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31 March 2005

I'm almost back to the Imax censorship crisis

Somewhere in an earlier post (when my Free Software let me post images) there's a homemade picture of the mysterious ghostly phenomenon in which supercold liquid Helium II creeps up and out of its glass tube to rejoin and equalize a lower level of He II. I mention it because I saw photos of it in a fancy Time/Life science book an aunt bought for me when I was 12, and it made lightning in my brain for the rest of my life. Forty years later I actually met a physics grad student (Helium Boy) who messed with the supercold goop, and he verified that I'd remembered this weird phenomenon accurately, just from seeing it once back in the days when I was a member of the Alice Deal Jr. High Duck & Cover Club (more about which coming soon).

Andrew Wiles, the Princeton mathematician who finally proved Fermat's Last Theorem, first got the bug when he read about FLT -- the greatest unsolved problem in mathematics for centuries -- in a recreational Boys' Math Book when he was about 12. (He later forgot the title of the book.) Okay, you know this, right? There are gazillions of all-whole-number solutions to the old Pythagorean thing

x² + y² = z²

... the most famous one being

3² + 4² = 5²

but can you find just one solution in all whole numbers to

x³ + y³ = z³

or in any higher whole-number exponent 4 or 5 or ... ?

And if you can't, can you prove that there are no whole-number solutions for any integer exponent greater than 2?

The real tease that drove the world nuts (and attracted droves of the world's nuts) for 300 years is that Fermat wrote: "I have discovered a truly remarkable proof which this margin is too small to contain." Nobody's sure if he did or not, the "proof" was never found anywhere else in his papers ... but with Fermat's Really Big Math Brain, he could have found a proof!

When Wiles first ran across this nifty puzzle (the question is South Park Simple ... but the answer is Cambridge Senior Wrangler Much Less Simple), he was 12 and didn't have the math skills to even try to solve FLT. But he stuck with it for 29 years. He did the work without a computer, just pencil and paper, in an attic room without a phone. And in secret, because FLT had acquired a bad rep among frustrated professional mathematicians that only lunatics tried to solve it.

Einstein began wondering what the world would look like if he could fly as fast as light when he was about 14.

Helium II, Fermat's Last Theorem, Relativity ... things in Science, Nature and Mathematics have the power to electrify the minds of children, and the spark illuminates their imaginations forever. One picture in a science book, one field trip to an Imax movie about the oceans can create Jonas Salk (the polio vaccine guy) or Banting and Best (the Canadian insulin guys), or Einstein, or Rosalind Franklin (who took the x-rays that revealed the structure of DNA) -- or the little girl who's growing up right now to discover the cure for AIDS. She could be on the school field trip bus to the Imax science center right now.

But we're all shit out of luck if the 6-story-tall documentary she was supposed to see was cancelled, because the narrator said living species evolved from earlier species over millions and billions of years.

These electric childhood conversions are also common in music, but music prodigies are luckier ... they can get up to speed and make world-recognized achievements, like Mozart or Glenn Gould, when they're still South Parkies. The ear and brain do the math automatically for gifted musicians.

But it's really artificial and misleading to separate the Little Mozarts from the Little Einsteins (he played the fiddle). In their little brains, it's the same stuff. The most talented soloists in my high school orchestra were also the school's top math and science students. Two of them are symphony conductors now, and the brilliant boy pianist who couldn't make a living at it became a biochemist. (Edward Teller, the Father of the H-Bomb, played Bach sublimely. I always thought he was Kubrick's model for Doctor Strangelove, but my Nephew Kwak says it's another Hungarian supergenius, John von Neumann.)

Sir William Herschel was the organist, composer and conductor for the English royal court, and his sister Caroline the choir soloist. They had a nighttime hobby, astronomy, built their own backyard telescope, and discovered the planet Uranus, a couple of its moons, new comets ... so the court musicians ended up as The King's Astronomer, and Assistant to the King's Astronomer (with life pensions). Herschel's position eventually morphed to the title of Astronomer Royal; there's still one of those today. (I'd kill for that job, and I think the AR's office is in Christopher Wren's Old Royal Observatory at Greenwich.)

Since Kepler became transfixed, mathematically and mystically, with The Music of the Spheres, the mathematics of the planets and the mathematics of music have been largely indistinguishable. You just need more math to compute comet orbits than you do to play Bix Beiderbecke's "In a Mist," but it's the same math, been the same since Pythagoras discovered its laws around 550 BC. (A fabulous new recording of Beiderbecke's dreamy jazz compositions is called "Private Astronomy.")

