Geometry sux

Updated: See below.
 
Originally posted on 9/19/2011
Could anything possibly be more useless than high school geometry (I avoided saying "pointless" - ha ha)? If ever there were a course better designed to drain the beauty out of math, I can't imagine what it might be. I think geometry is in the curriculum because it gives a fairly visual and intuitive introduction to the axiom / proof approach to math, which is what professional mathematicians do. But for most people math is worth studying because of its usefulness as a collection of tools applicable to the real world. And you can learn its beauty by learning the tools and gradually seeing how they hang together into a coherent architecture of quantitative thinking. But geometry, as taught, gets at virtually none of that. What's taught has virtually no value outside learning the axiom / proof stuff - or at least the applicable parts are a tiny portion of what's taught. And the rigor is of an extremely irritating "memorize these axioms" sort (which is what so much high school education seems to come down to).

It's not that there's no value in learning to distill the underpinnings of intuition into clearly stated basic inputs. Euclid did that (I'm told - I don't read greek) and it's worth understanding the how and why. But to spend an entire year on it is a crime. There's a lot of other useful math that could be taught instead. Basic probability and statistics, for example. Probability is an incredibly interesting subject and doesn't seem to be anywhere in the HS curriculum. But it's absolutely central to decisionmaking. It's intuitive, and sometimes counterintuitive, which is even better. And a lot of it can be taught without much math beyond basic algebra.

It probably won't surprise anyone that Anna has just started taking geometry and is not enjoying it...

Updated on 4/9/2013: I just stumbled on the passage below in a review of the essay "A Mathematician's Lament" by Paul Lockhart. The review is here. The original essay can be found here.

'The author reserves some of his strongest criticism for high school geometry, which he considers an “instrument of the devil.” In fact, his criticism is even more strongly stated: “A geometry class is by far the most mentally and emotionally destructive component of the entire K–12 mathematics curriculum.” Forcing students to follow a rigid and dogmatic format in laying out their proofs, he argues, destroys the very essence of what geometric proofs should be and undermines the students’ intuition.'

Desolation Wilderness

From Meek's Bay to Mt. Tallac, via Phipps and Dicks passes, in 3 1/2 days. Perfect weather, still lots of snow at higher elevations. Eaten alive by mosquitoes.

Stony Ridge Lake

Phipps Pass

Second night campsite at Fontanillis Lake.

Dicks Pass

Dicks Pass

360 degrees of Desolation Wilderness - view from the summit of Mt. Tallac

Mt. Tallac, on the way out

Apparently we haven't learned much

From Plutarch's Lives

...[A]mbitious men, who embrace the image and not the reality of virtue, produce nothing but ugly deeds. To become the people's leaders, they make themselves the slaves of public opinion. Steered by the applause of the multitude, they are really not leaders at all, no matter what title they claim. The wise and virtuous man has no need at all of glory, except inasmuch as it eases his way to action by greater trust. ...[W]hen the passion for popularity goes too far, it is dangerous in all men, and in the government it is utterly destructive. Those with power and authority are carried away into a sort of insanity, and they begin to think that glory is the cause, and not the effect, of goodness. Such men should tell the people, "I can't be both your leader and your slave," just as Phocion told Antipater, "I can't be both your flunky and your friend."

Leaders should learn from the snake in the fable: The tail complained to the head that, although the tail constituted a majority of the snake, the tail never got a turn to decide on its path. Taking the lead, the tail soon blundered into trouble, and the head suffered along with it -- justly punished for following, contrary to Nature, a guide without eyes or brains. Such has been the fate of many, who, submitting to be guided by the caprice of an uninformed and unreasoning multitude, could neither prevent, nor escape, the confusion and disaster that followed. So much for the glory that depends on the voice of large numbers.

Visit to Portland

Catherine & I went to Portland last weekend while Sam played Ultimate in Corvallis.

In our 20 hours we

• took the streetcar up to the north end of the Pearl District and went to a brew pub
• went to Powell's and spent an hour or so wandering around
• walked to the Japanese garden
• walked back to the hotel, on the river
• went to Andina, where the waitress drove me nuts by repeatedly calling us "you two", as in "How were the desserts, you two?" The food was excellent though.
• got up early and sped off to Corvallis

Very enjoyable city with a small-town feel and a pretty setting. We actually got a little sun while we were there, so it was a bit atypical.

How to keep track of your nuclear weapons

With bar codes!

The US Air Force has given a Team Excellence award to a contractor providing bar code tracking so they'll always know where their H-bombs are.

Our systems are failsafe

From today's New York Times, apropos of the meltdown at Fukushima:

Michael Tetuan, a spokesman for G.E.’s water and power division, staunchly defended the technology this week, calling it “the industry’s workhorse with a proven track record of safety and reliability for more than 40 years.”

Mr. Tetuan said there are currently 32 Mark 1 boiling water reactors operating safely around the globe. “There has never been a breach of a Mark 1 containment system,” he said.

From Dr. Strangelove or: How I Learned to Stop Worrying and Love the Bomb
...General Jack D. Ripper has sent B52s to drop H-bombs on targets inside the USSR... Dialogue ensues in the War Room
...
Muffley: General Turgidson! When you instituted the human reliability tests, you assured me there was no possibility of such a thing ever occurring!
Turgidson: Well, I, uh, don't think it's quite fair to condemn a whole program because of a single slip-up, sir.

Apropos of instructions from my Pilates trainer

Syphilophobiac Willy
Took precautions that seem rather silly
He'd step up quite gingerly
And pee intermittently
Fearing salmonlike swimming bacilli

(Not that she's got the clap... The Pilates instruction was a suggestion about how to find my pelvic floor muscles.)

The meter's a little off - feel free to propose adjustments.

Thanks, Tycho!

Violence and American Politics

The left’s fondness for violence largely went away in the early ’70s, with the demise of the Weathermen and similar groups. The right, on the other hand, continues to foster violence at its fringe, by word and deed. “Second amendment remedies,” “The tree of liberty must be refreshed from time to time with the blood of patriots and tyrants,” “Don’t retreat, reload,” etc. These are incitements. And the right’s obsession with guns makes it easy for nutjobs like this Arizona shooter to get them. The NRA continues to chip away at all efforts at reasonable limits on gun ownership and where they can be carried. Our craven legislatures are entirely complicit in this, as is the current supreme court. But “guns everywhere, all the time” is definitely a right wing obsession, not a lefty one.

All the hand-wringing about not blaming the politicians for the acts of a mentally ill man is specious. It’s pretty obvious where the blame lies. Right wingers who want to say “enforce the laws” as the solution to incidents like this need to explain what law and what enforcement would prevent this kind of occurrence.

We live in one of the most violent countries in the developed world. And it’s not because every one goes around with a loaded handgun in the other rich nations.

Safari Photos

Pictures are here.