Didacticism and the Ratchet of Progress

So my last two posts have focused on an idiosyncratic (and possibly nonsensical) view of creativity that I’ve developed over the past month or so. Under this picture, the intellect is divided into two categories: P-intelligence, which is the brain’s ability to perform simple procedural tasks, and NP-intelligence, which is the brain’s ability to creatively solve difficult problems. So far I’ve talked about how P- and NP-intelligence might vary independently in the brain, possibly giving rise to various personality differences, and how NP-intelligence is immune to introspection, which lies at the heart of what makes us label something as “creative”. In this post I’d like to zoom out a bit and talk about how the notion of P- and NP-intelligence can be applied on a larger, societal scale.

Before we can do that, though, we have to zoom in – zoom in to the brain, and look at how P- and NP-intelligence work together in it. I think something I didn’t emphasize quite enough in the previous two posts is the degree to which the two kinds of intelligence complement one another. P- and NP-intelligence are very different, but they form an intellectual team of sorts – they each handle different jobs in the brain, and together they allow us to bootstrap ourselves up to higher and higher levels of understanding.

What do I mean by bootstrapping? Well, I talked before about how the inner workings of NP-intelligence will always be opaque to your conscious self. Whenever you have a new thought or idea, it just seems to “bubble up” into consciousness, as if from nowhere. So there’s a sense in which NP-intelligence is “cut off” from consciousness – it’s behind a kind of introspective barrier.

By the same token, though, I think you could say that the reverse is also true – that it’s consciousness that is cut off from NP-intelligence. I picture NP-intelligence as essentially operating in the dark, metaphorically speaking. It goes through life stumbling about in what is, in effect, uncharted territory, trying to make sense of things that are at the limit of – or beyond – its ability to make sense of. And as a result, when your NP-intelligence generates some new idea or thought, it does so – well, not randomly, but…blindly.

I think that’s a good way of putting it: NP-intelligence is blind. When trying to solve some problem, your NP-intelligence has no idea in advance if the solution it will come up with will be a good one. How could it? We’re stipulating that the problems it deals with are too hard to immediately see the answer to. So your NP-intelligence is essentially reduced to educated guessing: How about this? Does this work? Okay, what about this? It offers up potential solutions, not knowing if they are correct or not.

And what exactly is it offering up these solutions to? Why, P-intelligence of course! P-intelligence may not be very bright – it could never actually solve the kind of problems NP-intelligence deals with – but it can certainly handle solution-checking. After all, solution-checking is easy. So when your NP-intelligence tosses up some half-baked idea that may be complete genius or may be utter stupidity (it doesn’t know), it’s your P-intelligence that evaluates the idea: No, that’s no good. Nope, total garbage. Yes, that works! Of course, it’s probably not just one-way communication – there’s probably also some interplay, some back and forth between the two: Yes, you’re getting better. No, not quite, but that’s close. Almost there, here’s what’s still wrong. By and large, though, P- and NP-intelligence form a cooperative duo in the brain in which they each stick to their own specialized niche: NP-intelligence is the suggester of ideas, and P-intelligence is the arbiter of suggestions.

That, in a nutshell, is my view of how we manage to make ourselves smarter over time. Your NP-intelligence is essentially an undiscriminating brainstormer, throwing everything it can think of at the wall to see what sticks, and your P-intelligence is an overseer that looks over what’s been thrown and ensures that only good things stick. Together they act as a kind of ratchet that lets good ideas accumulate in the brain and bad ones be forgotten.

Of course, saying that NP-intelligence acts “indiscriminately” is probably overstating things – that would amount to saying that NP-intelligence acts randomly, which is almost certainly not true. After all, while the above “ratchet” scheme would technically work with a random idea generator, in practice it would be far too slow to account for the rate at which humans manage to accumulate knowledge – it would probably take eons for a brain to “randomly” suggest something like General Relativity. No, NP-intelligence does not operate randomly, even if it does operate blindly – it suggests possible solutions using incredibly advanced heuristics that have evolved over millions of years, heuristics that are very much beyond our current understanding. And from the many ideas that these advanced heuristics generate, P-intelligence (faced only with the relatively simple task of identifying good ideas) is able to select the very best of them. The result? Whenever our NP-intelligence manages to cough up some brilliant new thought, our P-intelligence latches onto it, and uses it to haul ourselves up to a new rung on the ladder of understanding – which gives our NP-intelligence a new baseline from which to operate, allowing the process to begin all over again. Thus the ratchet turns, but only ever forward.

