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?