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The Social Life of Numbers: A Quechua Ontology of Numbers and Philosophy of Arithmetic
Gary Urton
I wanted to like this - I really did. But, it was boring and narrow and academic and literal and not really much fun.

The Grace of Great Things
Robert Grudin
Wonderfully written. Richly quotable. Speaks to me -- and makes me feel good. Problem: Grudin seems to want TOO much to believe that creativity is a journey that can only be truly undertaken and experienced by the virtuous. I know some evil geniuses and while I do feel a sense of the spiritual in connection with creative acts, it isn't clear that it is accessible only through virtue. It may be that one must tap into another plane of existence but it may also be that that plane is home to demons as well as angels. While we may and should pursue creation as a source of spiritual growth, it seems shallow to interpret creative skills as de facto evidence of goodness.

God's Secret Formula
Peter Plichta
Unrecognized genius? Hoax? Insanity? Paranoid conspiracy theories. Numerology gone amuck? Regardless of conclusion, a strange little book. Not written by any dummy. Exhaustively researched. Bizarrely self-referential (second only to Checkett's, a Rainbow to Share).

"A concept of the physical world can only be accurate to the degree permitted by the contemporary state of mathematics - a fact well known to all major thinkers of previous centuries. Today almost nobody is aware of it."

"The full extent of lies and distortions under the totalitarian Communist regimes was overwhelming. However, because no sound intellectual preparation had been made, the collapse of the system only brought the freedom to adopt the capitalist system. Perhaps now the question arises as to whether capitalism is not also doomed to extinction. It was quite clear to the three of us that the materialistic and rapacious capitalism prevailing in the West poses real danger sot humanity."

"It is perhaps characteristic that scarcely any physicist or chemist with the title of doctor has any knowledge of this limit of ten (maximum number of isotopes for any element). We are deliberately kept in the dark about the basic fact that there can be no more than ten isotopes because the number ten appears a bit too mystical for some people in high places."

"The number 81 is… (3^4). The numbers 3, 4, and 81 had been on my mind for years… If God has simply arranged the 81 elements according to the ordinal numbers 1,2,3,4…81, researchers would have discovered thi sfact long ago. (Bismuth has atomic number 83, but two elements are unstable and do not occur naturally)." (Then, there's a bunch of stuff about the reciprocal of 81, which does indeed have some unusual properties (accepting his math at face value)). "But could these durations of orbit - 27,32 days for the moon and 366 days per leap year for the earth - be only an expression of the reciprocal connection between these dual planets? (1/27.32 = 0.03660… and 1/366=0.002732). "It was a crime of literally astronomical proportions to hide this fact from the public… It seemed that nobody had had enough courage to publish a fact which could cast doubt on the power of coincidence."

(I have picked selective passages that may exaggerate the strangeness of the conclusions and theories. Such statements are sprinkled among rational, lucid, and scientifically accurate text.)

"I took up the phone and called the Technische Hochschule in Munich and asked for Professor Fischer. I then told him briefly about… my current ideas on the porphyrin ring of haemes as quadrupole magnets. Professor Fischer answered with the voice of excitement that only a passionate chemist has when he hears something new. My idea was the most astounding that he had ever heard in his life. I then told him how many years I had been try8ing to get behind the secret of the two missing elements of the periodic table, which had always appeared to me to be something of a mute warning, but which had been very cleverly avoided by our thick textbooks. "Are you telling me, Mr Plichta, that you have discovered something gin this field? As you know, the elements are the basis of all science." "Yes, it is linked to the basis of mathematics, the prime numbers, and the geometry of space. What I have discovered is in fact very simple, although nobody is prepared for it… I outlined my belief that at some time in the future, the Pythagorean notion that everything is number and Kepler's notion that everything is geometry would finally be accepted."

"One day around noon, at the end of February, I received a telephone call form Professor Fischer. His voice sounded very agitated. "Mr. Plichta, I have been in touch with Mr. Mossbauer and told him that the two of us wanted to c him to something new, and that there was some need for caution in this regard. He wanted to know whether your discovery would raise doubts about quantum mechanics. I told him that quantum mechanics would not even exist if what you discovered turned out to be true if what you discovered turned out to be true. Quantum mechanics would then simply turn out to be a figment of the imagination. My colleague, Mossbauer, then got very angry and accused me of putting everything we have accomplished at risk. Our great achievement, modern physics, was the result of tremendous efforts, and now everything would collapse should any doubts arise. Such people as yourself should not be given support under any circumstances. He refuse to meet you. He does even want to hear any of the new ideas. He gave mea very serious warning indeed."

(This is a very doubtful exchange. Hard to conceive of either Fischer or Mossbauer (or any respectable scientist) uttering such words. Easy to imagine them condemning Plichta as a crackpot but not as the architects of a great conspiracy.)