Now, there’s a sense in which what I’m saying is nothing new. After all, people have long recognized that “guess and check” is an important method of solving problems. But what this picture is saying is that at a fundamental level, guessing and checking is all there is. The only way problems ever get solved is by one heuristic or another in the brain suggesting a solution that it doesn’t know is correct, and then by another part of the brain taking advantage of the inherent (relative) easiness of checking to see if that solution is any good. There’s no other way it could work, really – unless you already know the answer, the creative leaps you make have to be blind. And what this suggests in turn is that the only reason people are able to learn and grow at all, indeed the only reason that humanity has been able to make the progress it has, is because of one tiny little fact: that it’s easier to verify a solution than it is to generate it. That’s all. That one little fact lies at the heart of everything – it’s what allows you to recognize good ideas outside your own current sphere of understanding, which is what allows that ratchet of progress to turn, which is what eventually gives you…the entire modern world, and all of its wonders. The Large Hadron Collider. Citizen Kane. Dollar Drink Days at McDonald’s. All of them stemming from that one little quirk of math.

(Incidentally, when discussing artificial intelligence I often see people say things like, “Superintelligent AI is impossible. How can we make something that’s smarter than ourselves?” The above is my answer to those people. Making something smarter than yourself isn’t paradoxical – we make ourselves smarter every day when we learn. All it takes is a ratchet)

Now, I started off this post by saying I wanted to zoom out and look at P- and NP-intelligence on a societal level, and then proceeded to spend like 10 paragraphs doing the exact opposite of that. But we seem to have arrived back on topic in a somewhat natural way, and I’m going to pretend that was intentional. So: let’s talk about civilizational progress.

Civilization, clearly, has made a great deal of progress over the past few thousand years or so. This is most obvious in the case of science, but it also applies to things like art and morality and drink deals. And as I alluded to above, I think the process driving this progress is exactly the same as the one that drives individual progress: the ratchet of P- and NP-intelligence. Society progresses because people are continually tossing up new ideas (both good and bad) for evaluation, and because for any given idea, people can easily check it using their P-intelligence, and accept it only if it turns out to be a good idea. It’s the same guess-and-check procedure that I described above for individuals, except operating on a much wider scale.

(Of course, that the two processes would turn out similar is probably not all that surprising, given that society is made up of individuals)

But the interesting thing about civilizational progress, at least to my mind anyway, is the extent to which it doesn’t just consist of individuals making individual progress. One can imagine, in principle at least, a world in which all civilizational progress was due to people independently having insights and getting smarter on their own. In such a world, everyone would still be learning and growing (albeit likely at very different rates), and so humanity’s overall average understanding level would still be going up. But it would be a very different world from the one we live in now. In such a world, ideas and concepts would have to be independently reinvented by every member of the population before they could be made use of. If you wanted to use a phone you would have to be Alexander Graham Bell; if you wanted to do calculus, you would have to be Newton (or at the very least Leibniz).

Thankfully, our world does not work that way – in our world, ideas only have to be generated once. And the reason for this is the same tiny little fact I highlighted above, that beautiful asymmetry between guessing and checking. The fact that checking solutions is easy means that the second an idea has even been considered in someone’s head, the hard part is already over. Once that happens, once the idea has been lifted out of the vast, vast space of possible ideas we could be considering and promoted to our attention, then it just becomes a matter of evaluating it using P-intelligence – which other people can potentially do just as easily as the idea-generator. In other words, ideas are portable – when you come up with some new thought and you want to share it with someone else, they can understand it even if they couldn’t have thought of it themselves. So not only does every person have a ratchet of understanding, but that ratchet carries with it the potential to lift up all of humanity, and not just themselves.

Of course, while this means that humanity is able to generate a truly prodigious number of good ideas, and expand its sphere of knowledge at an almost terrifying rate, the flip side is that it’s pretty much impossible for any one person to keep up with all that new knowledge. Literally impossible, in fact, if you want to keep up with everything – scientific papers alone come out at a rate far faster than you could ever read them, and there are over 300 hours of video uploaded to youtube every minute. But even if you just want to learn the basics of a few key subjects, and keep abreast of only the most important new theories and ideas, you’re still going to have a very tough time of it.

