There exists a number called i. It's called
i because it is an imaginary number.
i is equal to the square root of -1. No 'real'
number multiplied by itself produces a negative
number. But an imaginary number (which is a
real number times i), when multiplied by itself,
produces a negative (real) number. Here is the
Twist: We can't imagine what an imaginary number
is really like!
It turns out that to describe our world mathematically
you
need imaginary numbers. They
turn up everywhere in nature. If they are so
pervasive, why are we unconscious of imaginary
numbers? Ever drank
3i pints of bitter?
We are basically blind to imaginary numbers.
We only "sense" real numbers. We effectively
see a one dimensional numerical universe. Now
if you add imaginary numbers you get a 2D plane
of numbers, called complex numbers. Complex
numbers are composites of real numbers along
one axis and imaginary numbers aligning the
other.
If nature obeys imaginary numbers then perhaps
an intelligence could evolve that can perceive
imaginary numbers as easily as we perceive real
numbers. This alien intelligence would be frightening
to behold. Such an intelligence would see and
understand the secrets of nature that are fated
to be forever hidden from our senses and experience.
Actually things are even worse than that. What
follows is a bit of bullshit about weird numbers,
so don't worry if it makes no sense :)
Real numbers are one-dimensional, they exist
on an axis. Imaginary numbers exist in
two
dimensions, as explained above. What about three-dimensional
numbers? As it happens these do not obey laws
that are consistent. If you combine "ordinary"
2-D complex numbers you end up with 2-D complex
numbers, the results exist in the same plane
as the initial numbers. Three-dimensional numbers
are not
well behaved like that. However
Four-dimensional numbers (quarternions)
are
consistent. The next set of well behaved numbers
are the eight dimensional numbers (octonions).
So we have real, complex, quarternion and the
octonion numbers: 1-D, 2-D, 4-D and 8-D numbers.
The next in the sequence are the 16-D numbers.
But by some strange property of mathematics,
the algebraic rules become more dilute as the
dimensions of the numbers increases. No algebra
can be found for 16-D numbers, so it is as though
they do not exist. (If a number
can
be said not to exist, or conversely,
to
exist for that matter).
Complex numbers made from quarternions consist
of one real number and three different numbers
that, when multiplied by themselves, make -1.
Octonion complex numbers consist of one real
and seven octonion numbers that all equal -1
when multiplied by themselves. (But they are
distinct numbers: any two octonions multiplied
together produces a third, different octonion).
It turns out that octonion numbers crop up in
the Theory Of Everything that physicists are
searching for: in particular M-Theory, which
is physics on steroids. According to M-Theory,
we are made of minute particles that are really
strings of energy, or membranes or multi-dimensional
shapes. These vibrate in up to ten space dimensions,
but most of the dimensions are so tiny we don't
see them. Strange how we can only see one type
of number, when the universe may be made up
of eight of them.
We are all like Plato's captives gazing at shadows
cast on the wall of their prison cave and not
realising that they are shadows of 3 dimensional
- nay, make that 10 dimensional - objects. Everything
we see and touch in the world is a shadow of
a more complex, multi-dimensional, imaginary
entity.
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| From: |
Ted Erikson | Subject: | 2001-01-31 15:56:50 |
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| From: |
void | Subject: | 2002-05-13 16:55:25 |
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| From: |
Jake | Subject: | 2003-05-16 23:38:29 |
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| From: |
Kyle Baird | Subject: | 2003-09-09 18:47:24 |
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| From: |
Clayton Carter | Subject: | 2003-11-21 17:06:40 |
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| From: |
daa | Subject: | 2004-03-01 08:24:28 |
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| From: |
Stephen | Subject: | 2004-03-26 19:27:39 |
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| From: |
Thu P. Nguyen | Subject: | 2004-04-19 21:20:20 |
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Thu | Subject: | 2004-04-19 21:21:41 |
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| From: |
alex | Subject: | 2007-04-25 23:30:57 |
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| From: |
doug | Subject: | 2007-10-24 17:16:39 |
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