Drums That Talk
See first link above.
The Persistence of the Word
"In our world of ingrained literacy, thinking and writing seem scarcely related activities. We can imagine the latter (writing) depending on the former (thinking), but surely not the other way around (we cannot image thinking depending on writing): everyone thinks, whether or not they write. But Havelock was right. The written word -- the persistent word -- was a prerequisite for conscious thought as we understand it. It was the trigger for a wholesale, irreversible change in human psyche -- psyche being the word favored by Socrates/Plato as they struggled to understand."
By the way, that paragraph, I think explains why I like Virginia Woolf. She was trying to understand "thinking" and the "written word."
Paradoxes of "words:"
"Horses certainly have color. Hence, there are white horse. If it were the case that horses had no color, there would simply be horses, and then how could one select a white horse? A white horse is a horse and white. A horse and a white horse are different. Hence, I say that a white horse is not a horse."
One way to eliminate ambiguous words and wooly syntax, employ symbols that were rigorous and pure. To turn, that is, to mathematics. Because of these paradoxes of words, by the beginning of the 20th century, it seemed that only a system of purpose-built symbols could make logic work properly -- free of error and paradoxes. This dream was to prove illusory; the paradoxes would creep back in, but no one could hope to understand until the paths of logic and mathematics converged. -- p. 41And, for the first time I get it. Bertrand Russell: philosopher, logician, mathematician.
Mathematics, too, followed from the invention of writing. -- p. 41
Virginia Woolf taught herself Greek. She enjoyed Aristotle. Her sister, Vanessa, was an accomplished painter. Virginia felt that she painted with words; Vanessa painted with oils. And then this in Gleik:
I cannot help feeling, Paedrus, [says Socrates] that writing is unfortunately like painting; for the creations of the painter have the attitude of life, and yet if you ask them a questions they preserve a solemn silence ... You would imagine that they had intelligence, but if you want to know anything and put a question to one of them, the speaker always gives one unvarying power. -- p . 47
Chapter 4: To Throw the Powers of Though into Wheel-Work
The story of Charles Babbage, 1850's, and his aide, Augusta Ada Byron King (who always signed her notes to Charles with "A.A.L"), the daughter of Lord Byron who abandoned this daughter, and never saw her after her birth. The chapter is another incredible chapter, and reminds us again why Islam never left the 15th century: they marginalized one-half of their populace. Their children, sons and daughters, are raised by the members of their society who are not allowed to get an education.
Ms AAL came up with the definition of "operation." She defined an operation "as any process which alters the mutual relation of two or more things." Incredible. And she went further. The science of operations, as she conceived it,
is a science of itself, and has its own abstract truth and value; just as logic has its own peculiar truth and value, independently of the subjects to which we may apply its reasonings and processes ... One main reason why the separate nature of the science of operations has been little felt, and in general little dwelt on, is the shifting meaning of many of the symbols used.Wow, symbols and meaning. She was more prescient than Charles Babbage.
I just love the way they wrote in those days, and I love the way A.A.L. wrote, while struggling with sickness and ominous pains, her mind soaring (as Gleick says):
That brain of mine is something more than merely mortal; as time will show; (if only my breathing & some et-ceteras do not make too rapid a progress towards instead of from mortality).
Before ten years are over, the Devil's in it if I have not sucked out some of the life-blood from the mysteries of this universe, in a way that no purely mortal lips or brains could do.
No one knows what almost awful energy & power lie yet undeveloped in that wiry little system of mine. I say awful, because you may imagine what it might be under certain circumstances ...
I am doggedly attacking & sifting to the very bottom, all the ways of deducing the Bernoulli Numbers ... I am grappling with this subject, & connecting with others.
Chapter 5: A Nervous System for the Earth
Edgar Allan Poe -- p. 162
Augustus De Morgan and George Boole, p. 163
- Augustus De Morgan: Babbage's friend, Ada Byron's tutor, a professor at University College, London
- Boole: son of a cobbler and a lady's maid; a professor at Queen's College, Cork
- in 1847, they published separately and simultaneously books that amounted to the greatest milestone in the development of logic since Aristotle; the subject, esoteric as it was, had stagnated for centuries
- by post they exchanged ideas about converting language, or truth, into algebraic symbols
- Boole: only numbers allowed, he proposed, were zero and one, all or nothing
- until now, logic had belonged to philosophy; Boole was claiming possession on behalf of mathematics (again, Bertrand Russell)
- in doing so, he devised a new form of encoding
- wow
"Boole's influence was subtle and slow. He corresponded only briefly with Babbage; they never met. One of his champions was Lewis Carroll, who, at the very end of his life, a quarter century after Alice in Wonderland, wrote two volumes of instruction, puzzles, diagrams, and exercises in symbolic logic....As the century ended, Bertrand Russell paid George Boole and extraordinary compliment: "Pure mathematics was discovered by Boole, in a work which he called the Laws of Thought." It has been quoted often. What makes the compliment extraordinary is the seldom-quoted disparagement that follows on its heels:One might almost think Russell enjoyed paradoxes -- Gleick.
