Great Throughts Treasury

"Just like a computer, we must remember things in the order in which entropy increases. This makes the second law of thermodynamics almost trivial. Disorder increases with time because we measure time in the direction in which disorder increases. You can’t have a safer bet than that!"

"It will be difficult enough to avoid disaster on planet Earth in the next hundred years, let alone the next thousand, or million. The human race shouldn't have all its eggs in one basket, or on one planet. Let's hope we can avoid dropping the basket until we have spread the load."

"It seems Einstein was doubly wrong when he said, God does not play dice. Not only does God definitely play dice, but He sometimes confuses us by throwing them where they can't be seen."

"Let me describe briefly how a black hole might be created. Imagine a star with a mass 10 times that of the sun. During most of its lifetime of about a billion years the star will generate heat at its center by converting hydrogen into helium. The energy released will create sufficient pressure to support the star against its own gravity, giving rise to an object with a radius about five times the radius of the sun. The escape velocity from the surface of such a star would be about 1,000 kilometers per second. That is to say, an object fired vertically upward from the surface of the star with a velocity of less than 1,000 kilometers per second would be dragged back by the gravitational field of the star and would return to the surface, whereas an object with a velocity greater than that would escape to infinity."

"Many people do not like the idea that time has a beginning, probably because it smacks of divine intervention. The Catholic Church, on the other hand, seized on the big bang model and in 1951 officially pronounced it to be in accordance with the Bible."

"Life would be tragic if it weren’t funny."

"It surprises me how disinterested we are today about things like physics, space, the universe and philosophy of our existence, our purpose, our final destination. It's a crazy world out there. Be curious."

"It's the gravity that shapes the large scale structure of the universe, even though it is the weakest of four categories of forces"

"It would be hypocritical to complain. I can generally ignore it by going off to think in 11 dimensions. [On his lack of privacy]"

"Let's indulge in a little science fiction for a moment. Time travel movies often feature a vast, energy-hungry machine. The machine creates a path through the fourth dimension, a tunnel through time. A time traveler, a brave, perhaps foolhardy individual, prepared for who knows what, steps into the time tunnel and emerges who knows when. The concept may be far-fetched, and the reality may be very different from this, but the idea itself is not so crazy. Physicists have been thinking about tunnels in time too, but we come at it from a different angle. We wonder if portals to the past or the future could ever be possible within the laws of nature. As it turns out, we think they are. What's more, we've even given them a name: wormholes. The truth is that wormholes are all around us, only they're too small to see. Wormholes are very tiny. They occur in nooks and crannies in space and time. You might find it a tough concept, but stay with me. Nothing is flat or solid. If you look closely enough at anything you'll find holes and wrinkles in it. It's a basic physical principle, and it even applies to time. Even something as smooth as a pool ball has tiny crevices, wrinkles and voids. Now it's easy to show that this is true in the first three dimensions. But trust me, it's also true of the fourth dimension. There are tiny crevices, wrinkles and voids in time. Down at the smallest of scales, smaller even than molecules, smaller than atoms, we get to a place called the quantum foam. This is where wormholes exist. Tiny tunnels or shortcuts through space and time constantly form, disappear, and reform within this quantum world. And they actually link two separate places and two different times. Unfortunately, these real-life time tunnels are just a billion-trillion-trillionths of a centimetre across. Way too small for a human to pass through - but here's where the notion of wormhole time machines is leading. Some scientists think it may be possible to capture a wormhole and enlarge it many trillions of times to make it big enough for a human or even a spaceship to enter. Given enough power and advanced technology, perhaps a giant wormhole could even be constructed in space. I'm not saying it can be done, but if it could be, it would be a truly remarkable device. One end could be here near Earth, and the other far, far away, near some distant planet. Theoretically, a time tunnel or wormhole could do even more than take us to other planets. If both ends were in the same place, and separated by time instead of distance, a ship could fly in and come out still near Earth, but in the distant past. Maybe dinosaurs would witness the ship coming in for a landing."

"Maybe that is our mistake: maybe there are no particle positions and velocities, but only waves. It is just that we try to fit the waves to our preconceived ideas of positions and velocities.The resulting mismatch is the cause of the apparent unpredictability."

"Many people would claim that the boundary conditions are not part of physics but belong to metaphysics or religion. They would claim that nature had complete freedom to start the universe off any way it wanted. That may be so, but it could also have made it evolve in a completely arbitrary and random manner. Yet all the evidence is that it evolves in a regular way according to certain laws. It would therefore seem reasonable to suppose that there are also laws governing the boundary conditions."

