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Patrick Stevens

Former mathematics student at the University of Cambridge; now a software engineer.

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I have recently discovered the game of Agricola, a board game involving using resources (family members, stone, etc) to build a thriving farm. The game is turn-based, with the possible actions each turn being severely limited. This makes the game be in large part about optimising under constraint (the foundation of any good game). However, during gameplay I also detected a certain resonance between Agricola and the game of Magic: The Gathering, beyond the usual “constrained optimisation” theme. While I was playing Agricola, there was a kind of niggle in the back of my mind, telling me that “ooh, this is like Magic”. I notice a similar affinity when reading essentially anything by Douglas R Hofstadter, an author famed for his “metaness”. That is, when reading a good Hofstadter piece, I get a similar niggle (considerably weaker than the Magic-Agricola one) telling me that “ooh, this is a bit like Magic”. Hofstadter invents puns and connections which feel so natural that you’d be forgiven for thinking that he had invented English specially for the purpose, were it not for the fact that his book Gödel, Escher, Bach was translated (I am told) with the same level of scintillation into at least eight other languages 1. This leads me to wonder whether what I’m really noticing is not just constrained optimisation, but “metathought” - thought on a higher level of abstraction to the usual. With Hofstadter, it’s on the level of words as well as of the symbols of thought that the words invoke; with Magic, it’s thinking about plans and strategies involving the other player(s) and the interactions between their cards and mine; with Agricola it’s thinking about the aims of the other player(s) and how best to compete for the limited actions available to us both. I note that I don’t feel the resonance with chess - archetypical of “deterministic games”, where you know exactly what moves are available to both sides - so the resonance is not a marker for “putting myself in others’ shoes”. Rather, it seems to be a marker of interaction - between players’ plans, or between words and meaning, and so on.

Closely linked to this is the related concept of introspection. It’s a well-researched fact2 that people are (in general) bad at introspection (hence the existence of behaviourism and heterophenomenology). I’ve trained myself over the last year or so to be much better at introspection than I was 3 - I notice myself shying away from thinking things, I recognise when there’s a specific thing I can’t be bothered to think about, and so forth. Of course, I am (as yet) imperfect, but I am trying not to be.

How is this, as I have claimed, “closely linked”? I am slowly forming the opinion that it takes a reasonably good level of introspective ability just to be able to notice resonances between things. 4 I am waiting for experimental evidence on this (and it is possible that my subjects are reading this blog, so I won’t say what the tests are). However, I’ve noticed these resonances myself to a greater degree since learning introspection. 5 The feeling of “affinity” between things is very difficult for me to describe - it’s kind of a shade of extra interpretation laid on a concept, but it’s not linked to any of the commonly-recognised senses, so English isn’t very well set up to define it - but the feeling is very weak. I sometimes think of it as making an extra brushstroke on a watercolour - the added colour is there, but it’s very slight - perhaps slight enough as to go unnoticed by someone who is not in the habit of noticing eir thoughts. It also feels like an area of light (in both senses - “not dark” and “not heavy”) at the (literal) back of my mind. (Ah, how difficult to describe qualia accurately!) However it feels to me, it is my experience that people very rarely claim that one activity is similar to another in some abstract way (as I do with Magic and Gödel, Escher, Bach) - this may be because I don’t notice it when they so claim, or that they never so claim because no-one else ever so claims, or that they never so claim because they don’t notice the resonance, or that the resonance isn’t actually there and I’m delusional (although in this instance that seems a bit unlikely, if I say so myself).

Why do I think that what I’m noticing is “metathought” rather than merely “constrained optimisation”? Well, I very rarely feel the resonance, and I’m always solving constrained optimisation problems without feeling the resonance (how succinct can I make this post, how many chocolates can I get away with eating…) so I suspect that it’s not just the optimisation aspect. The only other link I have come up with at the moment is metathought. Magic, in particular, has the potential for very complicated interactions involving thinking hard about which strategies will be successful and when exactly to do things; Hofstadter’s punning is ridiculously meta anyway; while Agricola is heavily based on working out what the opponents will be doing and taking that into account (that is, it requires reflection, a key component of metathought), while juggling your own strategies. I note for completeness that I read Gödel, Escher, Bach well before I discovered the game of Magic, and I didn’t feel the resonance with GEB on first playing Magic - it was only once I’d played Magic that I started feeling the resonance. Alternatively put, I feel the “resonance with Magic”, rather than “resonance with things in the class to which Magic belongs”.

I get slight shades of the same resonance when solving crosswords, and maybe even sometimes when proving mathematical statements - but take this with a pinch of salt, because I’ve had time to create a pattern for “I feel this resonance when…”, and it’s much easier to fill that pattern than to actually work out whether I do feel that resonance. I explicitly noticed it and noted it to myself when playing Agricola and when reading the Ricercar from Gödel, Escher, Bach - any other examples are potentially suspect, now that I’ve thought the concept through, because the feeling of resonance is so weak compared to the thought “If my hypothesis is correct, I should feel resonance now”. (I came to this realisation while writing this paragraph.) It would appear that I may have accidentally corrupted my ability to feel this “resonance” in weak cases. Unfortunately, this makes it very hard to provide further tests: in particular, I need cases when I would predict feeling resonance but in fact do not.

Anyway, I hypothesised that “resonance” is only felt by people who naturally or artificially have good introspection. I would be very interested to hear of evidence on this point - if you feel (with some kind of justification) that you have unusually good introspection, or if you think you have felt the kind of resonance that I describe (of course, my description was poor!), do let me know - I don’t know which way causality runs, if any, and I would like to know whether it’s just some oddity of my own, or whether It’s A Thing that no-one bothers to mention for some reason.

  1. French, German, Spanish, Chinese, Swedish, Dutch, Italian and Russian, according to the bottom of this page [cached].

  2. The fact that the first stage of incompetence even exists, that of “not knowing that you are incompetent”, is a pointer here.

  3. Or at least, I hope I have - it certainly feels like it’s working, but then again, it would probably feel like that if I were getting worse at introspection, because I’d be getting worse at telling whether I was getting better or not.

  4. The resonance which is the main subject of this post is a single instance of a more general class of relations - for instance, there is a different kind of resonance between Scrabble and Countdown.

  5. A possible explanation is that I’ve just been doing more interrelated things recently, so I would be very likely to spot more interrelations.