[In “which” I use “scare” quotes a “lot”]
My last post turned out to be a fruitful one, at least in terms of giving me new things to think about. I find that the mark of a good thought is whether or not it begets other thoughts, and this one was a veritable begattling gun.
Recall the thesis from last time: people have two kinds of intelligence, P-intelligence and NP-intelligence (I’m not super crazy about the names by the way, but they’ll do for now). P-intelligence is the ability to recognize a good solution to a problem when it’s presented to you (where the “problem” could be anything from coming up with a math proof to writing an emotionally moving poem), and NP-intelligence is the ability to actually come up with the solution in the first place. Since it’s obvious that it’s much easier to verify solutions as correct than it is to generate them (where “obvious” in this case means “pretty much impossible to prove, but hey, we’ll just assume it anyway”), it’s clear that one’s P-intelligence will always be “ahead” of one’s NP-intelligence: the level of quality you can reliably recognize will always exceed the level you can reliably generate. In that post I then went on to speculate that the gap between P-intelligence and NP-intelligence might vary from person to person, and even within a person from one age to another, and that this gap might explain some behavioural patterns that show up in humans.
(By the way, I should probably point out here that I totally bungled the mathematical definition of NP problems in the last post. NP problems are not those that are hard to solve and easy to verify – they are simply those that are easy to verify, full stop. Thus a problem in P also has to be in NP, since being easy to solve guarantees being easy to verify. The hardest problems in the NP class (called NP-complete problems) do – probably – have the character I described, of being difficult to solve and easy to verify, and so I’m going to retroactively claim that those were what I was talking about when I described NP problems last time. Still, many thanks to the facebook commenter who pointed this out.)
Now, before I go any further, I should probably try to clarify what I mean when I talk about P-intelligence being “ahead” of NP-intelligence, because I managed to confuse myself several times while writing these posts – and if even the author is confused about what they’re writing, what chance does the reader have? So here’s my view of things: P-intelligence is actually the “dumber” of the two intelligences. It’s limited to simple, algorithmic tasks – things like checking solutions, yes, but also things like applying a formula you learned in calculus, or running through some procedure at work that you know off by heart. Plug’n’chug, in other words, for my physicist friends. So in retrospect I probably shouldn’t have portrayed P-intelligence as merely a “verifier” – P-intelligence essentially handles anything in the brain that’s been “taskified”, or reduced to a relatively simple algorithm, and one example of this is solution verification. NP-intelligence, on the other hand, is the smartest part of yourself, and handles the creative side of things. The strokes of genius and flashes of insight you sometimes get on oh-so-rare occasions? That’s NP-intelligence. In a sense, NP-intelligence is whatever you can’t taskify in the brain.
All of which is well and good. But if NP-intelligence is so smart, why then do I talk about P-intelligence being “ahead” of it? That’s what was causing the confusion for me – half the time I seemed to be thinking of P-intelligence as smarter than NP-intelligence, and half the time it was the other way around (which is never a good sign when you’re trying to flesh out a new concept in your mind). Eventually I managed to clarify things though, at least to my own satisfaction. Here’s what I would say on the matter: NP-intelligence is definitely smarter than P-intelligence, in that it can solve much more difficult problems. However, usually we’re not interested in a direct comparison of the two intelligences and their ability to solve problems. Usually what we’re comparing is the ability of NP-intelligence to generate a solution to a given problem, and the ability of P-intelligence to recognize a solution to that same problem. And for a given problem, solution recognition is of course much easier than solution generation. That’s why we can talk about P-intelligence being ahead of NP-intelligence – it faces a much easier task than NP-intelligence for any set level of problem difficulty, and so it can handle more difficult problems despite being “dumber”.
Now, hopefully that brings you up to at least the level of clarity I have in my own head (which, realistically, is probably not all that high). Moving forward, though, I’d like to de-emphasize the definition of P-intelligence as a solution-checker – it was useful in the last post, but I’ll be going in a somewhat different direction from here on out. Better now to think of P-intelligence as the part of your brain that handles simple, algorithmic tasks (one of which is solution checking) – in fact, if you like you can think of P-intelligence as standing for “Procedural Intelligence”, and NP-intelligence as standing for “Non-Procedural Intelligence”. That captures the idea pretty well.
Okay, so recaps and retcons aside, I’m pretty sure I was trying to write a blog post or something. As I was saying at the outset, this whole idea of P- and NP-intelligence seeded many new thoughts for me, some more profound than others. And first among them, in the “not-very-profound-but-still-edifying” category, was a clarified notion of creativity in art and science.
We’ve all heard the phrase, “It’s more of an art than a science”. It’s usually used to distinguish “intuitive” fields like literature and the arts from “logical” fields like math and science. The idea seems to be that creating a great work of art requires an ineffable, creative “spark” that is unique to humans and is (even in principle) beyond our understanding, whereas doing science requires merely the logical, “mechanical” operation of thought. There are countless fictional tropes that further the idea: the “rational” Spock being outwitted by the “emotional” Kirk, the “logical” robot losing some game to a “creative” human who can think outside the box, and so on and so forth.
Anyway, needless to say I’ve never liked the phrase, but until now it’s always been a vague sort of dislike that I lacked the vocabulary to really expand upon. Now, with P- and NP-intelligence added to my concept-set, I can finally explain myself, and it turns out that I have not just one but two problems with the phrase as it stands.
