February's Book: The Great Unknown

The Great Unknown by Marcus du Sautoy

Math/Physics (2016 - 428 pp.)

"How puzzling all these changes are! I'm never sure what I'm going to be, from minute to another." -Lewis Carroll, Alice's Adventures in Wonderland* (153)

In The Great Unknown, Oxford University mathematics professor Marcus du Sautoy outlines seven of the greatest questions in math and science that may never be solved. Between his introduction and his conclusion, there are seven "edges" of our current scientific understanding: Chaos, Matter, Quantum Physics, The Universe, Time, Consciousness, Infinity. The seven edges overlap in some of the scientists named,** as well as in framing devices used (such as du Sautoy's trusty red casino dice), but each tackles the boundaries of a different question as it has advanced through the history of scientific research. Du Sautoy readily admits his own blind spots, as must we all; in the introduction, he states that "I must admit that the arrogance of youth infused me with the belief that I could understand all that was known...", but then, as he has grown older, "Time is running out to know it all." (7) As someone almost a decade removed from my master's degree, I identify with that feeling.

Much of "Chaos" considers the early modern giants of math. Girolamo Cardano, a noted Lombardian mathematician of the 16th century, was "an inveterate gambler" (24) who spent much of his time devising strategies to win at dice games,*** (with mixed results, much to his family's chagrin) before correctly predicting his death date, in quasi-Machine of Death style. The origin of Pascal's triangle as a betting aid is less of a surprise when viewed through this lens, as its original application was to decide how a pot should be divided when the problem of points is incomplete; (28) in an inspired moment during 11th-grade math, I invented Gordon's Triangle, which provides far less insight.

Rows 0-7 of Pascal's Triangle, from Wikipedia. Note that each number is the sum of the two numbers directly above it.

In "Matter", the world's atomic, and even subatomic, building blocks comes to life, whizzing around and through each other with such startling speed we don't even notice them. Du Sautoy explains the development of particle theory, from 19th-century descriptions of atoms, followed by subsequent understandings of what makes atoms heavier than others (protons, neutrons), what orbits them (electrons), and what all of those are made of (quarks). Dmitri Mendeleev's part-discovery, part-invention of the periodic table (87) figures large here, including the use of octave theory to explain why elements repeat each other every eight atomic numbers, a recurring trend in The Great Unknown: what fills the gaps? Just as irrational numbers fill gaps between rational numbers, as in the case of the square root of 2, Mendeleev's discovery of the absence of an element with an atomic number of 31 inspired the later discovery of gallium. I have to disagree with du Sautoy's cello/trumpet metaphor to explain the duelling schools of thought regarding whether matter is continuous, like a cello's glissando, or discrete, like a trumpet's staccato. (119) As a classical and jazz trained trumpet player, I have played series of notes lasting 4+ bars when I tongued only two or three notes, despite playing entire scales at various volumes.

In "Quantum Physics", du Sautoy delves into realms that intimidate the average reader but are full of charming stories here. During Albert Einstein's annus mirabilis of 1905, he conducted significant amounts of work on photons; this, not the theory of relativity, would be the subject of his 1921 Nobel Prize. The question of whether light moves in waves or in quasi-particles stumped scientists until then. Du Sautoy makes the colourful analogy that waves would be like a series of taps on the shoulder, each incapable of knocking down the recipient, whereas a particle would be like one good push. (133-135) Oddly, a scientifically inclined friend brought this up during elementary school by asking me on the school bus one day, "would you rather receive a million taps on the shoulder or receive one huge tap with all the force of them combined?" I thought it was a silly question while having no idea he was (unintentionally?) quoting Einstein.

In "The Universe", du Sautoy educates the reader on all manners of cosmological bodies, including the fascinating observation that stars appear to be different colours and brightnesses depending on their distances. Measuring between them therefore requires a combination of trigonometry and colour theory - score one for art class? The 1915 sighting of Proxima Centauri, the closest star to our own, by Scottish astronomer Robert Innes, (192) is one of my favourite discoveries; he had the same name as one of my friends. Fittingly, beyond this edge, "Time", "Consciousness" and "Infinity" start collapsing into themselves...

