Saturday, May 3, 2008

Huh? re: Hey, Math Genius

This arose from an email my little sis, Beki, sent me:

Originally posted Aug 12, 2005

Dear Beki,

LOVE your subject line! I hope you do not mind me sharing this with ma
famille: what originally started as a response to your email has turned into
a full-blown Doug Auclair Entry (caps intentional), so ...

From: Rebecca Auclair
Date: Fri, 12 Aug 2005 07:27:11 -0400
Great emails, lately! I love the stories. Both the stories of what is happening in the Philippines with Diane and the girlies, and the stories about what is happening with you as you grow in your love for all of them.

"Leths." Diane has promised to send me a new photo with each of her emails, and I now have the three hat ladies smiling out a me from my desktop. Whenever I clear the screen, I smile right back, compelled, yet unbidden.

Did you see the movie /π/? [trans: pi; and snip]

Several times, actually: it is intense ... but I have fond recollection of the soundtrack, because someone found the scarab gun and demonstrated it set to the sound of the Pi soundtrack. The scarab gun can blow up a tank with one shot (so it's not what some would call a "balanced weapon" -- one only can hold it for a short time, at any rate).

I /DO/ act kinda like the main character: intense and (psychotically) focused -- I do notice in myself that I become fascinated with some detail and will not let it go until it's analyzed to death, like the character in the movie. Perhaps this behavior is a byproduct of mathematics or philosophy? Of course, unlike that dude, I don't go into the New York subway and poke at brains the size of cows under staircases.

So there it is.

So, it made me think about a cute little email I just sent my friend Holly. She does animal rescue, and so in closing I said "I hope that you and your forty seven dogs, eighty three cats and fifteen gerbils are all doing well..." I just pulled the numbers out of the air, trying to be cute. Then I looked back and thought, hey, are all those prime numbers? And then when I thought that they might be, I thought, I wonder if they have another relationship, besides that.

Any ideas?

I think, but I'm not sure, that kind of question is "hard" to answer: as the number line is infinite, there may or may not exist a relation between the numbers you mentioned, but it may take an infinite amount of effort to find out.


then again, number theorists do have inductive logic reasoning tools that allow them to prove that a supposition holds for all cases, so...

Anyway, 47 and 83 are prime; 15 is not.

But they are all odd numbers ... do they fit into a progression? ..., 15, 47, 83, ...

... so far, I haven't been able to find any. The most interesting progression so far is 1, 2, 15, 47, [but not 83] ... (named 'A041719') which is the progression of denominators of the fraction approaching the square root of 379.

But there were also sequences such as: "The sequence of the k-th natural number interlaced with the k-th prime number". I was not able to find a sequence for 15, 47, 83 at sequence research at AT&T. Which means when such a relation to dogs, cats and gerbils is found, you can then go about proclaiming your deep insights into the fundament of number theory.


Actually, I don't think I have much of a taste for pure number theory: it's depths seem impenetrable -- each mystery revealed shows only more mysteries; and there are absolutely no guide posts along the way. I equate it to the contemplative life -- tried it on a pre-wedding retreat for a week and went bonkers. The contemplative life is very hard, and very meager, work -- if one feels to have broken through to a better understanding of whatever (self, the universe, God), that feeling only shows how inadequately, stubbornly, wrong one is. When I worked at it, I felt angry, frustrated, and stupid -- tired and then glad to be returning to the business of the

Conversely, goal-directed pursuits are captivating (firing the imagination and providing motivation to essay the solution): breaking through elliptic curve encryption, finding a new golomb ruler, finding a new prime number (possibly a mersenne prime), and then, also, research that pays immediate dividends, such as the work I'm currently doing analyzing imperative programming through a logical lense or my research into combinators.

So, a rather round-about way to say that this progression may be your chance to break out into the big leagues! Wesleyan'd be calling you up to confer an honorary docatorate, 'n stuff.


Once again awake through the night, so now sleep is stealing into my blood vessels (or so it feels to me). I did exercise this morning (DDR, kenjutsu), and was pleased to see that I haven't lost the touch. Mike Wuerthele described watching my DDR technique as an experience akin to 'Riverdance' -- upper body erect and still while the legs whip about wildly.


Right about now I'm not feeling very spry, however, so off to bed for me.


beki said...

OK, so that's all sealed up. We have one confimed math genius in the family (Doug, in case there were any questions), and one nitwit. DUUUUUHHHHHH!!!!! Fifteen is OBVIOUSLY not a prime number. Sheesh. That's the end of my very short foray into number theory. At least I have other talents.

Hope all of your talents are shining today.


geophf said...

I hope you didn't read an implied 'DUHHHH!' in my email, 'cause it wasn't there. The first thing I did was run 15 through the prime number checker (it's called 'factor'), and that's when /I/ found out that 15 isn't prime, either. So, we both made the same mistake.

Humbling, really, when one builds this cathedral-like thesis, only to have it all fall to pieces because one little stone was chipped. I do that all the time, and sometimes, I manage to catch the problem /before/ I publish ... YIKES!

Besides, 15 not being prime means nothing for a progression of numbers ... it may be the stepping-stone to some amazing discovery -- that's how wide the field is: one could go of in nearly any direction and find something that no-one else has discovered. In fact, some go down the major superhighways of mathematics and find continent-wide fissures in the logic, creating, in that process of fixing the errors, whole new worlds to discover.

Anyway, just finishing work and on the way home for sleep.

Love Doug

cybele said...

Doug! My brain hurts reading about your mathematical deductions!!!! I'll
stick to checkers.

much love, Cybele

geophf said...

Tee-hee! K. I'll steer clear of the topic if it comes up in conversations, then. :-)

Love Doug

beki said...

Dear Doug,

I didn't think you were DUHHHing me. I was duhhing myself. Cuz, duh, 15 is dividable by 15, 1, 3, and 5. That took me about half a second to realize after I looked at your email. Oh well.

Sounds like your sleep schedule is getting a little more normal, so that's good. Just in time to go back to the PI, eh?