Hey Science! What are you trying to prove?

There is a certain thing that comes up from time to time in my courses and elsewhere. It's one of those things that is always mentioned in passing, cropping up like ugly little weeds along the path of discussion: bothersome, but fleeting enough that on no individual occasion is it really warranted to interrupt the discussion at hand to address it.

In class this morning, however, I spent half an hour listening to a presentation in which the presenter informed us of what the authors of a paper had aimed to prove, described how they tried to prove it, summarized what their results ended up proving, and went on to discuss the potential implications of what had been proven.

And every time the student uttered that P-word, I cringed inside (or I hope it was only inside). I wanted to stop him and proclaim: "This is science, not math! No one is trying to prove anything!"

Science is about uncovering truths to the best of our capabilities, with the understanding that there is always more to be uncovered and our capabilities themselves may improve over time -- that what we accept as true today may well be replaced with a new truth tomorrow. Scientists seek to uncover truths by making educated guesses about the nature of the world as well as predictions about what would happen, under specified conditions, if their guesses are correct. If what happens under those conditions turns out to match their predictions well enough, we might accept their guess as the Best Guess So Far regarding the nature of that aspect of the world. If the match isn't good enough, we go "Hm, nice idea, but guess again!" Similarly, if someone's guess conflicts with an older, previously accepted guess, but the predictions following from it match reality more closely than those of the old one, we might say "Gee, looks like that old guess wasn't quite right after all."

Rinse and repeat, and hopefully our Best Guesses So Far get ever closer to accurately representing how things actually work, enabling us to manipulate the world in ever cooler ways using this growing understanding of it. (And to the extent that these guesses allow us to manipulate the world as we'd like to, that degree of accuracy is good enough for the time being.)

A mentality of "trying to prove" that your guess is correct conflicts with the very basis of science. It hampers proper, rigourous experimental design. It poisons critical, unbiased evaluation of data. It makes drawing grounded, realistic conclusions nearly impossible.

Sadly, the science publication industry itself seems to reward only those who most convincingly "prove" the shiniest things, in spite of the value that all well-tested guesses contribute to our collective understanding of how the world works. (So maybe I'm wrong; maybe people end up trying to prove things after all. Publish or perish, as they say.) This distortion of science, as the authors of that essay put it, certainly doesn't help to give students the right idea of what science is all about, let alone a clear sense of what may or may not constitute good science.

And so this morning I sat listening to a classroom of graduate students talking, not about how convincing the authors' evidence was, nor whether their conclusions seemed reasonable, but about what the authors had proven, followed by sharing other examples they could think of that agree with what was proved. And suddenly this seminar course seemed to differ from a typical undergraduate one by barely more than the fact that it's not a professor who stands at the front of the room, but a student.

This Is Your Brain on Music (Part I)

This is a book I bought years ago because of my interest in cognition, my love of music, and the fact that my curiosity about how we experience music and why was driving me crazy. For some reason (probably because I'd bought another half-dozen books at the same time), I started reading it then, but didn't get that far before I got distracted by shiny things and forgot about it.

Recently, in my theory development class, we've been talking about design and perception, and music (the way we perceive it, and our preferences relating to it) came up; it reminded me of this book. My music- and dance-related experiences over the last couple of years have made my fascination with this subject much greater than it was even when I bought the book, so I was eager to pick it up again and start reading it from the beginning. Here are a couple of passages from the introduction that resonated with me in a way they couldn't possibly have when I first read them years ago:

What artists and scientists have in common is the ability to live in an open-ended state of interpretation and reinterpretation of the products of our work. The work of artists and scientists is ultimately the pursuit of truth, but members of both camps understand that truth in its very nature is contextual and changeable, dependent on point of view, and that today's truths become tomorrow's disproven hypotheses or forgotten objets d'art.

After I finished undergrad, during my final years of which I focused on molecular genetics and spent most of my non-classtime waking hours working on my school's team for the International Genetically Engineered Machine (iGEM) competition, I -- by no means deliberately -- gradually stepped back from the nitty gritty technical side of synthetic biology, and found myself spending more of my time focused on running and developing my team. Having receded from the land of the hardcore technical side of science, I came to realize that I am (would it be ironic to say "at heart"?) a scientist, in terms of the way I see and think about the world, the questions I'm given to asking, and the way I evaluate information on a day-to-day basis. Meanwhile, I'd become much more immersed in a world of art. Of music, and of dance, and of expression of whatever is alive inside us, trying to get out. And, feeling almost like two completely different people in each of them, I've all the while had a hard time reconciling these two worlds of Science and Art. I'm still not sure how I can do so in a practical sense (or whether I can), but reading that passage was strangely comforting; it made me feel more like a single person.

... I was going to include another excerpt here (actually, the one that I wanted to comment on in the first place), but I'll leave that for tomorrow.

