I pour tremendous time, thought, love, and resources into Brain Pickings, which remains free. If you find any joy and stimulation here, please consider supporting my labor of love with a recurring monthly donation of your choosing, between a cup of tea and a good dinner:
You can also become a one-time patron with a single donation in any amount:
And if you've already donated, from the bottom of my heart: THANK YOU.
|
|
 Hello, Larry! If you missed last week's edition – the love letters of Kahlil Gibran, the story behind "Do not go gentle into that good night," and how Rachel Carson spoke inconvenient truth to power to catalyze the modern environmental movement – you can catch up right here. And if you're enjoying this newsletter, please consider supporting my labor of love with a donation – each month, I spend hundreds of hours and tremendous resources on it, and every little bit of support helps enormously.
|
In case you missed them:
“Knowing what I do, there would be no future peace for me if I kept silent,†biologist Rachel Carson wrote to her most beloved friend as she was about to catalyze the modern environmental movement with the 1962 publication of Silent Spring.
My recent immersion in Carson’s world and her breathtaking correspondence with Dorothy Freeman led me down a curious path that circled back to our present moment with astonishing pertinence. In a letter to Freeman penned exactly ninety days before the release of Silent Spring, as Carson was coming to terms with the irreversible bravery of breaking her silence about the destruction of nature and the government’s attendant heedlessness, she shared a quotation that had bolstered her courage to speak out:
 To sin by silence, when we should protest makes cowards out of men.
The words reached across time to strike me with their extraordinary relevance today, and I set out to find their source. Literature being the original internet, as I’ve long believed, Carson’s letter became a de facto “hyperlink†to another text — the words she cited, though frequently misattributed to Abraham Lincoln, turned out to be the opening lines of a piercing poem titled “Protest†by Ella Wheeler Wilcox (November 5, 1850–October 30, 1919), from her 1914 book Poems of Problems ( public domain | public library), written at the peak of the Women’s Suffrage movement and just as WWI was about to erupt. 
Ella Wheeler Wilcox
A mighty and mobilizing anthem against silence, the poem stands as an anthem for our own time. So I asked my friend and fellow poetry-lover Amanda Palmer to record a reading of this timeless, timely masterpiece as an installment in our ongoing collaboration on poetry readings. (Previously: “Humanity i love you†by E.E. Cummings, and “Possibilities†and “Life While-You-Wait†by Polish Nobel laureate Wisława Szymborska.)
Amanda herself was so moved by the words that she invited her friend Jherek Bischoff — the brilliant composer and multi-instrumentalist with whom she collaborated on their David Bowie tribute — to set the words to music. The piece that buoys the poem is titled “Closer To Closure,†from Jherek’s entrancing album Cistern. Please enjoy:
PROTEST
To sin by silence, when we should protest,
Makes cowards out of men. The human race
Has climbed on protest. Had no voice been raised
Against injustice, ignorance, and lust,
The inquisition yet would serve the law,
And guillotines decide our least disputes.
The few who dare, must speak and speak again
To right the wrongs of many. Speech, thank God,
No vested power in this great day and land
Can gag or throttle. Press and voice may cry
Loud disapproval of existing ills;
May criticise oppression and condemn
The lawlessness of wealth-protecting laws
That let the children and childbearers toil
To purchase ease for idle millionaires.
Therefore I do protest against the boast
Of independence in this mighty land.
Call no chain strong, which holds one rusted link.
Call no land free, that holds one fettered slave.
Until the manacled slim wrists of babes
Are loosed to toss in childish sport and glee,
Until the mother bears no burden, save
The precious one beneath her heart, until
God’s soil is rescued from the clutch of greed
And given back to labor, let no man
Call this the land of freedom.
I’d be remiss not to mention that Amanda’s music, like my own work, is supported by donations. At a time when a ruthless administration seems intent on defundingthe National Endowment for the Arts and the National Endowment for the Humanities, supporting artists with our own patronage is a critical force of resistance and protest. So please join me in supporting Amanda on Patreon and supporting Jherek by buying his enchanting records.