First: “ineffable” doesn’t mean “magic”. When people say that some skill is an art rather than a science, they usually mean two things: one, it’s a creative skill (you can use it to generate new, original works), and two, it’s immune to introspection (you can’t just write down exactly how the skill works and thereby pass it on to someone else, because you yourself don’t know how it works). It’s this immunity to introspection that gets right down to the heart of the matter, I think: a skill is an art if you can’t verbalize, explicitly, how it works. And in that sense, saying that some skill is an art essentially amounts to saying that it requires NP-intelligence. In fact, the grouping of skills as “arts” and “sciences” actually corresponds very neatly to NP- and P-intelligence as I conceive of them. People frequently say “We’ve got it down to a science”, and what they mean is that they’ve figured out the skill to such an extent that they can say explicitly how it works – in effect, they’ve developed a procedure for implementing the skill, and so it falls under the purview of P-intelligence.
Here’s the problem, though. Yes, a skill that requires NP-intelligence (an “art”) will always be ineffable – that is, will always seem like a black box to the person who possesses the skill. If that weren’t the case – if the skill didn’t seem opaque to the person in question – then they would understand it at a conscious level and could presumably explicate exactly how it works, and then it would be an example of P-intelligence rather than NP-intelligence. So it seems as though creativity is doomed to always carry an element of mysteriousness with it, essentially by definition. But just because something seems mysterious doesn’t mean it is mysterious, and something being beyond your understanding is not the same thing as it being magic. Creativity, whatever it is, is implemented in the brain; it does not rely on some dualistic supernatural “spark” that transcends the physical. Just like everything else in the mind, creativity is an algorithm – it may be an algorithm that we lack introspective access to, but it’s an algorithm nonetheless. So there is zero reason to suspect that we couldn’t program a robot to be creative to the same extent that humans are creative. The leap from “I don’t understand how something works” to “It’s impossible to understand how this thing works” is a huge one, and it’s one that people are far too quick to make.
So that’s my first problem with the phrase “It’s more of an art than a science” – it elevates art (and by extension, creativity) to a category that’s fundamentally distinct from the “ordinary” workings of the brain, and I reject that distinction. Although now that I think about it, what I just described isn’t really a problem with the phrase per se – the phrase is actually pretty innocuous in that regard. It’s more of a problem with the set of connotations that have agglomerated around the word “creativity” in our culture, of which the phrase is kind of just a symptom.
Anyway, my second problem with the phrase actually pertains more to the phrase itself, so let’s move on to that one.
My second problem with the phrase is this: in choosing a skill to represent procedural, non-creative knowledge in contrast to art, you chose science? Seriously, of all things, SCIENCE? REALLY?
Doing science is the most creative, least procedural skill I can think of. Seriously, I’d be hard-pressed to come up with a way of getting it more backwards than describing science as non-creative. Scientists operate at the boundaries of humanity’s knowledge. They spend their days and nights trying to come up with thoughts that no one else has ever had before. They are most definitely not operating based on some set procedure – if they were, science would have been solved centuries ago. So if you want to say that they are not doing creative work, then I literally have no idea what the word creative means.
I suspect what’s going on here is that people have a warped, superficial view of what creativity is. They’ve internalized the idea that creativity belongs only to the domain of things that are “emotional” or “artistic” or “colourful”, whereas doing science only involves the manipulation of mere numbers and the use of cold, unfeeling “logic” – there’s no splattering of paint involved, so how can it be creative?
I hope that by now I’ve written enough that you can see why this idea is nonsense. If not, though, I’ll spell it out: creativity doesn’t care what your subject matter is. It doesn’t care if you’re working with reds and blues or with ones and zeros. It doesn’t care if you’re wearing a painter’s frock or a chemist’s lab coat. It doesn’t care if your tools are a pen and inkwell or an atomic force microscope. All that creativity cares about is originality: the generation of new ideas or thoughts or ways of doing something. Creativity is what happens when we employ the full extent of our intellect in solving a problem that is at the very limits of our ability to solve. Creativity is about NP-intelligence and non-proceduralizability and immunity to introspection; it’s not about some otherworldly spark of magical pixie dust. No, the demystified view of creativity is one that unifies the Sistine Chapel and Quantum Electrodynamics under one great heading of genius – the thing that separates humanity from everything else in the universe, the thing that makes homo sapiens unique.
Now, I suppose you could try to rescue the phrase. When people say “It’s more of an art than a science”, or perhaps more to the point, “We’ve got it down to a science”, what they really mean by “science” is “settled science”. They’re not talking about the actual process of doing science; they’re talking about things that scientists have already figured out, and that everyone else is trying to learn. There’s a big difference between learning something and discovering something, after all. And in that sense, what most people learn in high school science class is pretty algorithmic – certainly they’re not learning how to discover something new. Usually they’re just learning how to apply things that someone else has already discovered.
Still, though. Still I don’t like the phrase. I don’t like the idea of people associating science with a body of knowledge rather than a process of discovery. I don’t like the idea of people viewing science as a non-creative when it’s possibly the most creative thing that humanity does. And most of all I don’t like the idea of logic being the opposite of creativity.
No, I’d rather just say that science is science, and art is art, and that they’re both creative – and that they’re both genius, and that when you get right down to it, they’re both pretty special.
[Up next: more on P- and NP-intelligence, and how they pertain to AI-risk]