Archive for the 'math' Category

02
May
12

All linky, no thinky

Here’s Mike Boyle getting contemplative about the mechanics of deadlifting vs. squatting:

“It’s obvious”, right?  Go read.

——

And here’s Warren over at Coyote Blog, pointing out some rather shocking innumeracy from (who else?) Kevin Drum:

Warren spotlights this claim from Drum:

These two things together reminded me about an energy factoid that’s always struck me as slightly odd: virtually every form of energy seems to be almost as efficient as burning oil, but not quite.

For example, on either a power/weight basis or a cost basis, batteries are maybe 2x or 3x bigger and less efficient than an internal combustion engine. Not 50x or 100x. Just barely less efficient. And you see the same thing in electricity generation. Depending on how you do the accounting, nuclear power is maybe about as efficient as an oil-fired plant, or maybe 2x or 3x less efficient. Ditto for solar. And for wind. And geothermal. And tidal power.

I’m just noodling vaguely here. Maybe there’s an obvious thermodynamic explanation that I’m missing. It’s just that I wouldn’t be surprised if there were lots of ways of generating energy that were all over the map efficiency-wise. But why are there lots of ways of generating energy that are all surprisingly similar efficiency-wise? In the great scheme of things, a difference of 2x or 3x is practically invisible.

(Emphasis added.)

I… I just… wow.  Really, Kevin?  Suppose we were to reduce your salary by 50%.  Is that difference of 2x “practically invisible”?  How about we triple your taxes.  “Practically invisible” yet?  Give this one a try: Tonight, go out for a long, leisurely dinner at a nice brewpub, and have four pints of beer.  Tomorrow night, do the same, but have twelve pints.  Tell me if the difference is practically invisible.

——

While we’re on the subject of Arts majors being idiots, here’s a bit of the usual from the Daily Fail (h/t Jalopnik):

At $150,000, the Ford Mustang certainly doesn’t come in cheap.

The car in question:

That’s a Ford GT, you dumbfucks!  I thought journalism degrees were supposed to teach research skills and the importance of getting a few basic details right.  Quoth Jalopnik:

It’s not just that the DM confused a Ford GT with a Ford Mustang GT500, which is a mistake perhaps a blind person could make if told they’re writing about a fast Ford with racing stripes. It’s that they’re constantly wrong about anything to do with cars.

At least the comments over at the Daily Fail are amusing.

——

Next, Derek Lowe spotlights an interesting paper on resveratrol:

Yeah, it’s a mouse model paper, but kind of a nifty one.  The researchers in question showed some SIRT1-dependent effects, and some independent effects.

Sinclair’s quoted in this Nature News piece as saying that this reflects the nature of resveratrol as a compound. “Resveratrol is a dirty, dirty molecule, very non-specific”, he says. I think that’s a very fair characterization, which is one of the reasons why I wouldn’t take it myself.

And this being a resveratrol piece, the comments go from zero to stupid in the very first post.

In fact, resveratrol seems to be superior to targeted Sirt1 activators as it improves blood sugar levels and liver health.
Leave it to ‘modern science’ to attempt to disparage a wonderful, multifaceted, Natural molecule.

Capital-N Natural.  Yep.  Just like strychnine.

——

Finally, Ilya Somin makes a lot of sense on property rights absolutism:

Briefly: In the real world, absolutist moral intuitions are messy.  Click through and RTWT.

27
Nov
11

I missed something

You know that post where I was grateful for a bunch of things?  I just realized that I left off something really, really important:

Whew!

(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

02
Nov
11

Spoiler warning

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?

a) 25%
b) 50%
c) 60%
d) 25%”

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.

09
Sep
11

A wild statistical distribution appears!

So here’s another dreary example of a style of argument that sets me off:

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.

(And as with DADT, no-one seems to have bothered to check on what the Israelis are doing.  I don’t think those rifles are for show.)

28
Jul
11

Impress your friends with Richard’s paradox*

…and by “impress” I mean “insult”:

This is why no-one invites me to parties when I’m reading Douglas Hofstadter.

——

* What?  Here.

