Mr Greenspan, speaking to Congress on Wednesday, assessed the state of the US economy and the prospects for monetary policy. His testimony was woven through with a subdued astonishment at the state of America, currently in the throes of a fully-fledged expansion, yet with no apparent signs of a pick-up in inflation despite the lowest unemployment for nearly 30 years and a stock market that is racing ahead.
Perhaps, he speculated, the historical relationships that he had followed for nearly 50 years between growth, prices, labour markets and inflation had broken down. Maybe "we have, in a sense, moved beyond history". Or maybe not.
The job of a central banker is, famously, to take away the punch bowl before the party gets going. Mr Greenspan is moving among the guests, suspiciously, but despite the fact that it is getting late in the evening, they are all sipping their drinks decorously and getting along just fine. This clearly leaves him bewildered. The boisterous behaviour he expected to see is not there.
America's expansion has been challenged, but not beaten, by the Asian economic crisis. Mr Greenspan noted that the strong dollar, buoyant domestic demand and Asia had hit exports hard, reducing the annual growth rate of real GDP by 2.5 percentage points in the first quarter. None the less, the economy still grew amazingly fast, by 4.8 per cent. The domestic economy is racing ahead, and yet there are no signs so far of the inflationary pressure that would tip the Fed into raising rates.
"Our economy is still enjoying a virtuous cycle," he said. "Rising equity values are providing impetus for spending and, in turn, the expansion of output, employment and productivity-enhancing capital investment. The hopes for accelerated productivity growth have been bolstering expectations of future corporate earnings and thereby fuelling still further increases in equity values." Investors continue to believe that this will be sustained, and so it is.
But it was at this point that he sounded a note of concern. "These rising expectations have, in turn, driven stock prices sharply higher and credit spreads lower, perhaps to levels that will be difficult to sustain unless economic conditions remain exceptionally favourable - more so than might be anticipated from historical relationships."
In a previous experience, in 1996, Mr Greenspan had warned of "irrational exuberance" in the stock market; and clearly he is still worried that the continuing rise of stock markets is out of kilter with what anyone could reasonably expect from the real economy.
What concerns the Fed Chairman, above all, is the labour market. Unemployment is running at a 28-year low, yet so far there is no sign that is feeding through into inflationary wage claims. "The adverse wage-price interactions that played so central a role in pushing inflation higher in many past business expansions - eventually bringing those expansions to an end - do not appear to have gained a significant toehold in the current expansion."
Wage increases have kept pace with growth, partly because of job insecurity and the weakness of the union movement at the beginning of the expansion. But productivity growth is the main explanation, with new investment in technology benefiting the service sector and manufacturing industry alike. If workers get paid more and they produce more, that doesn't boost inflation, it just helps to stimulate a healthy economy.
In the past, wage rises have often tipped over into price rises, dragging a healthy economy into recession. But maybe everything has changed. Some economists speak of the New Paradigm in the US economy, whereby new technology, the defeat of inflation and the expansion of free markets removes the barriers to growth, creating a revolution in growth. Mr Greenspan alluded to this, speaking of "a major technological transformation of the economy". But he doubtless remembers similar arguments from the 1980s.
Above all, Mr Greenspan points to a set of very simple, unarguable numbers. There aren't enough people to allow the labour market to continue to expand as fast as it is. The working population is increasing by about 1 per cent a year; employment is rising by 2 per cent a year. The difference is about 1.2 million people a year.
The argument may be about the labour market, but it is addressed squarely to Wall Street. Interest rate rises aren't around the corner, but they will be if there is no adjustment.
The stock and bond markets clearly believe that Mr Greenspan will not do anything soon, to judge by the reactions yesterday. Partly that is because he still sees no direct evidence of inflation returning to the system. Partly, they believe he will not take away the punchbowl because the Asians have just arrived, and they need a drink. Raising interest rates now would send a shockwave through weak Asian economies and do further damage to Russia.
The Fed hasn't yet said anything to upset this conventional wisdom. Its chairman has, cautiously, subscribed to the New Paradigm thinking, without buying into it wholesale. Mr Greenspan is too good a central banker to appear complacent, or to shock the markets with a sudden change of mind. But clearly he is worried that when the time does come to change his mind, it may be too late.