Well, that's good to hear, you know, just in case I get in a plutonium-powered DeLorean and get shot back in time, I WON'T have to make sure my parents find each and get married so I can be born. Hell, I could even kill my grandfather.

Time Travel Simulation Resolves “Grandfather Paradox”

What would happen to you if you went back in time and killed your grandfather? A model using photons reveals that quantum mechanics can solve the quandary—and even foil quantum cryptography

Sep 2, 2014 | By Lee Billings



Entering a closed timelike curve tomorrow means you could end up at today.
Credit: Dmitry Schidlovsky
On June 28, 2009, the world-famous physicist Stephen Hawking threw a party at the University of Cambridge, complete with balloons, hors d'oeuvres and iced champagne. Everyone was invited but no one showed up. Hawking had expected as much, because he only sent out invitations after his party had concluded. It was, he said, "a welcome reception for future time travelers," a tongue-in-cheek experiment to reinforce his 1992 conjecture that travel into the past is effectively impossible.

But Hawking may be on the wrong side of history. Recent experiments offer tentative support for time travel's feasibility—at least from a mathematical perspective. The study cuts to the core of our understanding of the universe, and the resolution of the possibility of time travel, far from being a topic worthy only of science fiction, would have profound implications for fundamental physics as well as for practical applications such as quantum cryptography and computing.

Closed timelike curves

The source of time travel speculation lies in the fact that our best physical theories seem to contain no prohibitions on traveling backward through time. The feat should be possible based on Einstein's theory of general relativity, which describes gravity as the warping of spacetime by energy and matter. An extremely powerful gravitational field, such as that produced by a spinning black hole, could in principle profoundly warp the fabric of existence so that spacetime bends back on itself. This would create a "closed timelike curve," or CTC, a loop that could be traversed to travel back in time.

Hawking and many other physicists find CTCs abhorrent, because any macroscopic object traveling through one would inevitably create paradoxes where cause and effect break down. In a model proposed by the theorist David Deutsch in 1991, however, the paradoxes created by CTCs could be avoided at the quantum scale because of the behavior of fundamental particles, which follow only the fuzzy rules of probability rather than strict determinism. "It's intriguing that you've got general relativity predicting these paradoxes, but then you consider them in quantum mechanical terms and the paradoxes go away," says University of Queensland physicist Tim Ralph. "It makes you wonder whether this is important in terms of formulating a theory that unifies general relativity with quantum mechanics."

Experimenting with a curve

Recently Ralph and his PhD student Martin Ringbauer led a team that experimentally simulated Deutsch's model of CTCs for the very first time, testing and confirming many aspects of the two-decades-old theory. Their findings are published in Nature Communications. Much of their simulation revolved around investigating how Deutsch's model deals with the “grandfather paradox,” a hypothetical scenario in which someone uses a CTC to travel back through time to murder her own grandfather, thus preventing her own later birth. (Scientific American is part of Nature Publishing Group.)

Deutsch's quantum solution to the grandfather paradox works something like this:

Instead of a human being traversing a CTC to kill her ancestor, imagine that a fundamental particle goes back in time to flip a switch on the particle-generating machine that created it. If the particle flips the switch, the machine emits a particle—the particle—back into the CTC; if the switch isn't flipped, the machine emits nothing. In this scenario there is no a priori deterministic certainty to the particle's emission, only a distribution of probabilities. Deutsch's insight was to postulate self-consistency in the quantum realm, to insist that any particle entering one end of a CTC must emerge at the other end with identical properties. Therefore, a particle emitted by the machine with a probability of one half would enter the CTC and come out the other end to flip the switch with a probability of one half, imbuing itself at birth with a probability of one half of going back to flip the switch. If the particle were a person, she would be born with a one-half probability of killing her grandfather, giving her grandfather a one-half probability of escaping death at her hands—good enough in probabilistic terms to close the causative loop and escape the paradox. Strange though it may be, this solution is in keeping with the known laws of quantum mechanics.

In their new simulation Ralph, Ringbauer and their colleagues studied Deutsch's model using interactions between pairs of polarized photons within a quantum system that they argue is mathematically equivalent to a single photon traversing a CTC. "We encode their polarization so that the second one acts as kind of a past incarnation of the first,” Ringbauer says. So instead of sending a person through a time loop, they created a stunt double of the person and ran him through a time-loop simulator to see if the doppelganger emerging from a CTC exactly resembled the original person as he was in that moment in the past.

By measuring the polarization states of the second photon after its interaction with the first, across multiple trials the team successfully demonstrated Deutsch's self-consistency in action. "The state we got at our output, the second photon at the simulated exit of the CTC, was the same as that of our input, the first encoded photon at the CTC entrance," Ralph says. "Of course, we're not really sending anything back in time but [the simulation] allows us to study weird evolutions normally not allowed in quantum mechanics."

Those "weird evolutions" enabled by a CTC, Ringbauer notes, would have remarkable practical applications, such as breaking quantum-based cryptography through the cloning of the quantum states of fundamental particles. "If you can clone quantum states,” he says, “you can violate the Heisenberg uncertainty principle,” which comes in handy in quantum cryptography because the principle forbids simultaneously accurate measurements of certain kinds of paired variables, such as position and momentum. "But if you clone that system, you can measure one quantity in the first and the other quantity in the second, allowing you to decrypt an encoded message."

"In the presence of CTCs, quantum mechanics allows one to perform very powerful information-processing tasks, much more than we believe classical or even normal quantum computers could do," says Todd Brun, a physicist at the University of Southern California who was not involved with the team's experiment. "If the Deutsch model is correct, then this experiment faithfully simulates what could be done with an actual CTC. But this experiment cannot test the Deutsch model itself; that could only be done with access to an actual CTC."

Alternative reasoning

Deutsch's model isn’t the only one around, however. In 2009 Seth Lloyd, a theorist at Massachusetts Institute of Technology, proposed an alternative, less radical model of CTCs that resolves the grandfather paradox using quantum teleportation and a technique called post-selection, rather than Deutsch's quantum self-consistency. With Canadian collaborators, Lloyd went on to perform successful laboratory simulations of his model in 2011. "Deutsch's theory has a weird effect of destroying correlations," Lloyd says. "That is, a time traveler who emerges from a Deutschian CTC enters a universe that has nothing to do with the one she exited in the future. By contrast, post-selected CTCs preserve correlations, so that the time traveler returns to the same universe that she remembers in the past."