Tough love

Often, when I've dug a really deep hole for myself, and I know I've screwed myself over to the point where I couldn't undo it if I tried, I'm more than a little ambivalent when things work out alright anyway. And, as happy and relieved as my immediate reaction might be, part of me is disappointed in -- maybe even a little resentful of -- the person who made an exception and cut me way more slack than I deserve, because they've robbed me of the hard lesson I should have learned from my own behaviour.

Yesterday I fell in love. (Too bad it's unrequited.)

Strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.

- Ernst Mach

Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.

- Bertrand Russell

These two quotes were amongst many presented to my theory development class at the start of the term, and when I read them I thought, "Yeah, that's so true..." I thought they were great quotes. But I didn't really get them -- really *get* them -- until yesterday.

The lecture was on thinking and representation, and it included discussion of concepts and how we label them with words which are separate from the concepts themselves. We discussed a paper about concept maps as diagrammatic representations of concepts and the relationships between them: how Y changes as a result of a change in X (e.g., if X increases, Y inceases as well, depicted by a + on the line from X to Y).

Though useful, this type of model has at least one obvious limitation: it can't represent precisely how Y changes as a function of X. Many concepts, such as motivation or productivity, are not easy to quantify meaningfully. However, if we are able to measure X and then measure Y and we observe some kind of pattern as we vary them, we can apply a mathematical model instead. My prof used the example of Newton's Second Law, F=ma, and went on to talk about why it's a "perfect model", including the way it's quantitative, testable, generalizable, etc.

But then one student interjected and asked whether it really is such a great model -- does it really serve to convey the relationships between the concepts it relates? He elaborated to the effect of, sure, he "knows" that "force equals mass times acceleration" and can do the related computations, but conceptually, he doesn't *get* the relationship between these concepts from this equation: the prof agreed and went on to ask, "What does it even *mean* to multiply mass by acceleration? Or, if we want to determine acceleration, to divide force by mass??" Conceptually, how do these concepts relate to one another?

Here I suggested that this is where cognition comes into play: as humans, we obviously have cognitive limitations and can only represent so much and manipulate those representations so much before we run out of usable memory and processing ability. For me, I said, classical mechanics makes sense at a conceptual level. I have mental representations of force, mass and acceleration, and I can conceptualize the relationship between them independent of words, numbers or variables. But electromagnetism? V=IR? Sure, I can do all the math just as well as for anything else, but even if I can mentally represent (or "wrap my brain around") the concepts of potential, current and resistance per se, hell if I could successfully represent the *relationship* between them in terms of the concepts themselves. To think about the relationship itself, I have to resort to some kind of analogy involving, say, water and pipes.

And this is where I suddenly *got* it, what it means to say that abstraction is a tool -- that mathematics, the "highest form of abstraction in human thinking", is a tool. If I want to move a box from point A to point B, I can pick it up and carry it there. But if I want to move a whole skid of boxes, I need a forklift to help me.

Abstraction allows us to "[separate] the number concept from what [is] being counted" (Bronowski, 1976). As my prof had put it earlier in the lecture, "Back in the day, we'd think about five trees or five sheep. And then one day some guy comes along and says, 'To hell with the trees and sheep. I'm just interested in this concept of five.'"

Math in particular allows us to completely let go of mental representations of the concepts whose relationships we need to consider. If we can tie numbers to certain concepts by measuring them and observe, through scientific experimentation, a pattern that's consistent with an established mathematical relationship, we also don't have to worry about conceptualizing the literal relationship of these concepts to one another: mathematicians build various forklifts and describe for the rest of us where they'll go if we manipulate the controls in certain ways (and even, if they're especially brilliant/lucky, invent entirely new kinds of forklifts that can pick up different kinds of skids, or even objects that aren't on skids). So if I want to know what happens when I increase the mass and acceleration of an object by so much, I can get into my forklift, manipulate the controls according to some instructions that have been shown to drive the forklift from point A to point B, and not be bothered with actual the skid full of boxes until after I've already moved them. Then, I can get out of the forklift and see that, okay, this is how strong of a force I now have. Manipulating the controls has *nothing* to do with picking up the skid and carrying it myself (were it possible) except the result it achieves.

The magnitude of this sent my mind reeling -- how ridiculously powerful a tool math is, given how well our minds are able to represent concepts and the relationships between them (i.e., not very) versus all of the crazy things we're able to do as a result of circumventing these cognitive limitations. Constructing 50-storey buildings that won't collapse on us? Consider even just the chemical and mechanical properties of the metals, the woods, the concretes... let alone how those play into how much of each you'd need and where they ought to go. Here, those quotes from the beginning of the term came to mind:

Strange as it may sound, the power of mathematics rests on its evasion of all unnecessary thought and on its wonderful saving of mental operations.

