Near the end of an interesting post he says:
High frequency trading presents a lot of interesting puzzles. The Booth faculty lunchroom has hosted some interesting discussions: "what possible social use is it to have price discovery in a microsecond instead of a millisecond?" "I don’t know, but there’s a theorem that says if it’s profitable it’s socially beneficial." "Not if there are externalities" "Ok, where’s the externality?" At which point we all agree we don’t know what the heck is going on.
I guess I don't find this that puzzling. What's the benefit of having price discovery in a microsecond instead of a millisecond? How about a second instead of a minute? Or a minute instead of an hour? Or an hour instead of a week-long steamship journey? Or a week instead of a month of overland travel? The benefit is all the same and it's all perfectly real, but the marginal returns decline as we approach fundamental physical limits on how fast things can happen. As for externalities, it seems to me like a standard Red Queen's Race kind of thing. More and more resources are sucked into the game of trying to get better at HFT. If there's a harm to society it's not because the trading is imposing costs on others, it's because having the same personnel compete in some other field of endeavor might produce better returns for the rest of the world.
HFT seems to have become a proxy war for overall attitudes toward high finance, but the situation seems almost banal to me. There's no one point at which you can draw a line and pronounce conclusively "greater speed in price discovery is no longer socially valuable" but sometimes arbitrary limits are helpful. You could price stocks out to 9 or 27 or 81 decimal points and reap some kind of gains, but in practical terms it's useful to draw an arbitrary limit.