Newton
These are my notes from “The Life of Isaac Newton” by R.S. Westfall.
Childhood
Question: How come Newton invented calculus and made great scientific discoveries if he hadn’t even come across them in grammar school? Why didn’t anybody else do it?
The reader in the twentieth century, surrounded by the achievements of modern mathematics and the material culture it has generated, can scarcely believe that the man who would discover the calculus four years after he left grammar school was probably not even introduced there to the already thriving mathematical culture out of which the calculus would come. Neither is there any suggestion that he studied natural philosophy.
Genius?
Although they do not appear in his notes, most of his devices remembered in Grantham, including a windmill, were described in the book. Perhaps Newton’s adolescent genius shrinks a little in the light of Bate’s book.
Experimental Inquiries
Observation: Newton thought of experimental consequences of theories he read in books.
Observe if ye sea water rise not in days & fall at nights by reason of ye earth pressing from O uppon ye night water &c. Try also whither ye water is higher in mornings or evenings to know whither 0 [earth] or its vortex press forward most in its annuall motion …. Try whither ye seas flux & reflux bee greater in Spring or Autume in winter or Sommer by reason of ye 0s Aphelion & perihelion. Whither ye Earth moved out of its Vortexes center bye Moones pression cause not a monethly Parallax in Mars. &c.
– The Life of Isaac Newton, pg 28
To test the power of fantasy, he looked at the sun with one eye until all pale bodies seen with that eye appeared red and dark ones blue. After “v*1 motion of ^ spirits in my eye were almost decayed" so that things were beginning to appear normal, he closed his eye and “heightned [his] fantasie” of seeing the sun. Spots of various hues appeared to his eye, and when he opened it again pale bodies appeared red and dark ones blue as though he had been looking at the sun. He concluded that his fantasy was able to excite the spirits in his optic nerve quite as well as the sun.
– The Life of Isaac Newton, pg 28
Taboo “Genius”
What do you mean by “genius”? Which cognitive activities by Newton during college or during his miracle years constitute genius?
Did he read a book twice as fast anybody else? Did he remember it far better than others? Did he solve math problems faster?
If discovering something original is the only criterion you have for genius, then you raise the bar for later geniuses. How is a 20th century Newton supposed to discover the laws of motion? (He could if he never learned them in school.)
Hypothesis: The definition of genius should include only mental horsepower, problem-solving strategies, and domain-specific knowledge.
Two people with the same problem-solving ability should be considered as having the same level of genius.
Why care? Because the default definition of genius puts great achievements out of reach of people who haven’t yet been anointed. If you knew that you had the same mental horsepower as Hooke or Faraday, you could go forth and try to solve the important problems you need to solve. Otherwise, you might shrink away citing your lack of genius.
Focussing only on his Identity
Indeed, with 1664 Newton faced a crisis. Trinity held elections to scholarships only every three or four years. The election in 1664 was the only one during his career as a student. If Newton were not elected then, all hope of permanent residence in Cambridge would vanish forever. He chose exacdy that time to throw over the recognized studies and pursue a course that had no standing whatever in the college’s scheme of values.
– The Life of Isaac Newton, pg 33
He could abandon himself completely to the studies he had found. The capacity Newton had shown as a schoolboy for ecstasy, total surrender to a commanding interest, now found in his early manhood its mature intellectual manifestation. The tentativeness suggested by the earlier unfinished notes vanished, to be replaced by the passionate study of a man possessed. Such was the characteristic that his chamber-fellow Wickins remembered, having observed it no doubt at the time with the total incomprehension of the Woolsthorpe servants. Once at work on a problem, he would forget his meals. His cat grew very fat on the food he left standing on his tray.
– The Life of Isaac Newton, pg 35 (bolding mine)
One Problem at a Time
When we examine Newton’s grandiose adventure minutely, it turns out to be a mixture of discrete pieces rather than a homogeneous melange. His career was episodic. What he thought on, he thought on continually, which is to say exclusively, or nearly exclusively. What seized his attention in 1664, to the virtual exclusion of everything else, was mathematics.
– The Life of Isaac Newton, pg 40
Why Not Before?
Observation: Newton needed to read Descartes’ Geometry and modern analysis. That was his leverage, his competitive advantage.
Newton’s Level
“Your letter,” he wrote to Oldenburg immediately upon its receipt, “contains more numerous and more remarkable ideas about analysis than many thick volumes published on these matters ….
