Feminine(?) Role Models

Preface: Apparently the people at The Aperiodical are not as great as I think they are. You should make your own judgement, though. (In my undenied naivete, I think it's cool that somebody mentioned me on a podcast. Two, actually.)

 So recently some people at Michigan university did some research finding that feminine maths and science role models are not inspiring. I've been wondering for a little while why the article bothers me. Perhaps it's because I exhibit most of the characteristics that they say put girls off studying STEM (science, technology, engineering, mathematics, if I recall correctly) subjects. Which is, you know, kind of sad. I would not like to think that by wearing pretty skirts and getting good marks I send out a message that other people can't . . . can't what? Do mathematics? Understand physics? That sounds plain ridiculous.


Part of it is that the study was actually fairly limited -- it only looked a middle school girls. More significantly, from what I understand, 'feminine' here means something more like 'glamourous' than, say, 'womanly'. (The introduction to the paper proper refers to "pink-laptop-toting ‘‘Computer Engineer Barbie,’’" for instance.) That's not my immediate interpretation of feminine, but perhaps it's other people's. (If you're reading this, I'd love to know what you think.) I can believe that most girls don't think they have the potential to be the real-life version of Computer Engineer Barbie. I for one don't even want to. Does that make me unfeminine?

I like pretty dresses and I have a formidable collection of hair ribbons, but I can't be bothered to go through a fifteen minute make-up routine every morning. I own pretty high heeled sandals, but I don't wear them often. For one thing they're impractical for running up to the Physics department on the second (I think that's third in the USA, where people count funny) floor of Science block. For another, I'd feel overdressed when I arrived amidst the rest of the jeans-and-sneaker-clad students. If that's unfeminine, then I guess all those conclusions about STEM-successful women being unfeminine are probably true. Only I'd be inclined to think that most women are rather unfeminine then. (In fact this is semi-almost-implied in both the press release above and the paper proper.) Motherhood certainly doesn't sound feminine by this metric, which strikes me as rather odd.

If feminine means putting a fair amount of time and effort into satisfying certain perceptions of beauty, then being feminine means having less time to be good at anything else. It also means that anyone with a different idea of what beauty is will rather dislike being labelled as feminine. It wouldn't surprise me that many women who are successful in any number of other fields qualify as 'unfeminine'. On the other hand if being feminine is simply being typically female, I don't think it's nearly as likely to scare girls away from maths and science. (Of course STEM-successful women may still be perceived as unfeminine, which is not cool, but not something I really want to get into here.)

I do think the study is interesting and even useful, but I don't like the lack of definition of 'feminine'. It seems to mean something different every time I see it, until I find myself wondering how I've ended up in a world where it's referred to as counter-stereotypical for a woman to be feminine.

Perhaps I'm overthinking things, but that does strike me as a little odd.

Redefining Survival Mode

Every once in a while one is forced to go into survival mode, I think. It's simply not possible to do everything that one would like to, or even to do most of it altogether properly. So one ends up doing an okay job of the critical stuff until things improve. For instance, I may or may not have recently been heard to say 'I don't understand that, but it doesn't matter -- it's not in the exam.' It's not that I don't care about understanding things. It's that I have a fairly good argument for understanding the things that are in the exam first.

However, I've noticed that my definition of what exactly constitutes this survival mode seems to be changing. Survival mode used to mean sitting and staring tiredly at my cup of tea instead of getting on with my work. Now I sit and stare tiredly at my cup of tea, contemplating the curl of the tea velocity field and wondering if heat transfer would affect that velocity field. And what would the scalar heat field superimposed (as a colour map, say) on the velocity field look like? And if heat flow was treated as a vector? I may even pull up something like Mathematica or Gnuplot to get an idea of what those things would look like. All this still instead of the work I'm supposed to do, although I won't take it any further than that.

It still feels like survival mode, but it seems qualitatively different from the other kind of survival mode. I'm not quite sure where it comes from. Perhaps it's the increased 'mental fitness' after a couple of years of university maths and science; a gradual change in the way I think about things that's just highlighted by the fact that I'm survival mode-ing. Perhaps half a dozen things. I'd need to create an ensemble of identical systems and observe their evolution over time to be sure.

Whatever the cause, I think it's a kind of interesting phenomenon. I should probably stop staring tiredly at the computer screen and go figure out how to use a Cornu spiral, though.

This describes Fresnel diffraction. I'm still figuring out how.

