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[ by Charles Cameron — further thoughts on the advantages of seeing double ]
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I’ve said before that when I was at The Arlington Institute, my boss used to ask me to watch out for “early indicators”, and joked that in my book, two is the first number — I don’t see an “indicator” until I see a pattern emerging.

Dutch artists celebrate George Orwell's birthday by putting party hats on surveillance cams http://t.co/qOM7i8FL4u pic.twitter.com/0YjATl3sH5

— Aruna Sekhar (@aruna_sekhar) August 18, 2015

Putting it bluntly, one point is pointless — things could go anywhere from there. Two points suggest a line, a link, a connection — a possible, maybe even plausible, trend.

And so it is with the two photos above. Here the point is not to compare and contrast the two images of surveillance cameras wearing party hats, but to see that they represent a class — the presence of two concrete instances strongly implies the higher level abstraction: hah! they’re watching us!

It’s that sense I have of two being the beginning of thought that makes me so fond of the DoubleQuotes format — and of Arthur Koestler‘s insight, which I’m always quoting, about creation occurring at the intersection of two spheres..

If I’m a fundamentalist about anything, it’s the notion that it takes two to tango!

[ by Charles Cameron — cross-posted from Sembl ]
Following up on two previous posts on graph-based design: Preliminaries and Two dazzlers

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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:

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.

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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.

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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.

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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:

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.

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

Food for thought is food for play.

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Sources:

Check out the stunning physics — deeper than time and space? — if you don’t already know it, and explain it if you do!

And for Wolfram on the Petersen Graph:

[ by Charles Cameron — a grumpy grammatical plaint, plus Proclus for poet’s delight ]
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You know me, maybe — I’m not a quant, if anything I’m a qualit, but even so..

CEOs at the top 50 U.S. charities, including Samaritan’s Purse, earn in the $350,000 to $450,000 range, which makes Graham’s $622,000 salary from his aid organization alone about 40 percent to 50 percent higher than average, according to a Forbes story. He receives the rest of his $258,000 compensation as CEO of the Billy Graham Evangelistic Association.

That’s straight out of the Washington Post, who got it whole cloth from Religion News Service.

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OK, we know what the writer means to say, but.

If top US charity CEOs including Franklin Graham earn between $350,000 to $450,000, and Graham earns $622,000 as his CEO’s salary, then — bzztzz — top US chatioty CEOs earn in the $350,000 to $622,000 range, , not “in the $350,000 to $450,000 range” period.

Further, if Graham earns $622,000 from Samaritan’s Purse — which purse it seems I shall not be filling any time soon, and which might want to change its name to Sadducee’s Purse — the “rest of his $258,000 compensation” doesn’t make any sense at all — bzztzz. How can $622,000 plus an additional fee possibly sum to $258,000?

There is a language, English, and a numerical method, Arithmetic, and this paragraph is lacking in one, the other, or both.

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Or is Franklin Graham paid in irrational numbers?

Proclus, as quoted by Danziger:

It is told that those who first brought out the irrationals from concealment into the open perished in shipwreck, to a man. For the unutterable and the formless must needs be concealed. And those who uncovered and touched this image of life were instantly destroyed and shall remain forever exposed to the play of the eternal waves.

Play of the eternal waves?

Perhaps Graham’s expefrience is not unlike that of George Boole, who wrote a sonnet on the Trinity, and of whom Margaret Masterman wrote:

Towards mathematical truth he had indeed a consciously religious attitude, which he sometimes expressed to himself by the phrase, ‘For ever, O Lord, Thy word is settled in heaven.’ Boole’s behaviour during his last illness was characteristic of the man… When his mind had been wandering in fever, he told his wife that the whole universe seemed to be spread before him like a great black ocean, where there was nothing to see and nothing to hear, except that at intervals a silver trumpet seemed to sound across the waters, ‘For ever, O Lord, Thy word is settled in heaven.’ And as he lay in bed on the borders of delirium, all the little sounds of the house, such as the creaking of doors, resolved themselves into a chant of these words, which expressed for him the excellence of mathematical truth.

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Ah, but I drift.

[ by Charles Cameron — following on from the AI dog / ostrich, this ]
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No sooner had I posted my piece on the similarities and diffrerences between two humanly similar images — one of them identified as a dog by a neural net, the other as an ostrich — that I came across my friend Bill Benzon‘s piece, also posted today, Visual Resonance, in which he plays with Photoshop filters and a couple of his own images.

Synchronicity? Zeitgeist? GMTA?

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Here is one of Bill’s photos, which he claims “no sensible photographer would shoot”..

As Bill says:

The setting sun is low in the sky and reflecting strongly off a glass encased building, so strongly that the camera really can’t deal with it. Also, I’m shooting through the branches of a small tree or bush nearby and they show up as a mis-shaped dark area in the left half of the shot. I like to take such shots to see what I can pull out of them.

Here’s a second version, this one tweaked with a filter..

Frosted?

I think there’s a fairly peasily perceptible family resemblance there, no?

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But then we come to this one..

in which a different filter has been applied to the same image..

To my eye. this is very different from the original — almost pure jazz in fact, and yes, Billplays jazz trumpet — though the palette “seems the same”..

And then there’s this..

.. which seems to me discernibly similar to both the previous and the original images, and in fact consists, if I’m reading Bill right, of an overlay of the two of them.

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All this leads me to tentatively revise my formulation that “likeness and unlikeness appear to me to find themselves on a spectrum which approximates closely to identity at one end .. and absolute distinction at the other“, renaming my spectrum “same-same, same-diff, diff-same, diff-diff“.

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Sameness and Difference, One and Two, Three in One and One in Three — as the writer I referenced anonymously towards the end of my previous post said:

Even angels and the spirits of men were matter by Greek thinking. In a sense, there are only two substances in the universe. One is God — whatever the substance is that constitutes God — and the other is matter. Athenagoras, a Christian apologist writing in A.D. 168, tells us:

We employ language that makes a distinction between God and matter and the natures of both.

The question being asked at the Council of Nicea was …

Is Christ of the substance of God, or

is he made of matter like us and the angels?

Sameness and Difference, One and Two — we’re back in the heart of the Presocratics, of Pythagorean mathematics, of the Tao — the One and the Many.

One Another.

[ by Charles Cameron — a graphical analog to the inside outside koan ]
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Thinking one’s way inside that demmed box…

What’s even “inside”?

Eppur si muove! Or not?

I suppose this can be today’s Sunday Surprise.

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Source:

Wikipedia, Tesseract