Mathematical Universe Quotes

Even if there is only one possible unified theory, it is just a set of rules and equations. What is it that breathes fire into the equations and makes a universe for them to describe? The usual approach of science of constructing a mathematical model cannot answer the questions of why there should be a universe for the model to describe. Why does the universe go to all the bother of existing?

Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic, and abstract beauty.

Once upon a time, there was a girl who talked to the moon. And she was mysterious and she was perfect, in that way that girls who talk to moons are. In the house next door, there lived a boy. And the boy watched the girl grow more and more perfect, more and more beautiful with each passing year. He watched her watch the moon. And he began to wonder if the moon would help him unravel the mystery of the beautiful girl. So the boy looked into the sky. But he couldn't concentrate on the moon. He was too distracted by the stars. And it didn't matter how many songs or poems had already been written about them, because whenever he thought about the girl, the stars shone brighter. As if she were the one keeping them illuminated. One day, the boy had to move away. He couldn't bring the girl with him, so he brought the stars. When he'd look out his window at night, he would start with one. One star. And the boy would make a wish on it, and the wish would be her name. At the sound of her name, a second star would appear. And then he'd wish her name again, and the stars would double into four. And four became eight, and eight became sixteen, and so on, in the greatest mathematical equation the universe had ever seen. And by the time an hour had passed, the sky would be filled with so many stars that it would wake the neighbors. People wondered who'd turned on the floodlights. The boy did. By thinking about the girl.

Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

This most beautiful system of the sun, planets and comets, could only proceed from the counsel and dominion of an intelligent and powerful Being... This Being governs all things, not as the soul of the world, but as Lord over all; and on account of his dominion he is wont, to be called Lord God παντοκρατωρ or Universal Ruler.

Mathematics is the language in which God has written the universe

Physics depends on a universe infinitely centred on an equals sign.

As an orangutan cannot embrace higher mathematics or comprehend the architecture and operation of a computer, we humans __ so good at loudly proclaiming our intelligence and applauding our own doltish displays of cerebral gymnastics __ cannot begin to understand the true structure and functioning of the Universe.

Having solved all the major mathematical, physical, chemical, biological, sociological, philosophical, etymological, meteorological and psychological problems of the Universe except for his own, three times over, [Marvin] was severely stuck for something to do, and had taken up composing short dolorous ditties of no tone, or indeed tune. The latest one was a lullaby. Marvin droned, Now the world has gone to bed, Darkness won't engulf my head, I can see in infrared, How I hate the night. He paused to gather the artistic and emotional strength to tackle the next verse. Now I lay me down to sleep, Try to count electric sheep, Sweet dream wishes you can keep, How I hate the night.

We have a closed circle of consistency here: the laws of physics produce complex systems, and these complex systems lead to consciousness, which then produces mathematics, which can then encode in a succinct and inspiring way the very underlying laws of physics that gave rise to it.

A basic rule of mathematical life: if the universe hands you a hard problem, try to solve an easier one instead, and hope the simple version is close enough to the original problem that the universe doesn’t object.

Numbers written on restaurant bills within the confines of restaurants do not follow the same mathematical laws as numbers written on any other pieces of paper in any other parts of the Universe. This single fact took the scientific world by storm.

There’s no better guarantee of failure than convincing yourself that success is impossible, and therefore never even trying.

The 3-legged stool of understanding is held up by history, languages, and mathematics. Equipped with those three you can learn anything you want to learn. But if you lack any one of them you are just another ignorant peasant with dung on your boots.

The important thing to remember about mathematics is not to be frightened

God is a mathematician of a very high order and He used advanced mathematics in constructing the universe.

Some people majored in English to prepare for law school. Others became journalists. The smartest guy in the honors program, Adam Vogel, a child of academics, was planning on getting a Ph.D. and becoming an academic himself. That left a large contingent of people majoring in English by default. Because they weren't left-brained enough for science, because history was too try, philosophy too difficult, geology too petroleum-oriented, and math too mathematical - because they weren't musical, artistic, financially motivated, or really all that smart, these people were pursuing university degrees doing something no different from what they'd done in first grade: reading stories. English was what people who didn't know what to major in majored in.

The Hitchhiker's Guide to the Galaxy's definition of "Universe": The Universe is a very big thing that contains a great number of planets and a great number of beings. It is Everything. What we live in. All around us. The lot. Not nothing. It is quite difficult to actually define what the Universe means, but fortunately the Guide doesn't worry about that and just gives us some useful information to live in it. Area: The area of the Universe is infinite. Imports: None. This is a by product of infinity; it is impossible to import things into something that has infinite volume because by definition there is no outside to import things from. Exports: None, for similar reasons as imports. Population: None. Although you might see people from time to time, they are most likely products of your imagination. Simple mathematics tells us that the population of the Universe must be zero. Why? Well given that the volume of the universe is infinite there must be an infinite number of worlds. But not all of them are populated; therefore only a finite number are. Any finite number divided by infinity is zero, therefore the average population of the Universe is zero, and so the total population must be zero. Art: None. Because the function of art is to hold a mirror up to nature there can be no art because the Universe is infinite which means there simply isn't a mirror big enough. Sex: None. Although in fact there is quite a lot, given the zero population of the Universe there can in fact be no beings to have sex, and therefore no sex happens in the Universe.

…Our sunsets have been reduced to wavelengths and frequencies. The complexities of the universe have been shredded into mathematical equations. Even our self-worth as human beings has been destroyed.

I think that consciousness is the way information feels when being processed in certain complex ways.

Time was simple, is simple. We can divide it into simple parts, measure it, arrange dinner by it, drink whisky to its passage. We can mathematically deploy it, use it to express ideas about the observable universe, and yet if asked to explain it in simple language to a child–in simple language which is not deceit, of course–we are powerless. The most it ever seems we know how to do with time is to waste it.