This property of Lloyd's model would make CTCs much less powerful for information processing, although still far superior to what computers could achieve in typical regions of spacetime. "The classes of problems our CTCs could help solve are roughly equivalent to finding needles in haystacks," Lloyd says. "But a computer in a Deutschian CTC could solve why haystacks exist in the first place.”

Lloyd, though, readily admits the speculative nature of CTCs. “I have no idea which model is really right. Probably both of them are wrong,” he says. Of course, he adds, the other possibility is that Hawking is correct, “that CTCs simply don't and cannot exist." Time-travel party planners should save the champagne for themselves—their hoped-for future guests seem unlikely to arrive.

More:

• Can Quantum Bayesianism Fix the Paradoxes of Quantum Mechanics?
• Astrophysicist J. Richard Gott on Time Travel

Aaron Gordon - Does Randomness Actually Exist?

Does randomness exist? Can we even fathom the question? This is an interesting article from Aaron Gordan at Pacific Standard.

Does Randomness Actually Exist?

By Aaron Gordon • August 25, 2014 


An Enigma machine. (Photo: Wikimedia Commons)

Our human minds are incapable of truly answering that question.

•
All week long we’ll be posting stories about randomness and how poorly we tend to deal with it. Check back tomorrow for more.

Pick a number. Any number, one through 100. Got one? OK, so how did you pick it?

Humans are bad at creating and detecting randomness. Perceiving patterns has proven a great survival mechanism—the giant, spotted cats eat my children; this berry doesn’t make me sick—so we have evolved to be good at it. Perhaps too good. We misinterpret data all the time as a result of this desire for order. We believe that when a coin comes up heads five straight times, we are “due” for a tails, or we think that the stock market is predictable. It’s maybe unsurprising, then, that humans aren’t very good random number generators. And because of that, we’ve had to make some.

If you Google “Random Number Generators,” you’ll find several on the first page that are perfectly capable of mimicking a random process. After specifying a range, they will return a number. Do so 100 or 1,000 or 10,000 times, and you won’t find any discernible pattern to the results. Yet despite the name, the results are anything but random.

Computers are hyper-logical machines that can only follow specific commands. As explained by a BBC Radio broadcast from 2011, some of the random number generators you’ll find on Google follow something called the “Middle Squares” method: start with a seed number, which can be any number. Square that number. You’ll now have roughly twice as many digits. Take a few of the digits in the middle of that number and square that. Repeating this process is like shuffling a deck of cards. Still, if you know three basic pieces of information—the seed number, the number of digits taken from the middle of each square, and how many times the process will be repeated—you can calculate this supposedly “random” number every single time without fail.

Mathematicians have a word for this kind of randomness. They cleverly call it “pseudo-randomness”: the process passes statistical tests for randomness, yet the number itself is completely determined. On the BBC Radio broadcast, professor Colva Roney-Dougal of the University of St. Andrews says, “I can never prove that a sequence is random, I can only prove that it looks random and smells random.”

All of which brings us to this: Given the limits of human knowledge, how can we ever know if something is truly random?

A FEW ANCIENT THINKERS, known as Atomists, fathered a line of thought, which claims that, in fact, randomness doesn’t exist. The most deterministic among them, Democritus, believed the entire state of the universe could be explained through cause and effect. In other words, he was only interested in how the past dictated the present and future.

Once you learn about pseudo-randomness, it’s easy to see the world through Democritus’ eyes. Rolling dice isn’t random. Instead, the dice are governed by specific, mathematical laws, and if we knew the exact contours of the desk and the force applied to the dice, we could calculate which sides would come to rest facing upward. The same is true of shuffling cards. If we knew the exact height the cards were lifted, the exact force with which they were released, and the distance from each other, it’s completely feasible to calculate the order of the cards, time and time again. This is true for every game of chance, which are governed by Newtonian, or classical, physics. It all appears completely deterministic.

A lack of true randomness would be a huge problem, just like it was for the Germans during World War II with their revered but ultimately doomed Enigma enciphering machine. With its 150 quintillion different settings, many Allied cryptologists believed the code was unbreakable. Yet, because it was a mere matter of rotor settings and circuitry—or put simply, completely deterministic—the Allies were able to crack the code.

Since Newtonian physics has proven resistant to true randomness, cryptologists have since looked to quantum physics, or the rules that govern subatomic particles, which are completely different than Newtonian physics. Radioactive materials spontaneously throw off particles in a probabilistic manner, but the exact time when each particle will be discarded is inherently random. (We think.) So given a small window of time, the number of radioactive particles discarded can act as the seed for the random number generator.

Every time you buy something with a credit card, you’re relying on your information to be transmitted safely across a perfectly accessible network. This is where the difference between random and pseudo-random becomes vastly important. Pseudo-random patterns, like the ones created by the Enigma machine, are messages begging to be read. Random patterns are the cryptic ideal.

A company called PDH International is one of the patent-holders for Patent US6745217 B2, or “Random Number Generator Based on the Spontaneous Alpha-Decay,” the very process described above. PDH International, with an annual revenue of $10 to $25 million, specializes in the “fields of Privacy Protection, Authentication, Encryption and Electronic Document Protection.” PDH comes up with ways to safely encrypt data using true randomness from quantum physics.

BUT BACK TO THAT number you picked.

As with randomness, the more we learned about the precise nature of brain functions, we began to question whether free will was possible. If everything is the result of precise causal chains like the rolling of dice or shuffling of cards, some wondered how we can really be making genuine choices. However, as we’ve learned more about quantum physics, the possibility of genuine choice has been revitalized due to the break in the causal chain. In a way, quantum physics introduced a giant, unsolvable question mark, and question marks are good for free-will theorists. Ironically, quantum physics simultaneously undermines this line of thought, since randomness is bad for the idea that we are actually making rational choices.

So pick a number, any number. Maybe it is random after all.


Aaron Gordon is a freelance writer living in Washington, D.C. He also contributes to Sports on Earth, The New Yorker, Deadspin, and Slate.

Graham Priest - Beyond True and False

This is a cool article from Aeon Magazine about how modern mathematics is influencing Western philosophy in the direction of accepting contradictions - an influence of Buddhist thought that is finally getting traction in the West.

Graham Priest is a distinguished professor of philosophy at CUNY and professor emeritus at the University of Melbourne. He is the author of many books, including Logic: A Very Short Introduction (2001), The Law of Non-Contradiction (editor, 2007), and Towards Non-Being: The Logic and Metaphysics of Intentionality (2007). His new book, from Oxford University Press, is One: Being an Investigation into the Unity of Reality and of its Parts, including the Singular Object which is Nothingness (publishing on May 27, 2014).

