zenpundit.com » philosophy

Archive for the ‘philosophy’ Category

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

Monday, August 24th, 2015

[ by Charles Cameron — cross-posted from Sembl ]
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:

amplutihedron_span

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

droplet

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

But get this:

nima-permutation-grassmannian-final-picture

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.

**

Sources:

  • N. Arkani-Hameda et al, Scattering Amplitudes and the Positive Grassmannian
  • Nima Arkani-Hameda and Jaroslav Trnkab, The Amplituhedron
  • Check out the stunning physics — deeper than time and space? — if you don’t already know it, and explain it if you do!

  • Natalie Wolchover, A Jewel at the Heart of Quantum Physics
  • And for Wolfram on the Petersen Graph:

  • Eric W. Weisstein, Petersen Graph
  • On the Shoulders of Giants — Merton’s OTSOG illustrated?

    Saturday, August 22nd, 2015

    [ by Charles Cameron — I first saw the fish on @arlogilbert’s Twitter page, and I think I saw the turtle on someone’s FB? ]
    .

    The Turtle has gotta be a giant if it’s to carry elephants and a world on its back..

    SPEC turtle fish

    and moving from macro to micro, the Fish had best be sizeable if it’s to carry an island and village.

    **

    There are those who delight in the Turtle Hypothesis, but throw in a tiger atop the elephants, then extend the concept to encompass turtle upon turtle, Mr Justice Scalia (in Rapanos v. United States, 547 U.S. 715 [2006]. footnote 14) for instance:

    In our favored version, an Eastern guru affirms that the earth is supported on the back of a tiger. When asked what supports the tiger, he says it stands upon an elephant; and when asked what supports the elephant he says it is a giant turtle. When asked, finally, what supports the giant turtle, he is briefly taken aback, but quickly replies “Ah, after that it is turtles all the way down.”

    Likewise, there are those who reject it, as for example David Hume in his Dialogues Concerning Natural Religion

    How can we satisfy ourselves without going on in infinitum? And, after all, what satisfaction is there in that infinite progression? Let us remember the story of the Indian philosopher and his elephant. It was never more applicable than to the present subject. If the material world rests upon a similar ideal world, this ideal world must rest upon some other; and so on, without end. It were better, therefore, never to look beyond the present material world.

    Never to look beyond the present material world?

    Tsk, that’s a bit short-sighted, isn’t it?

    **

    Which brings me to Robert K. Merton‘s brilliant book familiarly known as OTSOG, which I’ve read, and Tristram Shandy, which I haven;t but would presumably like.

    As the saying goes, Odd Moves in a Mysterious Way.

    I’m also reminded of the Hendrix Hedge, but that’s another story..

    **

    Sources:

  • World on a tutle, The Science Behind Discworld’s Flat Earth on the Back of a Turtle
  • Island on a fish, Voted most likely to find a loophole
  • The Washington Post – can’t read, or can’t count?

    Thursday, August 20th, 2015

    [ by Charles Cameron — a grumpy grammatical plaint, plus Proclus for poet’s delight ]
    .

    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.

    **

    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.

    **

    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.

    **

    Ah, but I drift.

    The quantity of mercy is not strain’d?

    Wednesday, August 12th, 2015

    [by Charles Cameron — some remedial philosophy at age 71 ]
    .

    I seem to be doing remedial political philosophy this week. As it happens, I read a Chinese comedian in my youth and was admonished against “sitting down while running round in circles” and have been aerating my brain with too much conscious breathing ever since — neither leaving me much time or interest for what in Oxford in my day was known, somewhat dismissively, PPE — Philosophy, Politics and Economics.

    Which brings me today, and to grabbing lectures in just that sort of thing from Harvard’s Michael Sandel, courtesy of YouTube:

    The video shows Sandel’s lectures, “Justice: Putting a Price Tag on Life”, and “How to Measure Pleasure” — salted with some dark humor:

    Back in ancient Rome, they threw Christians to the lions in the Coliseum for sport. If you think how the utilitarian calculus would go, yes, the Christian thrown to the lion suffers enormous, excruciating pain, but look at the collective ecstasy of the Romans. .. you have to admit that if there were enough Romans delirious with happiness, it would outweigh even the most excruciating pain of a handful of Christians thrown to the lion.

    I enjoyed the two lectures immensely — maybe I should rewind fifty years, and try PPE at Harcard?.

    **

    All of which caused me to wonder:

    SPEC pinto and lincoln continental

    Sources:

  • Mark Dowie, Pinto Madness
  • W Michael Hoffman, Case Study: The Ford Pinto
  • See also:

  • ES Grush and CS Saunby, Fatalities Associated with Crash-Induced Fuel Leakage and Fires
  • **

    I mean, all of which made me wonder about Jeremy Bentham, I suppose.

    We had Locke at Christ Church, staring disdainfully from his portrait during dinners in the Great Hall — but Bentham? I don’t think I saw any utility in utilitarianism.

    **

    But then I also wondered:

    SPEC trolley problem torture

    I wondered: how close is the analogy between the trolly problem and the ticking bomb torture questionn? Do we start from numbers of likely victims in each case and decide from there, or should we instead start by contemplating torture — and recognize the abyss staring back at us?

    Sources:

  • Wikipedia, Trolly problem
  • Michael Sandel, Justice: Putting a Price Tag on Life & How to Measure Pleasure
  • See also:

  • Kyle York, Lesser-Known Trolley Problem Variations
  • **

    What Shakespeare said, though — getting back to my title — was “The quality of mercy is not strain’d” — not the quantity, the quality — unquantifiable.

    [2014] Gaza siege symmetry

    Monday, August 10th, 2015

    [ by Charles Cameron — a question in aesthetics-as-morality ]
    .

    Symmetry retains its beauty..

    Gaza-siege symmetry

    even when humans are to be found in the fireball?

    Note as appropriate — this was last year.

    **

    I am reminded of my most cherished passage from Plotinus, Enneads III.ii.15 — so very Shakespearean!

    Murders, death in all its guises, the reduction and sacking of cities, all must be to us just such a spectacle as the changing scenes of a play; all is but the varied incident of a plot, costume on and off, acted grief and lament. For on earth, in all the succession of life, it is not the Soul within but the Shadow outside of the authentic man, that grieves and complains and acts out the plot on this world stage which men have dotted with stages of their own constructing. All this is the doing of man knowing no more than to live the lower and outer life, and never perceiving that, in his weeping and in his graver doings alike, he is but at play; to handle austere matters austerely is reserved for the thoughtful: the other kind of man is himself a futility. Those incapable of thinking gravely read gravity into frivolities which correspond to their own frivolous Nature. Anyone that joins in their trifling and so comes to look on life with their eyes must understand that by lending himself to such idleness he has laid aside his own character. If Socrates himself takes part in the trifling, he trifles in the outer Socrates.

    **

    Chuang-Tzu, quoted by T’an Ssu-t’ung:

    That which is just born is already dead; that which is just dead is already born.

    Symmetry.


    Switch to our mobile site