or How I learned to Love Cherry Pies, Again
I'm enamoured with the great bit in Apocalypse Now when Robert Duvall, playing a seriously deranged unit commander named Kilgore, turns, stares at the sky and says,
“Smell that? You smell that?
Kilgore: Napalm, son. Nothing else in the world smells like that.
Kilgore: I love the smell of napalm in the morning. You know, one time we had a hill bombed, for 12 hours. When it was all over, I walked up. We didn't find one of 'em, not one stinkin' dink body. The smell, you know that gasoline smell, the whole hill. Smelled like -
[sniffing, pondering] Victory.
I had just the same experience the other day, simply by accident. I was reading A Brief History of Time by Stephen Hawking. Lots of really interesting stuff – if you are into esoterica.
I particularly liked the section where Hawking explains that the mathematical ideas involved in his speculations on Space/Time are so complex that only a very few specialists in the field could (or do) actually understand them. Great, sounds like the kind of maths I love!
To be more precise, it sounds like the kind of maths which got us into the present economic difficulties – for which the bankers are forever being blamed. They deserve it: that's true. But, perversely; the mathematicians, who provided the foundations for their folly, seemingly get off scot free.
Why? Because the bankers, if you care to believe them, protest that they were just following the mathematical models that they were given. The mathematicians, wisely, keep shtum. Good move!
But, I digress – back to Hawking. The idea that floored me is on page 149. Hawking is explaining some special numbers, called imaginary. Let him do it: “If we take any ordinary (or real) number and multiply it by itself, the result is a positive number. (For example, 2 times 2 is four, but so is -2 times -2) There are, however, special numbers (called imaginary) that give negative numbers when multiplied by themselves. (The one called i, when multiplied by itself, gives -1, 2i multiplied by itself gives -4 and so on.)”
Stephen, you are a genius. (This is not news – most folks accept this) You are now, in addition to all your other accolades the real founder of Cherry Pie Maths! (And I always thought it was me!!)
What he is saying, philosophically, is that if you require a particular system in order to produce a particular mathematical answer – go for it! So, if you can get a Hawking system to produce negative numbers when multiplied by itself – it's a short step to “imagining” numbers that produce positive sequences in the same scenario.
Thanks Stevie – I've been arguing this point for years! In my system, as you all know, when you multiply ½ times ½ you get one. If Steve says you can use imaginary numbers, then it's ok by me. Call it what you want.
I'm sticking to my system.
Just don't pull out some pseudo-math crapola – pick up the phone and call Steve.
Not my problem!
He's on my team!!