There are certain ideas in mathematics
that really tweak my head from time to time.
Infinity,
for instance. First you wrap your head around the idea that there
really is no “last number”, that they just keep going. You're
thinking of integers
when you first hear this, because you're pretty much used to using
them and nothing else. But there are negative
integers, too. And there are more
integers of both types than of either one, even though there are
an infinite number of each type.
And then you throw in rational
numbers and simple decimals.
And then irrationals.
And then transcendentals.
And then imaginary
numbers. There are an infinite number of each type, but if you
lump them all together, there are even more.
Or the Möbius
strip. Take a strip of paper, clearly a three-dimensional
object. Twist one end 180º
and tape it to the other end. What you now have is a one-sided,
one-edged object that still takes up space. If you reduce it to
mathematics, you can start with a two-dimensional object (no depth)
and come up with something truly impressive.
And
then there's Benoit
Mandelbrot. He's the guy that figured out that most real-world,
space-filling objects aren't three-dimensional. Wait, what? Of
course they're three-dimensional, height, width, depth, right? I can
see all three, that means they're three-dimensional, that's the
definition of three-dimensional!
Except
real objects, if measured properly, have something between 2 and 3
dimensions. Clouds are usually something like 2.72-dimensional
objects.
Oh,
and if you look at it right, the
length of the coast of Britain is infinitely long.
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