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[ by Charles Cameron — in which we glimpse the (female) divinity hidden behind infinity ]
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It is one of the curiosities of mathematics that the great Indian mathematician Srinivasa Ramanujan claimed to have received many, if not all, of his equations from the goddess Namagiri in dreams — and that this idea is all too often quietly omitted from discussions of his uncanny brilliance.

Now that The Man Who Knew Infinity is out in theaters, it might be wise to explore the connection between Namagiri and Ramanujan a little more closely.

Dream and waking, darshan and mathematics, inspiration and intuition, intuition and proof, quality and quantity — these polarities are all involved..

To its credit, the film contains the line:

You want to know how I get my ideas? God speaks to me.

However, the idea that “God” might be a goddess seems a reach too far for the screenwriters and director.

Viewing:

Matt Brown, The Man Who Knew Infinity

Here’s one version of the trailer:

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Stephen Wolfram posted a fine article on his blog last week, Who Was Ramanujan?. He was willing to mention that Ramanujan’s friend and collaborator, GH Hardy, “could be very nerdy — whether about cricket scores, proving the non-existence of God, or writing down rules for his collaboration with Littlewood” — but fails in 31 pages to mention Ramanujan’s own belief that he received his equations from a goddess.

All of which caused me to pose a question to Wolfram’s own algorithmic genie, Wolfram Alpha:

Did Namagiri reveal equations to Ramanujan?

WolframAlpha skipped the words “Did Namagiri reveal” and “to” and concentrated on responding to “equations” and “Ramanujan” — not quite up to par with AlphaGo, I’m afraid, let alone Ramanujan himself, or better, Namagiri.

Below’s the DoubleQuote I made to by way of comment — note that I’ve only had space for the first line of WolframApha’s extended response:

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Readings:

Stephen Wolfram, Who Was Ramanujan?

Hinduism Today, Computing the Mathematical Face of God

Huffington Post, Ramanujan’s Mock Modular Forms

The Hindu, American mathematicians solve Ramanujan’s “deathbed” puzzle

Sadhguru, Doorway to the Beyond

Paul Chika Emekwulu, Mathematical Encounters: For the inquisitive mind

The Hindu, The Man Who Knew Infinity: A misunderstood mind

[ by Charles Cameron — Robert Redford and Brad Pitt on a Berlin rooftop ]
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how do you draw a circle in an entirely linear medium?

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The movie is Spy Game, with Robert Redford and Brad Pitt.

To my mind, it’s a brilliant piece of film making: director Tony Scott chose a terrific location for Nathan Muir (Redford)’s debrief reaming of Tom Bishop (Pitt), in the course of which Muir very pointedly tells Bishop:

Listen to this, because this is important. If you’d pulled a stunt there and got nabbed, I wouldn’t come after you. You go off the reservation, I will not come after you.

That’s the heart of the movie, right there, in negative — because the whole movie is about Bishop going off reservation in China, pulling a stunt there, and getting nabbed by the Chinese, and Muir coming after Bishop and rescuing him, with great shenanigans and flashbacks along the way.

Scott wants to draw a circle around that point, to drive it home — but this is a movie, a totally linear sequence frames, whether celluloid or digital, so how do you draw a circle in a linear medium?

Scott shoots the scene atop a circular roof, and before, during and after the conversation between the two men, has the camera circle the building:

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I know, I stretch the limits of this blog mercilessly — and I’m spending this post on a piece of cinema technique. Let’s just say that I take Adam Elkus‘ words seriously:

Clausewitz himself was heavily inspired by ideas from other fields and any aspiring Clausewitzian ought to mimic the dead Prussian’s habit of reading widely and promiscuously.

I’m being promiscuous.

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There are two other major points caught in Scott’s tight circle. One offers the essence of Spy Game, emphasis on the spy:

Bishop: Okay, help me understand this one. Nathan, what are we doing here? Don’t bullshit me about the greater good.
Muir: That’s exactly what it’s about. Because what we do is, unfortunately, very necessary.

The other gets to the other half of the name Spy Game — game:

Bishop: It’s not a fucking game!
Muir: Yes, it is. That’s exactly what it is. It’s no kid’s game, either, but a whole other game. And it’s serious, and it’s dangerous, and it’s not one you want to lose.

So, in the gospel according to Spy Game, espionage is a deadly and death-dealing game, played unfortunately but very necessarily for the greater good. All that in three short minutes, with a circle drawn around it for emphasis.

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Thus a problem in geometry is artfully transcended.

[ by Charles Cameron — fitness landscapes and the Bonnie Banks o’ Loch Lomond ]
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With the rise and fall of sea levels, sky levels, land emerges or submerges, mountain ranges with scattered lakes in their valleys transform into archipelagos, island clusters surge up to become continents — rise and fall, ebb and flow, wave upon wave..

I mean, really, what of the moral high ground?

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Consider these:

Adaptive Basins and Strange Peaks

Biologists talk about adaptive landscapes. In these metaphorical places, species climb uphill towards optimal fitness. Going up is a struggle. Climbing takes energy. Optimal peaks can be hard to attain. Many species are distracted by getting stuck on sub-optimal false peaks, or waylaid by the intervening rugged landscape.

