[Epistemic status: no citations and mostly pulled straight out of my arse, but I think there’s something real here]
While I was away it looks like there was some kind of Two Cultures spat on rationalist-adjacent tumblr.
I find most STEM-vs-the-humanities fight club stuff sort of depressing, because the arguments from the humanities side seem to me to be too weak. (This doesn’t necessarily apply this time – I haven’t tried to catch up on everyone’s posts.) Either people argue that the humanities teach exactly the same skills in systematic thinking that the sciences do, or else you get the really dire ‘the arts teach you to be a real human being‘ arguments.
I think there’s another distinction that often gets lost. There are two types of understanding I’d like to distinguish, that I’m going to call explicit and tacit understanding in this post. I don’t know if those are the best words, so let me know if you think I should be calling them something different. Both are rigorous and reliable paths to new knowledge, and both are important in both the arts and sciences. I would argue, however, that explicit understanding is generally more important in science, and tacit understanding is more important in the arts.
(I’m interested in this because my own weirdo learning style could be described as something like ‘doing maths and physics, but navigating by tacit understanding’. I’ve been saying for years that ‘I’m trying to do maths like an arts student’, and I’m just starting to understand what I mean by that. Also I feel like it’s been a bad, well, century for tacit understanding, and I want to defend it where I can.)
Anyway, let’s explain what I mean by this. Explicit understanding is the kind you come to by following formal logical rules. Scott Alexander gives an example of ‘people who do computer analyses of Shakespeare texts to see if they contain the word “the” more often than other Shakespeare texts with enough statistical significance to conclude that maybe they were written by different people’. This is explicit understanding as applied to the humanities. It produces interesting results there, just as it does in science. Also, if this was all people did in the humanities they would be horribly impoverished, whereas science might (debatably) just about survive.
Tacit understanding is more like the kind you ‘develop a nose for’, or learn to ‘just see’. That’s vague, so here are some examples:
- Taking a piece of anonymised writing and trying to guess the date and author. This is a really rigorous and difficult thing my dad had to do in university (before pomo trashed the curriculum, [insert rant here]). It requires very wide-ranging historical reading, obviously, but also on-the-fly sensitivity to delicate tonal differences. You’re not combing through the passage saying ‘this specific sentence construction indicates that this passage is definitely from the late seventeenth century’. There might be some formal rules like this that you can extract, but it will take ages, and while you’re doing the thing you’re more relying on gestalt feelings of ‘this just looks like Dryden’. You don’t especially need to formalise it, because you can get it right anyway.
Parody. This is basically the same thing, except this time it’s you generating the writing to fit the author. Scott is excellent at this himself! Freddie DeBoer uses this technique to teach prose style, which sounds like a great way to develop a better ear for it.
Translation. I can’t say too much about this one, because I’ve never learned a foreign language :(. But you have the problem of matching the meaning of the source, except that every word has complex harmonic overtones of different meanings and associations, and you have to try and do justice to those as well as best as you can. Again, it’s a very skilled task that you can absolutely do a better or worse job at, but not a task that’s achieved purely through rule following.
I wish these kinds of tacit skills were appreciated more. If the only sort of understanding you value is explicit understanding, then the arts are going to look bad by comparison. This is not the fault of the arts!
Speaking as a logician, the whole idea that logic is dry and formal is as far from the truth as is possible. Some mathematicians pride themselves on being formalists but what they fail to say explicitly is that they are formalists in a very restricted sense; they only operate by classical logic (A lot of them can’t even construct the foundations of their subject formally [and by formal I mean fully formal, as in some sort of formal deductive system], even though they boast about it so much). And here’s another zinger: the foundation of mathematics relies on purely intuitive ideas which can’t be (at least not that I’m aware of anyway) defined in a non-circular way. Examples: Sets, set membership, strings, induction (a lot of mathematicians try to prove induction by using set theory and use the well-ordering principle to do it. This is a contrived load of bollocks; the well-ordering principle implies induction and induction implies the well-ordering principle so they are logicially equivalent. Using one to prove the other and then somehow saying they are not intuitive, foundational ideas is a load of bullshit), etc.. Mathematicians like those don’t understand logic in the philosophical sense, they are happy to be automatons and train hoards of students to be the same. It was pretty common practice even with the greats like Hilbert. Thank goodness for Godel and Turing! I’m one of the few people happy about the incompleteness and undecidability results, life is much more interesting because of them.
Any honest logician would tell people there are many logics out there, and so many things with some sort of structure which have logical rules, but are still informal at the same time (any natural language). Calling logic dry and formal means misunderstanding the whole enterprise or a sign of rejection of a vast section of it.
When one goes into a deep, serious study of logic it is obvious philosophy plays a very important role. Which rules of logic are ‘meaningful’ and ‘reasonable’? A lot of this comes down to choice (one only need look at intuitionistic and paraconsistent logics for examples). Mathematics is based on formal rules and intuition. Both are important. Intuition is greatly important when it comes to try and define things so we can do mathematics on those defined objects. Computers can be programmed to deduce things easily, but trying to get one to come up with ‘meaningful’, ‘useful’, and ‘good’ definitions is a much more difficult task (we don’t even know if it’s possible or not at the moment).
Epistemology is something which needs to be taught to both science and arts students. And art and science are just two parts of a wonderfully interconnected whole. Anyone trying to make a split is an ignoramus.
Apologise for the ranting and rambling but this is something that I learnt the hard way from a lot of spadework on my own and asking about. More students should be made aware of these issues, and earlier; it shouldn’t be shooed of as ‘PhD level topics’.
Sorry I’ve been slow replying to this. Agree with what you’re saying about formal rules and intuition here. And I definitely don’t mind some ranting! Not sure quite where the ranting is aimed at in this case – are you arguing against something specific in my post? Or is it more one of those spontaneous rants that just appears? (I have many of those…)
I think making a *sharp, defined* split between the sciences and arts is stupid, but I would still argue that the tacit/explicit distinction captures something useful, with explicit formal rules playing a bigger role in the sciences. Do you agree, or do you see it as basically the same mix of formal/intuitive everywhere?
We can all get pretty busy. My apologies for seeing your reply so late (I’ve been busy as well).
I think science, in general, has to be a mix of formal and intuitive. Mathematics itself benefits so much from physics. It is so much more satisfying looking at mathematics in relation to other applications. I myself love logic a lot, but I am against the Bourbakist way of turning mathematics into a logical game, instead of being inspired by problems from the sciences.
I think the problem we have today is the education system isn’t structured right. Students aren’t taught basic logic so they don’t really understand the more formal parts of mathematics (and computer science too). When it comes to teaching physics, the core principles aren’t explained (principle of least action, conservation laws, etc.); students are just thrown formulas to memorise. Most important of all, I think the connections between the domains of science aren’t emphasised.
I think what we’re seeing now in schools is the result of overspecialisation. If you pick up a book by great writers Vladimir Arnold, Cornelius Lanczos, etc. you’ll notice they jump between maths, physics, computer science, engineering, biology even, almost effortlessly. I think the reason they did so well, and could operate so broadly, is because they were given an education where principles were emphasised much more than techniques.