In November and December I’m going to shut up talking nonsense here, and also have a break from reading blogs, Twitter, and most of my usual other internet stuff. I like blogs and the internet, but being immersed in the same things all the time means I end up having the same thoughts all the time, and sometimes it is good to have some different ones. I’ve seen a big improvement this year from not being on tumblr, which mostly immerses you in other people’s thoughts, but stewing in the same vat of my own ones gets a bit old too. Also I have a bunch of stuff that I’ve been procrastinating on, so I should probably go do that.

I’ve pretty much accepted that I am in fact writing a real blog, and not some throwaway thing that I might just chuck tomorrow. That was psychologically useful in getting me started, but now writing just seems to appear whether I want it to or not. So I might do some reworking next year to make it look a bit more like a real blog and less like a bucket of random dross.

The topic of the blog has spread outwards a bit recently (so far as there is a topic — I haven’t made any deliberate effort to enforce one), but there does seem to be a clear thread connecting my mathematical intuition posts with my more recent ramblings.

One of the key things I seem to be interested in exploring in both is the process of being able to ‘see’ more, in being able to read new meaning into your surroundings. I’ve looked at examples in a couple of previous posts. One is the ‘prime factors’ proof of the irrationality of the square root of two, where you learn to directly ‘see’ the equation as wrong (both and have an even number of each prime factor, so dividing one by the other is never going to give a 2 on its own).

Another is the process of noticing interesting optical phenomena after reading Light and Colour in the Outdoors. I see a lot of sun dogs, rainbows and 22° halos that I’d have missed before. (No circumzenithal arcs yet though! Maybe I’m not looking up enough.)

They are sort of different: the first one feels more directly perceptual — I actually see the equation differently — while the second feels like more of a disposition to scan my surroundings for certain things that I’d previously have missed. I’m currently doing too much lumping, and will want to distinguish cases more carefully later. But there seems to be some link there.

I’m interested in the theoretical side of how this process of seeing more might work, but currently I’d mostly just like to track down natural histories of what this feels like to people from the inside. This sort of thing could be distributed all over the place — fiction? the deliberate practice literature? autobiographies of people with unusual levels of expertise? — so it’s not easy to search for; if you have any leads please pass them on.

I hadn’t really thought to explicitly link this to philosophy of science, even though I’d actually read some of the relevant things, but now David Chapman is pointing it out in his eggplant book it’s pretty obvious that that’s somewhere I should look. There is a strong link with Kuhn’s scientific revolutions, in which scientists learn to see their subject within a new paradigm, and I should investigate more. I used to hang around with some of the philosophy of science students as an undergrad and liked the subject, so that could be fun anyway.

We ended up discussing a specific case study on Twitter (Storify link to the whole conversation here): ‘The Work of a Discovering Science Construed with Materials from the Optically Discovered Pulsar’, by Harold Garfinkel, Michael Lynch and Eric Livingston. This is an account based on transcripts from the first observations of the Crab Pulsar in the optical part of the spectrum. There’s a transition over the course of the night from talking about the newly discovered pulse in instrumental terms, as a reading on the screen…

In the previous excerpts projects make of the optically discovered pulsar a radically contingent practical object. The parties formulate matters of ‘belief’ and ‘announcement’ to be premature at this point.

…to ‘locking on’ to the pulsar as a defined object:

By contrast, the parties in the excerpts below discuss the optically discovered pulsar as something-in-hand, available for further elaboration and analysis, and essentially finished. … Instead of being an ‘object-not-yet’, it is now referenced as a perspectival object with yet to be ‘found’ and measured properties of luminosity, pulse amplitude, exact frequency, and exact location.

This is high-concept, big-question seeing further!

I’m currently more interested in the low-concept, small-question stuff, though, like my two examples above. Or maybe I want to consider even duller and more mundane situations than those — I’ve done a lot of really low-level temporary administrative jobs, data entry and sorting the post and the like, and they always give me some ability to see further in some domain, even if ‘seeing further’ tends to consist of being able to rapidly identify the right reference code on a cover letter, or something else equally not thrilling. The point is that a cover letter looks very different once you’ve learned do the thing, because the reference code ‘jumps out’ at you. There’s some sort of family resemblance to a big fancy Kuhnian paradigm shift.

