My mind broke

...What? No model sailing frigate in the middle of all that? For shame!

Duuuuude.. WTF. I can't get high from this bong. Like, where do I put my mouth? And where do I light it?

...After a 42nd glance at this thing, it just hit me: is there three or four Klein bottles that are nested? And has anyone ever come up with a *use* for one?

There was once a mathmetician called Klein
Who thought the Moebius Strip was quite fine
He said "If you take two
and join their edges with glue
you'll end up with a bottle, like mine"

No idea who wrote it, but I love it

It's for Saurian Brandy.

--Charlie

Om, it's easy enough to put a frigate inside. All you have to do is set it next to the whole thing.

A Klein bottle is a surface which has no edges, no outside or inside and cannot properly be constructed in three dimensions.

if it "cannot properly be constructed in three dimensions", then how did they construct 3 and nest them? Did they construct them "improperly"?

I want to fill it up with water and see what happens

Actually, since the bottle has no proper outside or inside, we can wildly conclude the Universe is inside the bottle.

From appearances this is one ONE piece of blown glass! Eat your heart out Chihuly!

@8, GeekD,

Yes, they did construct them improperly. You see the places where the "bottle" self-intersects. That doesn't happen in a proper, 4D Klein bottle. It's similar to the fact that the edges of a 3D cube do not intersect, but when you draw one on paper, they usually do. (Of course, with a cube there *is* a way to draw it without self-intesection--draw the back face completely inside the front.) With a Klein bottle a 3D representation with no self-intersection is impossible, but these glass things do give you an idea of what it's "supposed to be".

The best glass Klein bottles pass through themselves without touching:

http://en.wikipedia.org/wiki/Mitsugi_Ohno

I count 4 klein bottles there.

And technically speaking, the entire universe is inside them.

Thank you. Some pure aesthetics to consider for the moment.
Of course, the metaphorical implications of these diminishing returns threaten to steer us back toward politics.

Here's a philosophical question for you. Since the entire universe is inside, is it half-empty or half-full?

Be a great design for a new designer Vodka.

There are only three Klein bottles there, but the innermost one's tube was widened to contain two tubes within it, so it looks sort of bottle-like. And yea, this easily beats the meter-tall glass Klein bottle for the coolest Klein creation in existence.

If the outermost one is "inside" the innermost one and vice versa , isn't this an imperfect representation of an infinite number of Klein bottles not just an imperfect representation of three Klein bottles?

This would be good to bait with honey, rotting meat, and pheromones and to hang in a tree to catch wasps.

Yes, as Trimeta points out, that's me behind the meter-tall Klein Bottle, at http://www.kleinbottle.com

There are several ways to make Klein Bottles; I usually make three separate sections for each, and then weld them together.

But for the meter-tall Kleinbot, we went with two sections, as can be seen on the website.

Alan Bennett's triple Klein Bottle at the London Science Museum uses about twenty intubations - it's a real corker!

Mathematically, one can either make a ring=seal at the cross-through, or leave it open, as Ohno did. Or, one can "break" the pass-through tube. All three cases represent valid /R3/ immersions of an /R4/ Klein Bottle. (I've made all three types, and prefer the first style, so as to allow the Kleinbot to hold liquids.

I've been working on a Klein Bottle Wine Bottle - made two so far. I'll post a couple photos on m'website.

Onesided cheers to all!

-Cliff

@Nanu: Taking into consideration dark matter, I´d say medium-rare.

wicked!

What purpose does it serve? Is it art or is it science? I'm confused.

I really wish people wouldn't make these things. After all, as many people have pointed out, each of these bottles contains the entire universe. They are made, without exception, of glass. Sooner or later one is going to get dropped. The contents of glass containers don't usually survive being dropped undamaged...

I'd rather have a trio of Calvin Klein bottles. BTW, when are these topological multidimensional theorist types finally going to convert a working monorail to a Mobius strip design?

It'd save me a ton of time off my commute. I figure I'd arrive at the train platform before I left.

Oooh, look at 21!

Holy crap! That's Clifford Stoll!

There's a number of achievements that make him super awesome, but his most important contribution to the field of awesomeness is the klein bottle knitted hat.

Easy to clean, as you need only wash one side., etc.

What happens if you pee in it?

As much as I like the sculpture (and I do), I really enjoyed all the clever and funny comments too :)

this is just about the most fascinating and useless looking thing I have seen all day

Oh, man... you get pee all over the universe!

LOL, Eustace!

I think you'd actually be peeing out of it.

@CliffStoll: Sorry if I offended with my comment; your work is still more awesome than anything I've ever constructed. I bought one of your Klein bottles a few years ago, and while I stupidly broke it after a year, I still think it was a good use of my money; everyone here should buy an Acme Klein Bottle. Anyway, the funny thing is that I first learned of Acme Klein Bottles from DHMO.org; the one time clicking on a banner ad led me to buy something.

Oh - no problem Trimeta! I'm honored that you mentioned my work alongside Alan Benett's Klein Bottle (and I completely agree with your comparison)! I've long admired that triple Kleinbot, and I've been tempted to further riff on his work ... if only I had a few extra months. (Goes without saying, Trimeta, that I really appreciate your buying one - your donation went straight to my kids' peanut butter sandwich fund.)

And Jame, thanks for your kind words! I check into BoingBoing every few days; this afternoon I was taken aback by that Kleinbot. Right now, I'm repairing an old oscilloscope for a possible garage physics class later this fall.

Again, warm cheers to all - thanks for the smiles!
-Cliff

i'd like to second Jaime's "Holy Crap its Cliff Stoll" ... after reading his adventures in "Cuckoo's Egg" I realized self-teaching is the BEST teaching, walked out of the masters program I was in; got a 'real' job to fund my learning, experimentation and participation in my true passion.

He totally changed my life, AND makes a heck of a great Klein... gave one to my pops for a birthday present.

Now if Cliff would advance his glassblowing skills to some Prince Rupert's Drops, I'd have my next (albeit dangerous) gift for dad....

Viva Cliff.

Um, okay.

I have a cute little red Stoll-made Klein bottle at work.

At least, it was purchased from Cliff Stoll. For all I know it is an empty beverage container from Hypercube Land. (That would explain the Mimsy Cola label.)

I was there last week, the display of mathematical objects it fantastic. I took some pics:

Here, on my Flickr

I saw this (or a similar bottle, certainly made by Bennett) at the excellent & gorgeous 'Beyond Measure: conversations across art and science' exhibition at Kettle's Yard earlier this year.

Warning: This post contains no comedy, math, or convoluted surrealistic|theoretical|philosophical conjecture:

It's just plain neato and I'd like to have one of those on my coffee table. I'd place a fresh gardenia bloom in it to adorn and complement its beauty.

:o)

#24: It's Sciartence!

Mathematician sarah-marie belcastro knits all kinds of cool topological surfaces and provides instructions for knitting your very own Klein bottle!

Thanks for bringing this to a wider audience - the Klein bottles on display at the museum invoke lots of curiosity and wonder. They're in the Mathematics gallery on the second floor of the Science Museum.

BTW if you fancy visiting when there are no kids around, we're open for Science Museum Lates on September 24, from 6.30-10pm. No under-18s allowed in.