We'll know the result of his deliberations today. Mr Greenspan has faced many momentous interest rate decisions in his time, but they don't come much heavier than this one.
One thing few would disagree with. At least there could be nobody better than Mr Greenspan wielding the sharp pin that might burst the market bubble. Steven Beckner, his biographer, records the Chairman's memories of the October 1987 crash. Wall Street lost 11 per cent of its value on "Black Monday". Mr Beckner writes: "Oddly enough, Greenspan recalls he slumbered peacefully that night, getting his usual five hours of sleep."
Besides his extraordinary stamina, Mr Greenspan has an obsessive interest in and memory for economic statistics. It is perhaps fortunate that someone does. Another anecdote reports him commenting on a 25 cent rise (to $1) in the price of checking in coats between one year and the next at smart Washington parties.
So if anybody can be trusted to get US interest rates right, he's the man. The balance of opinion amongst analysts is that borrowing costs will not go up today, although the statement might signal a change of stance. Having raised the ugly question of rising inflation in the minds of investors, so the idea of a rate rise gets into the market, the Fed's past pattern has been to let it stew for a while before taking the plunge.
Mr Greenspan has also run a remarkably inactive interest rate policy. In the two years during which the Bank of England's MPC has moved interest rates 12 times, the Fed has made only three moves, all of them cuts in reaction to the crisis last autumn.
Mr Greenspan will need to be smart as well as lucky for the verdict of posterity to remain as glowing as that of the present. Even the sage of the Federal Reserve can not predict how tumultuous a correction in stock prices we are eventually in for, when it will come, how long it will last, or how serious its economic consequences might be. But he knows as well as anyone that it is coming. The trick is going to be to let the market down gently in a way that will allow a degree of economic growth to persist. Possibly Mr Greenspan isn't losing any sleep over the enormity of the task, but an awful lot of other people are.