The book concludes thus: "An important author of technical books, Professor Hoimar von Ditfurth, had died a few years previously, and in an interview recorded shortly before his death he had spoken of his passionate wish to cast a glance behind the "great curtain." …

"Mr. Plichta, are you telling me that von Ditfurth was convinced that there was a secret puzzle hidden behind this world?" …

"The significance of the prime numbers in the resolution of cosmic theory." "Could you tell me in one sentence what is the real significance of your scientific work?"

"It was a decisive mistake that science began to interpret numbers as a human invention approximately one hundred years ago, just so that mysticism could be expelled form science and mathematics. In this way God was also expelled from nature… I can, however, prove that there is a divine structural plan behind this world. In this way the Big Bang and the apparently coincidental creation of life will be consigned to a period of our history from which we have now emerged. No great stretch of the imagination to guess the effect this will have on the book market."

"We will then use the means in our power to make sure this book reaches our readers. Go and write the book!"

Weird. Too weird. "The book market!" I see no adverse implications for quantum or cosmology. Think I'll stick with the conventional wisdom a while yet, but may leave a neuron or two wondering how much coincidence there is in some of his number games. It is true that there are some real numerical mysteries. The fine constant of 1/137. 137! Where'd that come from? The ratios of the four physical forces? We have to be honest and say that our present theories have a certain bricolage feel to them. I actually do tend to concur with Plichta that mathematics and geometry underpin our world or at least the way the matrix is perceived.

Seeing Like a State
James C. Scott
Could be subtitled, "Seeing Like a Corporation." Actually, it reflects the errors oftne perpetrated in the name of improvement by virtually any powerful monolithic entity. Of course, it would be nice if we could learn form history, but the lesson we are most likely to learn from history is that we can't. Perhaps we can at least become conscious of our own folly and temper its effects.

"... the most tragic episodes of state-initiated social engineering originate in a pernicious combination of four elements... first... the administrative ordering of society... second... a high-modernist ideology... third... an authoritarian state... fourth... a prostrate civil society."

"Designed or planned social order is necessarily schematic; it always ignores essential features of any real, functioning social order. This truth is best illustrated in the work-to-rule strike, which turns on the fact that any production process dependes on a host of informal practices and improvisations that could never be codified. By merely following the rules meticulously, the workforce can virtually halt production."

"The grid facilitated the commoditization of land as much as the calculation of taxes and boundaries. Administratively, it was also disarmingly simple. Land could be registered and titled from a distance by someone who possessed virtually no local knowledge... The more homogenous and rigid the geometric grid, however, the more likely it was to run afoul of the natural features of the non-comforming landscape."

"And the College of Cartographers set up a Map of the Empire which had the size of the Empire itslef and coincided with it point by point... Succeeding generations understood that this Widespread Map was Useless, and not without Impiety they abandoned it to the Inclemencies of the Sun and the Winters. --Suarez Miranda, Viajes de varones prudentes (1658)"

"States and city planners have striven, as one might expect, to overcome this spatial unintelligibility and to make urban geography transparently legible from without... Other things being equal, the city laid out according to a simple, repetitive logic will be easier to administer and to police."

"Legibility implies a viewer whose place is central and whose vision is synoptic. State simplifications of the kind we have examined are designed to provide authorities with a schematic view of their society, a view not afforded to those without authority... This priveleged vantage point is typical of all institutional settings where command and control of complex human activities is paramout. The monastery, the barracks, the factory floor, and the administrative bureaucracy exercise many statelike functions and often mimic its information structure as well."

"...Brasilia lacks the bustle of street life... it is almost as if the founders of Brasilia, rather than having planned a city, have actually planned to prevent a city... The plan did eliminate traffic jams; it also eliminated the welcome and familiar pedestrian jams that one of Holson's informants called the 'point of social conviviality'... They use the term 'brasilite' (Brasilia-itis) to refer to their feelings about a daily life without the pleasures -- the distractions, conversations, flirtations, and little rituals -- of outdoor life in other Brazilian cities... Compared to life in Rio and Sao Paulo with their color and variety, the daily round in bland, repetitive Brasilia must have resembled life in a sensory deprivation chamber. The recipe for high-modernist urban planning, while it may have created formal order and functional segregation, did so at the cost of a sensorily impoverished and monotonous environment -- an environment that inevitably took its toll on the spirits of its residents."

Notes on Synthesis of Form
Christopher Alexander
Deep design. Readable on at least three levels: architect's manual, design and function, purposefulness.

"Rather than face the responsibility of these difficult questions, designers turned instead to authority of resurrected "styles." The architectural decisions made within a style are safe from the nagging difficulty of doubt, for the same reason that decisions are easier to make under tradition and taboo than on one's own responsibility."

"We must face the fact that we are on the brink of times when man may be able to magnify his intellectual and inventive capability, just as in the nineteenth century he used machines to magnify his physical capability… as then, our innocence is lost… the loss demands attention, not denial."

"… every design problem begins with an effort to achieve fitness between two entities: the form in question and its context."

"We want to put the context and the form into effortless contact or frictionless coexistence."

