Thursday, May 26, 2011

The Number ...

... 8128

I have an affinity for the number 8128. Sometimes people ask me why. I apologize in advance for the self-aggrandizing nature of this post.

Back when I was a skinny, sports-averse lad of 12 or 13 years old, I read a lot of books. Reading was a lot more fun than standing out in left field praying that nobody would hit a softball in my direction, and then when it happened, acting like I was trying to catch it when, in fact, I really just wanted to get out of the way and avoid getting beaned or worse.

I read a lot of science fiction. I mean, a lot of it. I also read other things, including books about math. Not math textbooks, but things like George Gamow's One Two Three ... Infinity and the like. I don't remember which book specifically brought up the concept of "Perfect Numbers", but the concept resonated with me. For whatever reason, any book I found only listed the first 3 numbers in the series: 6, 28, 496, ... . I found this maddening -- what's the 4th number?!

You have to recall that this was circa 1973: we had a rotary phone, there was no internet or WWW, I was too young to drive so getting to the library took some effort, I lived in podunk where there were no bookstores, much less bookstores that had a "Computers" section, etc. I was pretty much on my own.

But at about this time I also got interested in computer programming. My family lived near a branch of Southern Illinois University, which had recently acquired a Control Data Corp Cyber mainframe, and was using it as a timeshare system. Through a friend I got access -- actually, people were extremely casual about usernames and passwords and you could find them written on abandoned punch-cards etc, I eventually had quite a collection. I realize that nowadays this is frowned upon, even illegal, but back then it was considered "cute". Before you condemn me, know that I had certain ethics about it, and I never deleted people's files or caused any kind of trouble. Mostly what I did at first was play games -- things like the old BASIC Star Trek game.

But eventually I wanted to know more, so I asked the wonderful lady (Mrs. Whelan) at the public library if she could find me some books on "basic computer programming". And in about a week she had a couple of books for me with titles like "Learning BASIC". I ate 'em up.

Yes, I was a serious geek as a boy. Geekitude was not popular in the small midwestern town in which I lived; the other kids gave me hell, I was "weird" and so forth. Today, it seems like "geek" is simply one of many accepted sub-cultures (like "jock", "goth", "rocker", "preppie", "skater", etc) that kids may identify with. I'm happy about this -- I think of myself as an "early adopter". But back in 1973, reading science fiction and writing computer programs just got you sucker-punched.

Anyway, long story short (and you can probably see where this is heading), one of the first things I did when I learned to program was write a program to generate the 4th Perfect Number. It was not especially efficient, but it chugged along and popped out 6, then 28, then 496, and then ... after a pregnant pause ... 8128!

Natch, first thing I did was rewrite the program to spit out the factors so that I could check the answer -- hey, it was an early effort! -- but 8128 checked out.

I went on to learn a whole bunch of different languages like FORTRAN and SNOBOL and LISP and APL (where, since I didn't have APL keyboards, the operators were all represented as escaped digraph "symbols" like $UP$ -- some things are too tedious even for an obsessed 13yo), and wrote a number of programs to play Conway's Life and several Turing Machine emulators and other nerdy delights. And this led to going to college and getting a couple of degrees in Computer Science, which have been "beddy beddy good" to me.

But at the beginning of it all was that 4th Perfect Number, 8128. Which, lest I sound too impressed with myself, I note that the Wikipedia article on Perfect Numbers says:

These first four perfect numbers were the only ones known to early Greek mathematics, and the mathematician Nicomachus had noted 8,128 as early as 100 AD.

Then, in 1456, an unknown mathematician recorded the earliest reference to a fifth perfect number, with 33,550,336 being correctly identified for the first time.

So it's not like I was blazing new trails on the frontiers of mathematics. But still, I've sort've 'adopted' the number and tend to use it in places where I need a handy integer. Like, for instance, a blog name. Although for obvious reasons I never use it for passwords or pin-codes or anything like that.

Anyhow, love it or hate it, that's the story.

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