Brain Pickings

Geometrical Psychology: Benjamin Betts’s 19th-Century Mathematical Illustrations of Consciousness

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“Imagination receives the stream of Consciousness, and holds apart and compares the different experiences.”

“What makes a mathematician is not technical skill or encyclopedic knowledge,” Paul Lockhard recently wrote, “but insatiable curiosity and a desire for simple beauty.” But what if this mathematical curiosity and desire for beauty were applied to questions that have perplexed scientists and philosophers for millennia — questions about consciousness, what it is, how it works, and how it shapes our lives? That’s precisely what New Zealander Benjamin Betts set out to do in the 19th century with his unusual diagrams of consciousness, collected in the 1887 tome Geometrical Psychology, or, The Science of Representation (public domain), a predecessor to Julian Hibbard’s geometric diagrams of love.

Editor Louisa S. Cook, who assembled Betts’s diagrams, writes in the introduction:

Mr. Betts has spent more than twenty years in studying the evolution of Man. He contemplates Man, not from the physical, but from the metaphysical point of view ; thus the evolution of Man is for him the evolution of human consciousness. He attempts to represent the successive stages of this evolution by means of symbolical mathematical forms. These forms represent the course of development of human consciousness from the animal basis, the pure sense-consciousness, to the spiritual or divine consciousness; both which extremes are not man — the one underlying, the other transcending the limits of human evolution.

Mr. Betts felt that consciousness is the only fact that we can study directly, since all other objects of knowledge must be perceived through consciousness.

Mathematical form, he considers, is the first reflection and most pure image of our subjective activity. Then follows number, having a close relation to linear conception. Hence mathematical form with number supplies the fittest symbols for what Mr. Betts calls “The Science of Representation,” the orderly representation by a system of symbolisation of the spiritual evolution of life, plane after place. “Number,” Philo said, “is the mediator between the corporeal and the incorporeal.”

Cook notes the form of Betts’s forms:

The symbolic forms which Mr. Betts has evolved through his system of Representation resemble, when developed in two dimensions, conventionalised but very scientifically and beautifully conventionalised leaf-outlines. When in more than two dimensions they approximate to the forms of flowers and crystals.

These mathematical curves might serve as a truer and more scientific basis of classification for Botany than de Candolle’s system or any other yet employed, many so-called amorphous developments of the Flora being readily reducible to law according to this method. For instance, the simple corollas, the horn-shaped corollas, and the bi-axial corollas would supply three main classes of flower forms, each of which might be divided into various distinct sub-classes.

The fact that he has accidentally portrayed plant-forms when he was studying human evolution is an assurance to Mr. Betts of the fitness of the symbols he has developed, as it affords presumptive evidence that the laws he is studying intuitively admit of universal application.

On Betts’s model of the imagination:

After the repeated recurrence of any sensation, though slightly varying in form, the individual develops the consciousness of its identity, and he begins to form an image or idea, both of the subjective sensation and of the accompanying objective perception, which he can retain in his mind though the sense affection of which it is the counterpart is transitory. Mr. Betts calls this power of ideation Imagination, using it in the literal sense of the word. As a prism receives a beam of light and deflects the rays, holding them apart so that the colours of the spectrum are separated and distinguished, so Imagination receives the stream of Consciousness, and
holds apart and compares the different experiences.

Comparison is represented in the diagrams by the angle-; Consciousness from one-dimensional becomes two-dimensional, the line is expanded to a surface.

[…]

And since every idea is dual — e.g., the positive idea of light brings with it the negative complementary idea of darkness — of a colour, its complementary colour — therefore the positive representative line on the right hand of the diagram is duplicated by a counterpart line on the left. The sensation of the present moment is not yet reflected as an idea, nor distinguished by comparison. In the diagram it is the apex of the form. When more than two senses occupy Consciousness the lines representing them are arranged radially round the centre. Although the distinction must then be represented by a smaller angle, it does not follow that it is less in amount, as the form itself of Consciousness has become enlarged. At the same time it is quite possible that when the number of modes of manifestation is very limited the sensations are more vivid, and consequently the distinctions more marked, than when more modes of consciousness are differentiated.