– Liebniz about Newton’s letter, pg 99
Quaestiones quaedam philosophicae (Certain Philosophical Questions)
He lists a bunch of questions he wants to answer:
Whither the conjunction of bodys be from rest: Neg: For then sand by rest might be united sooner than by a furnace &c
Why though both a dry bladder & water are perspicuous yet a wet blader is not. though oyle bee les diaphaneous than water yet it makes a paper more diaphaneous than it.
Why refraction is less in hot water than cold
Whither the parts of air be les than them of light or no.
Why light passeth easlier through white than black paper. & yet more efficaciously reflected from it.
The senses of divers men are diversly affected by the same objects according to the diversity of theire constitution To them of Java pepper is cold. [Ed: This made me LOL. Don’t know why.]
Why doth quicksilver sinke so readily into mettalls & into nothing else.
Of colours:
Try if two Prismas the one casting blew upon the other’s red doe not produce a white.
– ‘Quaestiones quaedam Philosophiae’ (‘Certain Philosophical Questions’), The Newton Project
Complete Focus
“Now I am upon this subject,” he told Flamsteed in January, “I would gladly know ye bottom of it before I publish my papers.” In getting to the bottom of it, he nearly cut himself off from human society. From August 1684 until the spring of 1686, his life is a virtual blank except for the Principia.
– The Life of Isaac Newton, pg 162
Insights
When he has sometimes taken a Turn or two [in the garden], has made a sudden stand, turn’d himself about, run up ye Stairs, like another Alchimedes [sic], with an [Eureka], fall to write on his Desk standing, without giving himself the Leasure to draw a Chair to sit down in.
– The Life of Isaac Newton, pg 162
Three does the Trick
What he sent to Halley was a short treatise concerned primarily with orbital mechanics. It implied that inverse-square centripetal attractions are general in nature because it asserted both that the satellites of Jupiter and Saturn, as well as the planets about the sun, conform to Kepler’s third law and that the motions of comets are governed by the same laws that determine planetary orbits.
He seems to have led towards universal gravitation by the three data points above. The satellites about the planets, the planets about the sun, and comets about stars are three diverse instances of the same curious structure.
On Hooke
Now is not this very fine? Mathematicians that find out, settle & do all the business must content themselves with being nothing but dry calculators & drudges & another that does nothing but pretend & grasp at all things must carry away all the invention as well of those that were to follow him as of those that went before.
…
Should a man who thinks himself knowing, & loves to shew it in correcting & instructing others, come to you when you are busy, & notwithstanding your excuse, press discourses upon you & through his own mistakes correct you & multiply discourses & then make this use of it, to boast that he taught you all he spake & oblige you to acknowledge it & cry out injury & injustice if you do not, I beleive you would think him a man of a strange unsociable temper.
Genius
Hypothesis: The word “genius” is like the word “magic”. It doesn’t explain anything.
“Magic,” said Professor McGonagall.
“That’s just a word! Even after you tell me that, I can’t make any new predictions! It’s exactly like saying ‘phlogiston’ or ‘elan vital’ or ‘emergence’ or ‘complexity’!”
The black-robed witch laughed aloud. “But it is magic, Mr. Potter.”
Harry slumped over a little. “With respect, Professor McGonagall, I’m not quite sure you understand what I’m trying to do here.”
Yes, you can predict that Newton was one of the best of his generation and solved problems that no one else could. But that definition is relative. How would we judge him today? What mental operations did he do better than us?
Age and Genius
The year 1693 witnessed the climax of the intense intellectual effort that followed the Principia; and if Newton had by no means lost his mental coherence after 1693, it remains true that he did not again inaugurate any new investigation of importance. He was no longer a young man. The crisis of 1693 terminated his creative activity. In theology as well as in natural philosophy and mathematics, he devoted the remaining thirty-four years of his life to reworking the results of earlier endeavors - insofar as he did not take refuge in administrative activity to absorb his time.
He had completed the two mathematical papers that he himself later published, published, which gave substance to his reputation as a mathematician. Nevertheless, he had not achieved the great synthesis at which he had grasped. The turning point of the Principia had come too late. Newton was now well over fifty. He knew that his powers had begun to fade.
What should they “fade” with age? Shouldn’t your scientific thinking skill grow with experience?
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