voice in the video, but what do I know :). Cliff turned me on to the "peoples republic of berkley" Does anyone call it that anymore?
"The 7 mm air space separates the inside from the outside, so ice water won't cause condensation. This extends the life of hot or cold drinks, saves energy, and helps stave off the dreaded local thermodynamic equilibrium."
But seriously just read the whole page, this is like a bear hug from a friend I didn't knew I had.
>WARNING! Acme constructs each Klein Bottle from genuine Baryonic matter. Do not allow your Acme Klein Bottle to come in contact with antimatter or unpredictable results may occur. Acme cannot guarantee the dimensionality of the result.
It's a joke. It has an inside as much as any bottle does, but the only point of a Klein Bottle is the topological form so they're using topological language to talk about it.
I think maybe it's just semantics. I seem to be incorrectly assuming that the inside of the bottle is the space where the liquid goes. And the inside of the möbius strip would be the gap where you put your neck if you were to wear it as a necklace.
Would it be more correct to say that there is no inside surface? And it was just a pun that went over my head?
As my friends (online and off) can attest, I make Klein bottles mainly for fun. It's a zero-volume home business, small enough to be run from one room; the warehouse occupies the crawlspace under our house.
Of course, the best part of Acme Klein Bottles is meeting people: via email, occasional visits, talks at schools & math colloquia, and chattering about physics & LTE & coding with friends at my day-job (Hi Newfield People!). Which is to say, it'll be a while before I recast my kleinbottle website - I'm having too much fun doing other things. -- from an earlier post
Oh my god the Cuckoo's Egg guy! That is a crazy book. Would never have connected them, but then again clearly this is someone who doesn't let go once he gets an idea between his teeth.
It was interesting to read the Cyberpunk by John Markoff after the Cockoo's egg, because this book covered the same case from the crackers point of view.
This is incredible. I LOVE stuff like this. It makes me so happy that people like this still exist in the world. I say 'still' because I feel like they're a dying breed. The rationale behind everything he's done is laid bare and it makes sense! People like this don't ever let a detail like "I have no idea how to achieve this" stand in their way. Everything is a challenge or problem that needs solving.
That is great! There were 2-3 that auto-played after it (only like 15 sec each) that were also good. Just sent these around to the team (over hipchat of course).
My favorite: PENTIUM PROCESSOR. Must know all pentium processes, including preprocessing, postprocessing, and past-pluperfect processing. Ideal candidate pent up at the Pentagon, penthouse, or penitentiary. Pays pennies. Penurious benefits include Pension, Pencil. Pentel, Pentax, and Pentaflex. Write to pensive@kleinbottle.con
In the next video he talks about how a Klein bottle is made, and how, contrary to a bottle, it has no edge.
I'm not sure I understand why a bottle "has to" have an edge? Surely it's possible to make a bottle with no edge? For example, if one takes a sphere and progressively turns it into a bowl (by punching into it), and then makes the bowl deeper, it still has just one surface and no edge, no?
The rim of your bowl is the edge: it's a point where the curvature changes suddenly. But that's not the important thing: the important thing is that not only is there only no edge, but only one surface.
Let's talk topology for a bit.
A manifold can be thought of as essentially a flat and infinitely thin sheet. If you have a spherical manifold (and your bowl would be a spherical manifold), it has two surfaces: one on the inside and another on the outside. Deforming the manifold doesn't change this.
The thing about a Klein bottle (and a Moebius strip) is that it only has one continuous surface, the difference between a Moebius strip and a Klein bottle is that the latter is a single surface with no edge whereas the former is a single surface with one edge, unlike the sphere (or your bowl), which has two surfaces and no edge.
So what's important here is the number of sides it has, not really that it has no edge. The lack of an edge is really only what separates a Moebius strip from Klein bottle.
But with an ordinary bottle, the edge is the point (if I may), because if a bottle had no edge, couldn't it be said that has just one ordinary surface?
So in fact, what I understand so far is:
- a (hollow) sphere has two surfaces, one inside and one outside, and you can't connect one to the other (you can't walk from one to the other)
- a potato, or a bowl also have the same properties: two distinct surfaces
- a bottle is not a special kind of bowl, it's more of a broken sphere (an egg the top of which has been removed) so that both surfaces (in and out) are accessible (but disjoint)
- to make a true bottle out of a bowl one needs to somehow "collapse" the inner and outer surfaces (therefore creating an edge)
- if you make a bottle that has a hollow space between the inside and the outside (think Thermos), then you actually have three surfaces
I think the confusion here is that you're taking what he's saying in terms other than those of topology.
In topology, you deal with manifolds. Manifolds have no thickness, but they do have area.
In topology, there's no such thing as a 'filled' sphere: a sphere in topology has no edges and an inside surface and an outside surface, much like a football.
There are two ways you can make a 'bottle': you can deform a sphere, which gives you a 'bottle' much like a vaccuum flask; or you can deform a planar manifold (which is like a sheet of paper). The former will have two surfaces and no edge, whereas the latter will have two surfaces and one edge, that being the rim.
A broken sphere would be a planar manifold.
A vaccuum flask is simply a deformed sphere in topological terms, and thus only has two surfaces, the inside and the outside.
