Via A., here’s a cool video about doodling in math class, that somehow keeps circling back to knot theory:
[youtube http://www.youtube.com/watch?v=heKK95DAKms&fs=1&hl=en_US]
This should be required viewing for anyone who doesn’t see what the appeal of math is, or who thinks math is only about numbers and formulas.
My favorite line is the one about the two snakes who can’t talk to each other because one only speaks parseltongue, and the other only Python.
I think most people, if you asked them, would say that teaching math in school is a good thing. If you ask why, the usual answer is something like, it allows you to figure out how much carpet and wallpaper you need to buy to redecorate your living room, to determine whether the 12-can pack of ravioli at Costco is cheaper than what you can find at Safeway, and so forth.
But that’s all elementary and High School level stuff: arithmetic, geometry, a dash of algebra. I’ve rarely used trigonometry after college, and I know one person who used calculus in quilting. I think it’s safe to say that most people never use calculus, differential equations, prepositional logic, etc. after college. But I still say there’s value in studying math beyond the practical.
Let me ask a contrasting question: why should kids play sports in school? Only a tiny minority of them will make a living playing or coaching sports, and less than half will even play on the office softball team or the like.
The answer I get most often is that sports teach teamwork: how to subsume your immediate desires for the greater good, make sure you do your part and trust your teammates to do theirs, and communicate effectively to make sure you’re not working at cross-purposes. You learn to win graciously and learn from your failures.
In other words, it’s not so much that playing sports develops muscle tone and general fitness. But rather, it’s an indirect way of teaching other skills like cooperation. They may not be taught explicitly, and there are other ways of teaching them, but this works.
The same thing, I think, applies to math. A few years after learning it, you probably won’t be able to prove that there is an infinite number of primes, or how to integrate a function. But that’s okay, because math teaches skills other than the purely pragmatic.
Proving theorems, for instance, forces you to distinguish between what you think is true, and what you can demonstrate; what looks right, and what is right. Geometry teachers always admonish students not to reason from the diagram because concrete examples are often misleading: just because line AB is perpendicular to line CD in this drawing doesn’t mean that that’s always the case. The point is to figure out what’s universally true, not just what’s true about this particular instance.
These are skills that apply to non-mathematical professions: judges and lawyers often deal with people who have clearly done something wrong, and need to distinguish between “I know that ain’t right” and whether the action in question is legal or not. Police officers likewise need to know the difference between “I know Jimmy’s been selling crack to students” and “I can prove to a jury that Jimmy’s been selling crack”. Programmers will find that they write code that works in situations that they didn’t imagine, because it’s a truism that end users will do weird things with your software that you never dreamed of. Financiers should be able to put together a portfolio that can survive unexpected catastrophic changes in the market. (And as much as it pains me to defend the Bush administration, Donald Rumsfeld was quite right in distinguishing between “known unknowns” and “unknown unknowns”, and trying to plan for both.)
Or take the discussion about defining information in the “I Get Email” thread; specifically, the exchange between Tom and Troublesome Frog on whether all living beings contain information. It seems that Tom doesn’t quite get the difference between ∀ x ∀ y p (no matter how you define information, all living beings contain information) and ∃ x ∀ y p (we can come up with a definition of “information” such that all living beings contain information).
Math is very big on abstraction. This starts in algebra, which is all about figuring things out about things that you know you don’t know much about. And it just gets more abstract from there. The first time you demonstrate that there is no solution for some equation, or better yet, that there can be no proof of a given proposition, can be quite a thrill.
And abstract thought is one of those things we humans are good at. It’s what allows us to formulate moral rules that apply to everyone, and see things like “the market” instead of a bunch of people trading stuff. It seems that we ought to learn to do it well.
One of my favorite types of SAT question is the one that presents a math problem, and one of the possible answers is “not enough information to solve the problem”. The lesson here isn’t just “know your limitations”. It also shows that just because something looks solvable doesn’t mean that it is; that just because something is printed in an official-looking book doesn’t make it kosher. And also, the sooner you figure out that a problem has no solution, the less time you’ll waste looking for one.
Finally, one thing that everyone should get out of any math class is that you can figure stuff out on your own, without looking the answers up in the back of the book. Yes, the same is true of science and other classes, but math is one of those branches where you don’t need fancy equipment to work on a problem and figure out the solution.
One problem I see is that a lot of people seem to think that knowledge is something that is handed down from on high, rather than something that can be created. This seems to be at the root of the claim that evolution is just another religion: “I have my priests who tell me that God created humans, and you have your priests who tell you humans evolved. The only difference between creation and evolution is which team you’re on.” There’s no arguing with someone who simply repeats what they were taught; but if you’re in an argument with someone who thinks that mere mortals can work out answers on their own, you might get somewhere. And that’s something we could use more of.
