Blaise Pascal was a
smart guy, and typically of such, he was a
flaming weirdo. The
following theory illustrates both:
In some of his
mathematical writings (yes, I've read pretty much all of them and no, I can't remember what one this was) Pascal gets into
Infinity, and what would
transpire if Infinity was--gulp--a real
place. Not just an
abstract point in thought, or a
numerological place, but a
part of space itself. To do this
twisted shit he uses
conic sections.
The (relevant) conic sections, for those of you
lucky enough to have
missed out on that particular (and
peculiar) subject of learning, are the
ellipse, the
parabola and the
hyperbola. Most of you know what these
look like, but if you don't know,
mathematically they are
very very weird. It is from the
conic sections that we get a lot of our
astronomy and even my pet
mathematical weirdness, the
asymptotic curve (which comes from the hyperbola). Now, here's where it gets
weird: A
parabola, which looks like an upside-down "U", has
parallel legs. Every single
point on a
parabola can be
mapped by
discovering the
point across from it (drawing a straight line), except for one--the point on the top. Because the legs are parallel,
assumedly, if you draw a
straight line from the
point on top downward, it would keep going forever, because the parallel legs would never meet.
Or rather,
according to Pascal, they wouldn't meet UNTIL Infinity, however far away that is. But because there's only
one point missing to be mapped on a Parabola, no matter how long it goes on, then
when you reach infinity you will find ONE POINT that "fills in" the parabola, which I guess would make it look like a really LONG ellipse. But if you think about an upside-down U, with the
legs extending to
infinity, and then try to understand that ONE POINT is all that's
missing mathematically; that AT INFINITY there would have to BE that point, and it would have to
fill in whatever space you see between those
sweet, sweet legs...well, that's pretty fucked up right there, to quote Stan. I mean, a
point with bigness?!
And it gets
one better: The
hyperbola is slightly
more complicated than the
parabola, so what Pascal does to it is even weirder. First of all, a hyperbola looks like a parabola, except instead of the legs being parallel lines, they're pointed
slightly outwards...er,
yes, it's a parabola with its legs spread. Thus, not only do the
legs never meet, they
wrap around Infinity and...um, well, they come all the way back. In fact, a FULL hyperbola is drawn as TWO spread-legged "U"s, one upside down on top of the other, touching only at their
apexes. The reason they draw them two-at-once like that is because,
mathematically, they really do
graph that way...the
infinite spreading legs of "one" hyperbola, if
graphed in numbers, will somehow end up
coming back and
creating the other half. Now, you can see there's a "missing bit" in the hyperbola too, but it's not just a point. It's like a big
swirling chunk of hyperbola is
missing, stuck in
Infinity.
Weird enough with
out Pascal, isn't it? But no, Pascal takes his parabola idea and expands it, effectively
proving that, if there is an Infinity, what you would find there if you
follow the hyperbola is...a
line. Come on,
think of that! Doodle yourself a
little hyperbola--I'd do it here but the
HTML would be
torturous--and try to
imagine a
line, a
single line, that would make all
four of those
ends sticking out meet.
But even after all that, Pascal admits what I'm about to admit--
Hey, it's Infinity. It's supposed to be
weird.