These are just the first few paragraphs - follow the title link to read the whole article.

Beyond true and false

Buddhist philosophy is full of contradictions. Now modern logic is learning why that might be a good thing

by Graham Priest | May 5, 2014

Illustration by Fumitake Uchida

Graham Priest is distinguished professor of philosophy at CUNY and professor emeritus at the University of Melbourne. His latest book, One, has just been published by Oxford University Press.

Western philosophers have not, on the whole, regarded Buddhist thought with much enthusiasm. As a colleague once said to me: ‘It’s all just mysticism.’ This attitude is due, in part, to ignorance. But it is also due to incomprehension. When Western philosophers look East, they find things they do not understand – not least the fact that the Asian traditions seem to accept, and even endorse, contradictions. Thus we find the great second-century Buddhist philosopher Nagarjuna saying:

The nature of things is to have no nature; it is their non-nature that is their nature. For they have only one nature: no-nature.

An abhorrence of contradiction has been high orthodoxy in the West for more than 2,000 years. Statements such as Nagarjuna’s are therefore wont to produce looks of blank incomprehension, or worse. As Avicenna, the father of Medieval Aristotelianism, declared:

Anyone who denies the law of non-contradiction should be beaten and burned until he admits that to be beaten is not the same as not to be beaten, and to be burned is not the same as not to be burned.

One can hear similar sentiments, expressed with comparable ferocity, in many faculty common rooms today. Yet Western philosophers are slowly learning to outgrow their parochialism. And help is coming from a most unexpected direction: modern mathematical logic, not a field that is renowned for its tolerance of obscurity.

Read the whole article.

Max Tegmark - How to See Yourself in a World Where Only Math Is Real

You (we) are little more than very elaborate braids in spacetime. Not sure what that means? Read this article from Nautilus and it will make a lot more sense.

Life is a Braid in Spacetime

How to see yourself in a world where only math is real,

By Max Tegmark
Illustration by Chad Hagen January 9, 2014

“Excuse me, but what’s the time?” I’m guessing that you, like me, are guilty of having asked this question, as if it were obvious that there is such a thing as the time. Yet you’ve probably never approached a stranger and asked “Excuse me, but what’s the place?”. If you were hopelessly lost, you’d probably instead have said something like “Excuse me, but where am I?” thereby acknowledging that you’re not asking about a property of space, but rather about a property of yourself. Similarly, when you ask for the time, you’re not really asking about a property of time, but rather about your location in time.

But that is not how we usually think about it. Our language reveals how differently we think of space and time: The first as a static stage, and the second as something flowing. Despite our intuition, however, the flow of time is an illusion. Einstein taught us that there are two equivalent ways of thinking about our physical reality: Either as a three-dimensional place called space, where things change over time, or as a four-dimensional place called spacetime that simply exists, unchanging, never created, and never destroyed.

I think of the two viewpoints as the different perspectives on reality that a frog and a bird might take. The bird surveys the landscape of reality from high “above,” akin to a physicist studying the mathematical structure of spacetime as described by the equations of physics. The frog, on the other hand, lives inside the landscape surveyed by the bird. Looking up at the moon over time, the frog sees something like the right panel in the figure, “The Moon’s Orbit”: Five snapshots of space with the Moon in different positions each time. But the bird sees an unchanging spiral shape in spacetime, as shown in the left panel.

  

The Moon’s Orbit: We can equivalently think of the moon as a position in space that changes over time (right), or as an unchanging spiral shape in spacetime (left), corresponding to a mathematical structure. The snapshots of space (right) are simply horizontal slices of spacetime (left). To keep things legible, I’ve drawn the orbit much smaller than to scale and made several simplifications. To get snapshots of space (right) from spacetime (left), you simply make horizontal slices through spacetime at the times you’re interested in.Max Tegmark

For the bird—and the physicist—there is no objective definition of past or future. As Einstein put it, “The distinction between past, present, and future is only a stubbornly persistent illusion.” When we think about the present, we mean the time slice through spacetime corresponding to the time when we’re having that thought. We refer to the future and past as the parts of spacetime above and below this slice.

This is analogous to your use of the terms here, in front of me, and behind me to refer to different parts of spacetime relative to your present position. The part that’s in front of you is clearly no less real than the part behind you—indeed, if you’re walking forward, some of what’s presently in front of you will be behind you in the future, and is presently behind various other people. Analogously, in spacetime, the future is just as real as the past—parts of spacetime that are presently in your future will, in your future, be in your past. Since spacetime is static and unchanging, no parts of it can change their reality status, and all parts must be equally real.

The idea of spacetime does more than teach us to rethink the meaning of past and future. It also introduces us to the idea of a mathematical universe. Spacetime is a purely mathematical structure in the sense that it has no properties at all except mathematical properties, for example the number four, its number of dimensions. In my book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, I argue that not only spacetime, but indeed our entire external physical reality, is a mathematical structure, which is by definition an abstract, immutable entity existing outside of space and time.

What does this actually mean? It means, for one thing, a universe that can be beautifully described by mathematics. That this is true for our universe has become increasingly clear over the centuries, with evidence piling up ever more rapidly. The latest triumph in this area is the discovery of the Higgs boson, which, just like the planet Neptune and the radio wave, was first predicted with a pencil, using mathematical equations.

That our universe is approximately described by mathematics means that some but not all of its properties are mathematical. That it is mathematical means that all of its properties are mathematical; that it has no properties at all except mathematical ones. If I’m right and this is true, then it’s good news for physics, because all properties of our universe can in principle be understood if we are intelligent and creative enough. It also implies that our reality is vastly larger than we thought, containing a diverse collection of universes obeying all mathematically possible laws of physics.

This novel way of viewing both spacetime and the stuff in it implies a novel way of viewing ourselves. Our thoughts, our emotions, our self-awareness, and that deep existential feeling “I am”—none of this feels the least bit mathematical to me. Yet we too are made of the same kinds of elementary particles that make up everything else in our physical world, which I’ve argued is purely mathematical. How can we reconcile these two perspectives?

 

Chad Hagen

The first step is to consider how we look as a spacetime structure. The cosmology pioneer George Gamow entitled his autobiography My World Line, a phrase also used by Einstein to refer to paths through spacetime. However, your own world line strictly speaking isn’t a line: It has a non-zero thickness and it’s not straight. The roughly 1029 elementary particles (quarks and electrons) that your body is made of form a tube-like shape through spacetime, analogous to the spiral shape of the Moon’s orbit (“The Moon’s Orbit”) but more complicated. If you’re swimming laps in a pool, that part of your spacetime tube has a zig-zag shape, and if you’re using a playground swing, that part of your spacetime tube has a serpentine shape.

