Blue is the Killer

Eye Bogglers by Gianni A. Sarcone and Marie-Jo WaeberEye Bogglers: A Mesmerizing Mass of Amazing Illusions, Gianni A. Sarcone and Marie-Jo Waeber (Carlton Books 2011; paperback 2013)

A simple book with some complex illusions. It’s aimed at children but scientists have spent decades understanding how certain arrangements of colour and line fool the eye so powerfully. I particularly like the black-and-white tiger set below a patch of blue on page 60. Stare at the blue “for 15 seconds”, then look quickly at a tiny cross set between the tiger’s eyes and the killer turns colour.

So what’s not there appears to be there, just as, elsewhere, what’s there appears not to be. Straight lines seem curved; large figures seem small; the same colour seems light on the right, dark on the left. There are also some impossible figures, as made famous by M.C. Escher and now studied seriously by geometricians, but the only true art here is a “Face of Fruits” by Arcimboldo. The rest is artful, not art, but it’s interesting to think what Escher might have made of some of the ideas here. Mind is mechanism; mechanism can be fooled. Optical illusions are the most compelling examples, because vision is the most powerful of our senses, but the lesson you learn here is applicable everywhere. This book fools you for fun; others try to fool you for profit. Caveat spectator.

Simple but complex: The café wall illusion

Simple but complex: The café wall illusion

This Mortal Doyle

Challenger chopped and changed. That is to say, in one important respect, Arthur Conan Doyle’s character Professor Challenger lacked continuity. His philosophical views weren’t consistent. At one time he espoused materialism, at another he opposed it. He espoused it in “The Land of Mist” (1927):

“Don’t tell me, Daddy, that you with all your complex brain and wonderful self are a thing with no more life hereafter than a broken clock!”

“Four buckets of water and a bagful of salts,” said Challenger as he smilingly detached his daughter’s grip. “That’s your daddy, my lass, and you may as well reconcile your mind to it.”

But earlier, in “The Poison Belt” (1913), he had opposed it:

“No, Summerlee, I will have none of your materialism, for I, at least, am too great a thing to end in mere physical constituents, a packet of salts and three bucketfuls of water. Here ― here” ― and he beat his great head with his huge, hairy fist ― “there is something which uses matter, but is not of it ― something which might destroy death, but which death can never destroy.”

That story was published just over a century ago, but Challenger’s boast has not been vindicated in the meantime. So far as science can see, matter rules mind, not vice versa. Conan Doyle thought the same as the earlier Challenger, but Conan Doyle’s rich and teeming brain seems to have ended in “mere physical constituents”. To all appearances, when the organization of his brain broke down, so did his consciousness. And that concluded the cycle described by A.E. Housman in “Poem XXXII” of A Shropshire Lad (1896):

From far, from eve and morning
  And yon twelve-winded sky,
The stuff of life to knit me
  Blew hither: here am I.

Now – for a breath I tarry
  Nor yet disperse apart –
Take my hand quick and tell me,
  What have you in your heart.

Speak now, and I will answer;
  How shall I help you, say;
Ere to the wind’s twelve quarters
  I take my endless way. (ASL, XXXII)

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The Brain in Train

I feel odd when I consider this possibility: that all my thoughts are strictly determined, no more under my control than a straw in a gale or a stone in an avalanche. It seems paradoxical to have strictly determined thoughts about strictly determined thoughts. But is it? And is strict determinism fatal for finding the truth? I don’t think so. In fact, I think that strict determinism is essential for truth. But irrelevant associations get in the way of our understanding this. If our thoughts are determined, they seem like automatic trains running on rigid tracks. We might want to go to the station marked “Truth”, but if the switches are set wrong, the train will never get there. Or it will thunder through and never stop.


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Rep-Tile Reflections

A rep-tile, or repeat-tile, is a two-dimensional shape that can be divided completely into copies of itself. A square, for example, can be divided into smaller squares: four or nine or sixteen, and so on. Rectangles are the same. Triangles can be divided into two copies or three or more, depending on their precise shape. Here are some rep-tiles, including various rep-triangles:

Various rep-tiles

Various rep-tiles — click for larger image

Some are simple, some are complex. Some have special names: the sphinx and the fish are easy to spot. I like both of those, particularly the fish. It would make a good symbol for a religion: richly evocative of life, eternally sub-divisible of self: 1, 9, 81, 729, 6561, 59049, 531441… I also like the double-square, the double-triangle and the T-tile in the top row. But perhaps the most potent, to my mind, is the half-square in the bottom left-hand corner. A single stroke sub-divides it, yet its hypotenuse, or longer side, represents the mysterious and mind-expanding √2, a number that exists nowhere in the physical universe. But the half-square itself is mind-expanding. All rep-tiles are. If intelligent life exists elsewhere in the universe, perhaps other minds are contemplating the fish or the sphinx or the half-square and musing thus: “If intelligent life exists elsewhere in the universe, perhaps…”

Mathematics unites human minds across barriers of language, culture and politics. But perhaps it unites minds across barriers of biology too. Imagine a form of life based on silicon or gas, on unguessable combinations of matter and energy in unreachable, unobservable parts of the universe. If it’s intelligent life and has discovered mathematics, it may also have discovered rep-tiles. And it may be contemplating the possibility of other minds doing the same. And why confine these speculations to this universe and this reality? In parallel universes, in alternative realities, minds may be contemplating rep-tiles and speculating in the same way. If our universe ends in a Big Crunch and then explodes again in a Big Bang, intelligent life may rise again and discover rep-tiles again and speculate again on their implications. The wildest speculation of all would be to hypothesize a psycho-math-space, a mental realm beyond time and matter where, in mathemystic communion, suitably attuned and aware minds can sense each other’s presence and even communicate.

The rep-tile known as the fish

Credo in Piscem…

So meditate on the fish or the sphinx or the half-square. Do you feel the tendrils of an alien mind brush your own? Are you in communion with a stone-being from the far past, a fire-being from the far future, a hive-being from a parallel universe? Well, probably not. And even if you do feel those mental tendrils, how would you know they’re really there? No, I doubt that the psycho-math-space exists. But it might and science might prove its existence one day. Another possibility is that there is no other intelligent life, never has been, and never will be. We may be the only ones who will ever muse on rep-tiles and other aspects of mathematics. Somehow, though, rep-tiles themselves seem to say that this isn’t so. Particularly the fish. It mimics life and can spawn itself eternally. As I said, it would make a good symbol for a religion: a mathemysticism of trans-biological communion. Credo in Piscem, Unum et Infinitum et Æternum. “I believe in the Fish, One, Unending, Everlasting.” That might be the motto of the religion. If you want to join it, simply wish upon the fish and muse on other minds, around other stars, who may be doing the same.

Double Bubble

The most mysterious thing in the universe is also the most intimate: consciousness. It’s an inti-mystery, something we experience constantly at first hand and yet cannot describe or explain. We are each a double bubble: a bubble of flesh and a bubble of conscious experience. The second bubble bursts regularly, when we sleep. Sooner or later, the first bubble will burst too, when we die. And that will be it for the second bubble, the bubble of consciousness. Or will it? Can consciousness survive death? Can it exist without a material substrate? Or without a particular kind of material substrate: the soggy, sparky substance of the brain? Can the clean, dry metal of a computer be conscious? Who knows? The double bubble attracts lots of double-u’s: what, where, why, when, (w)how. What is consciousness? What is its relation to matter? Is it king or courtier? Where does it exist? Why does it exist? When? And how?

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