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Transcript
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 MILLIONS
HUNDREDS 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 11dimensional Big Bang that
started everything.
Is all that really so
bad though?