Mornington Crescent with Ian Stewart, Doug Hofstadter and Dan Dennett

Just had a weird reading-linked-articles (Tennis-Elbow-Foot / Cow-Lake-Bomb / Rock-Paper-Scissors) experience: Ian Stewart is a popular maths writer I’ve enjoyed, but probably barely referenced here other than as the author of “Does God Play Dice? – The Mathematics of Chaos“.

I was also aware that the “non-game” Finchley Central was a forerunner to ISIHAC‘s Mornington Crescent, ever since Doug Hofstadter’s Metamagical Themas reference to it. But, I hadn’t twigged Ian Stewart was the inventor of Finchley Central in his time as editor of Warwick maths magazine Manifold.

If you follow me here on Psybertron, you’ll know I’m a big fan of Hofstadter and his connections to my hero Dan Dennett – the evolution of things complex, conscious and intelligent from nothing. One of the key contributions to my own agenda is Hofstadter’s game Tabletop (whose name has it’s own weird word-association evolution) but whose content, I now realise, is fundamentally a variant of Mornington Crescent (or Finchley Central).

In a game of no rules (a non-game) where the “board” permits any move of any piece  you might imagine, the progress – to something interesting – is by “conceptual slipping”. The basis of MC/FC is anyone can win the game at any time they choose after the first move, all moves are permitted, but the point is to spin it out into something interesting for as long as you can and still pre-empt your opponent’s winning move.

In Tabletop, and one variant of MC/FC, a strategy is to have some meta-rule (eg by some metaphorical association, A is to B as B is to C etc ) that allows you to make a next move but which looks random to your opponent. In that variant, an alternative way to beat your opponent is to guess their meta-rule before they make their winning move, or use that same (guessed) information to make your own winning move before they do. [The meta-rule may be very simple or pseudo-random to start with – when you first conceive it – but repeated, recursive, algorithmic action over many cycles can make the individual moves indecipherably complex – meta-(n x meta)-rule-result – from outside your head. That same feature makes it impossible for any outsider to know if you’ve been breaking or changing your own rule. The rule may be that there is no rule, other than the mental connection – the conceptual slipping – inside your head.]

The final synchronicity is that I’m pretty sure it was our maths master “Ester” Pearson, he who first introduced me to the Registry Assembly Programming exercise published later by Dennett, who also introduced us to listening to ISIHAC on the “Home Service” radio during our lunch breaks in 1972.

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