qmalzp

First project sounds like Coinbase.

Him, Tao, Emerton, Kisin, Coates, Calegari Bros... all Australian. Must be something in the water.

I'm not sure how many people care. It's like finding out Pepsi owns Aquafina.

N.b. the article uses d for the dimension, and n for the moment index. I haven't cranked out the details, but I believe that this is already true just assuming the fourth moments of the distance are integers. That is, for n != 1, 2, or 4, the fourth moment is never an integer. Idea of the "brute force" proof:

Take the formula in the article for the 4th moment of the d-dimensional sphere, which is always a rational number. Basically, for n=2^k, the denominator should be divisible by a larger power of two than the numerator (specifically, if I crunched the numbers right, the gap should be k-2). When n is not a power of two, then for any odd prime p dividing n, I believe the denominator should be divisible by a larger power of p than the numerator. This requires calculating exactly how many powers of p divide various factorial expressions, but you get the idea.

If you pass the interview as a generalist, Google absolutely prefers for people to work in their Mountain View office.

1. The cost of relocation is minuscule compared to the total cost of employing someone, so I don't buy that argument.

2. Do you have data to back up that Google engineers in Denver get paid less than their Mountain View counterparts? I believe this is true when comparing US to non-US salaries, but at least where I've worked, engineers get paid the same everywhere within the US (and indeed, you can relocate from the Bay Area to cheaper locales without taking a pay cut).

When talking about chess: "But even the most powerful program can be defeated by a skilled human player with access to a computer—even a computer less powerful than the opponent."

Is that true? Can a state-of-the-art chess engine plus a grandmaster really outperform just the state-of-the-art chess engine?

Google doesn't open a 500-engineer research lab in Grand Rapids, MI because there are not 500 Google-caliber engineers already living in Grand Rapids, MI. This is not a statement about the average talent there, but simply that the starting pool is not sufficiently large; hence the need to build offices in high density urban areas.

Google doesn't open an office in Denver so that Bay Area engineers have a slightly cheaper place to work, they do it to tap into the talent of folks who already live there.

Edit: I am basing these claims off of my own experience. I work at a satellite office of one of the big tech co's, and the vast majority of my coworkers are people who are either fresh out of a local university, or already lived here for many years before joining the company.

What if you replace it with

p(x|y) = 1, p(x|!y) = 0, and time(y) < time(x)

That rules out the rooster counter-example. If y is a boolean, I guess the only thing you can "do" to it is negate it.

As a former mathematican, I was at first a little offended and dismissive of his claim. But, perhaps what one can say is that mathematicians don't seem to distinguish "causation" with "implication". After all, if the barometer goes down, that does imply a storm is coming (perhaps with some increased probability), but it still doesn't cause the storm to come (even with increased probability).

In a simplified closed system, where all you have are barometers and storms, maybe there is no difference between implication and causation; all you know is these variables are correlated. Perhaps once you take every atom in the universe into account, the two start to look the same.

I think the first point is only true for symmetric matrices (which includes those that show up in multivariable calc). In general, the eigenvectors need not be orthogonal.

I completely disagree. One of the main reasons I prefer Instagram is precisely that it's not packed to the brim with features I don't use.

It does seem reasonable that there would be a cap, but I wonder how much cutting the pensions of a few thousand highly paid retirees will impact the budget.

Perhaps a more apt analogy is that mental arithmetic tricks are to math what stenography is to writing.

Category theory is basically a language. If one wanted to formulate an explicit conjecture corresponding to the original Langlands program, it could possibly be phrased as some kind of equivalence of a category of automorphic representations and a category of motives. Precisely defining those two categories is the hard part.

So even with this language, one still has to do the work of actually proving these things. It's like having a nice programming language; you still have to write the code to do the thing!

> 3. There are ways to make money online without ads begging you to click on them, and they involve real-world goods and services that your website can help connect people for?

Yeah, I could even imagine a scenario where you help connect people to real-world goods and services for free; the provider of those goods and services would be more than happy to help keep your bills paid, assuming there was some kind of mechanism that would drive people to their goods and services and not a competitor.

What would such a mechanism look like?