I like bullet points

• It's somehow less intimidating to write a bunch of not necessarily related points out of whatever vaguely interesting soup is floating around in my head than to pound out a nice set of linky paragraphs with a common theme. Let's not talk about why I might intimidate myself about posting to my own little blog in this corner of the internet. Test season and rationality do not have a high level of overlap.
• Let's not talk about test season either. I'd rather tell you that I started listening to the Math/Maths podcast and it's really awesome. Also, it makes me feel like I should actually remember to write about mathsy physicsy stuff on here more often. I thin we can call that a double win. The podcast assumes you know a little bit about maths (or math, for the Americans), but it certainly doesn't expect you to be at research level in anything. I like listening to something with a bit of meat to it without feeling like I've bitten off more than I can chew!
• I'm not sure whether or not that was a mixed metaphor.
• I've finished the first two of my final year courses! Our computational physics courses are largely based around actually writing code, so there's no final theory exam. The general consensus is that continuous assessment is actually more work than otherwise (I write a three hour theory exam for my 16 credit theoretical courses; I wrote a four hour final practical test for an 8 credit computational course), but it's lovely to be finished already!



Hydrogen molecule ion orbitals.

We get to make pretty pictures in comp. phys. too. Like this one, showing the electron orbitals (where the electron is most likely to occur) of a hydrogen molecule ion. This one was done in Mathematica, which is a wonderful tool for crunching through maths that's technically doable but not very much fun. Also, it draws pretty pictures.

(I haven't taken the care with formatting that I would in a proper report, so if there's anything odd about the image, that's probably why! You can look up molecular orbitals or the linear combination of atomic orbitals model if you're really interested in seeing the science done properly.)

• We spent some time yesterday trying to get Mathematica to draw rank two tensors for us, before realising that it was a rather silly idea. A rank zero tensor is just a scalar, or point on the number line, so it's pretty easy to understand. A rank one tensor is a vector (in R³), which you can visualise as an arrow in three dimensional space. A rank two tensor maps one three dimensional vector to another, which means, as far as I understand it, that you'd need a nine-dimensional blackboard to draw it out. Unfortunately (or perhaps fortunately), Mathematica doesn't have a Plot9D command. I can't imagine why not.
• One of the best parts about getting this far into my degree is that as a class we both know each other well enough and are sufficiently interested in physics that between lectures we (sometimes!) do stuff like trying to draw (potentially impossible) things in Mathematica or work out the details of a proof we glossed over in class. See also: hitting 'random' repeatedly on xkcd, and looking at graphs showing that the exponential growth rate for yoghurt is higher than that of gingerbeer or sourdough by a ridiculous amount.
• Are there physicsy versions of things like Math/Maths and Aperiodical? I can find stuff about science-in-general or maths-in-particular easily enough, perhaps because I already know where some of it is, but physics-in-particular doesn't seem to be very well represented. I don't know if maths gets more attention on it's own because it's sometimes excluded from 'science', if it's just considered more awesome than physics or if I just happen to have stumbled upon the online maths community and have yet to discover the physicsy* analogue.
 

*I have now used 'physicsy' three times. This makes it a real word. To quote the estimable Lewis Carroll (in The Hunting of the Snark) "I have said it thrice: // What I tell you three times is true."

For Us

Very Good Friday by ~eldersprite on deviantART

The thing about Good Friday is that we did -- we do, even -- all the very horriblest things to Him, but He will turn around and say "I love you. Be blessed." He reaches not just past, but through the pride, the selfishness, the ugliness of sin and offers Himself to us.

While we were still sinners, Christ died for us. -- Romans 5:8

Quantum mechanics is mind bending, but it's got nothing on this. Relativity is beautiful, but it's got nothing on this. Because the guy who dreamed up the universe whose description would be the source of so much joy and beauty and incredibly hard work? That guy chose to be incarnated inside the universe He'd created and to take the very hardest route out. For me. For you. For us.

There are not enough words to describe the awe (although many people have done a better job than me!). Better, though, to try and fall short than to refuse to try. A little like the parable of the talents, perhaps.

It turns out brick walls do exist

If you insist on verifying the existence of boundaries by repeatedly banging your head on them, you will end up bruised. That's just hearsay, of course. It's most certainly unrelated to the fact that I haven't found time to write here -- or 'most anywhere that's not a report to be handed in for marks -- in the last two months or so. Most certainly unrelated.

Having said that, I'm  sure it won't seem out of the way to ramble a little about how running out of time relates to number systems. I've been hooking a few ideas together and while none of this is rigourous or even necessarily true, I do think it's interesting. The thing about time is that it has to be continuous, kind of like the real numbers. If we allow it to be discrete -- like the integers, say -- we end up with Zeno's paradox:

Suppose Achilles is chasing a tortoise. In the first moment of his chase, we can say that he covers half the distance to the tortoise. In the next moment, he covers half the remaining distance. In the third moment, half of what is left then. Achilles always needs to cover half of the distance left before he can reach the tortoise, but he can continue like this indefinitely without actually catching up. So, says Zeno, it is impossible for Achilles to catch up with the tortoise.