This ad doesn’t actually say that the Q-Ray bracelet does a damn thing, but it sure as hellshit[] implies it:
Thanks to the Ask an Atheist guys for the pointer.
Hey, the Q-Ray people aren’t saying the bracelet does anything. That would be an invitation to get sued. No, the athlete is saying it. And she’s not saying it, either; she’s just saying it might.
And her testimonial is filmed in what appears to be a doctor’s office (or, more likely, a doctor’s office set. At least, my doctor doesn’t have any anatomical charts on his wall).
So it’s not actionable. But if you should happen to get the impression that this magic bracelet is part of a medical regimen endorsed by the medical profession, well, they won’t try to disillusion you.
The narrator says that magnets have been “used for centuries to promote a healthy lifestyle”. Of course, the same could be said of leeches.
As far as I can tell, the only verifiable claims made by the Q-Ray people are 1) it has magnets, and 2) “beautifully crafted, with an expandable steel band”.
This Hour Has 22 Minutes says pretty much the same thing, but won’t let me embed the video.
[] Text changed to refer to something for which there’s actual evidence.
(In which I play at being Ed Yong.)
Today is Bioscience Day at UMD. While I’m not a scientist, I am a science groupie, so on my lunch break I wandered over to the poster session to see what was being presented, and maybe score a pass to go backstage where the brown M&Ms and orgies are, and scientists would snort blow out of the small of my back before using me up and dumping me in some back alley with nothing but a case of antibiotic-resistant herpes and a couple of coauthor credits talk to the researchers.
For the most part, I lacked the vocabulary and the background to understand what was so cool about the research. But occasionally I understood enough to ask what was going on.
The Taboo Wiktionary: One problem with the sciences is that it uses big words, and so students are tempted to just memorize definitions without actually understanding the underlying ideas. So these folks devised a game similar to Taboo, in which students have to define terms without using certain words.
Attack! We’re right behind you! (Biological Nanofactories Target and Activate Epithelial Cell Surfaces for Modulating Bacterial Quorum Sensing and Interspecies Signaling): This was a rather cool notion. The idea is that bacteria like E. coli don’t attack the host organism until there’s a lot of them. The way this is coordinated is through chemical signals: the bacteria emit chemicals that their neighbors sense, so that each bacterium can tell whether it’s alone or part of a crowd. And if it’s part of a crowd, a bacterium will attack, confident that everyone else is, too.
So what these people figured was, what if you try to mimic the “crowd” signal? If there are only a handful of E. coli in your gut, but you fool them into thinking that there’s a bazillion of them, then they’ll attack. Your immune system will make mincemeat of them, and in the process, learn what that strain of E. coli looks like, in case they come back. I guess this is like beating the bushes to force potential enemies to show themselves.
Drug Delivery by Cucurbituril-Type Molecular Containers: The word that caught my eye was “Cucurbituril”. I seemed to remember that “cucurbit” is Latin for “pumpkin” or “gourd”, and that didn’t seem to match with the chemistry-heavy abstract.
I asked the author, figuring that cucurbiturils were originally derived from some gourd protein or something, but she explained that no, it’s because the molecule is sorta-spherical and has a lot of empty space inside, so it looks a little like a pumpkin. Sense of humor FTW!
Ant diversity from space: The way the title read (unfortunately, at that link they’ve replaced the poster’s title with “Assistant Research Scientist”, for some reason), I thought it was about detecting and mapping ants from satellites, which seemed rather hard to believe. It turns out that while there are some ant structures that can be seen from space (giant anthills in the African savannah, for instance), that wasn’t what they were talking about. Rather, they were using satellite imagery to map conditions like humidity, temperature, soil composition, etc., and from that predict the likely characteristics of native ants. In other words, if you’re looking for ants with a certain set of characteristics, this research can help narrow down the best places to look.
All in all, I found that all of the researchers I talked to were friendly, and more than happy to explain their work to a layman like myself.
The AP reports:
For 33 years, Maridjan spoke to Mount Merapi, believing he could appease its unpredictable spirits by throwing offerings of rice, clothes and chickens into the volcano’s gaping crater.
…Maridjan was believed by many to have the ability to speak directly to the mountain and led ceremonies every year to hold back its lava flows by throwing rice, clothes and chickens into its dome.
(emphasis added.)