04
Feb
11

Applying mathematics without a licence is discouraged in NC

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:

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.

13
Jan
11

I guess we’re doing the “violence in media” thing again

So amid the handwringing and anguish over violent political language — which almost certainly had nothing to do with Loughner’s attack on Rep. Giffords but maybe might inspire violence in the future, hey, it could happen, you can’t prove that it won’t — more than a few people have drawn the obvious comparisons between violent imagery in a campaign poster, violent imagery in a TV drama, and violent imagery in a video game.  Hey, I can play!  And so can Bill Gardner:

(Also?  Best academic blog title EVAR.)

Not surprisingly, it turns out that incidence of simple and aggravated assault began a sharp nose-dive in about 1993 with the release of DOOM, and incidence of rape began a sharp nose-dive in about 1991 as the WWW started to take off (you may also know this period as The Day Porn Became Free).  All of this is based on the Bureau of Justice Statistics Victimization Survey, rather than the fetid imaginings of sweaty-palmed demagogues.

Gardner is cautious about implying causation:

So, does that mean the experimental social psychology studies have been done wrong, and that media violence has no effect? No, and No. It is entirely possible that if we hadn’t had violent videogames during the last 15 years, the assault rates would have dropped even further. That said, the Figures above suggest that the effects of violent videogames on actual violence may be small relative to other social forces that have reduced rates of assault and rape, and similarly for the effects of pornography on sexual aggression.

[...]

So what do we make of this? It’s plausible to me that, as Austin suggests, the effect of violent rhetoric is something like the effect of violent videogames or pornography. The data suggest, then, that if media exposure to violent political rhetoric has an effect, it’s likely to be harmful, but if so the harm may be small.

I wouldn’t be shocked to discover that both increases in media and rhetorical violence and decreases in real physical violence come from the same root cause, which I’ll wildly and irresponsibly speculate to be a greater cultural willingness to confront and grapple with (whoops!  Violent imagery again) violent acts and their consequences.  Of course, I also wouldn’t be shocked to find that increased fake violence is offsetting behaviour for decreased real violence.  Either way, I’m a bit surprised that this still comes as a surprise.

04
Jan
11

Lotteries: Not so irrational

Seeing as how I hang out with a bunch of hard-science types, prevailing opinion in my monkeysphere is that lotteries are a bad damn idea.  The less authoritarian opinions usually lean towards annoyed exasperation at the Stupids — “lotteries are a tax on innumeracy”, and quite a regressive one at that — while the other side of the spectrum argues that lotteries are deliberate and malicious fraud against their participants.  All sides agree that the expected value of a lotto ticket is far less than its purchase price, and being snobs we can also agree that the money spent would be better put toward a good book — or at the very least a thought-provoking art-house movie.

Well, the expected dollar value of a lotto ticket is far less than its purchase price.  Cosma Shalizi points out that they aren’t meant as investment vehicles:

The benefit to playing the lottery comes entirely between buying the ticket, and when the winner is revealed. During this interval, someone who has bought the ticket can entertain the idea that they might win, and pleasantly imagine how much better their life could be with the money, what they would do with it, etc. It’s true that in some sense you always could just make yourself think about “what if I had $280 million?”, but many people find it very hard to get their imaginations going on sheer will-power. A plausible and concrete path to the riches, no matter how low the probability, serves as a hook on which to suspend disbelief. In this regard, indeed, lottery tickets are arguably quite cost-effective. If a $1 lottery ticket licenses even one hour of imagining a different life, I don’t see how people who spend $12 for two or three hours of such imagining at a movie theater, or $25 for ten hours at a bookstore, are in any position to talk.

…huh.  De gustibus non disputandum est, and in this case art-house movies and ten-hour books are poor substitutes for people who prefer lotto-winning fantasy.

Incidentally, it’s amusing to think of entertainment in terms of d$/dt.  A three hundred dollar bottle of single-malt scotch, divvied up into twenty-six drinks each savoured over the course of half an hour, starts to look like a bargain when held up to twelve-dollar tickets for a two-hour movie.




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