Alone in his workroom, a student contemplates his future. Piles of books teeter next to him. Boxes line the walls; and glass vials, the boxes. Sunbeams that struggle through the stained-glass window illuminate dust.

The student’s name is Faust. I met him during my last winter in college, while complementing Physics 42: Introductory Quantum Mechanics with German 44: The Faust Tradition. A medieval German alchemist, Faust has inspired plays, novels, operas, the short story “The Devil and Daniel Webster” about an American Congressman, and the film “Bedazzled” starring Brendan Frasier.

The Faust tradition in popular culture. Mephistopheles is the demon who buys Faust’s soul. (http://xkcd.com/501/)

As I wondered what to pursue a PhD in, so (roughly speaking) did Faust. In plays by Christopher Marlowe and Johann Wolfgang von Goethe, Faust wavers among law, theology, philosophy, and medicine. You’ve probably heard what happens next: Faust chooses sorcery, conjures a demon, and bargains away his soul. Hardly the role model for a college student. I preferred to keep my soul, though Maxwell’s demon had stolen my heart.

A few decades after Goethe penned Faust, English physicist James Maxwell proposed a thought experiment. Consider a box divided into two rooms, he wrote, and a demon controlling the door between the rooms. Since others have explained Maxwell’s paradox, I won’t parrot them. Suffice to say, the demon helps clarify why time flows, what knowledge is, and how information relates to matter. Quantum-information physicists, I learned in a seminar after German 44, study Maxwell’s demon. Via the demon, experiment, and math, QI physicists study the whole world. I wanted to contemplate the whole world, like Goethe’s Faust. By studying QI, I might approximate my goal. Faust, almost as much as my QI seminar, convinced me to pursue a PhD in physics.

Fast forward two years. Someone must have misread my application, because Caltech let me sign my soul to its PhD program. I am the newest Preskillite. Or Preskillnik. Whichever term, if either, irks my supervisor more.

For five years, I will haunt this blog. (Spiros will haunt me if I don’t haunt it.) I’ll try to post one article per month. Pure quantum information occupies me usually: abstract math that encodes physical effects, like entropy (a key to why time flows), decoherence (a system’s transformation from quantum to ordinary), and entanglement (one particle’s ability to affect another, instantaneously, from across a room).

In case I wax poetic about algebra, I apologize in advance. Apologies if I write too many stories about particles in boxes. In addition to training a scientist’s lens on atoms, I enjoy training it on science, culture, and communities. Tune in for scientists’ uses (and abuses) of language, why physics captivates us, and the bittersweetness of representing half our species in a roomful of male physicists (advantage: I rarely wait in line to use a physics department’s bathroom).

As I prepare to move to Caltech, a Faust line keeps replaying in my mind. It encapsulates my impression of a PhD, though written 200 years ago: “Nothing I had; and yet, enough for youth—/ delight in fiction, and the thirst for truth.”

Pleasure to meet you, Quantum Frontiers. Drink with me.

The article goes into some detail about the unusual life Feynman led, describing some of its high points without shying away from the idiosyncratic aspects of the master physicist’s life. Described in the article is this colorful animation that a graphic designer made of a brief excerpt from the now famous BBC interview of Feynman (The pleasure of finding things out):

As the Telegraph article describes, the little animation has gone viral, spreading the message that science actually adds to our ability to appreciate beauty in the world: Unlike popular belief would have us think, science is not dry, it is not cold, not clinical, or simply analytical, devoid of emotional impact on the ones that have devoted their lives to pursue it. Science is the one honest, brave (and obviously awesome) answer humanity has come up with to the burning question:

What just happened here?

The truth is that science always begins with the following answer: I don’t know. That is the honest part. Then comes the desire to know, otherwise known as curiosity. Whereas many of us will say of certain things: We can’t possibly know this, the scientist will say: I will try anyways. That is the brave part. Because some questions lead to answers that we don’t really want to accept – we are afraid that the answer may break something inside of us, something we invested time to construct, something we cherish, something important like the feeling of accomplishment for effortlessly appreciating the sublime beauty of a flower.

And then, of course, there is that thing about science being hard to do. It is. You can try to bs your way through science, and some do try, but then you might as well be a car salesman and make some good money in the process (actually, I met an honest car salesman just three weeks ago and I am still not sure what to make of it – he works for a Mini Cooper dealership in L.A. and that is all I am allowed to say in order to protect him and his family.)

But this is only half of the story…

The question that (too many) scientists are afraid to ask themselves is the following: What if my science doesn’t speak for itself? What if my science seems super-boring to others, or simply pointless (like studying fruit flies)? What if I actually need to go out into the unknown (the world that lies outside the Ivy Tower) in order to engage the public, to get the world excited about my discoveries?