"The experiment of putting a prototype form in the context itself is the real criterion of fit. A complete unitary description of the demands made by the context is the only fully adequate nonexperimental criterion. The first is too expensive, the second is impossible: so what shall we do?"

"With the invention of a teachable discipline called architecture (management), the old process of making form (leadership) was adulterated and its chance of success destroyed." (italics added)

"The search for realization through constructive diagrams is an effort to understand the required form so fully that there is no longer a rift between its functional specification and the shape it takes." "A design problem is NOT an optimization problem." (emphasis added)

Thus Spoke Zarathustra
Friedrich Nietzsche
Translated by Walter Kaufmann

To become more than an all-too-human animal man must become a creator… (through a) break with previous norms.

Our traditional virtues consecrate stereotyped mediocrity and make for sound sleep. The more he aspires to the height and light, the more strongly do his roots strive earthward, downward into the dark, the deep -- into evil.

…your industry is escape and the will to forget yourselves. If you believed more in life, you would fling yourselves less to the moment. But you do not have contents enough in yourselves for waiting – and not even for idleness.

Behold the superfluous! They steal the works of the inventors and the treasures of the sages for themselves; education they call their theft…

Flee my friend into your solitude! …Where solitude ceases the market place begins; and where the market place begins the noise of the great actors and the buzzing of the poisonous flies begins too.

Little do the people comprehend the great – that is, the creating. But they have a mind for all showmen and actors of great things. …and the people pride themselves on their great men, their masters of the hour. But the hour presses them; so they press you. And from you they want a Yes or No. Do not be jealous of these unconditional, pressing men, you lover of truth! Never has truth hung on the arm of the unconditional. Slow is the experience of all deep wells: long must they wait before they know what fell into their depth.

Far from the market place and from fame happens all that is great: far from the market place and from fame the inventors of new values have always dwelt. Flee my friend, into your solitude: I see you stung all over by poisonous flies. No longer raise up your arm against them. Numberless are they, and it is not your lot to shoo flies. Numberless are these small and miserable creatures; and many a proud building has perished of raindrops and weeds. You are no stone, but you have already become hollow from many drops. I see you wearied by poisonous flies, bloody in a hundred places; and your pride refuses even to be angry.

Blood is what they want from you in all innocence. But you, deep one, suffer too deeply even from small wounds; and even before you have healed, the poisonous worm crawls across your hand. You are too proud to kill these greedy creatures. But beware lest it become your downfall that you suffer all their poisonous injustice.

They hum around you with their praise too: obtrusiveness is their praise. They flatter you as a god or devil; they whine before you as before a god or devil. What does it matter? They are flatterers and whiners. And nothing more.

Often they affect charm. But that has always been the cleverness of cowards. Indeed, cowards are clever! They think a lot about you with their petty souls – you always seem problematic to them. They punish you for all your virtues. They forgive you entirely – your mistakes. Because you are gentle and just in disposition you say, “They are guiltless in their small existence.” But their petty souls think, “Guilt is every great existence.” …they are jubilant if for once you are modest enough to be vain.

Flee my friend into your solitude and where the air is raw and strong. It is not your lot to shoo flies.

A biographical sketch of Cantor and his work, particularly as it lead to his discovery and exploration of transfinite numbers. Cantor was hardly accepted in the inner circle of German mathematicians and spent his professional days in battle with Kronecker, an outstanding mathematician but one hidebound by limited vision.

Quoted from Plato's Republic: "Arithmetic has a very great and elevating effect, compelling the mind to reason about abstract number."

"The Kabbalist reads the Torah on four levels: Peshat (literal), Remez (homiletical), Derash (allegorical), and finally Sod (secret)… The letter aleph represents the infinite nature, and the oneness, of God."

"An infinite set can be "'equal' in number of elements to a smaller subset of itself - a set included as a smaller part of the original set. Infinity is an intimidating concept - one where our everyday intuition no longer serves to guide us."

"The rational numbers can be enumerated, or counted off, even though they are infinite. The irrational numbers are so infinite that they cannot be enumerated…"

"While algebraic and rational numbers are infinite, the transcendental numbers are of a higher order of infinity. If you could randomly choose a number on the real line, the number will be transcendental with probability one… Whether one could actually choose a number form an infinite collection of numbers is an important question…"

"There are just as many points on a plane as on a line… As far as infinity goes, dimension does not matter."

"Cantor advocated a doctrine of open exploration of new concepts and ideas… On the other hand, the mathematics of Kronecker and his followers was safe but benighted… Cantor believed that their arbitrary restrictions impeded the growth of the field… A few years earlier, he (Cantor) had been a student, and Kronecker and his colleagues were his teachers. From their point of view, he should have been shaped in their image, and he had no right to challenge his teachers' philosophy."

"Is there another cardinal number, another aleph, that lies between aleph-zero and the cardinal number of the continuum?"

"We know that the continuum hypothesis has no solution within our system of mathematics."