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.
Edit: Seriously, he seems like a fun parent.
Pure distilled mad science. He's like a living cartoon. I want to be him when I get old so very much!
I have his original book my shelf, it was fascinating when it came out.
His Klein Bottle company is here:
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.
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.
And he's funny. Mostly. ;-)
This was really fascinating read for a young nerd around very early 1990's.
From http://www.kleinbottle.com/drinking_mug_klein_bottle.htm :
"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.
Reading any page is a joy.
But seriously just read the whole page, this is like a
bear hug from a friend I didn't knew I had.
You could probably put a carbonated drink on it, though...
yes it does, you just pour in/out from the bottom.
That's basically the whole novelty of a Klein Bottle
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
But, aside from that, when I went to youtube to watch the video, the ad I had to watch was this:
First time I watched a youtube ad all the way through :p
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 firstname.lastname@example.org
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?
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.
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
Is this correct?
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.
Topology is an interesting area of study.
Can you do the same with your sphere/donut/bowl?
The abstract object doesn't, the 3d manifestation of it does.
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...)
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.
he says that a bootle has an edge (~3'40).
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.
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.
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 :)
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've always been amused by his 'Internet commerce will never work, give up' essay
I love my KB. :D
Eternity ... looping. Doh!
>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 was raised to believe it's extremely dangerous to health, people crawling there scare me. Of course it's easier with forklift.
Are you sure people were being honest with you? Or were they trying to stop an inquisitive young person from grabbing a handfull of it?
Cliff seems like a genuinely great guy.