“Optimism is an alienated form of faith, pessimism an alienated form of despair,†the great humanistic philosopher and psychologist Erich Fromm wrote in 1972 as he made his elegant case for rational faith in the human spirit, adding: “To have faith means to dare, to think the unthinkable, yet to act within the limits of the realistically possible.â€
That selfsame year, across the Atlantic, the philosopher Simone de Beauvoir (January 9, 1908–April 14, 1986) — another thinker of formidable foresight and abiding insight into the human experience — explored this osmotic relationship between optimism, pessimism, and hope in the fourth and final volume of her autobiography, All Said and Done ( public library). 
Simone de Beauvoir, 1952 (Photograph: Gisèle Freund)
De Beauvoir, who lived through two World Wars, devoted much of her work to the notion that happiness is not only possible but our moral obligation — a notion rooted not in a rosy wishfulness but in an incisive intellect that used every tool of skepticism to probe untruth and dispel ignorance. A devout lifelong atheist, she reflected at the end of her life that while many of her philosophical ideas evolved over the decades, her atheism remained unflinching. She held a strong conviction that the dogmas of religion preclude the critical thinking and analytical reasoning necessary for philosophical inquiry and for the evolution of human thought itself — an interference particularly pronounced when it came to the question of whether one is to take an optimistic or pessimistic attitude toward life and human nature. De Beauvoir writes:
Faith is often an appurtenance that is given in childhood as part of the middle-class equipment, and that is unquestionably retained together with the rest of it. If a doubt arises, it is often thrust aside for emotional reasons — a nostalgic loyalty to the past, affection for those around one, dread of the loneliness and banishment that threaten those who do not conform… Habits of mind, a system of reference and of values have been acquired, and one becomes their prisoner.
With an eye to the ultimate delusion of religion — that of personal immortality, to which the pious cling as a hedge against the terror of the void that death presents — De Beauvoir adds:
Faith allows an evasion of those difficulties which the atheist confronts honestly. And to crown all, the believer derives a sense of great superiority from this very cowardice itself.
But out of this courageous confrontation with difficulty arises an unexpected fountain of hope — that more lucid and muscular counterpart to blind optimism. De Beauvoir writes:
In what colors do I see this Godless world in which I live? Many readers tell me that what they like in my books is my delight in happiness, my love of live — my optimism. But others, particularly when they write to me about my last book, Old Age, deplore my pessimism. Both these labels are oversimplified.
[…]
My natural bent certainly does not lead me to suppose that the worst is always inevitable. Yet I am committed to looking reality in the face and speaking about it without pretense… It is just because I loathe unhappiness and because I am not given to foreseeing it that when I do come up against it I am deeply shocked or furiously indignant — I have to communicate my feelings. To fight unhappiness one must first expose it, which means that one must dispel the mystifications behind which it is hidden so that people do not have to think about it. It is because I reject lies and running away that I am accused of pessimism; but this rejection implies hope — the hope that truth may be of use. And this is a more optimistic attitude than the choice of indifference, ignorance or sham.
If the ancient Arab world had closed its gates to foreign travelers, we would have no medicine, no astronomy, and no mathematics — at least not as we know them today.
Central to humanity’s quest to grasp the nature of the universe and make sense of our own existence is zero, which began in Mesopotamia and spurred one of the most significant paradigm shifts in human consciousness — a concept first invented (or perhaps discovered) in pre-Arab Sumer, modern-day Iraq, and later given symbolic form in ancient India. This twining of meaning and symbol not only shaped mathematics, which underlies our best models of reality, but became woven into the very fabric of human life, from the works of Shakespeare, who famously winked at zero in King Lear by calling it “an O without a figure,†to the invention of the bit that gave us the 1s and 0s underpinning my ability to type these words and your ability to read them on this screen.
Mathematician Robert Kaplan chronicles nought’s revolutionary journey in The Nothing That Is: A Natural History of Zero ( public library). It is, in a sense, an archetypal story of scientific discovery, wherein an abstract concept derived from the observed laws of nature is named and given symbolic form. But it is also a kind of cross-cultural fairy tale that romances reason across time and space 
Art by Paul Rand from Little 1 by Ann Rand, a vintage concept book about the numbers
Kaplan writes:
If you look at zero you see nothing; but look through it and you will see the world. For zero brings into focus the great, organic sprawl of mathematics, and mathematics in turn the complex nature of things. From counting to calculating, from estimating the odds to knowing exactly when the tides in our affairs will crest, the shining tools of mathematics let us follow the tacking course everything takes through everything else – and all of their parts swing on the smallest of pivots, zero
With these mental devices we make visible the hidden laws controlling the objects around us in their cycles and swerves. Even the mind itself is mirrored in mathematics, its endless reflections now confusing, now clarifying insight.