However, the most interesting property of your spacetime tube isn’t its bulk shape, but its internal structure, which is remarkably complex. Whereas the particles that constitute the Moon are stuck together in a rather static arrangement, many of your particles are in constant motion relative to one another. Consider, for example, the particles that make up your red blood cells. As your blood circulates through your body to deliver the oxygen you need, each red blood cell traces out its own unique tube shape through spacetime, corresponding to a complex itinerary though your arteries, capillaries, and veins with regular returns to your heart and lungs. These spacetime tubes of different red blood cells are intertwined to form a braid pattern as seen in the figure “Complexity and Life” which is more elaborate than anything you’ll ever see in a hair salon: Whereas a classic braid consists of three strands with perhaps thirty thousand hairs each, intertwined in a simple repeating pattern, this spacetime braid consists of trillions of strands (one for each red blood cell), each composed of trillions of hair-like elementary-particle trajectories, intertwined in a complex pattern that never repeats. In other words, if you imagine spending a year giving a friend a truly crazy hairdo, braiding the hair by separately intertwining all their individual hairs, the pattern you’d get would still be very simple in comparison.

  

Complexity and Life: The motion of an object corresponds to a pattern in spacetime. An inanimate clump of 10 accelerating particles constitutes a simple pattern (left), while the particles that make up a living organism constitute a complex pattern (middle), corresponding to the complex motions that accomplish information processing and other vital processes. When a living organism dies, it eventually disintegrates and its particles separate from each other (right). These crude illustrations show merely 10 particles; your own spacetime pattern involves about 1029 particles and is mind-blowingly complex.Max Tegmark

Yet the complexity of all this pales in comparison to the patterns of information processing in your brain. Your roughly 100 billion neurons are constantly generating electrical signals (“firing”), which involves shuffling around billions of trillions of atoms, notably sodium, potassium, and calcium ions. The trajectories of these atoms form an extremely elaborate braid through spacetime, whose complex intertwining corresponds to storing and processing information in a way that somehow gives rise to our familiar sensation of self-awareness. There’s broad consensus in the scientific community that we still don’t understand how this works, so it’s fair to say that we humans don’t yet fully understand what we are. However, in broad brush, we might say this: You’re a pattern in spacetime. A mathematical pattern. Specifically, you’re a braid in spacetime—indeed, one of the most elaborate braids known.

Some people find it emotionally displeasing to think of themselves as a collection of particles. I got a good laugh back in my 20s when my friend Emil addressed my friend Mats as an “atomhög,” Swedish for “atom heap,” in an attempt to insult him. However, if someone says “I can’t believe I’m just a heap of atoms!’’ I object to the use of the word “just”: the elaborate spacetime braid that corresponds to their mind is hands down the most beautifully complex type of pattern we’ve ever encountered in our universe. The world’s fastest computer, the Grand Canyon or even the Sun—their spacetime patterns are all simple in comparison.

AT BOTH ENDS of your spacetime braid, corresponding to your birth and death, all the threads gradually separate, corresponding to all your particles joining, interacting and finally going their own separate ways (As seen in the right panel of “Complexity and Life”). This makes the spacetime structure of your entire life resemble a tree: At the bottom, corresponding to early times, is an elaborate system of roots corresponding to the spacetime trajectories of many particles, which gradually merge into thicker strands and culminate in a single tube-like trunk corresponding to your current body (with a remarkable braid-like pattern inside as we described above). At the top, corresponding to late times, the trunk splits into ever finer branches, corresponding to your particles going their own separate ways once your life is over. In other words, the pattern of life has only a finite extent along the time dimension, with the braid coming apart into frizz at both ends.1

This view of ourselves as mathematical braid patterns in spacetime challenges the assumption that we can never understand consciousness. It optimistically suggests that consciousness can one day be understood as a form of matter, a derivative of the most beautifully complex spacetime structure in our universe. Such understanding would enlighten our approaches to animals, unresponsive patients, and future ultra-intelligent machines, with wide-ranging ethical, legal, and technological implications.

This is how I see it. However, although this idea of an unchanging reality is venerable and dates back to Einstein, it remains controversial and subject to vibrant scientific debate, with scientists I greatly respect expressing a spectrum of views. For example, in his book The Hidden Reality, Brian Greene expresses unease toward letting go of the notions change and creation as fundamental, writing “I’m partial to there being a process, however tentative [...] that we can imagine generating the multiverse.” Lee Smolin goes further in his book Time Reborn, arguing that not only is change real, but that time may be the only thing that’s real. At the other end of the spectrum, Julian Barbour argues in his book The End of Time not only that change is illusory, but that one can even describe physical reality without introducing the concept of time at all.

If we discover the ultimate nature of time, this will answer many of the most exciting open questions facing physics today. Did time have some sort of beginning before our Big Bang? Will it ultimately end? Did it emerge out of some sort of timeless quantum fuzz into which it will eventually dissolve? We physicists haven’t found the mathematical theory of quantum gravity required to convincingly answer these questions, but whatever this “theory of everything” turns out to be, time will be the key to unlocking its mysteries.


~ Max Tegmark is an MIT physics professor who has authored more than 200 technical papers. Known as “Mad Max” for his unorthodox ideas and passion for adventure, his scientific interests range from precision cosmology to the ultimate nature of reality, all explored in his new popular science book Our Mathematical Universe.

Introducing the Amplituhedron: A Mathematical Object Encoding the Probabilities of Outcomes of Particle Interactions (Resembles a Jewel in Higher Dimensions)

Weird, cool, and marginally outside of my ability to fully grok without the aid of entheogens (or a bong, according to Conan). What I can grasp is the significance of it - with this simple object researchers can now perform calculations that once would have taken massive computers.

Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like “amplituhedron,” which yields an equivalent one-term expression.

“The degree of efficiency is mind-boggling,” said Jacob Bourjaily, a theoretical physicist at Harvard University and one of the researchers who developed the new idea. “You can easily do, on paper, computations that were infeasible even with a computer before.”

The article is well-written and easy to follow even for people (such as myself) who are bamboozled by math.

A Jewel at the Heart of Quantum Physics

By: Natalie Wolchover
September 17, 2013


Artist’s rendering of the amplituhedron, a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated — the probabilities of outcomes of particle interactions. Illustration by Andy Gilmore.
Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.

“This is completely new and very much simpler than anything that has been done before,” said Andrew Hodges, a mathematical physicist at Oxford University who has been following the work.