Mathematics is the language with which God has written the universe.

Real knowledge is to know the extent of one’s ignorance. —Confucius The highest form of ignorance is when you reject something you don’t know anything about. —Wayne Dyer

In the eighteenth century, philosophers considered the whole of human knowledge, including science, to be their field and discussed questions such as: Did the universe have a beginning? However, in the nineteenth and twentieth centuries, science became too technical and mathematical for the philosophers, or anyone else except a few specialists. Philosophers reduced the scope of their inquiries so much that Wittgenstein, the most famous philosopher of this century, said, "The sole remaining task for philosophy is the analysis of language." What a comedown from the great tradition of philosophy from Aristotle to Kant!

No doubt there are some who, when confronted with a line of mathematical symbols, however simply presented, can only see the face of a stern parent or teacher who tried to force into them a non-comprehending parrot-like apparent competence--a duty and a duty alone--and no hint of magic or beauty of the subject might be allowed to come through.

Film is one if three universal languages, the other two: mathematics and music.

I wanted very much to learn to draw, for a reason that I kept to myself: I wanted to convey an emotion I have about the beauty of the world. It's difficult to describe because it's an emotion. It's analogous to the feeling one has in religion that has to do with a god that controls everything in the whole universe: there's a generality aspect that you feel when you think about how things that appear so different and behave so differently are all run "behind the scenes" by the same organization, the same physical laws. It's an appreciation of the mathematical beauty of nature, of how she works inside; a realization that the phenomena we see result from the complexity of the inner workings between atoms; a feeling of how dramatic and wonderful it is. It's a feeling of awe — of scientific awe — which I felt could be communicated through a drawing to someone who had also had this emotion. It could remind him, for a moment, of this feeling about the glories of the universe.

Let's face it, the universe is messy. It is nonlinear, turbulent, and chaotic. It is dynamic. It spends its time in transient behavior on its way to somewhere else, not in mathematically neat equilibria. It self-organizes and evolves. It creates diversity, not uniformity. That's what makes the world interesting, that's what makes it beautiful, and that's what makes it work.

Why do we perceive the world as stable and ourselves as local and unique? Here’s my guess: because it’s useful.

Human thought, flying on the trapezes of the star-filled universe, with mathematics stretched beneath, was like an acrobat working with a net but suddenly noticing that in reality there is no net.

The universe is all mathematics and probabilities.

Universality is the distinguishing mark of genius. There is no such thing as a special genius, a genius for mathematics, or for music, or even for chess, but only a universal genius. The genius is a man who knows everything without having learned it.

I feel that my main responsibility as a teacher isn’t to convey facts, but to rekindle that lost enthusiasm for asking questions.

Do people believe in human rights because such rights actually exist, like mathematical truths, sitting on a cosmic shelf next to the Pythagorean theorem just waiting to be discovered by Platonic reasoners? Or do people feel revulsion and sympathy when they read accounts of torture, and then invent a story about universal rights to help justify their feelings?

This most beautiful system [The Universe] could only proceed from the dominion of an intelligent and powerful Being.

So I feel that the experimental verdict is in: the world is weird, and we just have to learn to live with it.

How did you know?” “I…” Thomas swallowed hard, his attention fixed on the painting. “The truth?” “Please.” “You’ve got a dress with orchid blossoms embroidered on it. Ribbons in the deepest purple. You favor the color, but not nearly as much as I find myself favoring you.” He took a deep breath. “As to the stars? Those are what I prefer. More than medical practices and deductions. The universe is vast. A mathematical equation even I have no hope of solving. For there are no limits to the stars; their numbers are infinite. Which is precisely why I measure my love for you by them. An amount too boundless to count.

Our mathematics is the symbolic counterpart of the universe we perceive, and its power has been continuously enhanced by human exploration.

Mathematics directs the flow of the universe, lurks behind its shapes and curves, holds the reins of everything from tiny atoms to the biggest stars.

As to the stars? Those are what I prefer. More than medical practices and deductions. The universe is vast. A mathematical equation even I have no hope of solving. For there are no limits to the stars; their numbers are infinite. Which is precisely why i measure my love for you by them An amount too boundless to count.

...The pages and pages of complex, impenetrable calculations might have contained the secrets of the universe, copied out of God's notebook. In my imagination, I saw the creator of the universe sitting in some distant corner of the sky, weaving a pattern of delicate lace so fine that that even the faintest light would shine through it. The lace stretches out infinitely in every direction, billowing gently in the cosmic breeze. You want desperately to touch it, hold it up to the light, rub it against your cheek. And all we ask is to be able to re-create the pattern, weave it again with numbers, somehow, in our own language; to make the tiniest fragment our own, to bring it back to eart.

In my own professional work I have touched on a variety of different fields. I’ve done work in mathematical linguistics, for example, without any professional credentials in mathematics; in this subject I am completely self-taught, and not very well taught. But I’ve often been invited by universities to speak on mathematical linguistics at mathematics seminars and colloquia. No one has ever asked me whether I have the appropriate credentials to speak on these subjects; the mathematicians couldn’t care less. What they want to know is what I have to say. No one has ever objected to my right to speak, asking whether I have a doctor’s degree in mathematics, or whether I have taken advanced courses in the subject. That would never have entered their minds. They want to know whether I am right or wrong, whether the subject is interesting or not, whether better approaches are possible… the discussion dealt with the subject, not with my right to discuss it. But on the other hand, in discussion or debate concerning social issues or American foreign policy…. The issue is constantly raised, often with considerable venom. I’ve repeatedly been challenged on grounds of credentials, or asked, what special training do I have that entitles you to speak on these matters. The assumption is that people like me, who are outsiders from a professional viewpoint, are not entitled to speak on such things. Compare mathematics and the political sciences… it’s quite striking. In mathematics, in physics, people are concerned with what you say, not with your certification. But in order to speak about social reality, you must have the proper credentials, particularly if you depart from the accepted framework of thinking. Generally speaking, it seems fair to say that the richer the intellectual substance of a field, the less there is a concern for credentials, and the greater is the concern for content.

