Originally invented for the purpose of counting, those peculiar creations known as "numbers" have become
endowed with special meaning. Numbers were originally created not as entities in themselves, but as conceptual tools
which turned out to be somewhat useful for solving problems, doing mathematics, and answering questions such as
"How many angels can fit on the head of a pin?" In recent times, geologically
speaking, numbers have gained an existence of their own. Certain numbers have become unlucky, while others have
become sexual innuendoes. Numbers can be natural, imaginary, or even perfect. I have spent
much time studying the history of numbers, and I have come up with some good advice for travellers
from afar.

1) Learn how many fingers the inhabitants have. The standard system for writing numbers on our planet is bsed on
the
number of fingers per person (barring injury and genetic mutation). This system is probably one of the more
clever things that we have generated, despite our awful choice of a base number. Since the number of fingers
per hand and the number of hands per person are both prime, our base number only has two factors, causing all sorts
of annoying little problems like repeating decimals for relatively simple fractions, and messy multiplication
algorithms. Many years ago, people
came into the habit of using letters as numbers. This caused a problem with paper, primarily because
there wasn't any. Writing materials were scarce, so when it came to large numbers, there wasn't enough space for
them. The Romans*, thought they had solved this problem by allowing certain letters to stand for very large numbers.
While this was
considered satisfactory for many years, people found the fact that CMXCIX and M were consecutive numbers just a
little counter-intuitive. It also neccessitated coming up with 2 new letters every time the number was multiplied by 10.

It was about this time that some genius realized that there already was a fantastically efficient method for keeping
track of arbitrarily large numbers. Contrary to popular belief, the abacus was not a musical instrument, nor was
it a convenient way for women to keep track of their jewlery. The abacus functioned on the simple principle that when
you ran out of beads on any particular column, you merely reset that column and flipped over one bead in the column
to the left. This brilliant person, who probably never really existed, used a set of 10 symbols to represent the number
of beads on any particular column and just strung them together exactly as if it were a tiny little abacus on paper (or
whatever they were using at the time). The only tricky part was that there needed to be a symbol for no beads. So,
borrowing a little symbol that the Babylonians had used to represent nothing**, the method
was complete!

2) Never argue with a mathematician over the reality of numbers. Humans have always enjoyed naming things,
and mathematicians are no different. While they usually name theorems, functions, formulae, and other gimmickry
after each other, they have adopted a different practice with respect to the naming of sets of numbers and number
classifications. Real numbers are just as real as imaginary numbers, irrational numbers do make sense, and surreal
numbers are not the labels on the soft watches in Dalhi's The Persistance of Memory. Way back in the times when
men got dates by thwacking them over the head with clubs and dragging them home by their hair, most cultures didn't
really have numbers. Some had rough equivalents of the words "a," "couple," and "lots."*** Eventually, the rest of
what have become known as the "whole numbers" were invented, and the long-standing tradition of adding more
numbers to the system had begun. The next number to be introduced to the ranks was zero. It's not as if people
didn't talk about nothing back then, but it wasn't really a number until it became useful as a place keeper in the digital
numbering system. This new numbering system, which started at zero instead of one, became known as the natural
numbers.****

Nobody is quite sure where negative numbers came from, but it was probably someone who made the
mistake of starting to count something in the middle. Measuring altitude from sea level or temperature from the
freezing point of water both raise problems because there are places below sea level and the temperature of the air
does indeed drop below freezing occasionally, as can be attested to by any skiier. The introduction of negative
numbers to the system results in what are called the integers. Elementary school students regularly put up quite a fuss
when told about these numbers. This is not because they have difficulties with the concepts, as is popularly believed,
but simply because they had been lied to. The practice of referring to certain mathematical operations as "illegal" or
"bad" is probably one of the biggest sources of the world-famous generation gap. It's not much of a jump from the
integers to what are called the rational numbers. Anyone who has ever ordered a coconut creme pie at a restaurant
and has been delivered the entire pie (as well as a bill for the entire pie) knows the neccessity of fractions.

It wasn't
long before everyone realized that not all numbers could be written as fractions. These numbers weren't particularly
nice, so they were instantly called irrational. Most examples of irrational numbers involve the square roots of numbers,
although cube roots, fourth roots, and even higher roots***** are also possible. Some of these annoying irrational
numbers were eventually incorporated into the number system, resulting in the set of algebraic numbers, so called
because all algebraic numbers are solutions to the algebraic equations consisting entirely of adding and multiplying
numbers and variables. For a very long time, mathematicians believed that they had finally found every possible
number that
made any sense whatsoever. They were so afraid of the possibility of more numbers that the first man to prove that
there were numbers that transcended the definition of algebraic numbers was immediately thrown over the edge of the
boat on which he was sailing. But you can't keep a good mathematician down, and eventually these transcendental
numbers were accepted into the numbering system, creating the real numbers. Incidentally, there are quite a lot more
transcendental numbers than there are algebraic numbers, even though there are an infinite number of both. This
doesn't make a whole lot of sense to most non-mathematicians, so I suggest seeing rule number four.

Most people don't have much difficulty with any of the real
numbers, however ugly they may be. But since mathematicians are perverse little buggers who aren't satisfied until
they are the only people on the planet who can understand what they're talking about, they decided that there needed
to be more numbers. Using the excuse that no one had ever decided what the square root of a negative
number was, they created a whole new set of numbers, all multiples of the square root of one. Since they quite
obviously were not real numbers, they were termed "imaginary numbers." This opened up a whole new realm of
complicated numbers consisting of real numbers, imaginary numbers, and any sum of the two which have become
quite understandably known as complex numbers.

3) Don't do arithmetic with infinity. This is one of the fastest ways to annoy a mathematician. Infinities don't play
nicely with other numbers, so avoid them at all costs.

* A now extinct race of people known in
modern times for wearing togas, saying things like "Et, tu Brute" with phony British accents, being holy, and having an
empire.

** It has been hypothesized that a species' intelligence is directly proportional to the number of different ways they
have for saying "nothing."

*** This fact has caused much confusion amongst students studying prehistory. Most books that discuss the
history of mathematics claim that prehistoric cultures couldn't count past two. These books have missed the boat
entirely; those cultures couldn't count at all.

**** There has been some debate over whether or not the natural numbers should include zero or not. Since the
phrase "whole numbers" isn't used often, it is quite common for either usage to appear in a math book. The first thing
covered in just about any advanced mathematics course is whether or not the instructor prefers to include zero in the
natural numbers. This debate has been going on for so long that nobody really cares anymore. Were someone to
come forward and declare as fact either opinion, everyone else would probably go along with that person, but there
isn't anyone who gives a flying kiwi one way or the other. The question will probably remain forever unanswered.

***** You might be tempted to call such high roots "branches," but don't. It only annoys the mathematicians.