the truth about math


Huh. So for some reason, when Henry Wallace was married to Carol Preston, he died in 1998. In the new timeline, he died in 1996. I wonder what influence made him die two years sooner/live two years longer.

In one study, for example, a group of French high school students was asked to rate the truth of stereotypes about gender difference in talent in math and the arts before rating their own abilities in these domains. So, for these students, gender stereotypes were very salient as they rated their own ability. Next, they were asked to report their scores in math and the arts on a very important national standardized test taken about two years earlier. Unlike students in a control condition, those in the stereotype-salient group altered the memory of their own objective achievements to fit the well-known stereotype. The girls remembered doing better than they really had in the arts, while the boys inflated their marks in math. They gave themselves, on average, almost an extra 3 percent on their real score while the girls subtracted the same amount from their actual math score. This might not seem like a large effect, but it’s not impossible to imagine two young people considering different occupational paths when, with gender in mind, a boy sees himself as an A student while an equally successful girl thinks she’s only a B.
—  Cordelia Fine, Delusions of Gender: How Our Minds, Society, and Neurosexism Create Difference
Reply to the archetypal "I can't wrap my head around science" comment

This was written as a reply to a tweet chain with @lordmookie, @milky​_candy and @PresidentIKOL on Twitter, but it was too big to tweet (wow, ya think?) and I noticed that it could be a standalone rant so I posted it here instead on twitlonger. Enjoy:

I don’t buy that argument and I think it’s damaging to, well, science and scientists in general.

Almost every single person that I talk to, that isn’t a scientist themselves, ends up eventually saying something like that. I have no idea how that weird culture managed to form. No matter how it formed, it’s actually a real problem, in my opinion, concerning science and scientists. I have my hypotheses on how it may have formed - I think that, in school, kids end up looking at science and mathematics as something scary and impossible to understand.

Anyway, when people think of “science”, they either think of the easily digestible version of science that is presented as popular science, or they think of horrifying, difficult and incomprehensible problems that make no contextual sense and that don’t seem like they have any real use.

People end up looking at science and math as something arcane and utterly abstract. But truth is, that couldn’t be any farther from the truth. Science and math are about looking at the most basic building blocks of the universe that surround us every day. Mathematics is the language used to describe the relations between things in the universe (and beyond), and physics (as the most fundamental form of applied math) is the order of implementation of mathematics - the mechanism that tells you which relations between things you have to look at. Mathematics can put the trajectory of a body moving around another body into equations, with no context or explanation, whereas physics can put things into appropriate context and tell you (and further describe) that those 2 objects are a helium atom, a planet orbiting around a star, or a galaxy in the slow cosmic dance with its galactic satellite.

There is nothing more fundamental, more childish than science, and mathematics is a language just like any other. And like any other language, it demands that you learn syntax and demands that you develop a certain intuition about using it - as well as developing an intuition about that language in different circumstances. For language, this is social circumstances. For mathematics, this applied to different kinds of problems, different theorems and physical applications.

Learning physics is like playing in a sandbox, and noticing how sand falls through your fingers, or seeing snow for the first time and making observations about how it feels on your skin - how it first feels pleasantly cold, but if you overdo it, starts to hurt. That’s exactly how science functions, especially if you have a good professor. You hear about simple, everyday things, and you use your mind to expand beyond those simple examples and to extrapolate to a general case using that knowledge. You know snow is cold and that it starts to hurt if you touch it too much, so you conclude that if you do the same with a cold metal plate, you’ll get the same result. You try it out and it turns out you were right. Then you keep thinking. What if you keep touching air that is the same temperature as that plate and the snow? You try it out and conclude that you can go for much longer (or indefinitely) if you touch air. You start wondering why. You try to think of an explanation - “maybe some things feel colder than others even if they’re not”. You open a biology book and learn a bit more about what “feel colder” means. Armed with that new knowledge, you rephrase your conclusion into “maybe some things drain (transfer) heat faster than others”. From a simple, childish example, you just concluded that different materials transfer heat faster, and some slower. Congratulations, you just reached a correct conclusion about a pretty complex physical property of materials, called heat capacity. Now you can measure stuff and conclude what that property depends on, and you’ve got yourself your very own physical.

