A number of years ago I used to have long, winding discussions about political philosophy, ethics, science and what not with Mikko Särelä. Some of the most influential ones to me concerned the nature of science, the scientific method, and by extension the role of rules in civilized discussion, the role of professional ethics in getting things done, and so on. Now that I've freshly had to apply those ideas to yet another piece of utter humbug, I thought I'd jot down the primary lesson I learnt about science then. It's also something I haven't seen written down concisely yet, and which might explain why I nowadays see no real schism between the so called hard, physical sciences on the one hand, and the soft, humanistic ones on the other.
Since I'm a mathematician-wannabe, the easiest example of the principle comes from that area. Mathematicians are after logical truth which follows from simple, formal presumptions. They want to prove certain things beyond any doubt, like the fact that if you cut out the corners of a triangle and place them side by side, what you always end up with is a straight line. "Given the axioms of Euclidean geometry, the sum of angles of any triangle will be 180 degrees."
But then, there are tons and tons of mathematical truths like that, and today you can even churn them out mechanically if you want to. The vast majority of them immediately seem dull and uninteresting. For example, it is a mathematical truth that there is a follower to the integer we call "9", another one is that in base ten we can systematically denote them all, with the follower then being called "10". That transition from single digits to double digits is rather interesting—and something I've used to instill the idea of number bases in small kids more than one time; they get binary and ternary in under ten minutes that way—but after that's done, the difference between 1999 and 2000 is pretty much a done deal. It ceases to be interesting somehow. Why is that?
The reason is generalization. Once we perceive the pattern inherent in enumeration in various number bases, we don't have to worry about the specifics anymore. What we need to know about the subject is already mostly covered, by means of applying a higher level abstraction. In this case mathematicians call that "induction".
My insight is then about what enables this kind of "productive laziness" (Linus Torvalds's words) in the first place. Because it isn't a given; not by a long shot. What enables it is that you're relying on a very carefully vetted set of concepts to bootstrap your intuition. Historically, not everybody had access to that, but many instead relied on haphazard, irregular notions of what numbers and their notation were.
Take for example the Roman numerals. Starting with them you'd be hard pressed to teach someone binary, because they behave in a fundamentally different and less organized fashion. It's much more difficult to show the analogy between going from III to IV to V, vis-à-vis 11 to 100 to 101, than to show how the carry mechanics of adding one work from 9 to 10, vis-à-vis adding one to 11 to get 100. Roman numerals simply aren't as organized or prone to generalizing thought as the Arabic ones have proven to be.
The history of mathematics is full of examples like this one: knowing some result for sure, even if it's as simple as to know what adding one to an integer leads to, isn't enough. It also matters how you structure your notation, and especially which concepts you structure your underlying thought upon. The Arabic derived place notation is a vast improvement upon the irregularities of the Mayan, Roman and other not so structured ones, and so won. Not because you couldn't do the same things with either, but because the different, more organized viewpoint brings a certain economy to your thinking which you would otherwise lack.
That neat, useful pivot for better, more economical thinking is not then a happenstance. It's a result of serious, long-term, scientific thought, reaching over tens of generations of cultural evolution. A process which tries not just to derive truths, but truths which have been packaged in an humanly consumable and easily applicable form. I seem to remember the fight claimed its casualties as well.
That is then the second, large task of science: to make increasing amounts of interconnected knowledge palatable and easily reapplied. It's why mathematicians try out alternative proofs, instead of being content with just knowing what will prove to be true. It's why physicists assign names like "quark" to something that is essentially a stable, more or less localized excitation in a much more difficult to understand quantum field theory. It's also why social scientists have to "formalize" and "operationalize" their findings, naming them and developing a story to explain their relevance to others. In essence, all of it is about choosing certain maximally humanly understandable base concepts and analogies into which to anchor/reduce much more variegated phenomena; a compression of knowledge against the nasty statistical-computational model which is the human consciousness. Partially societal-collective as well, since no scientist is an island either.
That is then, in my mind at least, also why the rules and etiquette of rational thought and scientific discussion are so full of seemingly banal rules of thumb, in addition to the simplistic empiricist protocol. While we do need protocols to shield us from wishful thinking and the like regarding the physical reality ("no, particles aren't truly minuscule ping-pong balls at the quantum level"), there's always the second, markedly human task of science which is to organize the knowledge, all knowledge, that we have into something both experts and laymen alike can use.
In nonempirical sciences like math or history, that Second Task then necessarily takes the forefront, ahead of teasing out unintuitive facts from Mother Nature. And that task is just as important, even if it doesn't go quite as closely in hand with human-unrelated physical truths as it does in the natural sciences. So whereas Rutherford said: "All science is either physics or stamp collecting", I'd rather claim physics too, at its best, is half the latter. And the better for it then.