Luckily, there are two things working in your favour. The first is just what I’ve been talking about for this whole post – P vs NP-intelligence, and the fact that it’s much easier to understand someone else’s idea than it is to come up with it yourself. Of course, easier doesn’t necessarily mean easy – you still have to learn calculus, even if you don’t have to invent it – but this is what gives you a fighting chance. Our whole school system is essentially an attempt to take people starting from zero knowledge and bring them up to the frontiers of our understanding, and it’s no coincidence that it operates mostly based on P-intelligence. Oh sure, there are a few exceptions in the form of “investigative learning” activities – which attempt to “guide” students toward making relatively small creative leaps – but for the most part, school consists of teachers explaining things. And it pretty much has to be that way – unless you get really good at guiding, it’s going to take far too long for students to generate on their own everything that they need to learn. After all, it took our best minds centuries to work all of this “science” stuff out. How’s the average kid supposed to do it in 12 years?

So that’s the first thing working in your favour – for the most part when you’re trying to learn, you “merely” have to make use of your P-intelligence to understand the subject matter, which in principle allows you to make progress much faster than the people who originally came up with it all.

The second thing working in your favour, and the reason I actually started writing this post in the first place (which at 2100 words before a mention is probably a record for me) is didacticism.

So, thus far I’ve portrayed the whole process of civilizational progress in a somewhat…overly simplistic manner. I’ve painted a picture in which the second an individual comes up with a brilliant new idea (or theory/insight/solution/whatever), they and everyone else in the world are instantly able to see that it’s a good one. I’ve sort of implied (if not stated) that checking solutions is not just easier than generating them, it’s actually fundamentally easy, and that everyone can do it. And to the extent that I’ve implied these things, I’ve probably overstated my case (but hey, in my defense it’s really easy to get swept up in an idea when you’re writing about it). I think I actually put things better in my first post about this whole mess – there I described P-intelligence as something that develops as you get older, and that can vary from person to person. And from that perspective it’s easy to see how, depending on your level of P-intelligence and the complexity of the idea in question, “checking” it could be anything from trivially easy to practically impossible. It all depends on whether the idea falls within the scope of your P-intelligence, or just at its limits, or well beyond it.

(Mind you, the important stuff I wrote about above still goes through regardless. As long as checking is easier than guessing – even if it’s not easy in an absolute sense – then the ratchet can still turn)

Anyway, so what does this all have to do with didacticism? Well, I view didacticism as a heroic, noble, and thus far bizarrely successful attempt to take humanity’s best ideas and bring them within the scope of more and more people’s P-intelligence. The longer an idea has been around the better we get at explaining it, and the more people there are who can understand it.

My view of that process is something like the following: when someone first comes up with a genuinely new idea (let’s say we’re talking about a physicist and they’ve come up with a new theory, since that’s what I’m most familiar with), initially there are going to be very few people who can understand it. Maybe a few others working in the same sub-sub-field of physics can figure it out, but probably not anyone else. So those few physicists get to work understanding the theory, and eventually after some work they’re able to better explain it to a wider audience – so now maybe everyone in their sub-field understands it. Then all those physicists get to work further clarifying the theory, and further working out the best way to explain it, and eventually everyone in that entire field of physics is able to understand it. And it’s around that point, assuming the theory is important enough and enough results have accumulated around it, that textbooks start getting written and graduate courses start being taught.

That’s an important turning point. When you’ve reached the course and textbook stage, that means you’ve gotten the theory to the point where it can be reliably learned by students – you’ve managed to mass-produce the teaching of the theory, at least to some extent. And from there it just keeps going – people come up with new teaching tricks, or better ways of looking at the theory, and it gets pushed down to upper-year undergraduate courses, and then possibly to lower-year undergraduate courses, and eventually (depending on how fundamentally complicated the theory is, and how well it fits into the curriculum) maybe even to high school. At every step along the way of this process, the wheel of didacticism turns, our explanations get better and better, and the science trickles down.

This isn’t just all hypothetical, mind you – you can actually see this process happening. Take my own research, which is on photonic crystals. Photonic crystals were invented in 1987, the first textbook on them was published in 1995, and just two years ago I sat in on a special photonic crystal graduate course, probably one of the first. So the didactic process is well on its way for photonic crystals – in fact, the only thing holding the subject back right now is that it’s of relatively narrow interest to physicists. If photonic crystals start being used in more applications, and gain importance to a wider range of physicists, then I would be shocked if they weren’t pushed down to upper-year undergraduate courses. They’re certainly no more complicated than anything else that’s taught at that level.