Illustrations abound in The Great Unknown. Two of my favourites are ones that were either familiar to me in concept, or familiar to me as in I had seen that exact illustration before. The latter is when du Sautoy shows the mathematical underpinning of human existence via the xkcd comic "Purity", (332) which surely connects with the Millennial crowd (full disclosure: I am a Millennial). The former is when du Sautoy demonstrates the limitation of Euclidean geometry to flat plane. Those of us who have studied any level of math take for granted that the sum of a triangle's angles is 180 degrees, but this axiom no longer holds true when the measurements take place on a curved surface. The best example of all is when a triangle is drawn on a sphere. (381) The ability to draw line segments and polygons on a sphere is crucial to navigation, flight paths, and nearly anything involving the curvature of Earth. This seemingly obtusely abstract concept is so obviously applicable to everyday life it is a testament to scientific education.

Back to dice: in the conclusion, du Sautoy mentions that there is a finite number of six-sided dice in his house, between his casino dice, his Monopoly set, and wherever else there might be dice, including stuck in the couch. He mentions that he does not know whether there is an odd or even number of dice, although he could find out if he wanted to count them. (418-419) This scenario made me reflect on du Sautoy's earlier observation of what might happen if he rolled a die (or threw magazines) into a black hole, beyond the event horizon, so that its result would be completely unknowable to him. (282) What if, as in the black hole example of the particles bouncing off the event horizon containing some aspect of the die, du Sautoy took his real-life dice and ground them into dust? Reassembling the particles would be practically impossible, and measuring dice powder on a scale could be defeated simply by wetting the dice into a sort of dice sludge, so... could du Sautoy theoretically know how many dice he has then?

The one thing I would have liked to see more of in The Great Unknown is a one-paragraph definition of the Riemann hypothesis and the PORC conjecture, two unsolved mathematical problems du Sautoy hints at many times near the end of the book but never explores. While I understand they are more useful as stand-ins than as illustrations of the book's ideas, their sheer complexity would have benefited from the book's clear, accessible language.

The world during, and since, The Great Unknown's release in 2016 contains themes present in the book. When du Sautoy frames the relationship between acceleration, gravity and time by using a thought experiment that sends one of his twin daughters into space at near-lightspeed while the other stays on Earth: "Ina returns younger because she has to accelerate to get to her constant speed." (264) This is an almost exact telling of the 2014 science fiction movie Interstellar, in which a father engages on a potentially Earth-saving interstellar mission while his daughter stays home; later in the movie, they are the same age. (Warning: movie spoiler!) The movie was released the year before the book's publication, making me wonder if du Sautoy read it while writing. Even more recently, Isaac Newton's isolation during the Great Plague of 1665,**** at age 22, marked the moment when many of his theories' seeds were planted in his head. (32) As someone currently in a jurisdiction with an emergency order due to COVID-19, but who hasn't felt particularly brilliant for much of that time... I hope someone's working on zeta functions as I write this.

Lastly, there's a great deal of material on scientists' and philosophers' beliefs in God, or lack thereof. How would God construct a black hole? Has God planned out the past, present and future, or does he "reset his watch" at certain intervals? All I have to say to these math plus science plus God questions is what The Great Unknown reminds us of our infinitesimal selves all the time: I don't know, and you don't either.

Ease of Reading: 5

Educational Content: 8

*In 18th-century novel style, du Sautoy opens each edge (chapter) with a quotation from some scientific or literary figure who has influenced our understanding of the unknown. Who better than Lewis Carroll, who wrote the most famous fiction book ever that was about abstract math? (I've blogged about Alice on here not once, but twice. No, not the heavy metal Alice.)

**For example, Albert Einstein is mentioned during the third edge for his work on photonics, and the fifth edge for his theory of general relativity.

***This Columbia University article contains a probability chart of rolling a total of 9-12 with three dice on page 5, Table 1. A similar chart appears in The Great Unknown at page 25.

****The Great Plague of 1665 differs from our present conundrum in that it was an outbreak of bubonic plague, the same bacterium that caused the Black Death and subsequent outbreaks. That said, there was an October 2020 news report using the bubonic plague as a case study, and a teenage Mongolian boy died of bubonic plague last July.