The revelation that particle interactions, the most basic events in nature, may be consequences of geometry significantly advances a decades-long effort to reformulate quantum field theory, the body of laws describing elementary particles and their interactions. Interactions that were previously calculated with mathematical formulas thousands of terms long can now be described by computing the volume of the corresponding jewel-like “amplituhedron,” which yields an equivalent one-term expression.

“The degree of efficiency is mind-boggling,” said Jacob Bourjaily, a theoretical physicist at Harvard University and one of the researchers who developed the new idea. “You can easily do, on paper, computations that were infeasible even with a computer before.”

The new geometric version of quantum field theory could also facilitate the search for a theory of quantum gravity that would seamlessly connect the large- and small-scale pictures of the universe. Attempts thus far to incorporate gravity into the laws of physics at the quantum scale have run up against nonsensical infinities and deep paradoxes. The amplituhedron, or a similar geometric object, could help by removing two deeply rooted principles of physics: locality and unitarity.

“Both are hard-wired in the usual way we think about things,” said Nima Arkani-Hamed, a professor of physics at the Institute for Advanced Study in Princeton, N.J., and the lead author of the new work, which he is presenting in talks and in a forthcoming paper. “Both are suspect.”

Locality is the notion that particles can interact only from adjoining positions in space and time. And unitarity holds that the probabilities of all possible outcomes of a quantum mechanical interaction must add up to one. The concepts are the central pillars of quantum field theory in its original form, but in certain situations involving gravity, both break down, suggesting neither is a fundamental aspect of nature.

In keeping with this idea, the new geometric approach to particle interactions removes locality and unitarity from its starting assumptions. The amplituhedron is not built out of space-time and probabilities; these properties merely arise as consequences of the jewel’s geometry. The usual picture of space and time, and particles moving around in them, is a construct.

“It’s a better formulation that makes you think about everything in a completely different way,” said David Skinner, a theoretical physicist at Cambridge University.

The amplituhedron itself does not describe gravity. But Arkani-Hamed and his collaborators think there might be a related geometric object that does. Its properties would make it clear why particles appear to exist, and why they appear to move in three dimensions of space and to change over time.

Because “we know that ultimately, we need to find a theory that doesn’t have” unitarity and locality, Bourjaily said, “it’s a starting point to ultimately describing a quantum theory of gravity.”

Clunky Machinery

The amplituhedron looks like an intricate, multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated, “scattering amplitudes,” which represent the likelihood that a certain set of particles will turn into certain other particles upon colliding. These numbers are what particle physicists calculate and test to high precision at particle accelerators like the Large Hadron Collider in Switzerland.


The iconic 20th century physicist Richard Feynman invented a method for calculating probabilities of particle interactions using depictions of all the different ways an interaction could occur. Examples of “Feynman diagrams” were included on a 2005 postage stamp honoring Feynman.
The 60-year-old method for calculating scattering amplitudes — a major innovation at the time — was pioneered by the Nobel Prize-winning physicist Richard Feynman. He sketched line drawings of all the ways a scattering process could occur and then summed the likelihoods of the different drawings. The simplest Feynman diagrams look like trees: The particles involved in a collision come together like roots, and the particles that result shoot out like branches. More complicated diagrams have loops, where colliding particles turn into unobservable “virtual particles” that interact with each other before branching out as real final products. There are diagrams with one loop, two loops, three loops and so on — increasingly baroque iterations of the scattering process that contribute progressively less to its total amplitude. Virtual particles are never observed in nature, but they were considered mathematically necessary for unitarity — the requirement that probabilities sum to one.

“The number of Feynman diagrams is so explosively large that even computations of really simple processes weren’t done until the age of computers,” Bourjaily said. A seemingly simple event, such as two subatomic particles called gluons colliding to produce four less energetic gluons (which happens billions of times a second during collisions at the Large Hadron Collider), involves 220 diagrams, which collectively contribute thousands of terms to the calculation of the scattering amplitude.

In 1986, it became apparent that Feynman’s apparatus was a Rube Goldberg machine.

To prepare for the construction of the Superconducting Super Collider in Texas (a project that was later canceled), theorists wanted to calculate the scattering amplitudes of known particle interactions to establish a background against which interesting or exotic signals would stand out. But even 2-gluon to 4-gluon processes were so complex, a group of physicists had written two years earlier, “that they may not be evaluated in the foreseeable future.”

Stephen Parke and Tommy Taylor, theorists at Fermi National Accelerator Laboratory in Illinois, took that statement as a challenge. Using a few mathematical tricks, they managed to simplify the 2-gluon to 4-gluon amplitude calculation from several billion terms to a 9-page-long formula, which a 1980s supercomputer could handle. Then, based on a pattern they observed in the scattering amplitudes of other gluon interactions, Parke and Taylor guessed a simple one-term expression for the amplitude. It was, the computer verified, equivalent to the 9-page formula. In other words, the traditional machinery of quantum field theory, involving hundreds of Feynman diagrams worth thousands of mathematical terms, was obfuscating something much simpler. As Bourjaily put it: “Why are you summing up millions of things when the answer is just one function?”

“We knew at the time that we had an important result,” Parke said. “We knew it instantly. But what to do with it?”

The Amplituhedron

The message of Parke and Taylor’s single-term result took decades to interpret. “That one-term, beautiful little function was like a beacon for the next 30 years,” Bourjaily said. It “really started this revolution.”


Twistor diagrams depicting an interaction between six gluons, in the cases where two (left) and four (right) of the particles have negative helicity, a property similar to spin. The diagrams can be used to derive a simple formula for the 6-gluon scattering amplitude. Arkani-Hamed et al.
In the mid-2000s, more patterns emerged in the scattering amplitudes of particle interactions, repeatedly hinting at an underlying, coherent mathematical structure behind quantum field theory. Most important was a set of formulas called the BCFW recursion relations, named for Ruth Britto, Freddy Cachazo, Bo Feng and Edward Witten. Instead of describing scattering processes in terms of familiar variables like position and time and depicting them in thousands of Feynman diagrams, the BCFW relations are best couched in terms of strange variables called “twistors,” and particle interactions can be captured in a handful of associated twistor diagrams. The relations gained rapid adoption as tools for computing scattering amplitudes relevant to experiments, such as collisions at the Large Hadron Collider. But their simplicity was mysterious.

“The terms in these BCFW relations were coming from a different world, and we wanted to understand what that world was,” Arkani-Hamed said. “That’s what drew me into the subject five years ago.”

