On the felicities of graph-based game-board design: four

[ following parts 1, 2 and 3 with a fourth ]

Back in my student days, I used to have a three dimensional tic-tac-toe board, 4 x 4 x 4, made of plexiglas sheets with holes drilled in them, and using colored golf-tees for markers. I could play pretty well on that board, but these ones would drive me nuts — whether for tic-tac-toe or for HipBone / Sembl.

with a chaser:

And that’s what I call a DoubleTweet.

On the felicities of graph-based game-board design: three

Following up on two previous posts on graph-based design: Preliminaries and Two dazzlers


Here are two old HipBone boards that have the curious property of looking very different while being, in fact, topologically identical. Moves played on either board will feature the same set of links — although, given the visual impac ts of proximity and distance, they may “feel” very different to the players themselves:

Petersen graph boards

I call them the Pentagram and Mercedes boards, for what I trust are obvious reasons. They are both based on versions of the Petersen graph, and I’m grateful to Walter Logeman and Miles Thompson for introducing me to them.


One of the vivid differences between my childhood memories and present experience has to do woth the time when the table, the place where food or whatever was, was above my head.

Of course, the table was flat — but it was flat above my head, and I had to reach up into that unknown flatland to grab what I could. Unless of course there was a tablecloth trailing over the edge of the flat, down towards eye-level, in which case.. voila!

Hence my ongoing notion that something tasty might be literally above my head, and my associated excitement. Hence, too, my excitement at the prospect that tasty ideas might also be above my head, and that I might reach up into unknown intellectual flatlands — or pull them down to my own level with a tug of the intellectual tablecloth.


That may sound foolish, but it’s entirely in line with Eric Drexler’s advice — and Drexler published the first scientific paper on molecular nanotechnology [.pdf] in 1981.

Here’s what Drexler has to say about reading scientific journals:

Read and skim journals and textbooks that (at the moment) you only half understand. Include Science and Nature.

Don’t avoid a subject because it seems beyond you – instead, read other half-understandable journals and textbooks to absorb more vocabulary, perspective, and context, then circle back.


Okay, I’m in over my head as they say.

Here’s an artist’s rendering of something called, I guess, an amplituhedron, a (relatively) newly discovered mathematical object that has the world of physics all excited:


Here’s another, titled for some reason “droplet”.:


Neither of those is anything I could conceivably use to come up with a HipBone or Sembl board, is it?

But get this:


This is another way of looking at the same corner of mathematical physics — one of over a hundred diagrams in the same paper— and here are the two “lesser” diagrams that caught my attention and made me think back to the Petersen graph boards earlier on today:

twistor-diagrams- scientists discover a jewel

Now my itch is to figure out what use the “filled” and “open” nodes in these two graphs might serve in game-playing terms, and how on earth to interpret in game terms the complex weavings of the colored lines in the larger image / board.


And hey, while we’re at it, Here are the Wolfram variants on the Petersen graph — striking, aren’t they?

PetersenGraphEmbeddings wolfram

Food for thought is food for play.



Metamap of the relationships between analogy, assemblage, cognition and so on

Cousin Metamaps

Toiling away on a project like Sembl can be lonely, so I was chuffed this week to make an acquaintance with Metamaps – or more particularly, Ishan Shapiro, one of its founders – and to discover some shared heritage.

Sembl is a descendant of the Glass Bead Game, and its purpose – or one of them – is to foster collaborative sensemaking. In its first form the game aspect of Sembl dominates its role as a sensemaking tool. But part of the reason I adopted this mission to bring Sembl into being was that I’ve been disappointed by every single mindmapping tool I’ve ever tried – because I want to be able to handcraft my own connections between nodes. For me, generic linking is a major limitation of most mindmapping software because the juice of a story is in the quality – and the nuance – of the relationships between the nodes. So my plan for Sembl has always included a de-gamified version, for personal or collaborative non-linear storytelling.

I was pretty excited to discover Metamaps, because it’s almost exactly the mindmapping tool I’ve always wanted. Then – thrill! – I learned that Metamaps was also inspired by the Glass Bead Game. By my reckoning, that makes Sembl and Metamaps cousins :)

Of course, my first exploratory exercise in Metamaps was Sembl-related, mapping the relationship between analogy-making, assembling and cognition, and their effects. Here’s the result:

Metamap of the relationships between analogy, assemblage, cognition and so on

I’m sharing a static PNG here because I wanted to show it with all the relationships visible. But (assuming you have requested and received access to Metamaps) you can see – and adapt! – the live version on the Metamaps site.

PR Beckman tweets on bridges and analogy

[ this post is for Cath Styles, who has been thinking bridges ]

Pooh bridge


My blog-friend PR Beckman, on a roll, has been tweeting Octavio Paz and Martin Esslin.

I’ve taken Beckman’s tweets out of 140 characters and put them back into paragraphs, and given a little more context to some of them, but greatly though I admire Octavio Paz and much though I have puzzled over the Theater of the Absurd, I wouldn’t have run across these particular passages if I hadn’t found them in my Twitter feed today. Important.


Octavio Paz, Children of the Mire: Modern Poetry from Romanticism to the Avant-garde:

Analogy is the science of correspondences. It is, however, a science which exists only by virtue of differences. Precisely because this is not that, it is possible to extend a bridge between this and that. The bridge does not do away with distance: it is an intermediary; neither does it eliminate difrerences: it establishes a relation between different terms. Analogy is the metaphor in which otherness dreams of itself as unity, and difference projects itself illusively as identity. By means of analogy the confused landscape of plurality becomes ordered and intelligible. Analogy is the operation nby means of which, thanks to the play of similarities, we accept differences. Analogy does not elimiate differences: it redeems them, it makes their existence tolerable.

Martin Esslin, The Theatre of the Absurd, pp 419:

the Theatre of the Absurd is concerned essentially with the evocation of concrete poetic images designed to communicate to the audience the sense of perplexity that their authors feel when confronted with the human condition

and 428:

The realization that thinking in poetic images has its validity side by side with conceptual thought and the insistence on a clear recognition of the function and possibilities of each mode does not amount to a return to irrationalism; on the contrary, it opens the way to a truly rational attitude.


Let me add a quote of my own choosing, this one from Winnie the Pooh:

Sometimes, if you stand on the bottom rail of a bridge and lean over to watch the river slipping slowly away beneath you, you will suddenly know everything there is to be known.

Illustration: Original, 1928 Illustration Of Pooh, Christopher Robin and Piglet Could Fetch Over $200K