In Einstein's general relativity the structure of space can change but not its topology. Topology is the property of something that doesn't change when you bend it or stretch it as long as you don't break anything.

I wouldn't have thought that a wrong theory should lead us to understand better the ordinary quantum field theories or to have new insights about the quantum states of black holes.

String theory is an attempt at a deeper description of nature by thinking of an elementary particle not as a little point but as a little loop of vibrating string.

There was a long history of speculation that in quantum gravity, unlike Einstein's classical theory, it might be possible for the topology of spacetime to change.

In Einstein's general relativity the structure of space can change but not its topology. Topology is the property of something that doesn't change when you bend it or stretch it as long as you don't break anything.

Having those extra dimensions and therefore many ways the string can vibrate in many different directions turns out to be the key to being able to describe all the particles that we see.

As far as extra dimensions are concerned, very tiny extra dimensions wouldn't be perceived in everyday life, just as atoms aren't: we see many atoms together but we don't see atoms individually.

You have that one basic string, but it can vibrate in many ways. But we're trying to get a lot of particles because experimental physicists have discovered a lot of particles.

Spreading out the particle into a string is a step in the direction of making everything we're familiar with fuzzy. You enter a completely new world where things aren't at all what you're used to.

Even before string theory, especially as physics developed in the 20th century, it turned out that the equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle.

Technically you need the extra dimensions. At first people didn't like them too much, but they've got a big benefit, which is that the ability of string theory to describe all the elementary particles and their forces along with gravity depends on using the extra dimensions.

Quantum mechanics brought an unexpected fuzziness into physics because of quantum uncertainty, the Heisenberg uncertainty principle.

On the other hand, we don't understand the theory too completely, and because of this fuzziness of spacetime, the very concept of spacetime and spacetime dimensions isn't precisely defined.

As of now, string theorists have no explanation of why there are three large dimensions as well as time, and the other dimensions are microscopic. Proposals about that have been all over the map.

It's indeed surprising that replacing the elementary particle with a string leads to such a big change in things. I'm tempted to say that it has to do with the fuzziness it introduces.

One of the basic things about a string is that it can vibrate in many different shapes or forms, which gives music its beauty.

But the beauty of Einstein's equations, for example, is just as real to anyone who's experienced it as the beauty of music. We've learned in the 20th century that the equations that work have inner harmony.

If I take the theory as we have it now, literally, I would conclude that extra dimensions really exist. They're part of nature. We don't really know how big they are yet, but we hope to explore that in various ways.

As for the forces, electromagnetism and gravity we experience in everyday life. But the weak and strong forces are beyond our ordinary experience. So in physics, lots of the basic building blocks take 20th- or perhaps 21st-century equipment to explore.

The theory has to be interpreted that extra dimensions beyond the ordinary four dimensions the three spatial dimensions plus time are sufficiently small that they haven't been observed yet.

So when you ask me how string theory might be tested, I can tell you what's likely to happen at accelerators or some parts of the theory that are likely to be tested.

I don't care about movies. I tend to play badminton once a week.

I have a tendency, more than most other physicists, to try to figure out everything all at once, before I publish. And even to try to figure out everything in my head, without pencil and paper.

I just think too many nice things have happened in string theory for it to be all wrong. Humans do not understand it very well, but I just don't believe there is a big cosmic conspiracy that created this incredible thing that has nothing to do with the real world.

I'm actually, for the most part, a complete agnostic politically.

If you are a researcher, you are trying to figure out what the question is as well as what the answer is.

One very important aspect of string theory is definitely testable. That was the prediction of supersymmetry, which emerged from string theory in the early '70s.

Quantum mechanics brought an unexpected fuzziness into physics because of quantum uncertainty, the Heisenberg uncertainty principle. String theory does so again because a point particle is replaced by a string, which is more spread out.

Regardless of any deviations, it was clear I was supposed to end up in math and physics.

We know a lot of things, but what we don't know is a lot more.

We used to think that revolutions are the cause of change. Actually it is the other way around: change prepares the ground for revolution.

I must stress here the point that I appreciate clarity, order, meaning, structure, rationality: they are necessary to whatever provisional stability we have, and they can be the agents of gradual and successful change.

Excuses change nothing, but make everyone feel better.

So, first you have to be able to play with a metronome. Then you take your freedom. If you play in an orchestra, you got to watch the conductor, he is like a metronome, but it is more difficult because he can change rhythms.

I wouldn't change Buffy for anything and I wouldn't change the course in which she has evolved but it is nice to be able to do something that is a little different.

For example, UNICEF works with governments to change legislation such as in India where a law was passed raising the age of compulsory school completion to keep children in school and away from the workplace for longer.

Great joy, especially after a sudden change of circumstances, is apt to be silent, and dwells rather in the heart than on the tongue.

I still feel that a movie has to attempt to say something - even if it fails miserably. But I've sort of given up on believing that I'm going to change the world with every film I choose to act in.

Don't knock the weather; nine-tenths of the people couldn't start a conversation if it didn't change once in a while.

You don't have to be the Dalai Lama to tell people that life's about change.

I knew that my staying up would not change the election result if I were defeated, while if elected I had a hard day ahead of me. So I thought a night's rest was best in any event.

It will always be a battle a day between those who want maximum change and those who want to maintain the status quo.

Being a father, well, I don't know if this is a change, but it makes me want to get out of here faster. Get off the clock. Just 'cause the baby is my reason for living, my reason for coming to work.

A liberal knows that the only certainty in this life is change but believes that the change can be directed toward a constructive end.

I was born not knowing and have had only a little time to change that here and there.

In their search for quality, people seem to be looking for permanency in a time of change.

The game has kept faith with the public, maintaining its old admission price for nearly thirty years while other forms of entertainment have doubled and tripled in price. And it will probably never change.

One day I actually took the list into the bathroom and I put it up against my face and looked in the mirror and I realized I had one of two choices, change the list or change myself.

But the real focus should be on people who are buying today because the base is so big it will take a long time for any change materialize on an overall basis.