Here is one example:

## 9. Klein Bottle

If you want to give a mathematician something to try to wrap their head around, a Klein bottle is a good place to start. A real Klein bottle is an object with no inside and no outside that can only exist in four dimensions. These glass models exist in three, which means that unlike the real thing, they can actually hold liquid.

The difference between the models and the real thing is that by adding an extra dimension, you can make it so that the neck of the bottle doesn’t actually intersect the side of the bottle. Take a couple aspirin and try to picture that in your head.

Price:$35

There are many others here. For the pointer I thank @induction_econ.

The person who makes the Klein Bottles is author and commentator Cliff Stoll, http://en.wikipedia.org/wiki/Clifford_Stoll

Gave an Acme Klein bottle to my math and science-loving daughter at her high school graduation and she loved it. Great gift.

http://www.kleinbottle.com

I let Cliff know why I was buying the bottle and he included a very nice and geeky note to my daughter. Well worth the money.

If someone says that he can envisage stuff in four dimensions, how would I know if he was telling the truth?

Stop making my head explode with weird thoughts! Kthxbye.

Ask him to solve NP-complete problems in polynomial time. That always works.

Of course, it would prove he’s god, so 4D imagining would be the least of his abilities.

A trick to seeing a Klein bottle in four dimensions is to forget what the bottle looks like, except locally.

…It’s kind of like a meditative koan.

How do you clean it?

Just wash off the outside….

Is it me or does the picture in this post look drastically better than the pictures on Acme’s site?

I’m trying to think how one could make it. Did he make a flask with a hollow handle and then drill the bottom out?

For a Klein Bottle – opener and other neat stuff check out:

http://www.bathsheba.com/

Thank you Curt for that interesting link

http://www.bathsheba.com

I have an Ezra Klein bottle. You put bullshit in the top and bullshit, after some tortuous travel, emerges unchanged from the underside.

It appears that DVICE and I have different definitions of the word “cheap”…

A mobius strip is a two-dimensional space that rotates through the third dimension. A klein botttle is a three-dimenstional space that rotates through the fourth dimension. Of course, we can hold real mobius strips in our hands, but only facsimiles – that is, three dimensional shadows – of klein bottles.

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