- Ernst Mach

Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.

- Bertrand Russell

I sat there in class, just basking in my little epiphany and contemplating the implications, completely oblivious to the ongoing class discussion for at least a good five minutes.

I have fallen in love with math. I'd say "all over again", after having allowed myself to become and remain entangled in the depths of mathless biology for years... but I didn't know it well enough before to justify calling it love. Infatuation, maybe? But now, finally seeing it more clearly, I realize that I don't understand it, and it's eating me alive.

‘‘Mathematics is only patterns... [It] is not just symbols as names for concepts but is a system of relations with logic and reason built into its inner structure." (Feynman, 1975, 1999)

It finally became obvious to me, in an epiphany aftershock, what math research is. In the past I'd asked several math-student friends of mine what one actually *does* as a grad student in math (compared to physics students who smash things, chemistry students who blow things up, biology students who kill things, or social sciences students who... recruit people for studies). I'd never gotten a satisfactory answer: "You think. You read, and you think. ... ... and you play around with ideas until something fits."

"Um... okay..."

But yes! Just as those quotes before merely sounded true but now so effectively sum up what I finally *get* about mathematics, this now is so obviously the truth... In science one seeks to discover relationships amongst natural things and describe them in terms of simpler such things that have been previously observed and described; so too in mathematics, where one seeks to discover relationships amongst abstract concepts or other relationships and prove them using more fundamental ones that have been proven before. However, whereas scientists' substrate for observation and description exists as concrete objects the natural world, that of mathematicians is represented abstractly inside their own minds. Hence math research is indeed just thinking after all...

But this is what plagues me now: what are the "most fundamental" patterns, relationships, or concepts? How were *they* proven? *Were* they proven? Are some things just accepted as "true" or "given" (or are they assumptions of some sort), and if so, which things?

What are the irreducible elements of math?

Multitasking and me

Nicholas Carr blogged last month about multitasking -- or, rather, hypermultitasking and its implications. How we sacrifice depth of attention for breadth: "... concentration, contemplation, reflection, introspection. The less we practice these habits of mind, the more we risk losing them altogether."

One commenter notes: "Scarily, it also appears to be highly addictive - sort of like acquired attention deficit disorder, making it quite difficult to focus on one thing, even when it's necessary/there's time to do so." Another wonders about whether this may affect personal happiness.

I'd mentioned to my supervisor today that I have a lot of trouble attending to things/people/whatever for very long. Even if I've just asked someone a question and they're in the middle of answering it, I *think* I'm listening, but then half the time it turns out that, really, I zoned out 20 seconds into their response. Never mind paying attention to an entire lecture. Hell, these days, it's not uncommon for me to forget what I'm saying mid-sentence, my train of thought having spontaneously jumped tracks against my will.

This is something that I've been struggling with to an increasing extent lately, and it's something that I really want to fix. I feel like I've all but lost my ability to get -- and remain -- engaged in a single task. To sit down and read something, start to finish, without punctuating my reading with five other things. Even the very blog post that got me thinking about this in the first place: I clicked to the page, read the title and the first paragraph or so, thought something to the effect of, "Oh, this is interesting; I want to read this,"... and yet, moments later, found that I had -- for some inexplicable reason and without consciously intending to do so -- flipped back to Google Reader and was checking my other feeds. Huh?

This wasn't always the case: I definitely didn't have this problem during the first couple years of my undergrad... and I'm not sure at what point my powers of attention started to waste away into practically nothing. By default I'd blame the undergrad education system somehow... the same way I blame it for turning me into a highly time-effective assessment-acing machine whose mental-bulimia approach to studying got her through three years of school with strong grades and no learning. (Not of the course material, anyway.) And by "turning me into", I suppose I really mean "letting me get away with being" -- since, in my view, no proper education system would let such student-bots through at anywhere near the top of their class.

But yeah... I think that in this case I can't rely solely on my good ol' scapegoat, The Postsecondary Education System, and must regretfully point the finger at what in fact *made* my undergrad experience (in a good way): my involvement in iGEM. Or, more accurately, the combination of iGEM and my need to see the whole picture and have a hand in everything. Heading up my team involved dealing with not only the project design stuff, but the lab work, the marketing, the funding proposals, the dozens of miscellaneous administration issues, as well as the management and coordination of people (full-time co-ops and other members) involved in each of the above... while somehow also doing my own coursework or research, as the case may have been. And I loved it; for however stressful it could get, it was also hugely rewarding. But I got really good at having a billion unrelated things flying around in my head at any given moment, ready to deal with whatever came up from one moment to the next, and I got really used to constantly switching tasks, switching modes... going from working on a proposal to helping someone troubleshoot in the lab to rescheduling some meeting or other at the last minute... somehow managing not to suffer from severe mental whiplash, but eventually relating all too well to the left side of this comic.