Or, if you’d like a more well-known example, take Special Relativity. Special Relativity is a notoriously counterintuitive and confusing subject in physics, and students always have trouble learning it. However, for such a bewildering, mind-bending theory it’s actually quite simple at heart – and so it stands the most to gain from good teaching and the didactic process in general. This is reflected in the courses it gets taught in. I myself am a TA in a course that teaches Special Relativity, and it’s not an upper year course like you might expect – it’s actually a first year physics course. And not only that, it’s actually a first year physics course for life-science majors. The students in this course are bright kids, to be sure, but physics is not their specialty and most of them are only taking the course because they need it to get into med school. And yet every year we teach them Special Relativity, and it’s actually done at a far less superficial level than you might expect. Granted, I’m not sure how much they get out of it – but the fact that it keeps getting taught in the course year after year puts a lower bound on how ineffective it could be.

Think about what that means – it means that didacticism, in a little over a hundred years, has managed to take Special Relativity from “literally only the smartest person in the world understands this” to “eh, let’s teach it to some 18-year-olds who don’t even really like physics”. It’s a really powerful force, in other words.

And not only that, but it’s actually even more powerful than it seems. The process I described above, of a theory gradually working its way down the scholastic totem pole, is only the most obvious kind of didacticism. There’s also a much subtler process – call it implicit didacticism – whereby theories manage to somehow seep into the broader cultural awareness of a society, even among those who aren’t explicitly taught the theory. A classic example of this is how, after Newton formulated his famous laws of motion, the idea of a clockwork universe suddenly gained in popularity. Of course, no doubt some people who proposed the clockwork universe idea knew of Newton’s laws and were explicitly drawing inspiration from them – but I think it’s also very likely that many proponents of the clockwork universe were ignorant of the laws themselves. Instead, the laws caused a shift in the way people thought and talked that made a mechanistic universe seem more obvious. In fact, I know this sort of thing happened, because I myself “came up” with the clockwork universe idea when I was only 14 or so, before I had taken any physics courses or knew what Newton’s laws were. And I take no credit for “independently” inventing the idea, of course, because in some sense I had already been exposed to it and had absorbed it by osmosis – it was already out there, had already altered our language in imperceptible ways that made it easier to “invent”. Science permeates our culture and affects it in very nonobvious ways, and it’s hard to overestimate how much of an effect this has on our thinking. Steven Pinker talks about much the same idea in The Better Angels of Our Nature while describing a possible cause of the Flynn effect (the secular rise in IQ scores in most developed nations over the past century or so):

And, Flynn suggests, the mindset of science trickled down to everyday discourse in the form of shorthand abstractions. A shorthand abstraction is a hard-won tool of technical analysis that, once grasped, allows people to effortlessly manipulate abstract relationships. Anyone capable of reading this book, even without training in science or philosophy, has probably assimilated hundreds of these abstractions from casual reading, conversation, and exposure to the media, including proportional, percentage, correlation,causation, [ . . . ]  and cost-benefit analysis. Yet each of them—even a concept as second-nature to us as percentage—at one time trickled down from the academy and other highbrow sources and increased in popularity in printed usage over the course of the 20th century.

-Steven Pinker, The Better Angels of Our Nature, p. 889

I have no idea if he’s right about the Flynn Effect, but what’s undoubtedly true is that right now we live in the most scientifically literate society to have ever existed. The average person knows far more about science (and more importantly, knows far more about good thinking techniques) than at any point in history. And if that notion seems wrong to you, if you’re more prone to associating modern day society with reality TV and dumbed-down pop music and people using #txtspeak, then…well, maybe you should raise your opinion of modern day society a little. A hundred years ago you wouldn’t have been able to just say “correlation does not imply causation”, or “you’ll hit diminishing returns” and assume that everyone would know what you were talking about. Heck, you wouldn’t have been able to read a blog post like this one, written by a complete layperson, even if blogging had existed back then.

All of which is to say: didacticism is a pretty marvelous thing, and we all owe the teachers and explainers of the world a debt of gratitude for what they do. So I say to them all now: thank you! This blog couldn’t exist without you.

When I put up this site I actually wrote at the outset that I didn’t want it to be a didactic blog. And while I do still hold that opinion, I’m much less certain of it than I used to be – I see now the value of didacticism in a way that I didn’t before. So I could see myself writing popular articles in the future, if not here then perhaps somewhere else. In some ways it’s hard, thankless work, but it really does bring great value to the world.

And hey, I know just the subject to write about…

[Up next: AI risk and how it pertains to didacticism. I was just going to include it here, but this piece was already getting pretty long, and it seems more self-contained this way anyway. So you’ll have to wait at least a few more days to find out why I think we’re all doomed]

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