He (Boole) was also mistaken in supposing that he was dealing with the laws of thought: the question how people actually think was quite irrelevant to him, and if his book had really contained the laws of thought, it was curious that no one should have though in such a way before.
Chapter 6: New Wires, New Logic
Ranchers used barbed wire fences as telegraph wires.
This is the chapter on Claude Shannon. I love the biography that James Gleick provides. It's only a paragraph or two about Claude and his future wife, Norma Levor, an adventurous nineteen-year-old Radcliffe student from New York. It reminds me of my first soul mate, my coming of age. Like those two, my wife and I were married by judge, no ceremony, but not in Boston like Shannon-Levor but in Las Vegas).
The invention of writing had catalyzed logic, by making it possible to reason about reasoning -- p. 177
... and now, all these centuries later, logic was reanimated with the invention of machinery that could work upon symbols. In logic and mathematics, the highest forms of reasoning, everything seemed to be coming together. -- p. 177.
The baton of perfectly precise expression: Leibniz --> Babbage --> Boole --> Bertrand Russell and Alfred North Whitehead --> Shannon, Gödel, and John von Neumann.
Somewhere around page 178, the text became very, very difficult to understand as Gleick started to work through Bertrand Russell, and then Kurt Gödel who "praised Russell before burying him."
Then, just as I was ready to put the book away to attack it again some other day (it had become too difficult to follow), Gleick introduces the man at the center of my attention right now: Neumann Janos, a Hungarian who would emigrate to the US and become known as Johnny (or John) von Neumann.
John von Neumann and Albert Einstein, among the first faculty members of the newly formed Princeton IAS, invited Gödel to the institute. Gödel vacillated; he was not Jewish; but in the end, a mathematician was just as much in danger, and in a very roundabout way, Gödel made it to Princeton -- via the Trans-Siberian Railway, Japan, ship to San Francisco, and then railroad to New Jersey.
Claude Shannon had also arrived at the institute to spend a postdoctoral year.
The gene.
Watson, Crick.
Rosalind Francis not mentioned.
Jacques Monad: a biologist; shared the Nobel Prize for working out the role of messenger RNA; the earth as a biosphere
This is the chapter on Claude Shannon. I love the biography that James Gleick provides. It's only a paragraph or two about Claude and his future wife, Norma Levor, an adventurous nineteen-year-old Radcliffe student from New York. It reminds me of my first soul mate, my coming of age. Like those two, my wife and I were married by judge, no ceremony, but not in Boston like Shannon-Levor but in Las Vegas).
The invention of writing had catalyzed logic, by making it possible to reason about reasoning -- p. 177
... and now, all these centuries later, logic was reanimated with the invention of machinery that could work upon symbols. In logic and mathematics, the highest forms of reasoning, everything seemed to be coming together. -- p. 177.
The baton of perfectly precise expression: Leibniz --> Babbage --> Boole --> Bertrand Russell and Alfred North Whitehead --> Shannon, Gödel, and John von Neumann.
Somewhere around page 178, the text became very, very difficult to understand as Gleick started to work through Bertrand Russell, and then Kurt Gödel who "praised Russell before burying him."
Then, just as I was ready to put the book away to attack it again some other day (it had become too difficult to follow), Gleick introduces the man at the center of my attention right now: Neumann Janos, a Hungarian who would emigrate to the US and become known as Johnny (or John) von Neumann.
John von Neumann and Albert Einstein, among the first faculty members of the newly formed Princeton IAS, invited Gödel to the institute. Gödel vacillated; he was not Jewish; but in the end, a mathematician was just as much in danger, and in a very roundabout way, Gödel made it to Princeton -- via the Trans-Siberian Railway, Japan, ship to San Francisco, and then railroad to New Jersey.
Claude Shannon had also arrived at the institute to spend a postdoctoral year.
Chapter 8: The Information Turn
Claude Shannon
What an incredible chapter
Cybernetics, the title of Wiener's first book
Bloomsbury, p. 253; British scientists meeting; Ratio Club; about 15 people who had Wiener's ideas before Wiener's book appeared; met for the first time in the basement of the National Hospital for Nervous Diseases, in Bloomsbury
McCulloch, a series of conferences, Beekman Hotel, Park Avenue, NYC; funded by "money from the Josiah Macy Jr. Foundation, endowed in the 19th century by heirs of Nantucket whalers."
A host of sciences were coming of age all at once -- so-called social sciences, like anthropology and psychology, looking for new mathematical footing; medical offshoots with hybrid names, like neurophysiology; not-quite-sciences like psychoanalysis -- and McCulloch invited experts in all these fields, as well as mathematics and electrical engineering....among the core group the already famous anthropologist Margaret Mead...recording the proceedings in a shorthand no one else could read, ....
Chapter 9: Entropy and Its Demons
Chapter 10: Life's Own Code
Chapter 10: Life's Own Code
The gene.
Watson, Crick.