"Most sets of values would give rise to universes that, although they might be very beautiful, would contain no one able to wonder at that beauty."

"My goal is simple. It is a complete understanding of the universe, why it is as it is and why it exists at all."

"My dreams at the time were rather disturbed. Before my condition had been diagnosed, I had been very bored with life. There had not seemed to be anything worth doing. But shortly after I came out of hospital, I dreamt that I was going to be executed. I suddenly realized that there were a lot of worthwhile things I could do, if I were reprieved. Another dream that I had several times was that I would sacrifice my life to save others. After all, if I were going to die anyway, it might as well do some good."

"My expectations we're reduced to zero when I was 21. Everything since then has been a bonus."

"Not to take this web of dualities as a sign we are on the right track would be a bit like believing that God put fossils into the rocks in order to mislead Darwin about the evolution of life."

"Nature Abhors a Naked Singularity."

"Now, I realize that thinking in four dimensions is not easy, and that wormholes are a tricky concept to wrap your head around, but hang in there. I've thought up a simple experiment that could reveal if human time travel through a wormhole is possible now, or even in the future. I like simple experiments, and champagne. So I've combined two of my favourite things to see if time travel from the future to the past is possible. Let's imagine I'm throwing a party, a welcome reception for future time travellers. But there's a twist. I'm not letting anyone know about it until after the party has happened. I've drawn up an invitation giving the exact coordinates in time and space. I am hoping copies of it, in one form or another, will be around for many thousands of years. Maybe one day someone living in the future will find the information on the invitation and use a wormhole time machine to come back to my party, proving that time travel will, one day, be possible. In the meantime, my time traveller guests should be arriving any moment now. Five, four, three, two, one. But as I say this, no one has arrived. What a shame. I was hoping at least a future Miss Universe was going to step through the door. So why didn't the experiment work? One of the reasons might be because of a well-known problem with time travel to the past, the problem of what we call paradoxes. Paradoxes are fun to think about. The most famous one is usually called the Grandfather paradox. I have a new, simpler version I call the Mad Scientist paradox. I don't like the way scientists in movies are often described as mad, but in this case, it's true. This chap is determined to create a paradox, even if it costs him his life. Imagine, somehow, he's built a wormhole, a time tunnel that stretches just one minute into the past. Through the wormhole, the scientist can see himself as he was one minute ago. But what if our scientist uses the wormhole to shoot his earlier self? He's now dead. So who fired the shot? It's a paradox. It just doesn't make sense. It's the sort of situation that gives cosmologists nightmares. This kind of time machine would violate a fundamental rule that governs the entire universe - that causes happen before effects, and never the other way around. I believe things can't make themselves impossible. If they could then there'd be nothing to stop the whole universe from descending into chaos. So I think something will always happen that prevents the paradox. Somehow there must be a reason why our scientist will never find himself in a situation where he could shoot himself. And in this case, I'm sorry to say, the wormhole itself is the problem. In the end, I think a wormhole like this one can't exist. And the reason for that is feedback. If you've ever been to a rock gig, you'll probably recognise this screeching noise. It's feedback. What causes it is simple. Sound enters the microphone. It's transmitted along the wires, made louder by the amplifier, and comes out at the speakers. But if too much of the sound from the speakers goes back into the mic it goes around and around in a loop getting louder each time. If no one stops it, feedback can destroy the sound system."

"My publisher told me that the number of readers of this book will be inversely proportional to the number of equations it contains."

"On seeing the Enterprise's warp engine while visiting the set of Star Trek: The Next Generation (where he would briefly play himself in the 1993 episode Descent, Part I), Hawking smiled and said: I'm working on that."

"Newton seems to have been an unpleasant character."

"One can imagine that God created the universe at literally any time in the past. On the other hand, if the universe is expanding, there may be physical reasons why there had to be a beginning. One could imagine that God created the universe at the instant of the big bang, or even afterwards in just such a way as to make it look as though there had been a big bang, but it would be meaningless to suppose that it was created before the big bang. An expanding universe does not preclude a creator, but it does place limits on when he might have carried out his job!"

"One cannot really argue with a mathematical theorem."

"One could say: The boundary condition of the universe is that it has no boundary. The universe would be completely self-contained and not affected by anything outside itself. It would neither be created nor destroyed. It would just BE."

"One does not have to appeal to God to set the initial conditions for the creation of the universe, but if one does He would have to act through the laws of physics."

