Bill Gates took Math 55 as a freshman at Harvard, which is the class designed for the most mathematically talented students at Harvard. During his sophomore year he did research which he later published a paper on with well known theoretical computer science professor Christos Papadimitriou.
Bill Gates’s father was an antitrust lawyer (focusing on the corporate, rather than government, side), and Gates is proficient at poker—the calculational, strategic, and human elements. Those seem stronger influences on his being able to create a monopolistic software juggernaut and get the better of his counterparties in several critical deals.
As Leo Atreides puts it, “A Mentat Duke would be formidable indeed.” But merely being a mentat is not enough! One must also train to be a duke, which is likely the harder part to convince this crowd of.
Sure, that’s plausible. Gates had other advantages as well. But even if those do dominate, his involvement in math is still (weak) Bayesian evidence for my claim.
There are so few people who do publishable TCS research as college sophomores that it’s very unlikely that the wealthiest person in the world is one of them by chance :D. I acknowledge that the correlation may be entirely spurious, but it still warrants a Bayesian update.
Weak bayesian evidence E is something which you can reasonable expect to find given either hypothesis (e.g. “math is useful” vs “math is useless”), but nevertheless results in P(H|E)/P(~H|E) > P(H)/P(~H).
Strong bayesian evidence would pretty much kill the alternative hypothesis, i.e. P(~H|E) ~ 0.
Bill Gates’s father was an antitrust lawyer (focusing on the corporate, rather than government, side), and Gates is proficient at poker—the calculational, strategic, and human elements. Those seem stronger influences on his being able to create a monopolistic software juggernaut and get the better of his counterparties in several critical deals.
As Leo Atreides puts it, “A Mentat Duke would be formidable indeed.” But merely being a mentat is not enough! One must also train to be a duke, which is likely the harder part to convince this crowd of.
Sure, that’s plausible. Gates had other advantages as well. But even if those do dominate, his involvement in math is still (weak) Bayesian evidence for my claim.
There are so few people who do publishable TCS research as college sophomores that it’s very unlikely that the wealthiest person in the world is one of them by chance :D. I acknowledge that the correlation may be entirely spurious, but it still warrants a Bayesian update.
I wish people would stop treating Bayes theorem as a magic box that solves causality for them.
Can you quantify what you mean with “weak”?
Weak bayesian evidence E is something which you can reasonable expect to find given either hypothesis (e.g. “math is useful” vs “math is useless”), but nevertheless results in P(H|E)/P(~H|E) > P(H)/P(~H).
Strong bayesian evidence would pretty much kill the alternative hypothesis, i.e. P(~H|E) ~ 0.
The world has more than just two categories. It’s useful to know whether we talk about updating by 1% or 0.001%.