Whether abstracting something as complex as consciousness in such concrete physical forms is a reasonable proposition remains a question for the metaphysicians — but the forms themselves are, unequivocally, pure visual mesmerism.

Betts’s diagrams are now in the public domain and the book is available for free in multiple digital formats from Open Library.

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Joan Didion on Keeping a Notebook

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“We are well advised to keep on nodding terms with the people we used to be, whether we find them attractive company or not.”

As a lover — and keeper — of diaries and notebooks, I find myself returning again and again to the question of what compels us — what propels us — to record our impressions of the present moment in all their fragile subjectivity. From Joan Didion’s 1968 anthology Slouching Towards Bethlehem (public library) — the same volume that gave us her timeless meditation on self-respect — comes a wonderful essay titled “On Keeping a Notebook,” in which Didion considers precisely that. Though the essay was originally written nearly half a century ago, the insights at its heart apply to much of our modern record-keeping, from blogging to Twitter to Instagram.

Portrait of Joan Didion by Mary Lloyd Estrin, 1977

After citing a seemingly arbitrary vignette she had found scribbled in an old notebook, Didion asks:

Why did I write it down? In order to remember, of course, but exactly what was it I wanted to remember? How much of it actually happened? Did any of it? Why do I keep a notebook at all? It is easy to deceive oneself on all those scores. The impulse to write things down is a peculiarly compulsive one, inexplicable to those who do not share it, useful only accidentally, only secondarily, in the way that any compulsion tries to justify itself. I suppose that it begins or does not begin in the cradle. Although I have felt compelled to write things down since I was five years old, I doubt that my daughter ever will, for she is a singularly blessed and accepting child, delighted with life exactly as life presents itself to her, unafraid to go to sleep and unafraid to wake up. Keepers of private notebooks are a different breed altogether, lonely and resistant rearrangers of things, anxious malcontents, children afflicted apparently at birth with some presentiment of loss.

[…]

[T]he point of my keeping a notebook has never been, nor is it now, to have an accurate factual record of what I have been doing or thinking. That would be a different impulse entirely, an instinct for reality which I sometimes envy but do not possess.

To that end, she confesses a lifelong failure at keeping a diary:

I always had trouble distinguishing between what happened and what merely might have happened, but I remain unconvinced that the distinction, for my purposes, matters.

What, then, does matter?

How it felt to me: that is getting closer to the truth about a notebook. I sometimes delude myself about why I keep a notebook, imagine that some thrifty virtue derives from preserving everything observed. See enough and write it down, I tell myself, and then some morning when the world seems drained of wonder, some day when I am only going through the motions of doing what I am supposed to do, which is write — on that bankrupt morning I will simply open my notebook and there it will all be, a forgotten account with accumulated interest, paid passage back to the world out there: dialogue overheard in hotels and elevators and at the hat-check counter in Pavillon (one middle-aged man shows his hat check to another and says, ‘That’s my old football number’); impressions of Bettina Aptheker and Benjamin Sonnenberg and Teddy (‘Mr. Acapulco’) Stauffer; careful aperçus about tennis bums and failed fashion models and Greek shipping heiresses, one of whom taught me a significant lesson (a lesson I could have learned from F. Scott Fitzgerald, but perhaps we all must meet the very rich for ourselves) by asking, when I arrived to interview her in her orchid-filled sitting room on the second day of a paralyzing New York blizzard, whether it was snowing outside. I imagine, in other words, that the notebook is about other people. But of course it is not. I have no real business with what one stranger said to another at the hat-check counter in Pavillon; in fact I suspect that the line ‘That’s my old football number’ touched not my own imagination at all, but merely some memory of something once read, probably ‘The Eighty-Yard Run.’ Nor is my concern with a woman in a dirty crepe-de-Chine wrapper in a Wilmington bar. My stake is always, of course, in the unmentioned girl in the plaid silk dress. Remember what it was to be me: that is always the point.

