Four ways

Following my review of the book Piranesi by Susanna Clarke, I wanted to say something about different ways of seeking knowledge. I see four fundamental options, which I list below, and illustrate graphically above (click to zoom).

P & P (agreement / synthesis)

I use the formula P & P to reflect the situation where different ways of thinking – such as Science, Art, and Religion – are all telling the same story, and therefore form part of a grand cultural synthesis. This was a characteristic of medieval thought in Europe, where Art frequently told religious stories, and Thomas Aquinas had integrated Religion with the best available Science of his day. Perhaps the pinnacle of the medieval approach is the poetry of Dante Alighieri (depicted above), where Religion and Science are combined together with poetic Art. But that was 700 years ago, of course.

P & Q (complementarity)

I use P & Q to reflect the situation where Science, Art, Religion, etc. are seen as complementary but incommensurable. They all produce their own kind of “truth” (P versus Q). I can study the stars, but independently of that, I can also see them as beautiful. For the case of Science and Religion, Stephen Jay Gould has called this approach non-overlapping magisteria.

The problem with this approach is a kind of fragmentation of life. Art is distinguished from Technology in ways that the ancient Greeks would have found bizarre. Increasingly, people seem to be fighting against this situation.

P > ~P (over-riding)

I use P > ~P to reflect the situation where Science, Art, Religion, etc. are seen as contradictory (P versus not P), but one source of “truth” is seen as superior to, and thus over-riding, the others. This includes the case of religious people who do not believe that observation of the universe can produce valid truth. It also includes scientism, or the belief that Science trumps everything else (a doomed approach, because the foundations of Science are themselves not scientific; they are philosophical and mathematical). I have illustrated this option with the depiction of Isaac Newton by William Blake. This was not intended to be a positive depiction; around about the same time Blake famously wrote “May God us keep / From Single Vision and Newton’s sleep.

The novel Piranesi touches on the problems of scientism: “It is a statue of a man kneeling on his plinth; a sword lies at his side, its blade broken in five pieces. Roundabout lie other broken pieces, the remains of a sphere. The man has used his sword to shatter the sphere because he wanted to understand it, but now he finds that he has destroyed both sphere and sword. This puzzles him, but at the same time part of him refuses to accept that the sphere is broken and worthless. He has picked up some of the fragments and stares at them intently in the hope that they will eventually bring him new knowledge.

P & ~P (contradiction / chaos)

Finally, I use P & ~P to reflect the situation where Science, Art, Religion, etc. are seen as contradictory (P versus not P) but the contradiction is embraced. Your “truth” may be completely contradictory to my “truth,” but that’s OK. The result of this is a kind of postmodernist chaos that seems to me fundamentally unstable. Indeed, former adherents of this approach seem now to be moving towards a new single dominant metanarrative.

So those are four ways of seeking knowledge. Can we indeed live with contradiction? Can the problems of complementarity be resolved? Or is it possible to construct some new synthesis of Science, Art, Religion, and other ways of seeking knowledge? The novel Piranesi raises some interesting questions, but gives no answers, of course.

Artwork from a Florentine artist, Ryan N. McFarlane/U.S. Navy, Auguste Rodin, William Blake, and Ivan Ayvazovsky.


Newton, gravity, and the apple


Isaac Newton and his apple (image: LadyofHats)

Among the numerous problems in this famous videoclip from South Africa (which I have previously mentioned) are some serious misunderstandings regarding Isaac Newton, gravity, and the apple story. According to William Stukeley (writing in 1726), “After dinner, the weather being warm, we went into the garden, and drank tea under the shade of some apple trees; only he [Newton], and myself. Amidst other discourse, he told me, he was just in the same situation, as formerly, the notion of gravitation came into his mind. ‘Why should that apple always descend perpendicularly to the ground,’ thought he to himself; occasion’d by the fall of an apple, as he sat in a contemplative mood. ‘Why should it not go sideways, or upwards?’

Of course, Newton was hardly the first person to think seriously about gravity. About 2,000 years earlier, Aristotle had recorded his theories on the subject. These had a great influence on the Greek-speaking world, the Muslim world, and Western Europe, up until the time of Galileo. Galileo demonstrated several flaws in Aristotle’s approach, and made measurements which showed that falling objects follow parabolic paths.


Parabolas traced out by a bouncing ball (photo: MichaelMaggs)

Newton’s genius lay in being able to explain both Galileo’s findings and Kepler’s laws of planetary motion using a single mathematical equation: F = G m1 m2 / d 2. This articulated the strength of the gravitational force, while leaving the true nature of gravity mysterious. Consequently, Newton’s work was hardly the last word on the subject. Einstein’s general relativity made considerable advances in the understanding of gravity, but several questions still remain.

The scientific understanding of gravity neither started nor ended with Newton, which means that the speaker in the video linked above is quite wrong in saying: “Western knowledge … is saying that it was Newton and only Newton who knew and saw an apple falling and out of nowhere decided gravity existed and created an equation and that is it. Whether people knew Newton or not‚ or whatever happens in Western Africa‚ Northern Africa‚ the thing is the only way to explain gravity is through Newton, who sat under a tree and saw an apple fall.

Western knowledge says nothing of the kind, of course. It is a sad thing that “decolonisation” is being driven by such radical misunderstandings, when what is needed may in fact be a review of the humanities and improvements in basic education.


Isaac Newton by James Gleick: a book review


Isaac Newton by James Gleick

I recently read the wonderful biography Isaac Newton by talented science writer James Gleick. This book was a Pulitzer finalist in 2004. The Guardian called it “a masterpiece of brevity and concentration,” and I would indeed have liked it to have been slightly longer, because the story it tells is fascinating.


Isaac Newton in 1689

Newton overcame a troubled childhood and made enormous contributions to the physics of motion and light, as well as to the calculus. However, he was also interested in theology and alchemy, and ran the Royal Mint. A complex man – and Gleick tells his story well.


Newton experimented extensively with lenses and prisms

Newton’s legacy transformed physics. For example, inspired by Newton’s formulation of gravity, Edmond Halley predicted the return of the comet that bears his name, as well as the eclipse of 1715. The descendants of Newton’s reflecting telescope helped develop modern astronomy.


Halley’s eclipse prediction

I can certainly recommend this short, but interesting, biography.

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Isaac Newton by James Gleick: 4 stars