Rosalind Francis not mentioned.
Chapter 11: Into the Meme Pool
Jacques Monad: a biologist; shared the Nobel Prize for working out the role of messenger RNA; the earth as a biosphere
Chapter 12: A Sense of Randomness
Complexity:
the complexity of an object is the size of the smallest computer
program needed to generate it. [The immediate problem: how do you define
a program; what is included in the program; embedded small programs?]
-- p. 337
But it's things like this that fascinate me about number theory, on page 339:
One who did not forget -- or who rediscovered it -- was John Archibald Wheeler, pioneer of nuclear fission, student of Bohr and teacher of Feynman, namer of black holes, the last giant of 20th-century physics. Wheeler was given to epigrams and gnomic utterances. A black hole has no hair was his famous way of stating that nothing but mass, charge, and spin can be perceived from outside.....In 1989 he offered his final catchphrase: It from Bit. His view was extreme. It was immaterialist: information first, everything else later. "Otherwise put," he said, "every it -- every particle, every field of force, even the space-time continuum itself -- derives its function, its meaning, its very existence ... from bits."
The black hole.
E=M
In a black hole, (T)ime = (S)pace -- p. 357.
A great bet that Stephen Hawking lost -- with grace. -- p. 359. The prize to the winner, John Preskill at California Institute of Technology: a copy of Total Baseball: The Ultimate Baseball Encyclopedia, weighing in at 2,688 pages.
At p. 367: "The puzzle of spooky action at a distance has not been altogether resolved. Nonlocality has been demonstrated in a variety of clever experiments all descended from the EPR thought experiment. Entanglement turns out to be not only real but ubiquitous. The atom pair in every hydrogen molecule, H2, is quantumly entangled. Bennett put entanglement to work in quantum teleportation across an arbitrary distance..... quantum computing.
This is the challenge that remains, and not just for scientists: the establishment of meaning. -- p 372
Information overload.
Kolmogorov: laid the groundwork for the renaissance in chaos theory to come in the 1970s
But it's things like this that fascinate me about number theory, on page 339:
Number theorists name entire classes of interesting numbers: prime numbers, perfect numbers, squares and cubes, Fibonacci numbers, factorials.
The number 593 is more interesting than it looks. It happens to be the sum of nine squared and two the ninth -- thus a "Leyland number" (any number that can be expressed xy + yx).
Wikipedia also devotes an entire article to the number 9,814,072,356. It is the largest holodigital square -- which is to say, the largest square number containing each decimal exactly once. [The square root can be found here: 99066.]
*********************
Of more relevance, perhaps, from page 347, in the chapter on randomness:Photographs are compressible because of their subjects' natural structure: light pixels and dark pixels come in clusters; statistically, nearby pixels are likely to be similar; distant pixels are not. Video is even more compressible, because the differences between one frame and the next are relatively slight, except when the subject is in fast and turbulent motion. Natural language is compressible because of redundancies [f u cn rd ths] and regularities...Only a wholly random sequence remains incompressible; nothing but one surprise after another [earlier, it was said, information = surprise].From p. 342:
Chaitin spent the rest of his career at the IBM Watson Research Center, one of the last great scientists to be so well supported in work of no plausible use to his corporate patron. He sometimes said he was "hiding" in a physics department; he felt that more conventional mathematicians dismissed him as "a closet physicist" anyway. His work treated mathematics as a sort of empirical science -- not a Platonic pipeline to absolute truth, but a research program subject to the world's contingencies and uncertainties.
Chapter 13: Information Is Physical
One who did not forget -- or who rediscovered it -- was John Archibald Wheeler, pioneer of nuclear fission, student of Bohr and teacher of Feynman, namer of black holes, the last giant of 20th-century physics. Wheeler was given to epigrams and gnomic utterances. A black hole has no hair was his famous way of stating that nothing but mass, charge, and spin can be perceived from outside.....In 1989 he offered his final catchphrase: It from Bit. His view was extreme. It was immaterialist: information first, everything else later. "Otherwise put," he said, "every it -- every particle, every field of force, even the space-time continuum itself -- derives its function, its meaning, its very existence ... from bits."
The black hole.
E=M
In a black hole, (T)ime = (S)pace -- p. 357.
A great bet that Stephen Hawking lost -- with grace. -- p. 359. The prize to the winner, John Preskill at California Institute of Technology: a copy of Total Baseball: The Ultimate Baseball Encyclopedia, weighing in at 2,688 pages.
At p. 367: "The puzzle of spooky action at a distance has not been altogether resolved. Nonlocality has been demonstrated in a variety of clever experiments all descended from the EPR thought experiment. Entanglement turns out to be not only real but ubiquitous. The atom pair in every hydrogen molecule, H2, is quantumly entangled. Bennett put entanglement to work in quantum teleportation across an arbitrary distance..... quantum computing.
This is the challenge that remains, and not just for scientists: the establishment of meaning. -- p 372
Chapter 14: After The Flood
Chapter 15: New News Every Day
Information overload.
Epilogue
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