Subject:
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Complex number theory (Was: God and the Devil and forgiveness)
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Newsgroups:
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lugnet.off-topic.debate
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Date:
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Tue, 14 Sep 1999 23:44:25 GMT
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Viewed:
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1348 times
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In lugnet.off-topic.debate, Todd Lehman writes:
> But pure logic transcends dimensionalities.
I finally figured out what it was about this statement that bothered me!
Math (a valid part of logic, arguably) has real difficulty resolving even
low-order functions on 4-dimensional complex numbers (1).
There are at least two main camps of thought on 4d complex numbers: quanterions
and hypercomplex numbers. Both are mutually incompatable, and quite
frustrating for the beginning student, because they both acknowledge that at
least one rule of mathematics has to be thrown out the window for higher-order
complex numbers.
For example, quanterions break the commutative law of multiplication. e.g.,
for any hypercomplex equation a x b = c , the equation b x a = c is not
necessarily true. Hypercomplex numbers, on the other hand, break the law that
guarantees a multiplicative inverse for non-zero numbers. That is, for any
non-zero (2) hypercomplex number h , the value 1 / h is not guaranteed to be
valid.
For higher-dimension math, not all the "laws" of math need apply. This
indicates that quite a few of these laws are merely conveniences. For me, this
promotes a heaping serving of doubt with a side-order of cynicism concerning
the perfectness of "pure" logic.
Cheers,
- jsproat
1. FRACTINT documentation (3),
http://spanky.triumf.ca/www/fractint/append_a_misc.html
2. Besides, we have enough problems working around the value 1 / 0 , even in
three-dimensional math. We've have come up with all kinds of arbitrary -- and
in some cases kludgy -- work-arounds for this issue.
3. I'll admit, quoting from this source proves that relying on a computer
pop-art application to supplement a college-level math education is a dangerous
thing! :-,
--
Jeremy H. Sproat <jsproat@io.com> ~~~ http://www.io.com/~jsproat/
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