"One is always a long way from solving a problem until one actually has the answer."

"One of the basic rules of the universe is that nothing is perfect. Perfection simply doesn't exist.....Without imperfection, neither you nor I would exist"

"One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?"

"One, remember to look up at the stars and not down at your feet. Two, never give up work. Work gives you meaning and purpose and life is empty without it. Three, if you are lucky enough to find love, remember it is there and don't throw it away."

"Our brains interpret the input from our sensory organs by making a model of the world. When such a model is successful at explaining events, we tend to attribute to it, and to the elements and concepts that constitute it, the quality of reality or absolute truth. But there may be different ways in which one could model the same physical situation, with each employing different fundamental elements and concepts. If two such physical theories or models accurately predict the same events, one cannot be said to be more real than the other; rather, we are free to use whichever model is most convenient."

"People who boast about their IQ are losers."

"Our search for understanding will never come to an end, and that we will always have the challenge of new discovery. Without it, we would stagnate."

"Primitive life [in the universe] is very common and intelligent life is fairly rare. Some would say it has yet to occur on Earth."

"Q: What is the value in knowing Why are we here? A: The universe is governed by science. But science tells us that we can't solve the equations, directly in the abstract. We need to use the effective theory of Darwinian natural selection of those societies most likely to survive. We assign them higher value. Q: You've said there is no reason to invoke God to light the blue touchpaper. Is our existence all down to luck? A: Science predicts that many different kinds of universe will be spontaneously created out of nothing. It is a matter of chance which we are in. Q: So here we are. What should we do? A: We should seek the greatest value of our action. Q: You had a health scare and spent time in hospital in 2009. What, if anything, do you fear about death? A: I have lived with the prospect of an early death for the last 49 years. I'm not afraid of death, but I'm in no hurry to die. I have so much I want to do first. I regard the brain as a computer which will stop working when its components fail. There is no heaven or afterlife for broken down computers; that is a fairy story for people afraid of the dark. Q: What are the things you find most beautiful in science? A: Science is beautiful when it makes simple explanations of phenomena or connections between different observations. Examples include the double helix in biology, and the fundamental equations of physics."

"Remember to look up at the stars and not down at your feet. Never give up work. Work gives you meaning and purpose and life is empty without it. If you are lucky enough to find love, remember it is there and don't throw it away."

"Quiet people have the loudest minds."

"Remember to look up at the stars and not down at your feet. Try to make sense of what you see and wonder about what makes the universe exist. Be curious. And however difficult life may seem, there is always something you can do and succeed at."

"Reports in magazine articles that I drank heavily are an exaggeration. I felt somewhat of a tragic character. I took to listening to Wagner."

"Science is beautiful when it makes simple explanations of phenomena or connections between different observations. Examples include the double helix in biology, and the fundamental equations of physics."

"Science predicts that many different kinds of universe will be spontaneously created out of nothing. It is a matter of chance which we are in. [Answer to question: You've said there is no reason to invoke God to light the blue touchpaper. Is our existence all down to luck?]"

"Scientists tend to risk theories they admire."

"So Einstein was wrong when he said, God does not play dice. Consideration of black holes suggests, not only that God does play dice, but that he sometimes confuses us by throwing them where they can't be seen."

"Simplicity is a matter of taste."

"So long as the universe had a beginning, we could suppose it had a creator. But if the universe is really completely self-contained, having no boundary or edge, it would have neither beginning nor end: it would simply be. What place, then, for a creator?"

"So next time someone complains that you have made a mistake, tell him that may be a good thing. Because without imperfection, neither you nor I would exist."

"Someone told me that each equation I included in the book would halve the sales. I therefore resolved not to have any equations at all. In the end, however, I did put in one equation, Einstein's famous equation, E = mc2. I hope that this will not scare off half of my potential readers."

"String theory cannot even describe the structure of the sun, let alone black holes."

"The danger is that global warming may become self-sustaining, if it has not done so already. The melting of the Arctic and Antarctic ice caps reduces the fraction of solar energy reflected back into space, and so increases the temperature further. Climate change may kill off the Amazon and other rain forests, and so eliminate once one of the main ways in which carbon dioxide is removed from the atmosphere. The rise in sea temperature may trigger the release of large quantities of carbon dioxide, trapped as hydrides on the ocean floor. Both these phenomena would increase the greenhouse effect, and so global warming further. We have to reverse global warming urgently, if we still can."

"Sports is to war as pornography is to sex."