With the help of leading mathematicians such as Pierre Deligne, Arkani-Hamed and his collaborators discovered that the recursion relations and associated twistor diagrams corresponded to a well-known geometric object. In fact, as detailed in a paper posted to arXiv.org in December by Arkani-Hamed, Bourjaily, Cachazo, Alexander Goncharov, Alexander Postnikov and Jaroslav Trnka, the twistor diagrams gave instructions for calculating the volume of pieces of this object, called the positive Grassmannian.

Named for Hermann Grassmann, a 19th-century German linguist and mathematician who studied its properties, “the positive Grassmannian is the slightly more grown-up cousin of the inside of a triangle,” Arkani-Hamed explained. Just as the inside of a triangle is a region in a two-dimensional space bounded by intersecting lines, the simplest case of the positive Grassmannian is a region in an N-dimensional space bounded by intersecting planes. (N is the number of particles involved in a scattering process.)

It was a geometric representation of real particle data, such as the likelihood that two colliding gluons will turn into four gluons. But something was still missing.

The physicists hoped that the amplitude of a scattering process would emerge purely and inevitably from geometry, but locality and unitarity were dictating which pieces of the positive Grassmannian to add together to get it. They wondered whether the amplitude was “the answer to some particular mathematical question,” said Trnka, a post-doctoral researcher at the California Institute of Technology. “And it is,” he said.


A sketch of the amplituhedron representing an 8-gluon particle interaction. Using Feynman diagrams, the same calculation would take roughly 500 pages of algebra. Nima Arkani-Hamed.
Arkani-Hamed and Trnka discovered that the scattering amplitude equals the volume of a brand-new mathematical object — the amplituhedron. The details of a particular scattering process dictate the dimensionality and facets of the corresponding amplituhedron. The pieces of the positive Grassmannian that were being calculated with twistor diagrams and then added together by hand were building blocks that fit together inside this jewel, just as triangles fit together to form a polygon.

Like the twistor diagrams, the Feynman diagrams are another way of computing the volume of the amplituhedron piece by piece, but they are much less efficient. “They are local and unitary in space-time, but they are not necessarily very convenient or well-adapted to the shape of this jewel itself,” Skinner said. “Using Feynman diagrams is like taking a Ming vase and smashing it on the floor.”

Arkani-Hamed and Trnka have been able to calculate the volume of the amplituhedron directly in some cases, without using twistor diagrams to compute the volumes of its pieces. They have also found a “master amplituhedron” with an infinite number of facets, analogous to a circle in 2-D, which has an infinite number of sides. Its volume represents, in theory, the total amplitude of all physical processes. Lower-dimensional amplituhedra, which correspond to interactions between finite numbers of particles, live on the faces of this master structure.

“They are very powerful calculational techniques, but they are also incredibly suggestive,” Skinner said. “They suggest that thinking in terms of space-time was not the right way of going about this.”

Read the whole article.

The Famous Feynman Lectures on Physics: The New Online Edition

Most of the material in the "famous Feynman lectures" is way beyond ability in the realms of mathematics and physics. However, I am sharing this anyway because Richard Feynman was simply a cool human being.

CalTech has converted all of his lectures into HTML5 format, and I'm sure there is a reason for that (and I suspect it has to do with readability on tablets and smart phones), and made them all available for free.

For those who would rather watch the lectures, that too is an option (a series of lectures at Cornell).

The Famous Feynman Lectures on Physics: The New Online Edition (in HTML5)

September 14th, 2013

Caltech and The Feynman Lectures Website have joined forces to create an online edition of Richard Feynman’s famous lectures on physics. First presented in the early 1960s as part of a two-year introductory physics course given at Caltech, the lectures were eventually turned into a book that became a classic reference work for physics students, teachers and researchers. You can still purchase the 560 page book online, or enjoy a new web edition for free.

Created with HTML5, the new site gives readers access to “a high-quality up-to-date copy” of Feynman’s lectures.” The text “has been designed for ease of reading on devices of any size or shape,” and you can zoom into text, figures and equations without degradation. Dive right into the lectures here. And if you’d prefer to see Feynman (as opposed to read Feynman), we would encourage you to watch ‘The Character of Physical Law,’ Feynman’s seven-part lecture series recorded at Cornell in 1964. Another 37 physics courses, most in video, can be found in our collection of Free Online Courses.

Feynman’s lecture are now listed in our collections of Free eBooks and Free Textbooks.

Photograph by Tom Harvey. Copyright © California Institute of Technology.
via Boing Boing

Related Content:

• The Richard Feynman Trilogy: The Physicist Captured in Three Films
• Richard Feynman’s Letter to His Departed Wife: “You, Dead, Are So Much Better Than Anyone Else Alive” (1946)
• Richard Feynman Presents Quantum Electrodynamics for the NonScientist

Podcast on Transrealism vs. Hyperrealism (w/ Transrealist Rudy Rucker)

This interesting piece comes from the Diet Soap podcast on the Critical Theory site. For a lot of people, mathematician, computer scientist, philosopher, and sci-fi author Rudy Rucker (Rudolf von Bitter Rucker) is best known as the author of the four cyberpunk novels comprising the Ware Tetralogy (the first two of which won the Philip K Dick Award). But he is also the author of several non-fiction books, most notably Infinity and the Mind: The Science and Philosophy of the Infinite (2004), as well as The Fourth Dimension: A Guided Tour of the Higher Universes (1985), Mind Tools: The Five Levels of Mathematical Reality (1988) and The Lifebox, the Seashell, and the Soul: What Gnarly Computation Taught Me About Ultimate Reality, the Meaning of Life, and How to Be Happy (2006), among many other books.

As a fiction author, Rucker identifies himself as a transrealist (from Wikipedia):

Transrealism is a literary mode that mixes the techniques of incorporating fantastic elements used in science fiction with the techniques of describing immediate perceptions from naturalistic realism. While combining the strengths of the two approaches, it is largely a reaction to their perceived weaknesses. Transrealism addresses the escapism and disconnect with reality of science fiction by providing for superior characterization through autobiographical features and simulation of the author's acquaintances. It addresses the tiredness and boundaries of realism by using fantastic elements to create new metaphors for psychological change and to incorporate the author's perception of a higher reality in which life is embedded. One possible source for this higher reality is the increasingly strange models of the universe put forward in theoretical astrophysics.

