Especially as he had been interested in programming, and the programming is the area where you can literally make a LOT of money in just a couple years while gaining the experience and gaining much better cred than childhood SAT.
What salary level is good enough evidence for you to consider someone clever?
Notice that your criteria for impressive cleverness excludes practically every graduate student—the vast majority make next to nothing, have few “concrete” things to show off, etc.
My impression is that he’s a spoiled ‘math prodigy’ who didn’t really study anything beyond fairly elementary math, and my impression is that it’s his own impression except he thinks he can do advanced math with little effort using some intuition while i’m pretty damn skeptical of such stuff unless well tested.
Except the interview you quoted says none of that.
JB: I can think of lots of big questions at this point, and I’ll try to get to some of those, but first I can’t resist asking: why do you want to study math?
EY: A sense of inadequacy.
[...]
[EY:] Even so, I was a spoiled math prodigy as a child—one who was merely amazingly good at math for someone his age, instead of competing with other math prodigies and training to beat them. My sometime coworker Marcello (he works with me over the summer and attends Stanford at other times) is a non-spoiled math prodigy who trained to compete in math competitions and I have literally seen him prove a result in 30 seconds that I failed to prove in an hour.
This is substantially different from EY currently being a math prodigy.
[EY:] I’ve come to accept that to some extent [Marcello and I] have different and complementary abilities—now and then he’ll go into a complicated blaze of derivations and I’ll look at his final result and say “That’s not right” and maybe half the time it will actually be wrong.
In other words, he’s no better than random chance, which is vastly different from “[thinking] he can do advanced math with little effort using some intuition.” By the same logic, you’d accept P=NP trivially.
[EY:] I’ve come to accept that to some extent [Marcello and I] have different and complementary abilities—now and then he’ll go into a complicated blaze of derivations and I’ll look at his final result and say “That’s not right” and maybe half the time it will actually be wrong.
In other words, he’s no better than random chance, which is vastly different from “[thinking] he can do advanced math with little effort using some intuition.” By the same logic, you’d accept P=NP trivially.
I don’t understand. The base rate for Marcello being right is greater than 0.5.
Maybe EY meant that, on the occasions that Eliezer objected to the final result, he was correct to object half the time. So if Eliezer objected to just 1% of the derivations, on that 1% our confidence in the result of the black box would suddenly drop down to 50% from 99.5% or whatever.
[EY:] I’ve come to accept that to some extent [Marcello and I] have different and complementary abilities—now and then he’ll go into a complicated blaze of derivations and I’ll look at his final result and say “That’s not right” and maybe half the time it will actually be wrong.
In other words, he’s no better than random chance, which is vastly different from “[thinking] he can do advanced math with little effort using some intuition.” By the same logic, you’d accept P=NP trivially.
If a device gives a correct diagnosis 999,999 times out of 1,000,000 and is applied to a population that has about 1 in 1,000,000 chance of being positive then a positive diagnosis by the device has approximately 50% chance of being correct. That doesn’t make it “no better than random chance”. It makes it amazingly good.
Notice that your criteria for impressive cleverness excludes practically every graduate student—the vast majority make next to nothing, have few “concrete” things to show off, etc.
It’s not criteria for cleverness, it is criteria for evidence when the prior is 0.0001 (for 1 in 10 000) . One can be clever at one in 7 billions level, and never having done anything of interest, but I can’t detect such person as clever at one in 10 000 level with any confidence without seriously strong evidence.
This is substantially different from EY currently being a math prodigy.
I meant, a childhood math prodigy.
In other words, he’s no better than random chance
If Marcello failed one time out of ten and Eliezer detected it half of the time, that would be better than chance. Without knowing failure rate of Marcello (or without knowing how the failures are detected besides being pointed out by EY), one can’t say whenever it is better than chance or not.
What salary level is good enough evidence for you to consider someone clever?
Notice that your criteria for impressive cleverness excludes practically every graduate student—the vast majority make next to nothing, have few “concrete” things to show off, etc.
Except the interview you quoted says none of that.
[...]
This is substantially different from EY currently being a math prodigy.
In other words, he’s no better than random chance, which is vastly different from “[thinking] he can do advanced math with little effort using some intuition.” By the same logic, you’d accept P=NP trivially.
I don’t understand. The base rate for Marcello being right is greater than 0.5.
Maybe EY meant that, on the occasions that Eliezer objected to the final result, he was correct to object half the time. So if Eliezer objected to just 1% of the derivations, on that 1% our confidence in the result of the black box would suddenly drop down to 50% from 99.5% or whatever.
Yes, but that’s not “no better than random chance.”
Sure. I was suggesting a way in which an objection which is itself only 50% correct could be useful, contra Dmytry.
Oh, right. The point remains that even a perfect Oracle isn’t an efficient source of math proofs.
You do not understand how basic probability works. I recommend An Intuitive Explanation of Bayes’ Theorem.
If a device gives a correct diagnosis 999,999 times out of 1,000,000 and is applied to a population that has about 1 in 1,000,000 chance of being positive then a positive diagnosis by the device has approximately 50% chance of being correct. That doesn’t make it “no better than random chance”. It makes it amazingly good.
It’s not criteria for cleverness, it is criteria for evidence when the prior is 0.0001 (for 1 in 10 000) . One can be clever at one in 7 billions level, and never having done anything of interest, but I can’t detect such person as clever at one in 10 000 level with any confidence without seriously strong evidence.
I meant, a childhood math prodigy.
If Marcello failed one time out of ten and Eliezer detected it half of the time, that would be better than chance. Without knowing failure rate of Marcello (or without knowing how the failures are detected besides being pointed out by EY), one can’t say whenever it is better than chance or not.