Sources:

ResearchGate, Schematic “adaptive” or “fitness” landscape

The Technium, Adaptive Basins and Strange Peaks

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Nemesis and the Prophets are agreed:

Every valley shall be exalted, every mountain and hill made low

— or as Mary said of her son’s father:

He buffets proud folk about like leaves in a gale.
He upsets those that hold themselves high and mighty
and rescues the least one of us.

Ursula le Guin voiced Lao Tzu for us in English:

True goodness
is like water.
Water’s good
for everything.
It doesn’t compete.

It goes right
to the low loathsome places,
and so finds the way.

Furthermore:

What’s softest in the world
rushes and runs
over what’s hardest in the world.

The immaterial
enters
the impenetrable.

**

O ye’ll tak’ the high road, and I’ll tak’ the low road, And I’ll be in Scotland afore ye

[ by Charles Cameron — Sun Tzu meets Willie Pep ]
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Sun Tzu‘s fightless victory is like the Platonic pearl, ideal, perfectly spherical. Pep‘s blowless round is like a cut diamond, multifaceted — some claim the tale is true, some that he fabricated the tale years later, some that it was a boast he made before the fight — one version suggests Pep told St. Paul sports writer Don Riley, who was covering the fight for Minnesota radio station WMIN:

Pick a round, I’ll throw punches, but I’ll never hit him. Check the scorecards after, and see if the judges fall for it.

Who knows? A good tale frays into a thousand fugal strands in the Ocean of Story.

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The curiosity:

The more facets a diamond built to approximate a sphere has, the closer it comes to the Platonic sphere.. Quite what the analogy with narrative variants would be, currently escapes me.

[ by Charles Cameron — paging birds and fishes, Chuang Tzu and Wm Blake ]
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Dwight Furrow, Wine Tasting and Objectivity:

The question is whether flavors are “in the wine” or “in the mind”. On the one hand, there are objectively measurable chemical compounds in wine that reliably affect our taste and olfactory mechanisms—pyrazines cause bell pepper aromas in Cabernet Sauvignon, malic acid explains apple aromas in Chardonnay, tannins cause a puckering response, etc. But we know that human beings differ quite substantially in how they perceive wine flavors. Even trained and experienced wine critics disagree about what they are tasting and how to evaluate wine. This disagreement among experts leads many to claim that wine tasting is therefore purely subjective, just a matter of individual opinion. According to subjectivism, each person’s response is utterly unique and there is no reason to think that when I taste something, someone else ought to taste the same thing. Statements about wine flavor are statements about one’s subjective states, not about the wine. Thus, there are no standards for evaluating wine quality.

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Is each mind inherently closed to every other, much as the bird’s mind is closed to ours in Blake‘s aphorism —

How do you know but every bird that cuts the airy way, is an immense world of delight, closed by your senses five?

— albeit not always so joyful?

In more contemporary terms — Is there encryption of the mind?

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I ask this in light of the DoubleQuote I posted a few days ago comparing Hesse and Hitchcock in terms of their metaphoric uses of “organ” — in, I hasten to add, the Bach sense of the word:

Here’s what I’m thinking. Hesse’s game influences the mind, as does art, but it is non-invasive; Hitchcock applauds the potential for art to move in a more invasive direction, as if by force rather than by enticement.

“”

Humans — or at least the philosophers and philosopher tagalongs among them — can’t even tell if what one human sees as “red” is what another sees as “red” — let alone what a given Burgundy tastes like on another’s palate.

If this means, more generally, that minds are effectively encrypted by virtue of their differences in wiring acquired with parentage, age and experience, then our communications media -– language, the arts, literature, number — would appear to be the available decryption keys, selectively available to the minds in question.

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Chuang-Tsu has this tale to tell:

Men claim that Mao-ch’iang and Lady Li were beautiful, but if fish saw them they would dive to the bottom of the stream, if birds saw them they would fly away, and if deer saw them they would break into a run. Of these four, which knows how to fix the standard of beauty for the world?

And this..

Chuang Tzu and Hui Tzu were strolling along the dam of the Hao River when Chuang Tzu said, “See how the minnows come out and dart around where they please! That’s what fish really enjoy!”

Hui Tzu said, “You’re not a fish – how do you know what fish enjoy?”

Chuang Tzu said, “You’re not I, so how do you know I don’t know what fish enjoy?”

Hui Tzu said, “I’m not you, so I certainly don’t know what you know. On the other hand, you’re certainly not a fish – so that still proves you don’t know what fish enjoy!”

Chuang Tzu said, “Let’s go back to your original question, please. You asked me how I know what fish enjoy – so you already knew I knew it when you asked the question. I know it by standing here beside the Hao.”

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Chuang Tzu said, “You’re not I, so how do you know I don’t know what fish enjoy?”

Blake said, “How do you know but every bird that cuts the airy way, is an immense world of delight, closed by your senses five?”