Its main proponent and prominent figure is science fiction author Rudy Rucker. Rucker coined the term "transrealism" after reading Philip K Dick's A Scanner Darkly described as "transcendental autobiography," and expounded the principles of transrealism in a short essay titled "A Transrealist Manifesto" in 1983. Rucker applied many of these principles in his short stories and novels, notably White Light and Saucer Wisdom. Damien Broderick has identified some other authors that have at some time utilized transrealist tropes to include Martin Amis, Margaret Atwood, Iain Banks, John Barth, J.G. Ballard, John Calvin Batchelor, Jonathan Carroll, Philip K. Dick especially, Karen Joy Fowler, Lisa Goldstein, James Morrow, Thomas Pynchon, Joanna Russ and James Tiptree Jr. [1]

While the Wikipedia entry sees transrealism as part of the slipstream literature genre, it sounds an awful lot like a form of postmodernist story-telling. Interested readers can check out Rucker's Transrealist Manifesto (1983).

Listen: Podcast on Transrealism vs. Hyperrealism

August 30th, 2013 | by Doug Lain

Rudy Rucker is a cyberpunk author, a mathematician, and a Transrealist. Known for his book Ware Tetralogy (four novels in one volume), Rucker’s most current book is “The Big Aha.” In this episode of the philosophy podcast Diet Soap the ideas of Transrealism and Baudrillard’s Hyperrealism are juxtaposed through sound clips and audio collage.

Rudy Rucker on Transrealism:

The Transrealist writes about immediate perceptions in a fantastic way. Any literature which is not about actual reality is weak and enervated. But the genre of straight realism is all burnt out. Who needs more straight novels? The tools of fantasy and SF offer a means to thicken and intensify realistic fiction. By using fantastic devices it is actually possible to manipulate subtext. The familiar tools of SF — time travel, antigravity, alternate worlds, telepathy, etc. — are in fact symbolic of archetypal modes of perception. Time travel is memory, flight is enlightenment, alternate worlds symbolize the great variety of individual world-views, and telepathy stands for the ability to communicate fully. This is the “Trans” aspect. The “realism” aspect has to do with the fact that a valid work of art should deal with the world the way it actually is. Transrealism tries to treat not only immediate reality, but also the higher reality in which life is embedded.

Listen below.

More awesomeness from Open Culture. Fractals: The Colors of Infinity takes us deep inside the world of fractal geometry, where we encounter what some people have called “the thumbprint of God.” Mostly, it's one of the most aesthetically beautiful discoveries in the history of mathematics.

Arthur C. Clarke Narrates Film on Mandelbrot’s Fractals; David Gilmour Provides the Soundtrack

August 29th, 2013


In 1995, Sir Arthur C. Clarke, the futurist and science fiction writer most well known for his novel 2001: A Space Odyssey, presented a television documentary on the 1980 discovery of the Mandelbrot Set (M-Set). Fractals: The Colors of Infinity brings us inside the world of fractal geometry, and soon enough we’re encountering what has been called “the thumbprint of God” and some of the most beautiful discoveries in the history of mathematics. Clarke narrates the 54-minute film, which includes interviews with important mathematicians, including Benoît Mandelbrot himself. David Gilmour, the guitarist for Pink Floyd, provides the soundtrack. It’s hard to imagine a more perfect combination. Fractals: The Colors of Infinity first appeared on Open Culture back in 2010, which means that a second viewing is long overdue. A book closely related to the film can be purchased here: The Colours of Infinity: The Beauty, The Power and the Sense of Fractals.

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• Pink Floyd’s David Gilmour Sings Shakespeare’s Sonnet 18
• Carl Sagan, Stephen Hawking & Arthur C. Clarke Discuss God, the Universe, and Everything Else
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This is pretty cool. Enjoy!

Envision the world in 11 dimensions: A TED-Ed lesson to blow your 3D mind

Posted by: Morton Bast
July 18, 2013

In our three-dimensional world, all we can experience is length, width and height. Unless one of your friends is a hypercube, it’s hard to imagine just what it would look like to live beyond the 3D. Would you like it? Would you understand it? Would you even believe it was real?

In this spunky TED-Ed lesson, Alex Rosenthal and George Zaidan lead us into a mathematical playland and test the very limits of our imagination. Inspired by Edwin Abbott’s 1884 novella, Flatland, they offer one way to conceive of a fourth, fifth or 11th dimension, and challenge us to open our eyes to a world outside what we’re built to perceive.

Does Math Objectively Exist, or Is It a Human Creation?

Thought-provoking video from PBS on a topic I seldom think about at all, which may be some kind of anxiety-based avoidance resulting from psychological trauma inflicted on me when last I took a math class, integral calculus. Oy vey! That was about the time I realized my strengths lie in the liberal arts and social science realms, not in the math and science realms.

Does Math Objectively Exist, or Is It a Human Creation? A New PBS Video Explores a Timeless Question

June 5th, 2013


In a famous scene from Boswell’s Life of Samuel Johnson, the biographer and his subject come to discuss the bizarre theories of Bishop Berkeley, who posited that everything is immaterial—nothing has any real existence; it’s all just ideal concepts held together by the mind of God. If God should lose his mind or fall asleep or die, everything would fall to pieces or cease to exist. Boswell insists there’s no way to refute the idea. Johnson, kicking a large stone with such force that his foot rebounds, cries, “I refute it thus.”

Johnson’s little demonstration doesn’t actually refute Berkeley’s radical idealism. It’s a conundrum still with us, like Plato’s Euthyphro stumper, which asks whether the rules governing human behavior exist independently of the gods, who simply enforce them, or whether the gods make the rules according to their whims. In other words, is morality objective or subjective? A similar problem occurs when we consider the existence of the rules that govern physical laws—the rules of mathematics. Where does math come from? Does it exist independently of human (or other) minds, or is it a human creation? Do we discover mathematical problems or do we invent them?

The question has engendered two positions: mathematical realism, which states that math exists whether we do or not, and that there is math out there we don’t know yet, and maybe never can. This position may require a degree of faith, since, “unlike all of the other sciences, math lacks an empirical component.” You can’t physically observe it happening. Anti-realists, on the other hand, argue that math is a language, a fiction, a “rigorous aesthetic” that allows us to model regularities in the universe that don’t objectively exist. This seems like the kind of relativism that tends to piss off scientists. But no one can refute either idea… yet. The video above, from PBS’s Idea Channel, asks us to consider the various dimensions of this fascinating and irresolvable question.

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~ Josh Jones is a writer and musician based in Washington, DC. Follow him at @jdmagness

Issues in the Metaphysics of Science - Bookforum Omnivore

From Bookforum's Omnivore blog, a collection recent links examining the metaphysics of science, from the meaning of a "second," to whether or not science is beautiful or must be elegant, to reality as a mathematical structure.


