The first one is pretty subtle; the second is rather less so; and the third is about as subtle as global nuclear war.
Archive for the 'math' Category
You know that post where I was grateful for a bunch of things? I just realized that I left off something really, really important:
- I’m grateful for the fact that I’m not a law professor.
(Hat tip: Orin Kerr.)
Well, back to saving the world with linear algebra*.
* I am dead serious: my job is saving the world with linear algebra**. It is awesome. Wish it paid more, and had benefits, but meh: still awesome.
** Also a bit of concrete mathematics.
*** Bonus unreferenced footnote: All of you Andrew Sullivans out there who’re dead set on insisting that science is destroying your sense of wonder: What the fuck do you make of Formula One? Seriously: incompressible fluid dynamics**** is easily explained by dirt-simple physics, and yet aero systems in ground effect are fucking magic. Just ask any Formula One aerodynamicist who isn’t Adrian Newey. The fact that HRT is multiple seconds off the pace at Interlagos vitiates your point (as does the fact that Hermann Tilke can’t capture the magic of Interlagos or Suzuka or Spa-Francorchamps without a fortuitous arrangement of elevation changes… but now I’m starting to sound like Scott Aaronson.)
**** Air is effectively incompressible at F1 speeds
So this image has been floating around the big truck:
“If you choose an answer to this question at random, what is the chance you will be correct?
It’s meant to be a gotcha, based on the reader’s (presumed) assumption that choosing an answer at random means each of the four answers is equally likely to be chosen. That gives a 1 in 4 chance of getting the “right” answer — but both a) and d) correspond to that probability, which means that there’s a 2 in 4 chance of getting an answer of 25%… which corresponds to the answer in b), but there’s only a 1 in 4 chance that you’ll select b). There’s no steady-state solution to this iterative process, so most people will mull it over and conclude “brain go splodey”, while a few math and comp-sci nerds will recognize a self-referential system and jump immediately to Russell and Gödel.
There is, of course, a satisfyingly smart-assed approach, which relies upon the fact that random numbers are chosen from some sort of distribution. This remains unspecified in the question. If we stipulate that random answers are distributed such that either b) is chosen 50% of the time or c) is chosen 60% of the time, we can make either one of those the correct answer.
Stupid math tricks: always fun on the internet.
So here’s another dreary example of a style of argument that sets me off:
- Why shouldn’t women serve in combat? Ctd. (Andrew Sullivan)
One of Andrew’s readers pontificates about averages:
Despite the amazing progress that women have made in many fronts on equality, they are still physically smaller, slower, and weaker than men. At the very least, one can look at the world records for just about any athletic event, and see how much faster men are. While this does not matter for pilots, or intelligence analysts, or ships captains, it matters very strongly to certain combat arms, such as the infantry. Carrying an 80-pound pack for miles is something where strength does matter. […] This, I think, is the fundamental stumbling block of putting women in the Infantry, or some of the other combat arms.
Oh, okay! Let’s look at the world records for an athletic event. I’m going to pick… Olympic weightlifting. The world record clean and jerk in the 69kg weight class — for men — is 195kg, set by Bulgaria’s Galabin Boevski at Sydney in 2000. The world record C&J for 69kg women is 158kg, set by the PRC’s Liu Chunhong at Beijing in 2008. From this we can conclude two things: First, like Andrew’s reader, we can deduce that men are (surprise, surprise) capable of greater strength and power development then women.
Second, holy fuck there are women out there who can pick up over twice their bodyweight and put it overhead!
You see what’s going on here? Our innumerate friend has taken a true statement (“At the mean, women tend to be smaller, slower, and weaker than men”), stated it obtusely (“Women are physically smaller, slower, and weaker than men”), and used a different interpretation of the obtuse restatement to derive a false conclusion (“There are no women big, strong, and fast enough to serve in the Infantry”). But s/h/its own source of justification — “world records for just about any athletic event” — indicates that there are a bunch of big/strong/fast enough women out there… though perhaps not as many of them as there are men.
While we’re on the subject: there are a lot of men out there who are not physically qualified to serve as light infantrymen — perhaps even a majority. This doesn’t seem to bother anyone.
Craig Scarborough had better stay out of North Carolina. “Scarbs”, if you’re not familiar with the gentleman and his work, is a freelance journalist who covers the technical aspects of Formula One with fantastic rigour, clarity, and depth. His analyses of the ongoing 2011 launch season are invaluable to those of us who’re trying to figure out just how F1’s top designers mean to do what they’re apparently doing. Case in point: speculating about blown outer diffuser sections days before Red Bull launched the RB7, which does precisely that.
For most of us
glib dilettantes interested observers, that’s the sort of intellectual trick to which we aspire: picking out the holes in the FIA’s technical regs by creative application of brain power. In North Carolina, that could be seen as practicing engineering without a license:
- Looks to me like you’ve been doing some unlicensed figurin’ (The Agitator)
A citizen in Raleigh, North Carolina presented the city a proposal to install traffic lights near his home. One city official responded by calling for the citizen to be investigated for what basically amounts to doing math without a license.
So. The city decides not to install traffic lights near David Cox’s house. Cox goes into the historical data, does some analysis, and presents a rather sophisticated report to the city arguing that those traffic lights would in fact be a pretty good idea. One of the neat things about math is that it doesn’t care about your credentials: if applied properly, it gives the same results to a computer, a fourth-grader, a civil engineer, a member of a homeowners’ association, or the Queen of fucking England. (Applying the math properly is of course the key component of the process.) So if you can walk into a city council meeting with a piece of analysis and walk them through the process to verify that it’s been properly constructed, you have a convincing argument no matter who you are.
Kevin Lacy, chief traffic engineer for the North Carolina DOT, seems to have been convinced. This is a problem for Lacy, because he evidently doesn’t want to install the traffic lights regardless of whether they’re a good idea. So Lacy falls back on his good friend the argumentum ad verecundiam — a logical fallacy so old it has three Latin names — and decides that he’s the only one in the council chambers professional enough to calculate traffic loads.
Instead, Lacy called on a state licensing agency, the N.C. Board of Examiners for Engineers and Surveyors, to investigate Cox[…]“When you start applying the principles for trip generation and route assignment, applying judgments from engineering documents and national standards, and making recommendations,” that’s technical work a licensed engineer would do, Lacy said.
Yeah, you know what? Those principles are in place because they work regardless of who uses them — if of course they’re used properly. Those national standards are in place (we presume) because they make sense regardless of who references them — if of course they’re interpreted properly. If Cox’s report committed technical errors, they should be easy for a licensed traffic engineer like Lacy to pick out those errors and show that they invalidate the analysis. The fact that he hasn’t speaks volumes about both Cox and Lacy.
Lacy said his complaint “was not an accusation” against Cox.
“I’m not trying to hush him up,” Lacy said.
I’ve got some more Latin for you, Lacy: factis non verbis.