Aristotle, the grandaddy of analytical thinking, wrote the most influential treatise on Rhetoric (the art of persuasion) for good reason. So here is my thesis: Every other Sunday morning, every church hosts a scientist to give a public lecture (no boring, arcane jargon allowed) on subjects ranging from the Big Bang Theory to the Theory of Evolution and Stem Cell research. No need to try to reconcile science with religion during the lecture, or be combative – just a good story based on scientific findings – let the audience decide if they want more. All I am saying is: Give it a try. Like pastors, there are scientists out there who love to tell a good story and provide some food for thought (and maybe raise some money from the parish for their good work). We can even use animations like the one above, or this one from PhD Comics.

What do you think?

Caltech sponsors the Earnest C. Watson lecture series (named after the same Earnest Watson mentioned in my post about Jane Werner Watson), which attracts very enthusiastic audiences to Beckman Auditorium nine times a year. I gave a Watson lecture on April 3 about Quantum Entanglement and Quantum Computing, which is now available from iTunes U and also on YouTube:

I did a Watson lecture once before, in 1997. That occasion precipitated some big changes in my presentation style. To prepare for the lecture, I acquired my first laptop computer and learned to use PowerPoint. This was still the era when a typical physics talk was handwritten on transparencies and displayed using an overhead projector, so I was sort of a pioneer. And I had many anxious moments in the late 1990s worrying about whether my laptop would be able to communicate with the projector — that can still be a problem even today, but was a more common problem then.

I invested an enormous amount of time in preparing that 1997 lecture, an investment still yielding dividends today. Aside from figuring out what computer to buy (an IBM ThinkPad) and how to do animation in PowerPoint, I also learned to draw using Adobe Illustrator under the tutelage of Caltech’s digital media expert Wayne Waller. And apart from all that technical preparation, I had to figure out the content of the lecture!

That was when I first decided to represent a qubit as a box with two doors, which contains a ball that can be either red or green, and I still use some of the drawings I made then.

Entanglement, illustrated with balls in boxes.

This choice of colors was unfortunate, because people with red-green color blindness cannot tell the difference. I still feel bad about that, but I don’t have editable versions of the drawings anymore, so fixing it would be a big job …

I also asked my nephew Ben Preskill (then 10 years old, now a math PhD candidate at UC Berkeley), to make a drawing for me illustrating weirdness.

The desire to put weirdness to work has driven the emergence of quantum information science.

I still use that, for sentimental reasons, even though it would be easier to update.

The turnout at the lecture was gratifying (you can’t really see the audience with the spotlight shining in your eyes, but I sensed that the main floor of the Auditorium was mostly full), and I have gotten a lot of positive feedback (including from the people who came up to ask questions afterward — we might have been there all night if the audio-visual staff had not forced us to go home).

I did make a few decisions about which I have had second thoughts. I was told I had the option of giving a 45 minute talk with a public question period following, or a 55 minute talk with only a private question period, and I opted for the longer talk. Maybe I should have pushed back and insisted on allowing some public questions even after the longer talk — I like answering questions. And I was told that I should stay in the spotlight, to ensure good video quality, so I decided to stand behind the podium the whole time to curb my tendency to pace across the stage. But maybe I would have seemed more dynamic if I had done some pacing.

I got some gentle criticism from my wife, Roberta, who suggested I could modulate my voice more. I have heard that before, particularly in teaching evaluations that complain about my “soporific” tone. I recall that Mike Freedman once commented after watching a video of a public lecture I did at the KITP in Santa Barbara — he praised its professionalism and “newscaster quality”. But that cuts two ways, doesn’t it? Paul Ginsparg listened to a podcast of that same lecture while doing yardwork, and then sent me a compliment by email, with a characteristic Ginspargian twist. Noting that my sentences were clear, precise, and grammatical, Paul asked: “is this something that just came naturally at some early age, or something that you were able to acquire at some later stage by conscious design (perhaps out of necessity, talks on quantum computing might not go over as well without the reassuring smoothness)?”

Another criticism stung more. To illustrate the monogamy of entanglement, I used a slide describing the frustration of Bob, who wants to entangle with both Alice and Carrie, but finds that he can increase his entanglement with Carrie only my sacrificing some of his entanglement with Alice.

Entanglement is monogamous. Bob is frustrated to find that he cannot be fully entangled with both Alice and Carrie.

This got a big laugh. But I used the same slide in a talk at the APS Denver meeting the following week (at a session celebrating the 100th anniversary of Niels Bohr’s atomic model), and a young woman came up to me after that talk to complain. She suggested that my monogamy metaphor was offensive and might discourage women from entering the field!

