zenpundit.com » mathematics

Archive for the ‘mathematics’ Category

On play as wildness

Saturday, September 24th, 2016

[ by Charles Cameron — what’s true of hex maps is true of all mental models ]
.

There’s a certain let-your-hair-down quality to play.

It appears that one Tausendsassa Friedensreich Regentag Dunkelbunt Hundertwasser said or perhaps wrote, muttered, whispered, shouted, or simply thought out loud, “the straight line is a godless line” — at any rate, someone noticed and recorded the phrase, and now it’s scattered across the net and difficult to track to its source.

**

But we do love order, don’t we?

hex-grid

And so the rivers on our hexagonal maps all too easily follow the hexagons..

rivers-and-tree-clusters-hexagonal-map

when they’d more realistically cross over them, following their own courses:

free-rivers

and note how easily even our efforts to bring natural variety to our hexagonal mappings conform more to hexagons than to variety.

hexmaptopo

**

Zennist Thich Nhat Hanh in Listening Deeply for Peace writes:

A traditional Vietnamese Zen garden is very different from a Japanese Zen garden. Our Zen gardens, called hon non bo, are wild and exuberant, more playful than the formal Japanese gardens with their restrained patterns. Vietnamese Zen gardens are seriously unserious. For us, the whole world is contained in this peaceful place. All activities of life unfold in true peace in the garden: in one part, children will be playing, and in another part, some elderly men will be having a chess game; couples are walking; families are having picnics; animals are free to wander around. Beautiful trees are growing next to abundant grasses and flowers. There is water, and there are rock formations. All ecologies are represented in this one microecology without discrimination. It is a miniature, peaceful world. It is a beautiful living metaphor for what a new global ethic could bring.

**

Here is the wrestling of a tree with such angels as gravity, sun, wind and rain:

methuselah-bristlecone-pine-tree

Here is the wild calligraphy of the Rio Mamoré across the forests of the Amazon basin:

meanders_oli_2014194

From medieval gold leaf to Olympic gold

Monday, August 15th, 2016

[ by Charles Cameron — a voyage into nondualism via the coincidentia oppositorum ]
.

Here from Dr Emily Steiner may be the widest rigorous gap-bridging DoubleQuotes I’ve ever seen:

Kudos to Anthony Ervin for his gold!

I’m not entirely sure there’s gold leaf in the image Dr Steiner uses to represent medieval manuscripts, though it certainly works for the genre as a whole, and I think I detect some gold leaf in the hearts of the flowers depicted..

**

It would be foolish for me to claim to follow JL Usó-Doménech et al’s Paraconsistent Multivalued Logic and Coincidentia Oppositorum: Evaluation with Complex Numbers, but the general notions of Cardinal Nicholas of Cusa (Cusanus), “That in God opposites coincide” and “That God is beyond the coincidence of opposites” rae pretty basic (with appropriate variations) to Carl Jung‘s psychology — and to my own thinking.

Here, in Dr Steiner’s tweet, we have something that comes delightfully, playfully close to a coincidence of opposites. Indeed it is that possibility of evoking and annotating opposites in a manner than allows us to transcend them — as we could be said to transcend the two streams of vision in binocular vision, the two streams of hearing in stereophonic audition — that lies at the heart of my focus on DoubleQuoting.

**

If the “new atheists” were a little more widely read, they might find themselves perplexed by the trans-logical implications of a God described thus by Cusanus:

When we attempted to see Him beyond being and not-being, we were unable to understand how He could be visible. For He is beyond everything plural, beyond every limit and all unlimitedness; He is completely everywhere and not at all anywhere; He is of every form and of no form, alike; He is completely ineffable; in all things He is all things, in nothing He is nothing, and in Him all things and nothing are Himself; He is wholly and indivisibly present in any given thing (no matter how small) and, at the same time, is present in no thing at all.

That’s a far harder concept — if it can even be called a concept — to deal with than the “seven day creator” God that is their usual mark. And yet there is no great logical space between Cusanus’ “He is completely ineffable” and the Athanasian Creed‘s ” The Father incomprehensible, the Son incomprehensible, and the Holy Spirit incomprehensible .. The Father eternal, the Son eternal, and the Holy Spirit eternal .. And yet they are not three eternals but one eternal .. As also there are not three uncreated nor three incomprehensible, but one uncreated and one incomprehensible.”

Jasper Hoskins proposes [Jasper Hopkins, A concise introduction to the philosophy of Nicholas of Cusa] that in Cusanus’ view, “no finite mind can comprehend God, since finite minds cannot conceive of what it is like for God to be altogether undifferentiated.”