[…]
As we follow the meanderings of zero’s symbols and meanings we’ll see along with it the making and doing of mathematics — by humans, for humans. No god gave it to us. Its muse speaks only to those who ardently pursue her.
With an eye to the eternal question of whether mathematics is discovered or invented — a question famously debated by Kurt Gödel and the Vienna Circle — Kaplan observes:
The disquieting question of whether zero is out there or a fiction will call up the perennial puzzle of whether we invent or discover the way of things, hence the yet deeper issue of where we are in the hierarchy. Are we creatures or creators, less than – or only a little less than — the angels in our power to appraise?
Like all transformative inventions, zero began with necessity — the necessity for counting without getting bemired in the inelegance of increasingly large numbers. Kaplan writes:
Zero began its career as two wedges pressed into a wet lump of clay, in the days when a superb piece of mental engineering gave us the art of counting.
[…]
The story begins some 5,000 years ago with the Sumerians, those lively people who settled in Mesopotamia (part of what is now Iraq). When you read, on one of their clay tablets, this exchange between father and son: “Where did you go?†“Nowhere.†“Then why are you late?â€, you realize that 5,000 years are like an evening gone.
The Sumerians counted by 1s and 10s but also by 60s. This may seem bizarre until you recall that we do too, using 60 for minutes in an hour (and 6 × 60 = 360 for degrees in a circle). Worse, we also count by 12 when it comes to months in a year, 7 for days in a week, 24 for hours in a day and 16 for ounces in a pound or a pint. Up until 1971 the British counted their pennies in heaps of 12 to a shilling but heaps of 20 shillings to a pound.
Tug on each of these different systems and you’ll unravel a history of customs and compromises, showing what you thought was quirky to be the most natural thing in the world. In the case of the Sumerians, a 60-base (sexagesimal) system most likely sprang from their dealings with another culture whose system of weights — and hence of monetary value — differed from their own.
Having to reconcile the decimal and sexagesimal counting systems was a source of growing confusion for the Sumerians, who wrote by pressing the tip of a hollow reed to create circles and semi-circles onto wet clay tablets solidified by baking. The reed eventually became a three-sided stylus, which made triangular cuneiform marks at varying angles to designate different numbers, amounts, and concepts. Kaplan demonstrates what the Sumerian numerical system looked like by 2000 BCE:
This cumbersome system lasted for thousands of years, until someone at some point between the sixth and third centuries BCE came up with a way to wedge accounting columns apart, effectively symbolizing “nothing in this column†— and so the concept of, if not the symbol for, zero was born. Kaplan writes:
In a tablet unearthed at Kish (dating from perhaps as far back as 700 BC), the scribe wrote his zeroes with three hooks, rather than two slanted wedges, as if they were thirties; and another scribe at about the same time made his with only one, so that they are indistinguishable from his tens. Carelessness? Or does this variety tell us that we are very near the earliest uses of the separation sign as zero, its meaning and form having yet to settle in?
But zero almost perished with the civilization that first imagined it. The story follows history’s arrow from Mesopotamia to ancient Greece, where the necessity of zero awakens anew. Kaplan turns to Archimedes and his system for naming large numbers, “myriad†being the largest of the Greek names for numbers, connoting 10,000. With his notion of orders of large numbers, the great Greek polymath came within inches of inventing the concept of powers, but he gave us something even more important — as Kaplan puts it, he showed us “how to think as concretely as we can about the very large, giving us a way of building up to it in stages rather than letting our thoughts diffuse in the face of immensity, so that we will be able to distinguish even such magnitudes as these from the infinite.â€
“Archimedes Thoughtful†by Domenico Fetti, 1620
This concept of the infinite in a sense contoured the need for naming its mirror-image counterpart: nothingness. (Negative numbers were still a long way away.) And yet the Greeks had no word for zero, though they clearly recognized its spectral presence. Kaplan writes:
Haven’t we all an ancient sense that for something to exist it must have a name? Many a child refuses to accept the argument that the numbers go on forever (just add one to any candidate for the last) because names run out. For them a googol — 1 with 100 zeroes after it — is a large and living friend, as is a googolplex (10 to the googol power, in an Archimedean spirit).