The flaw in this argument is the assumption that time is discretised. It's modelled using integers: moment 1, moment 2, moment 3. We can get a better description of time by using real numbers: between time 3 and and time 4 is time 3.5. Between 3.5 and 4 is 3.75. Between 3.75 and 4 -- well, I could go on forever, which is how Achilles manages to catch the tortoise. (What he does with it next is still up for debate.) However, despite time's going on forever, I still can't manage to get everything I want done.

I can sort of explain that by looking at a mathematical kind of density. Suppose S is a set of numbers. If I can pick any two real numbers and find a third number that's between them and in the set S, then I can say that 'S is dense in the reals'. The rational numbers (numbers that can be written as fractions) are dense in the reals, for instance, but the integers are not. If I pick 1/2 and 1/4, I can't find an integer between them. I can find a rational number between them: 1/3 is perhaps the most obvious. (If you think about it, being dense in the reals actually implies that S has an infinite number of members between any two real numbers.) It seems to me that my perception, or perhaps my experience, is not dense in time. There may, in some sense, be an infinite amount of time between now and tomorrow morning, but I'm certainly not going to get an infinite amount of stuff done in it! In the same way, there are infinitely many (real) numbers between 0 and 100, but only 101 integers (or 99 on the open interval).

I guess I could link in things like response time here too or the fact that movies, which are obviously finite, give the impression of being continuous simply by being more densely packed than our perception. Or I could ditch the biology and go play Mouse Guard with the rest of the family. Mmm.

Numerical Analysis on a Calculator

Today in my differential equations class, we ended up trying to solve the equation x=cos x. And couldn't. Well, I'm not sure everyone was trying very hard, but I had scribbled trig identities all over my page without making any progress whatsoever. Eventually the lecturer took pity on us (or decided that giving us any longer was a waste of his time, perhaps!) and told us to take out our calculators. Oh! So all that analytical fiddling wasn't helpful. It's quite easy to solve the equation numerically on a pretty standard scientific calculator, though, and quite a pretty technique too, I think. I thought I'd share it.

Pick any number you like. If you pick it close to the right answer, the process will be a little quicker, but it doesn't really matter. From the picture below (drawn with Gnuplot), 1 seems like a reasonable starting point.

Now you put cos(1) into your calculator. You don't get 1 back out, so that's not your solution. But if you take cos of that answer, and then cos of that answer and so on for a little while (you can probably do something like just hitting '=' over and over) the answer eventually stops changing. You've found a value which - at least to the accuracy your calculator displays - is it's own cosine. That's the solution. Quite neat! (I think that method is the numerical form of Picard integration, but I could be quite wrong.)

Having started playing with Gnuplot, I don't want to stop, so before I go back to work, why don't I show you a picture of the probability densities we're calculating for the particle-in-a-box problem? It's pretty, at least.

Probabilities of finding an electron at different points in an infinite potential well for five different energy states. (I hope.)

Details

Despite appearance, I am neither dead nor gone. I'm landing. Working out how to cook for two. Working out how four people with three cars can share a single garage. Hoping that the university internet will be a little more reliable once the registration hordes have faded.

Lectures start on Monday morning. In preparation, I have worked out my timetable. I haven't worked out my lecture venues yet. Or labelled my files. Or actually registered for the extra elective which is making my timetable look as scary as it does. (There are six timetable blocks, running 07:45 - 17:30, Monday to Friday. I have  courses in five of those blocks.) I most certainly haven't looked over last years notes so that I'm ready to pick up where we left off, or more than half thought about doing that so-lauded preparatory reading for any of my courses.

Probably, none of that is necessary. Certainly, it's more important that I know how to work the kitchen of the house we're staying in, that I've got the best route from the fridge to the supermarket and back worked out, that I've met the lovely people who are helping our church youth group get organised again, that I'm working out how to do the things I do 'just for fun', but which are really rather important to my sanity.

So tonight I'm going to work out how to make handwritten file tags look just as snazzy as computer-designed ones. I'm going to work on the Baltic myth I'm retelling for a deviantART contest/project. (I don't expect to win, but I want to enter anyway.) I'll have a go at cooking for one, since my sister and partner-in-crimeooking is going out.

Nothing fancy; nothing tragic; nothing exciting, perhaps. But life is taking shape. Sometimes the drama is in the details.