Wiles was an English clergyman's son when Fermat's little puzzle first teased him. From centuries before the Enlightenment to the Victorian Age, British science is lousy with Christian divines sticking their noses, often brilliantly, into science; and on the Continent, Catholic priests and friars (Mersenne, Clavius, Copernicus et al.) were also outstanding figures in the development of math and science. Charles Darwin was heading toward a career as an Anglican clergyman when the talented geology student was invited aboard the round-the-world voyage of HMS Beagle as its naturalist.

The Rev. Thomas Malthus must have suspected that his amateur scientific inquiries might get him into a bit of professional trouble with Organized Christianity, because he published his "Essay on the Principle of Population" anonymously in 1798. You only need simple junior-high algebra to understand his troubling conclusion.

At its most optimistic, food production can only grow arithmetically: a constantly steep up-ramp with time. But human population always increases geometrically or exponentially: an increasingly steep exponential curve with time. No matter how few people you start with, and how efficient your farmers are, eventually population will overtake and outstrip food production. (Because of Malthus, economics is nicknamed "the Dismal Science.")

Malthus said so (but didn't want to sign his name to it). Eventually there's going to be a food shortage, crisis, or famine.

If you disagree, please explain your disagreement in a Comment, I want to see that. Please use at least as much algebra as Malthus did.

Or, if you like, ignore arithmetic entirely and argue that we'll never run out of food because God or Jesus will never let that happen. (This argument relies on Faith.) What the hell, argue whatever you want.

* * *

Okay, now I have to go to the Recycling Center. Hang with me and eventually we'll get back to the Imax Censorship Crisis, which sucks, it really sucks, and it's really going to get us all into very big trouble. It's poisoning the minds of our South Park kids.

We were sort of hoping a few of them would grow up to cure cancer, AIDS, Parkinson's and Alzheimer's Disease, spinal cord injuries, figure out how to get limitless non-polluting electricity from seawater, and prove the Riemann Hypothesis.

But because of this Fundie faith-based creation-science intelligent-design crap going on down at the Imax, we are shit out of luck, they're going to grow up to be Fundie Bushie Moral Majority 700 Club politicians who will get down on their knees and pray while they forbid stem cell research and all sorts of other divinely-inspired holy junk science laws and government policies.

A mind is a terrible thing to waste down at the Imax.


Blogger Newphew Kwak said...

Just to clarify, _I_ didn't say that Von N. was the model for Dr. Strangelove; all I said was that whatsisname who wrote that book whatsitcalled said in the intro that Von N. was the model. Apparently Von N. strenuously urged the POTUS to make like a genocidal bunny and quickly launch a full-out nuclear attack against the damn Ruskies. Clearly a fool in the academic department, the POTUS failed the final exam of his private tutoring classes in Game Theory when he decided to allow life to continue on the face of the earth (for now). Will the same be true if and when we elect a certified genius Economist as POTUS sometime in the future? After all, look at our Senators. The Honorable William Frist (R-Tenn) is, to quote the Washington Post, a "renowned heart surgeon," yet he thinks himself able to diagnose the neurological condition of Terri Schiavo merely by viewing a few minutes of home video; he furthermore can't make himself say the words, "AIDS is not transmitted through sweat," though 110% of all research evidence points towards that conclusion. And some other Senator or Congressperson is supposedly a PhD in Economics but fat chance that they know diddly squat about people actually getting jobs and being paid decently and having hope for their kids to get the same treatment. But they've got a piece of paper that says they are certifiably "smarter than you." What would either of these two certifiably smart people have done if one of the most mega-ultra-math geniuses and (co) inventor of Game Theory insisted that the winning strategy was to "BOMB THE LIVING SHIT OUT OF EVERY SPECK OF MOVING LIFE OVER THERE BEYOND THAT HORIZON, AND MAKE IT SNAPPY!"? I'm sure there are lots of reason to think that Eisenhower can kiss my ass, but his refusal to fall for the trap of smart-people's advice trumps all of that and makes him OK in my book. Seriously, what, of all the really large-scale terrible things that have happened in human history, was instigated by smart people and what by so-called dummies? I'm sure my Uncle will buy you a slice of pizza if you can identify more than one dummy that did anything more than get fooled by some stoopid ass genius.

Blogger Newphew Kwak said...

Comment part 2: Here are two simple reasons that Malthus has been so very, very wrong up until now, though they do not guarantee that he will be wrong regarding some point in the future.
1) Food production is not restricted to mere arithmetical increase.
2) Human reproduction is not restricted to geometric growth.

Blogger Newphew Kwak said...

Comment 3: furthermore, much of what was "dismal" about Malthus's "science" was not just that he predicted famine, but that he made the following political policy suggestion -- because famine appears to be likely in the future, we must avoid it by maintaining a socio-economic system that promotes starvation among the poor. Thus starvation deaths in the future are prevented by inducing starvation deaths in the present. His math may have been technically correct, but his logic left something to be desired.


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