Finally, the same goes for thought overall. Such basically scientific prepercepts as this one are fully applicable at every level and to everyone. I'm no scientist, but I continue to benefit over and over from the lessons I've learnt from the doers in the field. Some historical figures, some friends of mine, but still. It's not just that science has its markedly human side; it's also that good, useful, human thought too possesses its markedly scientific side.
Since I'm a mathematician-wannabe, the easiest example of the principle comes from that area. Mathematicians are after logical truth which follows from simple, formal presumptions. They want to prove certain things beyond any doubt, like the fact that if you cut out the corners of a triangle and place them side by side, what you always end up with is a straight line. "Given the axioms of Euclidean geometry, the sum of angles of any triangle will be 180 degrees."
But then, there are tons and tons of mathematical truths like that, and today you can even churn them out mechanically if you want to. The vast majority of them immediately seem dull and uninteresting. For example, it is a mathematical truth that there is a follower to the integer we call "9", another one is that in base ten we can systematically denote them all, with the follower then being called "10". That transition from single digits to double digits is rather interesting—and something I've used to instill the idea of number bases in small kids more than one time; they get binary and ternary in under ten minutes that way—but after that's done, the difference between 1999 and 2000 is pretty much a done deal. It ceases to be interesting somehow. Why is that?
The reason is generalization. Once we perceive the pattern inherent in enumeration in various number bases, we don't have to worry about the specifics anymore. What we need to know about the subject is already mostly covered, by means of applying a higher level abstraction. In this case mathematicians call that "induction".
My insight is then about what enables this kind of "productive laziness" (Linus Torvalds's words) in the first place. Because it isn't a given; not by a long shot. What enables it is that you're relying on a very carefully vetted set of concepts to bootstrap your intuition. Historically, not everybody had access to that, but many instead relied on haphazard, irregular notions of what numbers and their notation were.
Take for example the Roman numerals. Starting with them you'd be hard pressed to teach someone binary, because they behave in a fundamentally different and less organized fashion. It's much more difficult to show the analogy between going from III to IV to V, vis-à-vis 11 to 100 to 101, than to show how the carry mechanics of adding one work from 9 to 10, vis-à-vis adding one to 11 to get 100. Roman numerals simply aren't as organized or prone to generalizing thought as the Arabic ones have proven to be.
The history of mathematics is full of examples like this one: knowing some result for sure, even if it's as simple as to know what adding one to an integer leads to, isn't enough. It also matters how you structure your notation, and especially which concepts you structure your underlying thought upon. The Arabic derived place notation is a vast improvement upon the irregularities of the Mayan, Roman and other not so structured ones, and so won. Not because you couldn't do the same things with either, but because the different, more organized viewpoint brings a certain economy to your thinking which you would otherwise lack.
That neat, useful pivot for better, more economical thinking is not then a happenstance. It's a result of serious, long-term, scientific thought, reaching over tens of generations of cultural evolution. A process which tries not just to derive truths, but truths which have been packaged in an humanly consumable and easily applicable form. I seem to remember the fight claimed its casualties as well.
That is then the second, large task of science: to make increasing amounts of interconnected knowledge palatable and easily reapplied. It's why mathematicians try out alternative proofs, instead of being content with just knowing what will prove to be true. It's why physicists assign names like "quark" to something that is essentially a stable, more or less localized excitation in a much more difficult to understand quantum field theory. It's also why social scientists have to "formalize" and "operationalize" their findings, naming them and developing a story to explain their relevance to others. In essence, all of it is about choosing certain maximally humanly understandable base concepts and analogies into which to anchor/reduce much more variegated phenomena; a compression of knowledge against the nasty statistical-computational model which is the human consciousness. Partially societal-collective as well, since no scientist is an island either.
That is then, in my mind at least, also why the rules and etiquette of rational thought and scientific discussion are so full of seemingly banal rules of thumb, in addition to the simplistic empiricist protocol. While we do need protocols to shield us from wishful thinking and the like regarding the physical reality ("no, particles aren't truly minuscule ping-pong balls at the quantum level"), there's always the second, markedly human task of science which is to organize the knowledge, all knowledge, that we have into something both experts and laymen alike can use.
In nonempirical sciences like math or history, that Second Task then necessarily takes the forefront, ahead of teasing out unintuitive facts from Mother Nature. And that task is just as important, even if it doesn't go quite as closely in hand with human-unrelated physical truths as it does in the natural sciences. So whereas Rutherford said: "All science is either physics or stamp collecting", I'd rather claim physics too, at its best, is half the latter. And the better for it then.
Finally, the same goes for thought overall. Such basically scientific prepercepts as this one are fully applicable at every level and to everyone. I'm no scientist, but I continue to benefit over and over from the lessons I've learnt from the doers in the field. Some historical figures, some friends of mine, but still. It's not just that science has its markedly human side; it's also that good, useful, human thought too possesses its markedly scientific side.
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