The whole world in a grain of salt.

Where to start ?

You maybe don’t need me to point out

that these are anagrams of each other?

Table-Top

Battle-Op

Ob-Platte

Potel-Bat

Bel-Patto

Plato-Bet

But what are they ? It might help if you knew that they are the title of Chapter 8 of Douglas Hofstadter’s book “Fluid Concepts and Creative Analogies” (*Computer models of the fundamentals of thought*.) The book is a collection of papers in collaboration with Daniel Defays, David Chalmers, Robert French, Melanie Mitchell and Gary McGraw with prologues by Douglas Hofstadter, all compiled in the mid-nineties.

If I was to sum up the book / collection I’d say that whilst it seems at first to be a study of thought processes – strategies to find answers to problems – it is really an analysis of “the concept of concept”, which proceeds through abstractions, analogy and “slipping”. At a simple level an analogy has some self-evident sameness to an original subject. But, how self-evident or more-subtly-creative that analogy is, turns out to be a matter of looking for that sameness at different levels of abstraction – lateral thinking, hunting for the “essence” – the Platonic form. But in typical Hofstadter style, the whole book is actually one long number, letter, word game. So much so that if you don’t share his enthusiasm for searching for patterns in near-cyclical sequences (of numbers, letters, words, etc … fonts even) the near-repetition is a long slog.

The whole book is a million

different ways of expressingA:B :: X:Y

(As is to B as X is to Y)“Get a life” you might think.

Chapter 8 is worth the slog.

At the simplest level A is to B, as B is to C, as C is to D, etc … is the definition of a series. Given a starting situation (the known history of the series so far) find the next term, given what you can infer about the “is to” relationship. The point is the “best” next may not be an obvious value, but involves a sense of “elegance” or “creativity”. The archetypal example for me (my paraphrase) …

What is the next number in the series 0, 1, 2, … ?

Obviously it’s 3, right ?

Well no. How about 720! (*1)

(You’re missing that the shared relation

between A and B, is [n(!n)]

ie the series is 0, 1!, 2!!, 3!!!, 4!!!!, etc …)Think about it.

If someone actually asked you the question “What is the next number in the series 0, 1, 2, … ?” surely the very first thing you would know for sure would be, well presumably, since you’re not a two-year old, the answer you’re looking for is not 3 or you wouldn’t have asked me, right ?

And in fact your first response would probably be that rhetorical question – to confirm the premise, to check you hadn’t misheard.

Chapter 8 takes this by analogy – given ** the history of the world** up to this point – what should I do next. Shall I have a donut for breakfast? or what decision / action should my government take next in the current situation? It’s about decision-making strategies. Occam (or Buridan’s Ass) might lead you to say the best answer is the obvious one (the 3, or either bale of hay will do), but the point is the obvious answer is not the only possibility, nor necessarily the best in the overall analysis.

Looking at the strategies for finding the more creative “better” answers what is most striking is that the problem domain may appear closed and bounded as in the Tabletop analogy – all explicit knowledge and choices are laid out in front of you on the table – the “best next thing” reasoning involves thinking which is abstracted above it and slipped more broadly sideways (outside the explicit problem domain).

[*Tabletop game described further here*.]

Choosing your grain of salt involves its relationships to the whole world of possibilities; evaluating / filtering the most significant relations is the tricky, creative bit.

When I say “do this” and touch my nose – you already knows (by analogy) that I mean touch your own nose. “This” is the same by analogy. The Tabletop process simply extends this to – if I touch this object from my perspective of the table in front of us which should you touch next from yours. In all but the most trivial tit-for-tat cases (*2) the choice involves analogies – patterns of related essence – well beyond what actually exists on the tabletop – the *apparent* theatre of operations.

Q. What is the Ob of Nebraska ? A. The Platte. Because the Ob is to Siberia (a large river flowing across its desolate wastes) as the Platte is to Nebraska. If that really was published in 1890 by Belpatto then the whole anagram sequence is truly spooky. Meta-fascinating.

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[*Post Note (*1) In fact, that fourth term or the next term after the 720, or ANY subsequent term can be almost anything you choose. Scientifically, there are an infinity of hypotheses to fit any given set of data so far, all that is required is creativity and ingenuity. There’s a whole debate to be had – a la Occam’s Razor – if we were talking about truth and beauty in science, which we’re not particularly, but the best or most elegant solution isn’t necessarily the simplest or most obvious. See Sabine Hossenfelder “Lost in Math”.*]

[*Post Note (*2) for a treatment of “tit-for-tat” and the infinite possibility of other strategies in a real world of incomplete trust, imperfect information and levels of ironic intent, see this later post on Basic Evolutionary Game Theory and the truly excellent Evolution of Trust Simulator created by Nicky Case based on Axelrod’s 1984 work.*]

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