Have you noticed something in the paragraph above? Have you noticed how many times I suggested that you assume and extrapolate, and then check if it’s correct or not? Yeah. That’s something that most school systems in the world root out in children (and teens, and young adults). There is right and there is wrong, supposedly. But no, that’s not how science works and that’s not how the world works. You look at the world, you make observations and you allow yourself to think freely, you allow yourself to assume, and then you test whether your assumptions are correct or not. The inability - no, the FEAR of doing that, and the anxiety of being potentially wrong, is the only thing that separates you and me, that separates someone who studies (or truly understands, even if they don’t study it, of course) science, and someone who sees science as something as something they can’t wrap their mind around.

That’s the ONLY difference. Scientists are not more “intelligent” than you (the concept of intelligence is utter bollocks anyway IMO). We (well, I’m a primary author of a paper and a science student, I’m technically one >.>) do not understand the world in a way that you don’t. The only thing that is different between us is that we chose to study science despite how scary it looks, and (if we stayed in science and didn’t drop out) we learned to deal with the fear of being wrong, which is 100% necessary for science.

If I was to read to you a chapter from my mathematical physics (a subject I have this year, introducing a mathematical basis that I will be using for all kinds of physics, including even quantum physics) book, you would be JUST as dumbfounded as I am when I read it for the first time. Sure, I understand some of the words, since I took earlier mathematics classes, but most of it is new. But if you’re a scientist, something you have to do is to take every single of those words that you don’t understand and to learn what it means. In the explanation for that word, you’ll find other words that you don’t understand. This will continue to a few degrees. Instead of getting scared shitless, what you’d need to do is to keep at it. Soon, you’d know every one of those smaller terms, and you’d be able to continue and to look at the larger picture. You’d repeat the process, but now on entire theorems instead of terms. Slowly but steadily, you’d be able to grasp the whole thing, you’d be able to see the entire puzzle and how it all fits together, almost perfectly describing a tiny sliver of the universe that you now deeply understand - and it’d feel great. You’d be incredibly proud of yourself.

And I believe that pretty much every single person on the planet is able to do this. The question is not whether you CAN wrap your head around it. The question is whether it’s something you WANT to do, whether it’s something you’re interested enough in. Every single person is capable of becoming a great scientist. Yes, I still do believe that praising great scientists is good, but when that praise is combined with self-deprecation, it feels unfair towards the person giving the praise. Scientists are humans, not transhumans who understand things better than you. I got into the hardest (or second hardest) university in my country (and we tend to be even harder/more thorough than universities in the west) with very little knowledge of physics and mathematics, and purely because of my passion for physics, I passed the first year on the budget.

So encourage people to get into science and mathematics, because everybody is welcome and everybody is capable of it, the only thing that is needed is some effort and persistence, but you need that for any field of education. Science requires a bit more, but if it’s what you WANT in life, that part will not be an issue. You CAN understand those things, you just don’t yet (which is fine, if you’re not interested). But the important thing to learn is that you can do it, period. That’s basically what this entire rant boils down to - “you can do it!”.

tjdaviss  asked:

About your post on the quadratic formula. It goes back up in September every year, because that is when students are forced to start to learn about it. Down in the summer because nobody likes what they teach in school.

You’re not exactly right.

For most students, the quadratic formula is indeed a gruesome encounter with some non-trivial mathematics. They don’t know where it comes from, have to learn it by heart, and know how to use it only in straightforward but artificial exercises. No creativity to be found. It can even be disapproved to try something new instead of sticking to the plan.

The source of that problem doesn’t lie with the math itself: it’s the system of education that’s inherently wrong. To make students appreciate mathematics, they should be taught to think, instead of to calculate. Creativity, intuition and interest should be stimulated, by letting students try to solve problems, instead of giving them a magic formula to apply and to learn by heart. Math is not solving quadratics by a formula, it’s understanding why the formula works.

If you’re the lucky student who understands math is about deducing real life truths, and not about calculations with contrived interpretations, you just may be wanting to learn about cool mathematics during summer. I do. But then you wouldn’t need to waste time on looking up the quadratic formula, because you’d know where it comes from.

Don’t blame mathematics for being boring, blame school.