At some point I got past the micromanaging tendencies I once had and *actually* wanted to give other people oversight of things... and I got into the habit of looking things over only to the extent necessary to pass them off to the right person -- that is to say, very superficially, without any serious thinking involved. And despite all of the books and papers I once used to read at great length, these days I have to actively focus on reading continuously, forcing my eyes not to flit down through the beginning and end of each paragraph on a hasty hunt for the key points. (Okay, so maybe my days as a student-bot are partially to blame after all.)

I suppose, considering that haste is what got me here in the first place, there is no quick fix for my problem. Perhaps curling up in bed with a nice, long book will be a good first step toward rehabilitation.

Day One

Yesterday was the first day of the new term. My first class was cancelled, but since I currently know, like, two people in my entire program and wish for this not to be the case, I sat around in the classroom chatting with a couple other students for the entire length of the class. My program is interesting since there are so many students from such varied backgrounds. Most of them come from engineering, but some are just out of undergrad while others have worked in industry for years before coming back to build on their education.

Sitting and listening to one fellow talk about things he's done (including a failed business venture and how he studied for some kind of project management certification test requiring 1500 hours of experience) and his views on the types of companies/firms he's worked for (I hadn't even realized there was a distinction between the two :|), I thought he fell into the latter category. But it turned out that he'd just graduated last year and, because of the economy, decided to continue into grad school instead of braving the bleak job market just yet, predicting that prospects for entry-level jobs in his area would improve by the time he's done.

I guess that's what co-op does for you: being able to come out of undergrad with experience working for several different companies (not to mention at least some kind of sense about things like The Job Market) seems like an incredibly valuable thing, and if I could have appreciated this back then in the way that I do now, I probably would have chosen a different undergrad program and done co-op. That's not to say that I regret opting for the program I did -- quite the opposite, in spite of my opinion of the program itself: on the path I chose, I met some incredible people who have without question, and without even trying, changed my life, and I think I learned a great deal during my undergrad, even if it wasn't what my profs were trying to teach us in class.

Part of me wonders how my experience compares to those of the people I'd be working/competing with if I chose the academia route versus The Real World. I currently have little idea of what The Real World is like, and I can't help but listen to people who live in The Real World and be in awe of their vast wisdom and experience, feeling like my little Academia Bubble self would never stand a chance out there. And so it feels especially bizarre to receive any sort of oohing and aahing at my description of the things I've been doing so far, relating to school and to iGEM (as outstanding as I think iGEM is, from the inside), from such vastly wise and experienced folks. I don't feel impressive at all (more like woefully inadequate, half the time), and hearing people make impressed noises in my direction makes me feel more or less like a fraud. As if I said one thing, but they heard something else altogether, and suddenly I've inadvertently but unavoidably lied to them.

I've now steered myself into a program in which I'm not only doing a thesis, but also a considerable amount of coursework, and I've signed up for the co-op option to boot (which is extremely uncommon for a thesis-based program). I suppose, really, there's no point in comparison with other people, even if it were possible; regardless of where in the pack I stand, all I can do is do what I can, the best that I can, and that will get me wherever it'll get me. If I can figure out where I want that somewhere to be, so I can direct my efforts accordingly, all the better.

But lately I've been finding it increasingly difficult to direct much effort anywhere. Maybe it's partly because I spent most of last term being sick, but I think it has a lot to do with how I feed off of other people's motivation. When I'm around people who want to do things, I want to do things myself. Thinking back to fourth year, I still can't believe how productive I was, with courses, grad school and scholarship applications, trips to various places to visit potential labs (and all the research that went along with it) and of course iGEM, the task set of which naturally expanded to fill every waking moment. I remember spending all day at the lab and coming home only to collapse into bed. Scraping ice off my windshield at 2 am before finally heading home. I probably complained at the time, but now I miss it. ... okay, maybe not the midnight car-cleaning, but I miss the non-stop Doing Things, and the seemingly endless well of Desire to Do Things. Whatever it was that compelled me to do the things that I miss in spite of the things that I don't miss. But it wasn't just me: it was me and my friend, who got me into iGEM in the first place. It's so easy to get -- and stay -- excited about things when you're doing it alongside someone. It's more than how spending all day working doesn't feel so much like working (and can even be enjoyable) in the right company: it's how the right energy from some people can make you want to push forward even when they're not actually around. A wonderful positive-feedback loop of passion and drive. That's what I miss most, I think. It's exciting. From time to time I still somehow find myself in a super-motivated sort of phase, but without the feedback loop it tends to fizzle out pretty quickly.

At the moment, however, I'm quite excited for the new term. The courses I'm taking seem really interesting, I'm eager to get going on my thesis, and there's a really promising group of students involved in iGEM this term, including our two new co-ops. This is the best part of the term: everything is so fresh and full of possibilities!