Well, duh. Of course he could speak to the volcano. Anyone can talk to a mountain, or a river, or dead ancestors. To quote Shakespeare’s Henry IV, Part I:
Glendower: I can call spirits from the vasty deep.
Hotspur: Why, so can I, or so can any man;
But will they come when you do call for them?
The real question is, does anything happen as a result of talking to a mountain?
Do you want to restore sanity and rationality to political discourse? Sure, we all do!
But do you also want to promote sanity and rationality in general? Then you should join the Washington Coalition of Reason this Saturday on the National Mall as they participate in the Rally to Restore Reason.
Look for the #unitedcor hashtag on Twitter.
Oh, and the guys from the American Freethought podcast will be there as well. They’ll also be announcing their location on Twitter, so find out where they are, then stop by and say hi.
At the end of Wednesday’s meeting of the UMD Society of Inquiry, the local student skeptic group, I conducted a psychological experiment on those attendees who didn’t need to rush off for other appointments.
It was a variation on the game of Twenty Questions. But instead of a person or thing, I’d think of a rule or category, which the players had to guess. And instead of trying to guess directly what category I had in mind, the players would call out a specific example, and I’d tell them whether it was in the category I was thinking of. Actually, I asked them to name both the category they were thinking of, and a specific example; but I’d only tell them whether the specific example fit my category, not whether the category they were thinking of was correct.
For example, I might think of the category “types of cake”. A player might say, “the category is vegetables
, and the example is carrot
“. I would then say yes, because carrot cake is a type of cake. The next player knows that “carrot” matches the rule, and might say “orange things, and the example is red hair”. To which I’d say no, because there’s no such thing as red hair cake.
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This news item caught my eye because it’s a “news of the weird” type of story:
NEW YORK — A New York City man who plunged 40 stories from the rooftop of an apartment building has survived after crashing onto a parked car.
But then there was this bit:
The car’s owner, Guy McCormack, of Old Bridge, N.J., told the Daily News he’s convinced that rosary beads he kept inside the Dodge saved Magill’s life.
Can we please stop lending credibility to such obvious superstitious nonsense by repeating it uncritically?
If the car’s owner had attributed the man’s survival to a statuette of Ganesh on his dash, or a voodoo amulet, or a lucky Mickey Mantle rookie card, would it be taken as seriously? If not, then why are magic beads more plausible?
ObPunchline: You’re a mean drunk, Superman.
There’s a phrase that’s been annoying me lately. I don’t know whether it’s a new thing, or something that’s been floating around for years but only recently came to my attention, but it’s been bugging me.
“We should respect everyone’s ideas.”
This is exactly wrong. There are plenty of ideas out there that don’t deserve respect: the idea that women shouldn’t be allowed to vote, that the ACLU hates America, that the Earth is flat, that good deeds are pointless unless you also believe in a Jewish zombie, that farts should be used as currency, and many more.
Respecting people, now that’s something else entirely. Everyone is entitled to certain rights, simply by virtue of being human. People can lose those rights, like a criminal who goes to prison and loses his rght to go where he likes, but every person starts out with a core set of rights. A more pedestrian example is that I tend to start out believing that you are a basically decent, honest person until you demonstrate otherwise.
But ideas are not people. They don’t suffer when they’re abandoned or overturned. They don’t feel shame when they’re shown to be idiotic, nor do they get lonely when held only by a handful of loons. Eliminating an idea is nothing like killing a person.
Of course, the problem is that many ideas, particularly religious or ideological ones, are tightly wrapped up in people’s sense of identity or self-worth; so saying that someone has a stupid idea or holds a stupid belief feels to them as if they’re being told that they themselves are stupid.
And so “all ideas should be respected” is really cover for “don’t criticize my religion”. The reasoning seems to be, “We both hold ideas that we’re not willing to abandon, even though we realize that they can’t stand up to critical examination. So I’ll agree not to shoot down your weak ideas if you’ll agree not to attack mine.” This seems to be the truce entered into in civilized countries where religions and other ideologies aren’t allowed to impose themselves through force of arms anymore.
But of course it all depends on all participants having weak beliefs that they want to protect. Along come skeptics who don’t want to hold weak beliefs, who want people to point out their false beliefs so they can get rid of them, and upset this unstable balance.
So fuck beliefs. They don’t automatically deserve my respect.
Now, I have friends (of the “I’d help them move a corpse, and vice-versa” variety) who hold wacky beliefs. (Mostly religious ones, as you might expect.) And yes, there are topics that, by mostly-unspoken agreement, we venture into only rarely. But that’s because I don’t want to upset my friends (see “sense of identity and self-worth”, above). In other words, it’s about respecting the person, not the belief.