**

There’s an exchange in Cusanus’ Trialogus de possest (“On actualized-possibility”) in Hoskins’ op. cit.., that sets forth instructions for reading propositions about God — which also make interesting reading in terms of the flexibility ofmmind andimagination necessary for reading poetry, myth, and scriptures:

Bernard: I am uncertain whether in similar fashion we can fittingly say that God is sun or sky or man or any other such thing.

Card. Nicholas of Cusa: We must not insist upon the words. For example, suppose we say that God is sun. If, as is correct, we construe this [statement] as [a statement] about a sun which is actually all it is able to be, then we see clearly that this sun is not at all like the sensible sun. For while the sensible sun is in the East, it is not in any other part of the sky where it is able to be. [Moreover, none of the following statements are true of the sensible sun:] “It is maximal and minimal, alike, so that it is not able to be either greater or lesser”; “It is everywhere and anywhere, so that it is not able to be elsewhere than it is”; “It is all things, so that it is not able to be anything other than it is”— and so on. With all the other created things the case is simnilar. Hence is does not matter what name you give to God, provided that in the foregoing manner you mentally remove the limits with respect to its possible being.

We’re close here, to the zen notion of the finger pointing at the moon — except that here is is the moon pointing at what cannot even be located in either physical spacetime or conceptual space..

**

and that’s the touch of gold in the heart of all flowers..

Sunday’s second surprise — the Van Gogh DoubleQuote

Sunday, July 17th, 2016

[ by Charles Cameron — Van Gogh, Rilke, El Greco, Von Kármán. Hokusai, Jakob — rich correspondences between singificant items in widely separate disciplines ]
.

My friend Steve Engel suggested this variant on my personal favorite DoubleQuote — the one pairing Van Gogh with Von Kármán — and as a lover of Rainer Maria Rilke I very much appreciate his suggestion, which bridges painting and poetry as my original DQ brdges arts and sciences:

SPEC DQ Gogh Rilke Steve Engel

**

I’ve also featured that particular van Gogh painting in another DQ, this one showing the sky as painted by El Greco and Van Gogh:

SPEC DQ greco gogh

El Greco was first among my loves in painting, and I’ve long thought that the differences between how El Greco sees the sky and how Van Gogh sees it could stand in for the differences between religions — you don’t see Van Gokkites attacking El Grekkites in museums on account of the different visions of their preferred painters, and if we could view religions as visionary rather than prescriptive, taking from them what a poetic, metaphoric, non-literal, non-fundamentalist, non-reductionist reading would approve, we might be a little farther on our way towards interfaith harmony, and away from religiously-sanctionable violence.

I’m thinking here of St Francis‘ meeting with the Sultan Malik al-Kamil, and more recently Thomas Merton‘s meetings with Buddhist contemplatives, Sufis and the like..

**

Here’s the Von Kármán / Van Gogh DQ, which I value in light of Hermann Hesse‘s Glass Bead Game as a clear bridge between one of the crucial dualities of recent centuries — the needless and fruitless schism between the arts and sciences, which has given rise not only the rantings of Christopher Hitchens and his less elegant disciple Bill Maher, but to such other matters as the Papal condemnation and “forgiveness” 359 years later of Galileo Galilei, Charles Babbage‘s Ninth Bridgewater Treatise, Andrew White‘s A History of the Warfare of Science With Theology in ChristendomW, and CP Snow‘s The Two Cultures:

karman gogh

**

And finally, here’s an ugraded version of the other DQ of mine that seeks to bridge the arts and sciences — featuring Hokusai‘s celebrated woodblock print, The Great Wave off Kanagawa (upper panel, below) and Jakob aka nikozy92‘s fractal wave, which I’ve flipped horizontally to make its parallel with the Hokusai clearer (lower panel) — Jakob‘s is a much improved version of a fractal wave compared with the one I’d been using until today:

SPEC-DQ-Hokusai-fractal v 2.0 minikozy92

Prof Pogge teaches ethics at Yale, but does he shave himself?

Wednesday, June 22nd, 2016

[ by Charles Cameron — Pogge’s ethics, Russell’s barber paradox, and self-reference ]
.

It’s that old ouroboros [1, 2, 3, 4] rearing its ugly head again, with its tail firmly between its teeth:

DQ 600 ethicists & barbers

**

The riddle, koan or potential paradox posed in the upper panel alludes to the matter of Yale’s professor Thomas Pogge, a noted ethicist, and some unbecoming behavior of which he has been accused — but as professor Judith Stark writing at Conversation suggests, there’s further interest beyond the case of Pogge and his accusers.