Cindy, have you heard of the second law of thermodynamics?” “Yes. Something about heat energy can never be created or destroyed?” “That’s the first law of thermodynamics. The second one is this…all organized systems tend to slide slowly into chaos and disorder. Energy tends to run down. The universe itself heads inevitably towards darkness and stasis. Our own star system eventually will die, the sun will become a red giant, and the earth will be swallowed by the red giant.” “Cheery thought.” “But mathematics has altered this concept; rather one particular mathematician. His name was Ilya Prigogine, a Belgian mathematician.” “Who and what does that have to do with your being a PI and a great psychologist?” “Are you being sarcastic? Of course you are. Anyway, what I was trying to say was that Prigogine used the analogy of a walled city and open city. The walled city is isolated from its surroundings and will run down, decay, and die. The open city will have an exchange of materials and energy with its surroundings and will become larger and more complex; capable of dissipating energy even as it grows. So my point is, this analogy very much pertains to a certain female. The walled person versus the open person. The walled person will eventually decline, fade, and decay.

All the hypotheses about the early universe . . . are pure speculation. They're modern creation myths written in the language of mathematics.

economics was largely a form of intellectual prostitution where you got rewarded for saying what the powers that be wanted to hear.

There cannot be a language more universal and more simple, more free from errors and obscurities...more worthy to express the invariable relations of all natural things [than mathematics]. [It interprets] all phenomena by the same language, as if to attest the unity and simplicity of the plan of the universe, and to make still more evident that unchangeable order which presides over all natural causes

I needed to wander… whenever and wherever I wanted! I’d found myself at the end of my rope as far as school was concerned; there seemed no particular reason for me to stay. The teachers didn’t want to teach, and I didn’t want to learn—from them. I wanted my education to come from living life, getting out there in the world, seeing and doing and moving amongst the other vagabonds who had had the same sneaking suspicion that I did, that there would be no great need for high-end mathematics, nope… I was not going to be doing other people’s taxes and going home at 5:37 p.m. to pat my dog’s head and sit down to my one meat and two vegetable table waiting for Jeopardy to pop on the glass tit, the Pat Sajak of my own private game show, in the bellybutton of the universe, Miramar, Florida.

A man craves ultimate truths. Every mortal mind, I think, is that way. But what is ultimate truth? It's the end of the road, where there is no more mystery, no more hope. And no more questions to ask, since all the answers have been given. But there is no such place. The Universe is a labyrinth made of labyrinths. Each leads to another. And wherever we cannot go ourselves, we reach with mathematics. Out of mathematics we build wagons to carry us into the nonhuman realms of the world.

She needs to be educated. She needs to know the contents of those books, there. She needs to understand the movements of the stars and the origins of the universe and the requirements of kindness. She needs to know mathematics and poetry. She must ask questions. She must seek to understand. She must understand the laws of cause and effect and unintended consequences. She must learn compassion and curiosity and awe. All of these things. We have to instruct her, Glerk. All three of us. It is a great responsibility.” The

The world of strict naturalism in which clever mathematical laws all by themselves bring the universe and life into existence, is pure (and, one might add, poor) fiction. To call it science-fiction would besmirch the name of science.

When she was a teenager D’Agostino told a friend that she wanted to go to university to study Death, Stars and Mathematics. Inexplicably the University of Manchester didn’t offer such a course, so she settled for Mathematics.

Srinivasa Ramanujan was the strangest man in all of mathematics, probably in the entire history of science. He has been compared to a bursting supernova, illuminating the darkest, most profound corners of mathematics, before being tragically struck down by tuberculosis at the age of 33... Working in total isolation from the main currents of his field, he was able to rederive 100 years’ worth of Western mathematics on his own. The tragedy of his life is that much of his work was wasted rediscovering known mathematics.

The theory of computation has traditionally been studied almost entirely in the abstract, as a topic in pure mathematics. This is to miss the point of it. Computers are physical objects, and computations are physical processes. What computers can or cannot compute is determined by the laws of physics alone, and not by pure mathematics.

In the early universe—when the universe was small enough to be governed by both general relativity and quantum theory—there were effectively four dimensions of space and none of time. That means that when we speak of the “beginning” of the universe, we are skirting the subtle issue that as we look backward toward the very early universe, time as we know it does not exist! We must accept that our usual ideas of space and time do not apply to the very early universe. That is beyond our experience, but not beyond our imagination, or our mathematics.

In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of thirty or thirty-five years, I can state that their imprint upon the mathematics of our time has not been very profound. They've all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they've remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birthright, as it was mine: the capacity to be alone.

All high mathematics serves to do is to beget higher mathematics.

Although in principle we know the equations that govern the whole of biology, we have not been able to reduce the study of human behavior to a branch of applied mathematics.

I’ve come to believe that genius is an exceedingly common human quality, probably natural to most of us. I didn’t want to accept that notion — far from it: my own training in two elite universities taught me that intelligence and talent distributed themselves economically over a bell curve and that human destiny, because of those mathematical, seemingly irrefutable scientific facts, was as rigorously determined as John Calvin contended.

So, I convinced myself that, because the statistical likelihood of something happening in real life exactly the way I imagined it was so low, if I imagined the worst possible things in vivid detail, I could mathematically reduce the odds of them happening. I convinced myself that my brain had power over the probability projections of the universe. I’d lie awake at night thinking about all the worst stuff that could happen like it was my job, and I don’t know if I ever really broke the habit.

All nature has come to expect from God a sense of orderliness. Whatever God does carries with it His fingerprint. And in the world around us His fingerprint of orderliness is evident to anybody who is honest with the facts. If you look at nature, you will discover a mathematical exactness. Without this precision, the entire world would be in utter confusion. One plus one always equals two no matter what part of the universe you happen to be in. And the laws of nature operate in beautiful harmony, a harmony that is ordered by God Himself.

I believe we can keep what feels wondrous about the search for a mathematical description of the universe while disconnecting this work from its historical place in the hands of violently colonial nation-states.

In 1982, Raphael Nachman, visiting lecturer in mathematics at the university in Cracow, declined the tour of Auschwitz, where his grandparents had died, and asked instead to visit the ghetto where they had lived.

We should reject the view that high culture, as the possession of an elite, is of no use to those who don’t possess it. This is as false as the view that science or higher mathematics are useless to those who don’t understand them. Scientific knowledge exists because a few talented people are prepared to devote their energy to pursuing it. That is what a university is for: and since you cannot pass on difficult knowledge without discriminating between the students who can absorb it and those who cannot, discrimination is a social good. The same is true of high culture. Those able to acquire it will be a minority and the process of cultural transmission will be critically impeded if that teacher must teach Mozart and Lady Gaga side by side to satisfy some egalitarian agenda.

Mathematics has always shown a curious ability to be applicable to nature, and this may express a deep link between our minds and nature. We are the Universe speaking out, a part of nature. So it is not so surprising that our systems of logic and mathematics sing in tune with nature.

When I was young, most teachers of philosophy in British and American universities were Hegelians, so that, until I read Hegel, I supposed there must be some truth to his system; I was cured, however, by discovering that everything he said on the philosophy of mathematics was plain nonsense.

Study after study has shown almost all behavioral and psychological differences between the sexes to be small or nonexistent. Cambridge University psychologist Melissa Hines and others have repeatedly demonstrated that boys and girls have little, if any, noticeable gaps between them when it comes to fine motor skills, spatial visualization, mathematics ability, and verbal fluency.

To make this condition mathematically clearer, it is convenient to assert it in the form that the space-time can be continued smoothly, as a conformal manifold, a little way prior to the hypersurface . To before the Big Bang? Surely not: the Big Bang is supposed to represent the beginning of all things, so there can be no ‘before’. Never fear—this is just a mathematical trick. The extension is not supposed to have any physical meaning! Or might it …?

Philosophy is written in that great book which ever lies before our eyes — I mean the universe — but we cannot understand it if we do not first learn the language and grasp the symbols, in which it is written. This book is written in the mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

Why a journey into space? Because science is now learning that the infinite reaches of our universe probably teem with as much life and adventure as Earth's own oceans and continents. Our galaxy alone is so incredibly vast that the most conservative mathematical odds still add up to millions of planets almost identical to our own — capable of life, even intelligence and strange new civilizations. Alien beings that will range from the fiercely primitive to the incredibly exotic intelligence which will far surpass Mankind. (The Hollywood Reporter, Sept. 8, 1966)

The laws of Nature are written in the language of mathematics.” Math is a way to describe reality and figure out how the world works, a universal language that has become the gold standard of truth. In our world, increasingly driven by science and technology, mathematics is becoming, ever more, the source of power, wealth, and progress. Hence those who are fluent in this new language will be on the cutting edge of progress.

Ever since I was a child, I’ve had the gut sense that there’s a consciousness behind the universe. When I witness the precision of mathematics, the reliability of physics, and the symmetries of the cosmos, I don’t feel like I’m observing cold science; I feel as if I’m seeing a living footprint…the shadow of some greater force that is just beyond our grasp.

The basic principle of the new education is to be that dunces and idlers must not be made to feel inferior to intelligent and industrious pupils. That would be ‘undemocratic’. These differences between the pupils—for they are obviously and nakedly individual differences—must be disguised. This can be done on various levels. At universities, examinations must be framed so that nearly all the students get good marks. Entrance examinations must be framed so that all, or nearly all, citizens can go to universities, whether they have any power (or wish) to profit by higher education or not. At schools, the children who are too stupid or lazy to learn languages and mathematics and elementary science can be set to doing the things that children used to do in their spare time. Let them, for example, make mud-pies and call it modelling. But all the time there must be no faintest hint that they are inferior to the children who are at work. Whatever nonsense they are engaged in must have—I believe the English already use the phrase—‘parity of esteem’. An even more drastic scheme is not impossible. Children who are fit to proceed to a higher class may be artificially kept back, because the others would get a trauma—Beelzebub, what a useful word!—by being left behind. The bright pupil thus remains democratically fettered to his own age-group throughout his school career, and a boy who would be capable of tackling Aeschylus or Dante sits listening to his coaeval’s attempts to spell out A CAT SAT ON THE MAT.

Our experience teaches us that there are indeed laws of nature, regularities in the way things behave, and that these laws are best expressed using the language of mathematics. This raises the interesting possibility that mathematical consistency might be used to guide us, along with experimental observation, to the laws that describe physical reality, and this has proved to be the case time and again throughout the history of science. We will see this happen during the course of this book, and it is truly one of the wonderful mysteries of our universe that it should be so.

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth. —Galileo Galilei, The Assayer, 1623

A black man, Benjamin Banneker, who taught himself mathematics and astronomy, predicted accurately a solar eclipse, and was appointed to plan the new city of Washington, wrote to Thomas Jefferson: I suppose it is a truth too well attested to you, to need a proof here, that we are a race of beings, who have long labored under the abuse and censure of the world; that we have long been looked upon with an eye of contempt; and that we have long been considered rather as brutish than human, and scarcely capable of mental endowments. . . . I apprehend you will embrace every opportunity to eradicate that train of absurd and false ideas and opinions, which so generally prevails with respect to us; and that your sentiments are concurrent with mine, which are, that one universal Father hath given being to us all; and that he hath not only made us all of one flesh, but that he hath also, without partiality, afforded us all the same sensations and endowed us all with the same facilities. . . . Banneker asked Jefferson “to wean yourselves from those narrow prejudices which you have imbibed.

Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that Galilei ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that Copernicus ascertained the true position of the earth and accounted for all celestial phenomena; that Kepler discovered his three laws—discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that Newton gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that Euclid, Cavalieri, Descartes, and Leibniz, almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of Galvani, Volta, Franklin and Morse, of Trevithick, Watt and Fulton and of all the pioneers of progress—that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that Æschylus and Shakespeare, Burns, and Beranger, Goethe and Schiller, and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God?

For the next half hour it continued. Dr. Joseph would call on someone who looked half bright, then he would call on someone whom he felt was just the opposite. In the upper grades—fourth, fifth, and sixth—he asked grammatical, mathematical, and geographical questions. And besides looking at hands, now he began inspecting teeth. Open wide, say “Ahhh”—and he would have the poor children spreading out their lips as far as they could while he peered into their mouths. At the university I had read about slave masters who had done the same when buying new slaves, and I had read of cattlemen doing it when purchasing horses and cattle. At least Dr. Joseph had graduated to the level where he let the children spread out their own lips, rather than using some kind of crude metal instrument. I appreciated his humanitarianism.

If memory within nature sounds mysterious, we should bear in mind that mathematical laws transcending nature are more rather than less so; they are metaphysical rather than physical. The way mathematical laws can exist independently of the evolving universe and at the same time act upon it remains a profound mystery. For those who accept God, this mystery is an aspect of God's relation to the realm of nature; for those who deny God, the mystery is even more obscure: A quasi-mental realm of mathematical laws somehow exists independently of nature, yet not in God, and governs the evolving physical world without itself being physical.

Because, you see, everything you know about the way this universe works is correct—except for the little problem that this isn’t the only universe we have to worry about. Information can leak between one universe and another. And in a vanishingly small number of the other universes there are things that listen, and talk back—see Al-Hazred, Nietzsche, Lovecraft, Poe, et cetera. The many-angled ones, as they say, live at the bottom of the Mandelbrot set, except when a suitable incantation in the platonic realm of mathematics—computerised or otherwise—draws them forth. (And you thought running that fractal screen-saver was good for your computer?)

THE BOTTOM LINE •  Parallel universes are not a theory, but a prediction of certain theories. •  Eternal inflation predicts that our Universe (the spherical region of space from which light has had time to reach us during the 14 billion years since our Big Bang) is just one of infinitely many universes in a Level I multiverse where everything that can happen does happen somewhere. •  For a theory to be scientific, we need not be able to observe and test all its predictions, merely at least one of them. Inflation is the leading theory for our cosmic origins because it’s passed observational tests, and parallel universes seem to be a non-optional part of the package. •  Inflation converts potentiality into reality: if the mathematical equations governing

What was magic, after all, but something that happened at the snap of a finger? Where was the magic in that? It was mumbled words and weird drawings in old books, and in the wrong hands it was as dangerous as hell, but not one half as dangerous as it could be in the right hands. The universe was full of the stuff; it made the stars stay up and the feet stay down. But what was happening now . . . this was magical. Ordinary men had dreamed it up and put it together, building towers on rafts in swamps and across the frozen spines of mountains. They’d cursed and, worse, used logarithms. They’d waded through rivers and dabbled in trigonometry. They hadn’t dreamed, in the way people usually used the word, but they’d imagined a different world, and bent metal around it. And out of all the sweat and swearing and mathematics had come this . . . thing, dropping words across the world as softly as starlight.

If he would just work with pure ideas like a proper mathematician he could go as fast as thought. As it happens, Alan has become fascinated by the incarnations of pure ideas in the physical world. The underlying math of the universe is like the light streaming in through the window. Alan is not satisfied with merely knowing that it streams in. He blows smoke into the air to make the light visible. He sits in meadows gazing at pine cones and flowers, tracing the mathematical patterns in their structure, and he dreams about electron winds blowing over the glowing filaments and screens of radio tubes, and, in their surges and eddies, capturing something of what is going on in his own brain. Turing is neither a mortal nor a god. He is Antaeus. That he bridges the mathematical and physical worlds is his strength and his weakness.

Doing a geographic” is a term alcoholics often use for acting on the impulse to start over by moving to a new town, or state, instead of making any internal changes. It’s the anywhere-but-here part of the disease that says, “Remove yourself from this, go someplace new, and everything will be better.” Two years into our Florida stint, my mother pulled a geographic as radical as the move from Rochester. The new plan was to head for California. She enrolled in the mathematics graduate program at the University of California’s shiny new campus in San Diego, and as soon as our elementary school let out for the summer, she put us into a new Buick station wagon – a gift from her parents – and drove us across the country. You’d think we’d have protested at yet another move. After all, having been duped before, we were in no position to believe that the next move would be any different. But I have no memory of being unhappy about the news. Because that’s what often happens when an alcoholic parent is doing a geographic. She pulls you in and, before you know it, you, too, believe in the promise of the new place.

But the point is, when the writer turns to address the reader, he or she must not only speak to me—naively dazzled and wholly enchanted by the complexities of the trickery, and thus all but incapable of any criticism, so that, indeed, he can claim, if he likes, priestly contact with the greater powers that, hurled at him by the muse, travel the parsecs from the Universe’s furthest shoals, cleaving stars on the way, to shatter the specific moment and sizzle his brains in their pan, rattle his teeth in their sockets, make his muscles howl against his bones, and to galvanize his pen so the ink bubbles and blisters on the nib (nor would I hear her claim to such as other than a metaphor for the most profound truths of skill, craft, or mathematical and historical conjuration)—but she or he must also speak to my student, for whom it was an okay story, with just so much description.

It seems to be one of the fundamental features of nature that fundamental physical laws are described in terms of a mathematical theory of great beauty and power, needing quite a high standard of mathematics for one to understand it. You may wonder: Why is nature constructed along these lines? One can only answer that our present knowledge seems to show that nature is so constructed. We simply have to accept it. One could perhaps describe the situation by saying that God is a mathematician of a very high order, and He used very advanced mathematics in constructing the universe. Our feeble attempts at mathematics enable us to understand a bit of the universe, and as we proceed to develop higher and higher mathematics we can hope to understand the universe better.

Why does the universe go to all the bother of existing? Is the unified theory so compelling that it brings about its own existence? Or does it need a creator, and, if so, does he have any other effect on the universe? And who created him? Up to now, most scientists have been too occupied with the development of new theories that describe what the universe is to ask the question why. On the other hand, the people whose business it is to ask why, the philosophers, have not been able to keep up with the advance of scientific theories. In the eighteenth century, philosophers considered the whole of human knowledge, including science, to be their field and discussed questions such as: Did the universe have a beginning? However, in the nineteenth and twentieth centuries, science became too technical and mathematical for the philosophers, or anyone else except a few specialists. Philosophers reduced the scope of their inquiries so much that Wittgenstein, the most famous philosopher of this century, said, 'The sole remaining task for philosophy is the analysis of language.' What a comedown from the great tradition of philosophy from Aristotle to Kant! However, if we do discover a complete theory, it should in time be understandable in broad principle by everyone, not just a few scientists. Then we shall all, philosophers, scientists, and just ordinary people, be able to take part in the discussion of the question of why it is that we and the universe exist. If we find the answer to that, it would be the ultimate triumph of human reason--for then we would know the mind of God.

Meanwhile, someplace in the world, somebody is making love and another a poem. Elsewhere in the universe, a star manyfold the mass of our third-rate sun is living out its final moments in a wild spin before collapsing into a black hole, its exhale bending spacetime itself into a well of nothingness that can swallow every atom that ever touched us and every datum we ever produced, every poem and statue and symphony we’ve ever known—an entropic spectacle insentient to questions of blame and mercy, devoid of why. “In four billion years, our own star will follow its fate, collapsing into a white dwarf. We exist only by chance, after all. The Voyager will still be sailing into the interstellar shorelessness on the wings of the “heavenly breezes” Kepler had once imagined, carrying Beethoven on a golden disc crafted by a symphonic civilization that long ago made love and war and mathematics on a distant blue dot. But until that day comes, nothing once created ever fully leaves us. Seeds are planted and come abloom generations, centuries, civilizations later, migrating across coteries and countries and continents. Meanwhile, people live and people die—in peace as war rages on, in poverty and disrepute as latent fame awaits, with much that never meets its more, in shipwrecked love. I will die. You will die. The atoms that huddled for a cosmic blink around the shadow of a self will return to the seas that made us. What will survive of us are shoreless seeds and stardust.

Here is the essence of mankind's creative genius: not the edifices of civilization nor the bang-flash weapons which can end it, but the words which fertilize new concepts like spermatoza attacking an ovum. It might be argued that the Siamese-twin infants of word/idea are the only contribution the human species can, will, or should make to the reveling cosmos. (Yes, our DNA is unique, but so is a salamander's. Yes, we construct artifacts, but so have species ranging from beavers to the architecture ants... Yes, we weave real fabric things from the dreamstuff of mathematics, but the universe is hardwired with arithmetic. Scratch a circle and pi peeps out. Enter a new solar system and Tycho Brahe's formulae lie waiting under the black velvet cloak of space/time. But where has the universe hidden a word under its outer layer of biology, geometry, or insensate rock?)

Turing attended Wittgenstein's lectures on the philosophy of mathematics in Cambridge in 1939 and disagreed strongly with a line of argument that Wittgenstein was pursuing which wanted to allow contradictions to exist in mathematical systems. Wittgenstein argues that he can see why people don't like contradictions outside of mathematics but cannot see what harm they do inside mathematics. Turing is exasperated and points out that such contradictions inside mathematics will lead to disasters outside mathematics: bridges will fall down. Only if there are no applications will the consequences of contradictions be innocuous. Turing eventually gave up attending these lectures. His despair is understandable. The inclusion of just one contradiction (like 0 = 1) in an axiomatic system allows any statement about the objects in the system to be proved true (and also proved false). When Bertrand Russel pointed this out in a lecture he was once challenged by a heckler demanding that he show how the questioner could be proved to be the Pope if 2 + 2 = 5. Russel replied immediately that 'if twice 2 is 5, then 4 is 5, subtract 3; then 1 = 2. But you and the Pope are 2; therefore you and the Pope are 1'! A contradictory statement is the ultimate Trojan horse.

And yet sometimes she worried about what those musty old books were doing to her. Some people majored in English to prepare for law school. Others became journalists. The smartest guy in the honors program, Adam Vogel, a child of academics, was planning on getting a Ph.D. and becoming an academic himself. That left a large contingent of people majoring in English by default. Because they weren't left-brained enough for science, because history was too dry, philosophy too difficult, geology too petroleum-oriented, and math too mathematical--because they weren't musical, artistic, financially motivated, or really all that smart, these people were pursuing university degrees doing something no different from what they'd done in first grade: reading stories. English was what people who didn't know what to major in majored in.

Sexuality is the only drive that is in itself hindered, perverted: simultaneously insufficient and excessive, with the excess as the form of appearance of the lack. On the one hand, sexuality is characterized by the universal capacity to provide the metaphorical meaning or innuendo of any activity or object–any element, including the most abstract reflection can be experienced as ‘alluding to that‘ (suffice it to recall the proverbial example of the adolescent who, in order to forget his sexual obsessions, takes refuge in pure mathematics and physics–whatever he does here again reminds him of ‘that’: how much volume is needed to fill out an empty cylinder? How much energy is discharged when two bodies collide?…). The universal surplus–this capacity of sexuality to overflow the entire field of human experience…is not the sign of preponderance. Rather, it is the sign of a certain structural faultiness: sexuality strives outwards and overflows the adjoining domains precisely because it cannot find satisfaction in itself, because it never attains its goal.

Only women could bleed without injury or death; only they rose from the gore each month like a phoenix; only their bodies were in tune with the ululations of the universe and the timing of the tides. Without this innate lunar cycle, how could men have a sense of time, tides, space, seasons, movement of the universe, or the ability to measure anything at all? How could men mistress the skills of measurement necessary for mathematics, engineering, architecture, surveying—and so many other professions? In Christian churches, how could males, lacking monthly evidence of Her death and resurrection, serve the Daughter of the Goddess? In Judaism, how could they honor the Matriarch without the symbol of Her sacrifices recorded in the Old Ovariment? Thus insensible to the movements of the planets and the turning of the universe, how could men become astronomers, naturalists, scientists—or much of anything at all?

From the moment I bought my ticket, I had a premonition I wasn’t returning to New York anytime soon. You Know, this happens a lot to Russians. The Soviet Union is gone, and the borders are as free and passable as they’ve ever been. And yet, when a Russian moves between the two universes, this feeling of finality persists, the logical impossibility of a place like Russia existing alongside the civilized world, of Ann Arbor, Michigan, sharing the same atmosphere with, say, Vladivostok. It was like those mathematical concepts I could never understand in high school: if, then. If Russia exists, then the West is a mirage; conversely, if Russia does not exist, then and only then is the West real and tangible. No wonder young people talk about “going beyond the cordon” when they talk of emigrating, as if Russia were ringed by a vast cordon sanitaire. Either you stay in the leper colony or you get out into the wider world and maybe try to spread your disease to others.

Magic is like a lot of other disciplines that people have recently begun developing, in historic terms. Working with magic is a way of understanding the universe and how it functions. You can approach it from a lot of different angles, applying a lot of different theories and mental models to it. You can get to the same place through a lot of different lines of theory and reasoning, kind of like really advanced mathematics. There's no truly right or wrong way to get there, either--there are just different ways, some more or less useful than others for a given application. And new vistas of thought, theory, and application open up on a pretty regular basis, as the Art develops and expands through the participation of multiple brilliant minds. But that said, once you have a good grounding in it,you get a pretty solid idea of what's possible and what isn't. No matter how much circumlocution you do with your formulae, two plus two doesn't equal five. (Except maybe very, very rarely, sometimes, in extremely specific and highly unlikely circumstances.)

Of course, I’ve only brought up two examples. Other universal laws of physics have been used as weapons as well, though we don’t know all of them. It’s very possible that every law of physics has been weaponized. It’s possible that in some parts of the universe, even … Forget it, I don’t even believe that.” “What were you going to say?” “The foundation of mathematics.” Cheng Xin tried to imagine it, but it was simply impossible. “That’s … madness.” Then she asked, “Will the universe turn into a war ruin? Or, maybe it’s more accurate to ask: Will the laws of physics turn into war ruins?” “Maybe they already are.… The physicists and cosmologists of the new world are focused on trying to recover the original appearance of the universe before the wars more than ten billion years ago. They’ve already constructed a fairly clear theoretical model describing the pre-war universe. That was a really lovely time, when the universe itself was a Garden of Eden. Of course, the beauty could only be described mathematically. We can’t picture it: Our brains don’t have enough dimensions.” Cheng Xin thought back to the conversation with the Ring again. Did you build this four-dimensional fragment? You told me that you came from the sea. Did you build the sea? “You are saying that the universe of the Edenic Age was four-dimensional, and that the speed of light was much higher?” “No, not at all. The universe of the Edenic Age was ten-dimensional. The speed of light back then wasn’t only much higher—rather, it was close to infinity. Light back then was capable of action at a distance, and could go from one end of the cosmos to the other within a Planck time.… If you had been to four-dimensional space, you would have some vague hint of how beautiful that ten-dimensional Garden must have been.” “You’re saying—” “I’m not saying anything.” Yifan seemed to have awakened from a dream. “We’ve only seen small hints; everything else is just guessing. You should treat it as a guess, just a dark myth we’ve made up.” But Cheng Xin continued to follow the course of the discussion taken so far. “—that during the wars after the Edenic Age, one dimension after another was imprisoned from the macroscopic into the microscopic, and the speed of light was reduced again and again.…” “As I said, I’m not saying anything, just guessing.” Yifan’s voice grew softer. “But no one knows if the truth is even darker than our guesses.… We are certain of only one thing: The universe is dying.” The

Whether or not we subscribe to any particular religion or philosophy, it would be hard to deny that knowing our cosmic destiny must have some impact on how we think about our existence, or even how we live our lives. If we want to know whether what we do here ultimately matters, the first thing we ask is: how will it come out in the end? If we find the answer to that question, it leads immediately to the next: what does this mean for us now? Do we still have to take the trash out next Tuesday if the universe is going to die someday? I’ve done my own scouring of theological and philosophical texts, and while I learned many fascinating things from my studies, unfortunately the meaning of existence wasn’t one of them. I may just not have been cut out for it. The questions and answers that have always drawn me in most strongly are the ones that can be answered with scientific observation, mathematics, and physical evidence. As appealing as it sometimes seemed to have the whole story and meaning of life written down for me once and for all in a book, I knew I would only ever really be able to accept the kind of truth I could rederive mathematically.

The aborted research project wasn’t important in and of itself. What mattered was the instruction that Ye Wenjie had given him, so that’s where Luo Ji’s mind was stuck. Over and over again he recalled her words: Suppose a vast number of civilizations are distributed throughout the universe, on the order of the number of detectable stars. Lots and lots of them. The mathematical structure of cosmic sociology is far clearer than that of human sociology. The factors of chaos and randomness in the complex makeups of every civilized society in the universe get filtered out by the immense distance, so those civilizations can act as reference points that are relatively easy to manipulate mathematically. First: Survival is the primary need of civilization. Second: Civilization continuously grows and expands, but the total matter in the universe remains constant. One more thing: To derive a basic picture of cosmic sociology from these two axioms, you need two other important concepts: chains of suspicion and the technological explosion. I’m afraid there won’t be that opportunity.… Well, you might as well just forget I said anything. Either way, I’ve fulfilled my duty. He

I grew up in Brooklyn, New York.. a city neighborhood that included houses, lampposts, walls, and bushes. But with an early bedtime in the winter, I could look out my window and see the stars, and the stars were not like anything else in my neighborhood. [At age 5] I didn’t know what they were. [At age 9] my mother … said to me, “You have a library card now, and you know how to read. Take the streetcar to the library and get a book on stars.” … I stepped up to the big librarian and asked for a book on stars. … I sat down and found out the answer, which was something really stunning. I found out that the stars are glowing balls of gas. I also found out that the Sun is a star but really close and that the stars are all suns except really far away I didn’t know any physics or mathematics at that time, but I could imagine how far you’d have to move the Sun away from us till it was only as bright as a star. It was in that library, reading that book, that the scale of the universe opened up to me. There was something beautiful about it. At that young age, I already knew that I’d be very happy if I could devote my life to finding out more about the stars and the planets that go around them. And it’s been my great good fortune to do just that.

Evolution endowed us with intuition only for those aspects of physics that had survival value for our distant ancestors, such as the parabolic orbits of flying rocks (explaining our penchant for baseball). A cavewoman thinking too hard about what matter is ultimately made of might fail to notice the tiger sneaking up behind and get cleaned right out of the gene pool. Darwin’s theory thus makes the testable prediction that whenever we use technology to glimpse reality beyond the human scale, our evolved intuition should break down. We’ve repeatedly tested this prediction, and the results overwhelmingly support Darwin. At high speeds, Einstein realized that time slows down, and curmudgeons on the Swedish Nobel committee found this so weird that they refused to give him the Nobel Prize for his relativity theory. At low temperatures, liquid helium can flow upward. At high temperatures, colliding particles change identity; to me, an electron colliding with a positron and turning into a Z-boson feels about as intuitive as two colliding cars turning into a cruise ship. On microscopic scales, particles schizophrenically appear in two places at once, leading to the quantum conundrums mentioned above. On astronomically large scales… weirdness strikes again: if you intuitively understand all aspects of black holes [then you] should immediately put down this book and publish your findings before someone scoops you on the Nobel Prize for quantum gravity… [also,] the leading theory for what happened [in the early universe] suggests that space isn’t merely really really big, but actually infinite, containing infinitely many exact copies of you, and even more near-copies living out every possible variant of your life in two different types of parallel universes.

If we analyse the classes of life, we readily find that there are three cardinal classes which are radically distinct in function. A short analysis will disclose to us that, though minerals have various activities, they are not "living." The plants have a very definite and well known function-the transformation of solar energy into organic chemical energy. They are a class of life which appropriates one kind of energy, converts it into another kind and stores it up; in that sense they are a kind of storage battery for the solar energy; and so I define THE PLANTS AS THE CHEMISTRY-BINDING class of life. The animals use the highly dynamic products of the chemistry-binding class-the plants-as food, and those products-the results of plant-transformation-undergo in animals a further transformation into yet higher forms; and the animals are correspondingly a more dynamic class of life; their energy is kinetic; they have a remarkable freedom and power which the plants do not possess-I mean the freedom and faculty to move about in space; and so I define ANIMALS AS THE SPACE-BINDING CLASS OF LIFE. And now what shall we say of human beings? What is to be our definition of Man? Like the animals, human beings do indeed possess the space-binding capacity but, over and above that, human beings possess a most remarkable capacity which is entirely peculiar to them-I mean the capacity to summarise, digest and appropriate the labors and experiences of the past; I mean the capacity to use the fruits of past labors and experiences as intellectual or spiritual capital for developments in the present; I mean the capacity to employ as instruments of increasing power the accumulated achievements of the all-precious lives of the past generations spent in trial and error, trial and success; I mean the capacity of human beings to conduct their lives in the ever increasing light of inherited wisdom; I mean the capacity in virtue of which man is at once the heritor of the by-gone ages and the trustee of posterity. And because humanity is just this magnificent natural agency by which the past lives in the present and the present for the future, I define HUMANITY, in the universal tongue of mathematics and mechanics, to be the TIME-BINDING CLASS OF LIFE.