It is a difficult point to admit. We are brought up in the ethic that others, any others, all others, are by definition more interesting than ourselves; taught to be diffident, just this side of self-effacing. (‘You’re the least important person in the room and don’t forget it,’ Jessica Mitford’s governess would hiss in her ear on the advent of any social occasion; I copied that into my notebook because it is only recently that I have been able to enter a room without hearing some such phrase in my inner ear.) Only the very young and the very old may recount their dreams at breakfast, dwell upon self, interrupt with memories of beach picnics and favorite Liberty lawn dresses and the rainbow trout in a creek near Colorado Springs. The rest of us are expected, rightly, to affect absorption in other people’s favorite dresses, other people’s trout.

Once again, Didion returns to the egoic driver of the motive to write:

And so we do. But our notebooks give us away, for however dutifully we record what we see around us, the common denominator of all we see is always, transparently, shamelessly, the implacable “I.” We are not talking here about the kind of notebook that is patently for public consumption, a structural conceit for binding together a series of graceful pensées; we are talking about something private, about bits of the mind’s string too short to use, an indiscriminate and erratic assemblage with meaning only for its maker.

Ultimately, Didion sees the deepest value of the notebook as a reconciliation tool for the self and all of its iterations:

I think we are well advised to keep on nodding terms with the people we used to be, whether we find them attractive company or not. Otherwise they turn up unannounced and surprise us, come hammering on the mind’s door at 4 a.m. of a bad night and demand to know who deserted them, who betrayed them, who is going to make amends. We forget all too soon the things we thought we could never forget. We forget the loves and the betrayals alike, forget what we whispered and what we screamed, forget who we were.

[…]

It is a good idea, then, to keep in touch, and I suppose that keeping in touch is what notebooks are all about. And we are all on our own when it comes to keeping those lines open to ourselves: your notebook will never help me, nor mine you.

The rest of Slouching Towards Bethlehem is brimming with the same kind of uncompromising insight, sharp and soft at the same time, on everything from morality to marriage to Hollywood.

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Andrew Zuckerman’s Extraordinary Portraits of Flowers

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Blossoms like you’ve never seen them before.

Thanks to his ethos of curiosity and rigor as the key to creativity, photographer Andrew Zuckerman has consistently managed to captivate the imagination and stir the soul with his crisp portraits of nature’s creatures, celebrated musicians, and our era’s most beloved elders. He now brings his singular lens to nature’s most vibrant and whimsical flora with Flower (public library) — a collection of mesmerizing, luminous close-ups of more than 150 species, making the familiar sparkle with newfound curiosity and shedding scintillating light on the exotic.

Here is but a tiny taste — though it’s worth noting the screen does Zuckerman’s lush, rich artwork absolutely no justice.

Datura fastuosa 'Double Purple'

Andrew Zuckerman :: flowerthebook.com

fiddlehead fern

Andrew Zuckerman :: flowerthebook.com

Rosa Charlotte

Andrew Zuckerman :: flowerthebook.com

Aechmea 'Del Mar'

Andrew Zuckerman :: flowerthebook.com

Brugmansia suaveolens

Andrew Zuckerman :: flowerthebook.com

Cannabis sativa species Indica cultivar

Andrew Zuckerman :: flowerthebook.com

Chrysanthemum 'Coral Reef'

Andrew Zuckerman :: flowerthebook.com

Couroupita guianensis

Andrew Zuckerman :: flowerthebook.com

Maxillariella picta

Andrew Zuckerman :: flowerthebook.com

Paeonia cultivar 6

Andrew Zuckerman :: flowerthebook.com

Paphiopedilum Pink Fred

Andrew Zuckerman :: flowerthebook.com

Strongylodon macrobotrys

Andrew Zuckerman :: flowerthebook.com

In addition to the photographs, Zuckerman also produced a series of breathtaking short timelapse films with fantastic sound design:

Flower comes on the heels of Zuckerman’s Bird, the sequel to Creature.

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