The small questions are lacking somewhat in grandeur and impressiveness, but make it up in sheer number. Breakthroughs like the pulsar observation don’t come along very often, and full-scale scientific revolutions are even rarer, but millions of people see further in their boring office jobs every day. There’s much more opportunity to study how it works!

Written quickly and probably not very clear – it’s a workbook post not a polished-final-thoughts post. Vaguely inspired by this exchange between Julia Galef and Michael Nielsen.

One of my favourite things is the point in learning a new topic where it starts to get internalised, and you begin to be able to see more. You can read into a situation where previously you had no idea what was going on.

Sometimes the ‘seeing’ is metaphorical, but sometimes it’s literal. I go walking quite a lot, and this year I’m seeing more than before, thanks to an improved ability to read into the landscape.

I got this from Light and Colour in the Outdoors, a classic 30s book on atmospheric phenomena by the physicist Marcel Minnaert. It’s really good, and I’m now regretting being cheap and getting the Dover version instead of the fancy coffee-table book (note to self: never buy a black-and-white edition of a book with the word ‘colour’ in the title).

I’ve only read a few sections, but already I notice more. Last weekend I got the coach to London, and on the way out I saw a sun dog I’d probably have missed before. And then on the way back it was raining with the sun shining onto the coach windscreen in front, and I thought to myself, ‘I should probably look behind me’. I turned, and right on cue:

This is entry-level reading into the landscape, but still quite satisfying. Those with exceptional abilities seem to have superpowers. George Monbiot in Feral talks about his friend Ritchie Tassell:

… he has an engagement with the natural world so intense that at times it seems almost supernatural. Walking through a wood he will suddenly stop and whisper ‘sparrowhawk’. You look for the bird in vain. He tells you to wait. A couple of minutes later a sparrowhawk flies across the path. He had not seen the bird, nor had he heard it; but he had heard what the other birds were saying: they have different alarm calls for different kinds of threat.

This is the kind of learning that fascinates me! You can do it with maths as well as with sparrowhawks…

This has been on my mind recently as I read/reread Venkatesh Rao’s posts on ambiguity and uncertainty. I really need to do a lot more thinking on this, so this post might look stupid to me rather rapidly, but it’s already helping clarify my thoughts. Rao explains his use of the two terms here:

I like to use the term ambiguity for unclear ontology and uncertainty for unclear epistemology…

The ambiguity versus uncertainty distinction helps you define a simpler, though more restricted, test for whether something is a matter of ontology or epistemology. When you are missing information, that’s uncertainty, and an epistemological matter. When you are lacking an interpretation, that’s ambiguity, and an ontological matter.

Ambiguity is the one that maps to the reading-into-the-landscape sort of learning I’m most fascinated by, and reducing it is an act of fog-clearing:

20/ In decision-making we often use the metaphors of chess (perfect information) and poker (imperfect information) to compare decision-makers.

21/ The fog of intention breaks that metaphor because the game board /rules are inside people’s heads. Even if you see exactly what they see, you won’t see the game they see.

22/ Another way of thinking about this is that they’re making meaning out of what they see differently from you. The world is more legible to them; they can read/write more into it.

I think this is my main way of thinking about learning, and probably accounts for a fair amount of my confusion when interacting with the rationalist community. I’m obsessed with ambiguity-clearing, while the rationalists are strongly uncertainty-oriented.

For example, here’s Julia Galef on evaluating ‘crazy ideas’:

In my experience, rationalists are far more likely to look at that crazy idea and say: “Well, my inside view says that’s dumb. But my outside view says that brilliant ideas often look dumb at first, so the fact that it seems dumb isn’t great evidence about whether it will pan out. And when I think about the EV here [expected value] it seems clearly worth the cost of someone trying it, even if the probability of success is low.”

I’ve never thought like that in my life! I’d be hopeless at the rationalist strategy of finding a difficult, ambitious problem to work on and planning out high-risk steps for how to get there, but luckily there are other ways of navigating. I mostly follow my internal sense of what confusions I have that I might be able to attack, and try to clear a bit of ambiguity-fog at a time.

That sounds annoyingly vague and abstract. I plan to do a concrete maths-example post some time soon. In the meantime, have a picture of a sun dog: