Klein Bottles

http://www.kleinbottle.com

In 1882, Felix Klein imagined sewing two Möebius loops together to create a single-sided bottle with no boundary. It’s inside is it’s outside, so it contains itself.

Klein Steins?

Why Is This Man Smiling?

What Is Man’s Place

In The Universe?

Ancient Man:

The Earth is the center of the Universe. We know

this because everything in the sky turns around the

Earth. It’s obvious man!!

Copernicus (15??):

The Sun is the center of the Universe. I know this because

the orbital calculations come out with less overall error this way. The orbits are perfect circles.

Kepler (16??):

The Sun sits at one of the focal points of each planet’s elliptical orbit. I know this because I stole Tycho Brahe’s data and there’s

simply less error in the calculations if you assume elliptical orbits.

1700’s to early 1900’s:

The Sun is just one of:TENS OF THOUSANDS

TENS OF MILLIONSHUNDREDS OF MILLIONS

HUNDREDS OF BILLIONS of other stars in the Universe.

1920-ish:

“Hey, those fuzzy spiral blobs in the sky are other galaxies! And

the Milky Way is just one galaxy out of HUNDREDS OF BILLIONS of others!!”

Does this mean we are on an insignificant planet orbiting an average star which is a member

of an ordinary galaxy?

Is there nothing special about us?

Edwin Hubble (19??):

Hey – all those other galaxies are running away from us! Maybe

we’re special after all?

Nope – it turns out that in an expanding universe, everyone sees it as if all the other stars are running away from them.

1950’s:

Hey – none of these galaxies seem like they have enough visible mass to explain their

rotation speeds!

1970’s:

Hey – none of these galaxy clusters seem to have enough

visible mass to explain the motions of the galaxies inside

them!

1980’s:

No problem. That just means that there’s “more than meets the eye”

when it comes to Astronomy.

We’ll just call that missing stuff “dark matter”, and try to look for

different kinds of it.

1990’s:

Y’know what? We’ve found lots and lots of dark matter, but it

STILL doesn’t add up to enough to explain anything. It’s as if 70% to 90% of the Universe’s mass is

hidden. What’s this mean?

The ultimate insult:

We aren’t even made of the most common type of matter in the

universe.

What could be more humbling than that?

Well . . . .

If the current thinking is correct, then we might be aware of only 3 of the 10 or 11 dimensions that

exist.

Or, worse yet?

We might be living in just one universe out of an infinite

number of universes that were created all together in the 11-

dimensional Big Bang that started everything.

Is all that really so bad though?