Issues in the metaphysics of science

26 2013 

10:00AM

• From Studia Philosophica Estonica, a special issue on practical realist account of science. 
• It may have been awhile since you wondered, what exactly is a second? But think about it now and the question will nag at you. 
• Are there parallel universes? The answer is "possibly". 
• Stephen Mumford is cool, calm and collected as he broods on the big issues in the metaphysics of science. Is scientific truth always beautiful? 
• David Orrell says the quest for elegance leads too many researchers astray. 
• According to Max Tegmark, it’s not enough to say that math governs our universe; rather, he believes that reality itself is a mathematical structure. 
• Philosophy under attack: Patrick Stokes on Lawrence Krauss and the new denialism. 
• An “embarrassment” to science: Brad Plumer on a simple breakdown of why physicists still can't agree on how to interpret quantum mechanics — and why it matters. 
• What is the purpose of the Universe? Here is one possible answer.

If you are an MC Escher fan this is pretty rad - if not, it's still pretty cool. As is usually the case, this comes from Open Culture.

Metamorphose: 1999 Documentary Reveals the Life and Work of Artist M.C. Escher

October 2nd, 2012

Made in 1999 by Dutch director Jan Bosdriesz, the documentary Metamorphose: M.C. Escher, 1898-1972 takes its title from one of Escher’s more well-known prints in which the word “metamorphose” transforms itself into patterns of abstract shapes and animals. It’s one of those college-dorm prints one thinks of when one thinks of M.C. Escher, and it’s wonderful in its own way. But the documentary reveals other sides of the artist—his art-school days, his sojourn in Italy—that produced a very different kind of work. Escher began as a student of architecture, enrolled in the School for Architecture and Decorative arts in Haarlem by his parents, who struggled to help him find his way after he failed his high school exams.

Once in Haarlem, the lonely and somewhat morose Escher finds himself drawn to graphic art instead. One of his teachers, accomplished Dutch artist Samuel Jessurun de Mesquita, whose influence is evident in Escher’s work and life, sees some of Escher’s linocuts and likes them. In archival footage of an interview with Escher, the artist says that Jessurun de Mesquita asked him, “Wouldn’t you rather be a graphic artist instead of an architect?” Escher admits, “I wasn’t all that interested in architecture.” It’s a little bit of a surprising admission given Escher’s wild architectural imagination, but perhaps what he meant was that he wasn’t interested in the conventional, but rather in the architecture of the fantastic, the impossible spaces he imagined in much of his work.

We learn other things about Escher: One of his woodcuts from this period is titled “Never Think before You Begin,” showing a lonely figure on a dark and treacherous path with only a tiny light to guide him, a representation of Escher’s decision to pursue graphic art. The narrator informs us that “it took more than thirty years for him to earn enough from his work to live on.” Luckily, as with many artists who struggle for years, Escher had rich parents. We can thank them for their patronage.  To give you some idea of Escher’s morbid character, we learn that he chose the topic “Dance of Death” for a three-hour lecture to his fellow art students in Haarlem. Escher told them, “The dance of death and life are two expressions with the same meaning. What else do we do other than dance death into our souls?”

Metamorphose is an impressive documentary, beautifully shot and edited, with a balance of stock footage of the period, interviews with the artist himself, and long, lingering shots of his work. The film covers Escher’s entire artistic life, ending with footage of the artist at work. These “last images” of Escher, the narrator says, “are not gloomy. We see an artist in his studio, doing the things he enjoys,” a man “proud of his success.” At the end of his life, he still honored his teacher, de Mesquita, and the South Italian coast that sheltered him during his formative years.

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• Mathematics Made Visible: The Extraordinary Art of M.C. Escher
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Josh Jones is a doctoral candidate in English at Fordham University and a co-founder and former managing editor of Guernica / A Magazine of Arts and Politics.

Open Culture - Face to Face with Bertrand Russell: ‘Love is Wise, Hatred is Foolish’

Nice little video of the timeless Bertrand Russell talking about mathematics, love, and hate. Russell sat down with John Freeman of the BBC program Face to Face - in April, 1959.

Face to Face with Bertrand Russell: ‘Love is Wise, Hatred is Foolish’

August 31st, 2012
by Mike Springer 

In April of 1959 the British philosopher and mathematician Bertrand Russell sat down with John Freeman of the BBC program Face to Face for a brief but wide-ranging and candid interview. Russell reminisced about his early attraction to mathematics. “I got the sort of satisfaction that Plato says you can get out of mathematics,” he said. “It was an eternal world. It was a timeless world. It was a world where there was a possibility of a certain kind of perfection.”

Russell, of course, distinguished himself in that rarified world as one of the founders of analytic philosophy and a co-author of Principia Mathematica, a landmark work that sought to derive all of mathematics from a set of logical axioms. Although the Principia fell short of its goal, it made an enormous mark on the course of 20th century thought. When World War I came along, though, Russell felt it was time to come down from the ivory tower of abstract thinking. “This world is too bad,” Russell told Freeman. “We must notice it.”

The half-hour conversation, shown above in its entirety, is of a quality rarely seen on television today. The interviewer Freeman was at that time a former Member of Parliament and a future Ambassador to the United States. Russell talks with him about his childhood, his views on religion, his political and social activism, even his amusing conviction that smoking extended his life. But perhaps the most famous moment comes at the end, when Freeman asks the old philosopher what message he would offer to people living a thousand years hence. In answering the question, Russell balances the two great spheres that occupied his life:

I should like to say two things, one intellectual and one moral:

The intellectual thing I should want to say to them is this: When you are studying any matter or considering any philosophy, ask yourself only what are the facts and what is the truth that the facts bear out. Never let yourself be diverted either by what you wish to believe or by what you think would have beneficent social effects if it were believed, but look only and solely at what are the facts. That is the intellectual thing that I should wish to say.

The moral thing I should wish to say to them is very simple. I should say: Love is wise, hatred is foolish. In this world, which is getting more and more closely interconnected, we have to learn to tolerate each other. We have to learn to put up with the fact that some people say things that we don’t like. We can only live together in that way, and if we are to live together and not die together we must learn a kind of charity and a kind of tolerance which is absolutely vital to the continuation of human life on this planet.

Related content:

• Bertrand Russell on the Existence of God and the Afterlife
• Three Passions of Bertrand Russell (and a Collection of Free Texts)
• Face to Face with Carl Jung: ‘Man Cannot Stand a Meaningless Life’