[…]
By not using zero, but naming instead his myriad myriads, orders and periods, Archimedes has given a constructive vitality to this vastness — putting it just that much nearer our reach, if not our grasp.
Names belong to things, but zero belongs to nothing. It counts the totality of what isn’t there. By this reasoning it must be everywhere with regard to this and that: with regard, for instance, to the number of humming-birds in that bowl with seven — or now six — apples. Then what does zero name? It looks like a smaller version of Gertrude Stein’s Oakland, having no there there.
Zero, still an unnamed figment of the mathematical imagination, continued its odyssey around the ancient world before it was given a name. After Babylon and Greece, it landed in India. The first surviving written appearance of zero as a symbol appeared there on a stone tablet dated 876 AD, inscribed with the measurements of a garden: 270 by 50, written as “27°†and “5°.†Kaplan notes that the same tiny zero appears on copper plates dating back to three centuries earlier, but because forgeries ran rampant in the eleventh century, their authenticity can’t be ascertained. He writes:
We can try pushing back the beginnings of zero in India before 876, if you are willing to strain your eyes to make out dim figures in a bright haze. Why trouble to do this? Because every story, like every dream, has a deep point, where all that is said sounds oracular, all that is seen, an omen. Interpretations seethe around these images like froth in a cauldron. This deep point for us is the cleft between the ancient world around the Mediterranean and the ancient world of India.
But if zero were to have a high priest in ancient India, it would undoubtedly be the mathematician and astronomer Āryabhata, whose identity is shrouded in as much mystery as Shakespeare’s. Nonetheless, his legacy — whether he was indeed one person or many — is an indelible part of zero’s story.
Ä€ryabhata (art by K. Ganesh Acharya)
Kaplan writes:
Āryabhata wanted a concise way to store (not calculate with) large numbers, and hit on a strange scheme. If we hadn’t yet our positional notation, where the 8 in 9,871 means 800 because it stands in the hundreds place, we might have come up with writing it this way: 9T8H7Te1, where T stands for ‘thousand’, H for “hundred†and Te for “ten†(in fact, this is how we usually pronounce our numbers, and how monetary amounts have been expressed: £3.4s.2d). Āryabhata did something of this sort, only one degree more abstract.
He made up nonsense words whose syllables stood for digits in places, the digits being given by consonants, the places by the nine vowels in Sanskrit. Since the first three vowels are a, i and u, if you wanted to write 386 in his system (he wrote this as 6, then 8, then 3) you would want the sixth consonant, c, followed by a (showing that c was in the units place), the eighth consonant, j, followed by i, then the third consonant, g, followed by u: CAJIGU. The problem is that this system gives only 9 possible places, and being an astronomer, he had need of many more. His baroque solution was to double his system to 18 places by using the same nine vowels twice each: a, a, i, i, u, u and so on; and breaking the consonants up into two groups, using those from the first for the odd numbered places, those from the second for the even. So he would actually have written 386 this way: CASAGI (c being the sixth consonant of the first group, s in effect the eighth of the second group, g the third of the first group)…
There is clearly no zero in this system — but interestingly enough, in explaining it Ä€ryabhata says: “The nine vowels are to be used in two nines of places†— and his word for “place†is “khaâ€. This kha later becomes one of the commonest Indian words for zero. It is as if we had here a slow-motion picture of an idea evolving: the shift from a “named†to a purely positional notation, from an empty place where a digit can lodge to “the empty numberâ€: a number in its own right, that nudged other numbers along into their places.
Kaplan reflects on the multicultural intellectual heritage encircling the concept of zero:
While having a symbol for zero matters, having the notion matters more, and whether this came from the Babylonians directly or through the Greeks, what is hanging in the balance here in India is the character this notion will take: will it be the idea of the absence of any number — or the idea of a number for such absence? Is it to be the mark of the empty, or the empty mark? The first keeps it estranged from numbers, merely part of the landscape through which they move; the second puts it on a par with them.
|
Forward to a friend
Facebook
Twitter
Instagram
Tumblr
No comments:
Post a Comment
Please leave a comment-- or suggestions, particularly of topics and places you'd like to see covered