will then be reflected back much more than the other colours. In the same way, an object will appear blue because it reflects blue more than the other colours (those that Newton called ‘the swifter rays’). The ability to absorb or reflect different parts of the spectrum depends on the nature of the object and produces the rich diversity of colour that we observe in the universe.*
Following this discovery, Newton copied out an extract from Descartes’s Dioptricks and wrote after it:
Of Light
Light cannot be by pressure for we should see in the night as well or better than in the day we should see a bright light above us because we are pressed downwards … there could be no refraction since the same matter cannot press 2 ways, the Sun could not be quite eclipsed, the Moon & planets would shine like suns. A man going or running would see in the night …27
Throughout the summer and autumn of 1664 Newton conducted further experiments and observed diffraction through feathers and different fabrics held up to the light: ‘A feather or a black riband put between my eye and the setting Sun makes glorious colours,’ he observed.28 But then his fervour for experiment seemed to take him over. Within days he performed two experiments that left him almost totally blind.
The first near-catastrophe was when he looked directly at the Sun for too long, with the intention of observing coloured rings and spots before the eyes – a practice he repeated over and over again. In a letter to his friend the political philosopher John Locke, written a quarter of a century later, in 1691, he describes the experience:
I looked a very little while upon the Sun in a looking glass with my right eye and then turned my eyes into a dark corner of my chamber & winked to observe the impression made & the circles of colours which encompassed it & how they decayed by degrees & at last vanished … And now in a few hours’ time I had brought my eyes to such a pass that I could look upon no bright object … but I saw the Sun before me, so that I could neither write nor read but to recover the use of my eyes shut myself up in my chamber made dark for three days together & used all means to direct my imagination from the Sun.29
This mishap could be put down to Newton’s ignorance of the true danger involved, but what is the explanation for the following experiment?
I took a bodkin [from the illustration accompanying this entry in the notebook, astonishingly, this appears to be a small dagger similar to an envelope knife], and put it between my eye and the bone as near to the backside of my eye as I could: & pressing my eye with the end of it (so as to make the curvature in my eye) there appeared several white, dark and coloured circles. Which circles were plainest when I continued to rub my eye with the point of the bodkin, but if I held my eye and the bodkin still though I continued to press my eye with it yet the circles would grow faint often disappear until I resumed them by moving my eye or the bodkin.30
Youthful enthusiasm and dedication are one thing, but most people would agree that sticking a blade into one’s own eye goes far beyond the call of duty. As a result, by nearly causing permanent blindness, he came close to destroying his scientific career almost before it had begun.
In spite of these set-backs, Newton was learning rapidly from his experiments. The synthesis of Baconian method, innate talent and theoretical rigour was almost complete, but one crucial element was still missing.
There is general disagreement regarding the timing and even the exact method by which Newton acquired the mathematical knowledge that transformed his approach. No mathematics appear in the Philosophical Notebook, but early in 1664, and before his optical experiments, he began to make mathematical notes in what he called the ‘Waste Book’, the barely used notebook of his stepfather, Barnabas Smith.31 By late that summer he was already familiar with the most complex mathematical ideas of the times, gleaned largely from major texts of the period, including John Wallis’s Arithmetica Infinitorum (1655) and Descartes’s Geometry.32
Until his entry into Cambridge University, Newton’s mathematical knowledge had been limited to simple arithmetic, perhaps some algebra and a little trigonometry. But it is a mark of his genius that during the course of only two years he taught himself advanced mathematics and developed the calculus.
From letters and a collection of private papers which a few privileged disciples were allowed to rake through towards the end of his life, it is clear that Newton approached mathematics with the same autodidactic fervour he had shown as an adolescent pursuing his quest for knowledge at the Clarks’ home. But this time, in his enthusiasm, he skipped the fundamentals. The French mathematician Abraham Demoivre made the most intense study of Newton’s earliest mathematical work, and in a memorandum he wrote in 1727 he gives us an account of Newton’s stumbling, maverick approach:
In ’63 [Newton] being at Stourbridge fair brought a book of astrology to see what there was in it. Read it ‘til he came to a figure of the heavens which he could not understand for want of being acquainted with trigonometry. Bought a book of trigonometry, but was not able to understand the demonstrations. Got Euclid to fit himself for understanding the ground of trigonometry. Read only the titles of the propositions, which he found so easy to understand that he wondered how anybody would amuse themselves to write any demonstrations of them.33
Whether or not Newton had any official help with mathematics towards the end of his second year at Cambridge is difficult to ascertain. In March 1664 Isaac Barrow began a series of mathematical lectures as part of his duties as the first Lucasian Professor – a position he had accepted that winter. We know that Barrow and Newton were acquainted closely a few years after this, and that Barrow surrendered his chair to Newton in 1669, but it is by no means certain that Newton attended Barrow’s mathematics lectures. According to statutes laid down by the King, these lectures were for fellow-commoners only. This may have prevented Newton; however, such rules were flaunted openly and, being the sort of student he was, Newton may have worked his way in despite his lowly social position within the university.
For the future advancement of science, his efforts at teaching himself advanced mathematics were of the utmost significance. Without an understanding of algebra, Newton could not have developed the calculus, and without that he could not have manipulated and communicated his physics – calculus provided the formal structure needed to turn his notions of gravity from concept to hard science.
In 1664 such grand designs were some way ahead; more pressing were the demands of the university. Although he had been working consistently hard, his efforts had been exerted almost entirely outside the curriculum. Like Darwin, Einstein, Hawking and many other great scientists after him, Newton found himself ill-prepared for the various exams he needed to pass in order to continue as a student.
Having realised that his charge was more interested in mathematics and the latest philosophical ideas from Europe than in the official curriculum, Newton’s tutor, Benjamin Pulleyn, referred him to Isaac Barrow for his scholarship appraisal. Newton was required to pass an examination in April 1664 which would make him an undergraduate scholar, allowing him to sit for his BA the following spring. Pulleyn presumed that Barrow would be the most useful fellow to access the young man’s talents. Unfortunately, Barrow decided to quiz Newton on Euclid. This could have spelled disaster, because Newton had paid little attention to simple Euclidean theorems en route to more advanced mathematics. Conduitt tells us:
When