Yeah but last time I heard, a Klein bottle being only a one sided surface can only be rendered in 4D space with the 'passing through' funnel not breaking or intersecting the curved surface and this can't be rendered in 3D space. Unless recently they've decided to relax that restriction. Nice model though and worth getting but I wonder how best to mount it in a display case.
IE, cross-sections or projections. Would be interesting if there were a way to render a Klein bottle using techniques similar to those used when 'impossible triangles' are modeled with boards and 2x4s in fields which then seem to work when viewed from a certain angle. But then what would non-intersecting intersecting lines look like. Sounds like double-think.
Run your finger around a möbius strip. Your finger touches all parts of the surface without travelling over an "edge". You can do the same with the klein bottle.
I could paint the inside of your surface red and the outside blue (where by "inside" I mean the part you've trapped air in). That's not the case with Cliff's bottles.
I had to think about what that meant for a moment, as it's sort of part of the weirdness of the bottle. Really, putting a cork in it is probably closer to putting a lid on a bowl, no?
It's just sealing the local minimum. (Maximum? I don't really know what the sign should be for this. Probably maximum, for enclosed volume, since I'm not sure if it's reasonable to talk about the topology having a minimum in this context...)
If I needed to close one, I'd stick a cork in the hole in the bottom. So I think that is a reasonable way to describe closing it.
I don't think I can reason clearly about the 4 dimensional object, part of pointing out that a 3d manifestation does not have the same properties is me trying to do that.
Well, I'm not sure about that. The top of my bowl is the top-half of a doughnut if you will: it really does not seem to have an edge. At what point does an "edge" appear?
the object that have only one surface, but no edge, is a klein bottle. A sphere (or if you will, a ball pressed into a bowl shape) has two surfaces - the outer one, and the "inner" one (where the "inner one" is the one you cannot reach from the outer one, as tho the surface is infinitely thin, and the bowl/sphere is made of hollowness.
A sphere does not have an "inner surface", it has just one surface. So does a potato. If you go from sphere to potato to bowl, when does an edge appear and does it have to appear, is my question.
Well. A bottle is topologically equivalent to a solid sphere. It only has one surface.
The inside and outside of a bottle is just by convention. Usually you would say something is inside the bottle if it is past the opening. (As he says in the video.)
So your example with the bowl-shaped "sphere" is correct. There's no clear limit when a bottle has an inside and an outside.
I do like Cliff. This reminds me, I dropped my bottle last year; time to replace it.
If Klein bottles catch your fanvcy, there's another and very different artist doing metal and glass algorithmic artwork in 3D printers: Bathsheba (at http://bathsheba.com). I had Cliff's bottle sitting on top of her laser etched known universe cube at work. Each contains the other. Too bad nobody there gets the joke. But I saw the same combo in a documentary about String Theory, in one of the scientists' office, so I'm not alone :)
I confess that my first hope was that it was some kind of klein-bottle glassblowing robot bodged togetehr out of bits of scrap wood and insulated with glass-fibre.
The reality was almost as good though, it's a cute little forklift-bot, and appears to work really well for his use (although I suspect if he started stacking boxes on top of each other it would get a lot harder).
So, who's going to kickstart Kiva for your attic/crawlspace? :)
I got one of those Klein bottles from him, and it's really beautifully done. If you are careful, you can even store some liquid or other stuff in it. I wonder if the mathematical original could do that, too.
I suppose I am compelled to get one too. Not that I want one, it's just that I already have his books - and methinks he deserves a little extra money for this video.
AFAIK, Chris is the only person to have blown a Klein bottle. I don't think the mass produced version is hand-blown like his original. Maybe there are a few shy chemistry equipment blowers, but not many if so.
Perfect model for Amazon's new distribution system! Transform people's basements into small warehouses, complete with autonomous robots. Then ship everything locally, as they are needed!
Its practical uses are both guaranteed and finite!
>You can convert your Acme Klein Bottle into an astonishing amount of energy, over 1023 ergs! Enough to power a small city for years. To get you started, we'll supply the necessary equation for free.
>At any time -- day or night -- you can easily check on the Euler Characteristic of your Acme Klein Bottle. Just add the number of vertices to the number of faces, then subtract the number of edges. So simple, even a grad student can do it!
I bought one of these a few years ago and was touched by the personal note written in it. I hadn't realised until now that it was Clifford Stoll who actually sent these! Fascinating video.
jup, just don't handling it sucks (it gets everywhere and itches if it penetrates your skin. construction workers often don't seem to give much of a * though...)
I used to work with ceramic wool and in big letters on the box it says that it's known to be a possible carcinogen. Not only does it kill you slowly, it hurts more than itches unlike regular insulation. The fibers are longer and sharper and really sting and take a few freezing cold showers to really get it out of your skin. I certainly don't miss those days :)
I thought I was just swinging by to pick up the bottle and pay the check, but I ended up staying for about 45 minutes (because he just kept going!), chatting about the crawlspace, the robot, and life in general. He talked about eschewing a big career so that he and his wife could focus on making life great for their kids. And it certainly seemed to have paid off for both kids and dad: I've never met anyone who seemed to be having so damned much fun just existing. It was refreshing to see that it's totally possible to be driven almost entirely by intrinsic factors and still exist in the real world. He left an impression as being an all-around fantastic human being. The bottle was pretty cool, too.