4 December
Dear Ananyo Bhattacharya,
[highlight=transparent]Dear Ananyo,[/highlight][highlight=transparent]Thank you so much for making the time to write back. I really enjoyed reading what you had to say. And I’m sure that others will too. You gave me a lot to ponder about.[/highlight][highlight=transparent]You are right, of course. The education systems of advanced economies today are generally better than they were before. And there is certainly more opportunity for women and minorities to flourish. While we still have a long way to go, we have made good progress on many fronts of society and education.[/highlight][highlight=transparent]Still, I wonder how many more geniuses we might have if we could replicate the upbringing that von Neumann had. We agree, for instance, that it is easier to spot a prodigy today. But I cannot help but wonder how much potential in children stays dormant due to our inability to maximize their learning and inclinations during the sensitive periods of their brain development. It is no wonder that geniuses are rare when so many things in nature, nurture, and chance have to go just right over many years or generations even.[/highlight][highlight=transparent]You mention Srinivasa Ramanujan, who is certainly a fascinating case. I could not find much information on his upbringing online. So I wonder how much his parents and teachers played in his prodigy and cultivation. At the very least, it seems that he had access to a lot of books, which helped him to nurture his unique brand in mathematics. I also wonder what kind of mathematical career he might have had later in life with better nutrition, healthcare, and advanced training. I am struck by one of his [/highlight][color=rgb(17, 85, 204)][highlight=transparent][url=https://writings.stephenwolfram.com/2016/04/who-was-ramanujan/#:~:text=He%20says%20that%20his%20first%20goal%20is%20just%20to%20get%20someone%20like%20Hardy%20to%20verify%20his%20results%E2%80%94so%20he%E2%80%99ll%20be%20able%20to%20get%20a%20scholarship%2C%20since%20%E2%80%9CI%20am%20already%20a%20half%20starving%20man.%20To%20preserve%20my%20brains%20I%20want%20food%E2%80%A6%E2%80%9D]letters to G.H. Hardy[/url][/highlight][/color][highlight=transparent] in which he writes: “I am already a half starving man. To preserve my brains I want food.” To die at the age of thirty-two with so much potential is just so sad.[/highlight][highlight=transparent]It does warm me, however, to hear of initiatives like the Parallel Project and the Liverpool Maths School. Perhaps in time, we can extend these programs to more vocations, more age-groups, and more walks of life. But it will take time. I think society is only beginning to tap into the potential of education. And delivering effective education at scale is no easy thing.[/highlight][center][highlight=transparent]***[/highlight][/center][center][/center][highlight=transparent]I believe Laszlo Polgar elected chess for his daughters because it was the intellectual vocation with the smallest number of uncontrollable variables. For one, it is easy to measure our success in chess via the ELO ratings system. We can say with confidence when somebody is a good player, a great player, or a genius in chess. But the spectrum is less obvious in mathematics or science. How many publications or prizes would the Polgar sisters need to justify such a claim? In chess, we are also somewhat less dependent on unreliable variables like one’s birthplace, connections, institutions, supervisors, wealth, and research opportunities. Personally, there is also something symbolic about Judit Polgar’s achievements in a head-to-head sport that was once dominated almost exclusively by arrogant and often sexist men.[/highlight][highlight=transparent]You write, however, that one does not “necessarily have to be a genius to achieve chess mastery”. But I think that depends on how strictly we define mastery or genius. True, “high mathematical ability [may be] more closely allied with IQ” and the traditional genius, as you say. But that may be because mathematics is also more general-purpose than chess. After all, math is the language of logic and science. And it is a readily transferable one at that. This problem of generalizability is also probably why Michael Jordan was transcendent in basketball but abysmal in baseball. And John von Neumann, likewise, for all his genius and cross-walking feats, would surely fail as a professional Formula One driver if we recall your humorous anecdotes on his driving prowess.[/highlight][highlight=transparent]I do believe that geniuses arise in all walks of life, from chess to football to filmmaking. (Although these forms of genius may not lend itself to cross-walking as mathematics does for the likes of von Neumman.) I cannot help but watch the grandmaster games of Mikhail Tal, Bobby Fischer, or Magnus Carlsen in awe. They play chess with a type of creativity and personality that does appear to be replicable through training alone. That said, the chess schools of India and China seem to be producing an ever-growing number of creative world class talent. Perhaps in time their results may help to further clarify the nature-nurture debate.[/highlight][highlight=transparent]Genius comes in degrees, of course. And von Neumann does seem to be one of a kind. A historical anomaly. A man from the future. I remember reading his transcript for ‘The Computer and the Brain’ and wondering what other mischief this brilliant man might have gotten up to had life given him just a bit more time. Thankfully, we can also take solace in knowing that humanity is built in with some redundancy. If Charles Darwin was felled by illness or accident or the wrong track, we would have Alfred Russel Wallace to take the mantle. Sure, we might need a legion of men and women to fill von Neumann’s cross-walking shoes had he not existed. But I believe humanity would have filled in some of the gaps, sooner or later, one way or another.[/highlight][highlight=transparent]Ananyo, I am perhaps a bit more optimistic now, having had time to mull over our letters. But given the amount of knowledge one must assimilate before reaching the frontier of science, cross-walking may favor the collaborative team over the brilliant lonewolf. Perhaps what we need now are more scientists with a genius for people.[/highlight][highlight=transparent]But if I had to bet on a future cross-walking individual, I would put my money on a quantitative biologist or computer scientist with a strong theoretical bent—a flexible contrarian who marches to the beat of his or her own drum. Such a daring person may have what it takes to bring the trees of biology, neuroscience, computing, artificial intelligence, and economics into a single garden. I think we are seeing inklings of this already in the mathematics for networks and the science of complex systems. But there must still be tremendous room for cross-pollination and cross-walking in these fields. Will such an individual or team “range as successfully” as von Neumann? Probably not, as for reasons you’ve already explained. But it will be nonetheless inspiring. I hope to live long enough to see some of it. [/highlight][center][highlight=transparent]***[/highlight][/center][center][/center][highlight=transparent]To your broader point, my instinct is to agree with you that students should study some more math and logic until they leave school. On the other hand, I also worry about a world in which everyone thinks like a Godelian logician. Might society lose something else in turn? What might happen to art or music or cinema? But if the goal is to constrain the baloney and charlatans that surround us, then I actually feel it more prudent that students take more subjects in history, anthropology, biology and ethics. The imperative, as I see it, is to foster an intuition for intellectual honesty and a wide-ranging perspective of our complex world. For the average classroom, I would cut back on William Shakespeare, and add more Martin Luther King Jr, more Charles Darwin, more George Orwell, and the likes. I’m not sure if you and others would agree?[/highlight][highlight=transparent]Either way, thank you again for giving myself and others so much food for thought, both in your wonderful book and letter. I know you are a busy man. So I will not be offended if you do not reply. But I do humbly request that you write another book someday, if it pleases you. [/highlight][highlight=transparent]Warm regards and happy holidays,[/highlight][highlight=transparent]Toby[/highlight][highlight=transparent]PS. I too am excited for Christopher Nolan’s Oppenheimer film next year. I think he has the track record to get the story right. The later years of Oppenheimer’s story is well suited to Nolan’s mind-bending style. At the very least, it should be nothing like Ron Howard’s A Beautiful Mind. Still, I hope there will be more well-meaning attempts at portraying the history of science. Perhaps they can engage you as an advisor on set someday. :) [/highlight]
Tobias Lim
Tobias Lim