Responding to the question posed by the title of her own piece, Should ethics professors observe higher standards of behavior?, she writes:

This is an enduring dilemma in the area of ethics and one that has recently come to light with charges of unethical behavior brought against a prominent philosopher, Professor Thomas Pogge of Yale University. Pogge has been accused of manipulating younger women in his field into sexual relationships, a charge he has strenuously denied.

Without making any judgment on the case itself, this situation raises larger questions about how the behavior of the experts in ethics is to be reviewed and evaluated.

Profession and practice are, in their own way, like word and act — or are they?

**

In the lower panel, I’ve placed a discussion of Bertrand Russell‘s “barber” paradox that in Russell’s view partially but not fully resembles his paradox of the “class of all classes that are not members of themselves” — the question there being whether this class is a member of itself or not. I’m not in a position to argue such matters with Russell, so I’ll just say that he views both the “classes” and “barber” paradoxes as (different but similar) seeming knots which, when you pull on their loose ends, disentangle themselves, pop!:

Russell writes of the “barber” paradox that it is a variant on the “classes” paradox in which “the contradiction is not very difficult to solve.” The “classes” paradox is harder, he says, but he finally dismisses it as “nonsense, i.e., that no class either is or is not a member of itself, and that it is not even true to say that, because the whole form of words is just a noise without meaning.”

Or as Wm. Shakespeare might have said, “a tale told by an idiot, full of sound and fury, signifying nothing” — to which Witty Wittgenstein might have quipped, “Whereof one cannot speak, thereof one must be silent” — which, alas, has the air of a tautology, with the entire Tractatus thereby eating its own tail..

**

What do you think? Is the entire question of ethicists behaving ethically or unethically moot? a koan? does it eat its own tail? does it just melt into thin air, and leave not a rack behind?

Sources:

  • Judith Stark, Should ethics professors observe higher standards of behavior?
  • Esther Inglis-Arkell, The Barber Paradox Shook the Foundations of Math
  • Bertrand Russell, Logic and Knowledge: Essays, 1901-1950
  • Considering Viv, Wolfram Language, Syntience, and the GBG

    Wednesday, June 8th, 2016

    [ by Charles Cameron — expanding the computable to include qualitative ideation ]
    .

    Let’s start with Viv. It looks pretty phenomenal:

    That video is almost exactly a month old, and it’s pitched at “the universe of things” with a marked tilt towards e-commerce. Fair enough.

    **

    It’s instructive to compare it with Wolfram Language, although here I’ve had to go with a video that’s a couple of years old:

    Stephen Wolfram, the creator of both Mathematica and Wolfram Alpha, is focused on the world of numbers — and incidentally, that includes graphs of the sort I’ve been discussing in my series here On the felicities of graph-based game-board design, as you can see in the video above.

    It will be interesting to see how the two of them — Viv and Wolfram — interact over time. After all, one of the purposes of these lines of development is to dissolve the “walled gardens” which serve as procrustean beds for current thinking about the nature and possibilities of the web. Do these two gardens open to each other? If so, why? If not, why not?

    **

    I’ve talked enough for my purposes about AlphaGo and it’s narrowly focused though impressive recent triumph, and the wider picture behind it, as expressed by Monica Anderson — and tying the two together, we have this video from Monica’s timeline, Bob Hearn: AlphaGo and the New Era of Artificial Intelligence:

    Bob Hearn: AlphaGo and the New Era of Artificial Intelligence from Monica Anderson on Vimeo.

    Monica’s Syntience, it seems to be, is a remarkable probing of the possibilities before us.

    **

    But I’m left asking — because Hermann Hesse in his Nobel-winning novel The Glass Bead Game prompts me to ask — what about the universe of concepts — and in particular for my personal tastes, the universe of musical, philosophical, religious and poetic concepts. What of the computational mapping of the imagination?

    My question might well have large financial implications, but I’m asking it in a non-commercially and not only quantitative way. I believe it stands in relationship to these other endeavors, in fact, as pure mathematics stands in relation to physics, and hence also to chemistry, biology and more. And perhaps music stands in that relationship to mathematics? — but I digress.

    If I’m right about the universe of concepts / Glass Bead Game project, it will be the most intellectually demanding, the least commercially obvious, and finally the most revelatory of these grand-sweep ideas..

    From my POV, it’s also the one that can give the most value-add to human thinking in human minds, and to CT analysts, strategists, journos, educators, therapists, bright and playful kids — you name them all!

    Seeing it in terms of counterpoint, as Hesse did — it’s the virtual music of ideas.


    Switch to our mobile site