Penetrating thoughts

Usage examples of insights.

But now, through the insights of the second superstring revolution, physicists have realized that M-theory is the unifying pachyderm of the five string theories.

Foremost among these are the nineteenth-century mathematical insights of Georg Bernhard Riemann that firmly established the geometrical apparatus for describing curved spaces of arbitrary dimension.

Perturbative methods can, at best, give skeletal insights, since the extremes of energy, temperature, and density require precision analysis.

David Steinhardt read the manuscript with great care and generously provided sharp editorial insights and invaluable encouragement.

So central are these remarkable insights into the nature of space and time that we shall use them as a guiding theme in all that follows.

Einstein formalized this idea, one that actually goes back to insights of Galileo, by proclaiming that it is impossible for you or any fellow traveler to perform an experiment within the closed compartment that will determine whether or not the train is moving.

It is one of the deepest insights into the nature of reality ever discovered.

By 1977, insights of Ferdinando Gliozzi of the University of Turin, Scherk, and David Olive of Imperial College put this pairing into the proper light.

One of the main insights of quantum mechanics is that our predictive power is fundamentally limited to asserting that such-and-such outcome will occur with such-and-such probability.

Aspinwall, Morrison, and I had almost daily impromptu meetings with Witten at which he would show us new insights following from his approach.

And then we must follow the subtle reasoning that makes use of these techniques to find the remarkable insights alluded to above.

Inspired by earlier works of Duff, Hull, Townsend, and building on insights of Schwarz, the Indian physicist Ashok Sen, and others, Witten announced a strategy for transcending the perturbative understanding of string theory.

In one stroke, Strominger had made use of the exciting new insights of string theory to resolve one of the thorniest issues surrounding the curling up of extra dimensions into a Calabi-Yau space.

These conditions, as is by now familiar, require that both quantum mechanics and gravity be taken into account, and hence the birth of the universe provides a profound arena for exercising the insights of superstring theory.

But, as with most successful theories, our new insights raise yet more detailed questions.