I've always had a really hard time with numbers. In spite of the fact that I work with and program computers,
mathematics has always been nearly opaque to me. This is not from a lack of trying mind you. Several times in
my career I've felt stymied by my lack of understanding, and have tried real hard to learn the principles
behind both basic and advanced mathematics. I nearly always come away with a fuzzed brain and not much
more understanding than I had to begin with.
Discreet mathematics was the worst. In this, you must not answer "what is 3x3?", but rather "why is 3x3
= 9?", and "prove that 3x3 always = 9. Now." At the time I had the very real problem of wanting
to know who cared why 3x3=9, but I now see learning to answer these basic questions would've lead
me to understand the principles behind figuring out how to prove stuff you don't already know. I
honestly regret that I just can't do these sorts of things, and envy people who can.
Because of this difficulty, I developed any number of apparently unique "crutches" to help me get through the
daily hell of the various math classes I was forced to take throughout my life. Ellen thought these crutches
were bizarre and interesting enough that they would make a good essay, so here goes:
You must remember that this stuff was cooked up by a particularly imaginative six to eight year old kid trying
really hard not to do his homework, because a) it was unbelievably boring and b) it was a foregone conclusion
the answer he arrived at would be wrong.
Basic Math According to a 6 Year Old Math Clutz
- Numbers have sex. No, not like that, 6 year olds don't think like that. There are boy and girl numbers. 1,
2, 4, 5, 7, 10, 11, and 12 are boys, 3, 6, 8, and 9 are girls. Teens after that are the same sex as their last
number. Beyond teens, they're the sex of the first number.
- Some numbers "fit" together. 6 & 4 "fit" by turning 4 upside down and dropping it into 6. This turns it
into 10. 8 & 2 the same way. In fact, in general, numbers over 5 always have "sockets" to accept numbers under
- If a number "overflows" it's socket, you subtract the socket amount from the number, and add that to 10
and the answer is always right (I still do math this way. Really!)
- Some numbers "get along", others don't. Some numbers are ambitious, others aren't. Some have ages.
- All numbers like to be added and multiplied, because it makes them bigger. Some numbers like to be
subtracted, but only when it's easy to figure out the difference. No number likes to be divided, because
division, especially long division, is confusing and hard.
- 1 is a cool guy because nobody can get very far with him, so they mostly leave him alone. Even division is
easy with 1.
- 2 is a tired old man sick of people making him turn stuff even.
- 3 is a mean number because she's the mother of 6 and 9 and 12 (first 3 multiples of 3) and she's sick of
- 4 likes 3 because she allows him to turn into 12 when multiplied and 7 when added. 4 likes 6 because she
lets him turn into 10 when added. 4 likes 8 cos 8 is his daughter 2 different ways (multiplication and
- 5 cooler than 1 because he can turn any number into an easy-to-figure-out product. He also helps turn all
the small numbers into big numbers when added. 5 gets along with everyone because of this. 5 doesn't have a
"socket", he has a platform that other numbers stand on to turn into bigger numbers when added, but the small
numbers aren't real happy about it because the platform isn't tall enough to turn them into 10 or more.
- 6 is very ambitious, and likes anyone that can turn her into 12 (she likes herself a lot). 7 is a
particular favorite, because that gets her to 13, one more than 12. 8 is not so good, because 6 thinks 4 is a
dork and 8 turns her into 14. She doesn't like 5 one bit, because 5 will only get her to 11. 6's socket holds
- 7 is a cool customer but sort of intimidating, because adding him to and multiplying him by stuff can lead
to unpredictable things. 7 gets along with 6 but is embarrassed by her because she's always trying to get him
to turn her into 13. He likes 8 a lot because multiplying by her turns him into 42, which is about as close as
anyone can get to 40 without being 8. 7's socket holds exactly 3.
- 8 is intimidating because she's so big and multiplication can do really wonky things sometimes when it
involves her. 8 likes 7 because he's cool and they can make really big numbers together. She likes 9 even
more. She likes 5 best of all because 5 turns her into 40 and everyone knows 40 is a cool number. 8's socket
holds exactly 2.
- 9 is a nice number. Everyone likes 9 because it's so easy to figure out what happens when you do nearly
anything with 9. Adding and subtracting and even multiplication are a breeze. 9 is taller than everyone else,
but is cool about it so it doesn't cause a lot of friction. 1 likes 9 a lot because he gets to turn into 10
when added to her. 9's socket holds exactly 1.
- 10 wears a tuxedo because he is excellent at multiplication, and everyone really likes him because
of this. He's even easy with division when you learn about decimals.
- 11 is a quirky professor type number, because he kind of clones all the other numbers when you multiply
them by him. He hates numbers bigger than 9, and figuring out the bigger numbers
is always really hard because of this.
- 12 is the school professor of numbers. He makes you have to remember all these really weird combinations
that don't make much sense. Nobody likes 12 very much, except 6, but even she doesn't like to be multiplied by
12 all that much. This all changed completely when I figured out that 12 was half a day and 24 was a full day.
Then 12 was really cool because you could divide up all his results into day sections.
- 13 and above was where "dragons be". You didn't have to learn multiplication tables past 12 (thank god),
so they represented the infinite jungle where you always got F's no matter how hard you tried.
- 0 by itself isn't even a person, it's a mysterious force. Since it's so easy to figure out what happens
when you tinker with 0s, they don't have time to develop a personality. A zero at the end of a number just
multiplies the number by 10.
- Negative numbers are cool because they're kind of like antimatter and turn all the rules upside down. They
also confuse other people, which is even better. Negative numbers all have goatees (even the girls) because
that's how you tell evil star trek people apart on that episode where the transporter breaks.
These were the rules that got me through school. Yes, they're really weird, and no, they didn't (and still
don't) work very well. The biggest problem was that they were slow. I've always pictured normal people as
having these calculators in their heads that just squeeze out the right numbers like a playdough toy. I was
always the last one to finish a math test, which affects me to this day when I take other kinds of
tests (must finish fast, must hurry must hurrymustnotbelast). It made tutoring me in math
nearly impossible, because what was going on inside my head didn't even vaguely resemble
what was going on inside the tutor's head. It was always a case of getting the right answer
for the wrong reasons.
They also broke down completely when confronted
with complex mathematics like algebra, calculus, and the aforementioned discreet mathematics. A visualization
system like mine just can't cope when the numbers get replaced by letters and everything gets abstracted and
distorted, like looking through a prism.
Fortunately computers aren't just about math (otherwise I'd be out of a job), they're also heavily based on
logic. And logic is where I really shine... boolean math, which is all about logic, is very easy for me
and I can reduce a complex logic statement, and get the answer right, in a big hurry. I sometimes think
that doing boolean math for me must feel like what doing arithmetic feels like for others... natural and
Of course, this doesn't help all that much when it's time to figure out the tip. That's why I let Ellen pay