With that kind of superhuman knowledge, you could get an early warning of emerging imbalances between pessimists and optimists, between likely sellers and buyers.
Such imbalances set the groundwork for a crash - specifically, when the number of potential buyers gets very small.
Of course, no one has access to such mental information.
Yet Donier and Bouchaud found a clever way to estimate it, and to do so using only publicly available data.
They turned to the bitcoin market because it has a unique feature, perhaps related to the fact that it is still fairly young and exotic: Traders place their buy and sell orders early and leave them there for all to see.
Of course, the picture is constantly changing as price movements prompt traders to enter new orders.
Still, the orders visible at any moment already make it possible to predict crashes.
In a recent paper, Donier and Bouchaud found that the market is prone to crash specifically when buy orders are scarce, and estimated how much a typical-size sell order should move the price when matched with such buy orders.
Using this method, they were able to predict the size of the biggest 14 single-day drops in bitcoin value between January and April 2013 to a high degree of accuracy.
Most other markets are not like bitcoin. Participants don't place orders well in advance.
Instead, traders post and cancel orders much more frequently, often working hard to hide their true intentions, which become evident only as prices begin to move and they respond.
To deal with the lack of transparency, Donier and Bouchaud employed a much more sophisticated mathematical analysis to estimate the likely size of a downward price movement as signalled by a dearth of buy-side demand.
The exact result is highly technical. But, as they show, it turns out to be almost identical to a much simpler formula - market volatility divided by the square root of trading volume - which can be calculated purely from public data.
If they're right, this measure alone should predict big market movements.
Will it work? We'll see.
Bouchaud and some other physicists initially proposed the formula a couple of years ago, and some preliminary tests by economists on data from five historic market crashes - including the crash of 1929 and the Flash Crash of May 6, 2010 - suggest that it has promise.
It will take a lot more research to clarify the conditions under which the indicator should and should not be trusted.
What's not surprising is that the predictive ability comes from carefully teasing out information on emerging trading imbalances, especially the drying up of buy orders.
This approach isn't the hocus-pocus of chartists identifying weird patterns in past price movements.
It also doesn't predict a crash's precise timing, which is almost certainly determined by more or less random factors, such as a chance coincidence of sales that - under the right conditions - sets off a larger avalanche.
Now, you might assume that if the formula does turn out to work, markets will adapt and render it obsolete.
Donier and Bouchaud don't think so.
This simple formula, they believe, reflects such fundamental mechanics of market behaviour that it will hold predictive value even if everyone comes to understand it.
Market movements, in this sense, might not be as unpredictable as we've been led to think.
Mark Buchanan, a physicist and Bloomberg View columnist, is the author of the book "Forecast: What Physics, Meteorology and the Natural Sciences Can Teach Us About Economics."