After discussing the issue with Roberta, I decided to address the problem by swapping the gender roles. The next day, during the question period following Stephen Hawking’s Public Lecture, I spoke about Betty’s frustration over her inability to entangle fully with both Adam and Charlie. But is that really an improvement, or does it reflect negatively on Betty’s morals? I would appreciate advice about this quandary in the comments.

In case you watch the video, there are a couple of things you should know. First, in his introduction, Tom Soifer quotes from a poem about me, but neglects to name the poet. It is former Caltech postdoc Patrick Hayden. And second, toward the end of the lecture I talk about some IQIM outreach activities, but neglect to name our Outreach Director Spiros Michalakis, without whose visionary leadership these things would not have happened.

The most touching feedback I received came from my Caltech colleague Oskar Painter. I joked in the lecture about how mild mannered IQIM scientists can unleash the superpower of quantum information at a moment’s notice.

Mild mannered professor unleashes the superpower of quantum information.

After watching the video, Oskar shot me an email:

“I sent a link to my son [Ewan, age 11] and daughter [Quinn, age 9], and they each watched it from beginning to end on their iPads, without interruption.  Afterwards, they had a huge number of questions for me, and were dreaming of all sorts of “quantum super powers” they imagined for the future.”

After graduating from MIT with a degree in Mathematics with Computer Science (18C), I found myself in the following predicament: I was about to start doing research on Quantum Computation as a PhD candidate at UC Davis’ Department of Mathematics, but I had taken exactly two physics courses since 9th grade (instead of Chemistry, Biology and Physics, I had no choice but to take Anthropology, Sociology and Philosophy throughout high school; which I blame for starting a fashion line…) The courses are well-known to MIT undergraduates – 8.01 (Classical Mechanics) and 8.02 (Electromagnetism) – since they are part of MIT’s General Institute Requirements (GIRs). Modesty and common sense should force me to say that I found the two MIT courses hard, but it would not be true. I remember getting back my 8.01 midterm exam on rocket dynamics with a score of 101%. I didn’t even know there was a bonus question, but I remember the look on my friend’s face when he saw my score and Prof. Walter Lewin announced that the average was 45%. It doesn’t take much more than that to make you cocky. So when my PhD adviser suggested years later that I take graduate Quantum Mechanics with no background in anything quantum, I accepted without worrying about the details too much – until the first day of class…

Prof. Ching-Yao Fong (Distinguished Professor of Physics at UC Davis) walked in with a stack of tests that were supposed to assess how much we had learned in our undergraduate quantum mechanics courses. I wrote my name and enjoyed 40 minutes of terror as it dawned on me that I would have to take years of physics to catch up with the requirements needed for any advanced quantum mechanics course. But out-of-state (worse, out-of-country) PhD students don’t have the luxury of time given the fact that we cost three times as much as in-state students to support (every UC is a public university). So I stayed in class and slowly learned to avoid the horrified looks of others (all Physics PhD candidates), whenever I asked an interesting question (thanks Dr. Fong), or made a non-sense remark during class. And then the miracle happened again. I aced the class. I have already discussed my superpower of super-stubbornness, but this was different. I actually had to learn stuff in order to do well in advanced quantum mechanics. I learned about particles in boxes, wavefunctions, equations governing the evolution of everything in the universe – the usual stuff. It was exhilarating, a whole new world, a dazzling place I never knew! In all my years at MIT, I never took notes on any of my classes and I continued the same “brilliant” tactic throughout my PhD, except for one class: Quantum Mechanics. I even used highlighters for the first time in my life!

It was a bonafide love affair.

Thinking about it years later, comfortable in my poly-amorous relationship with Paul Dirac (British), Werner Heisenberg (German), Erwin Schrödinger (Austrian) and Niels Bohr (Danish), I realize that some people may consider this love one-sided. Not true. Here is proof: Dirac himself teaching quantum mechanics like only he could.

Note: The intrepid Quantum Cardinal, Steve Flammia, scooped us again! Check out his post on the Dirac lectures and virtual hangouts for quantum computation lectures on Google+.

Questions on the many-worlds interpretation always make me think back to my early student days, when I also obsessed over these issues. In fact, I got so frustrated with the question, that I started having heretic thoughts: What if it is all in our minds? What if the quantum superposition is always there, but maybe evolution had consciousness always zoom in on one possible outcome. Maybe hunting a duck is just easier if the duck is not in a superposition of flying south and swimming in a pond. Of course, this requires that at least you and the duck, and probably other bystanders, all agree on which quantum reality it is that you are operating in. No problem – maybe evolution equipped all of our consciousnesses with the ability to zoom in on a common reality where all of us agree on the results of experiments, but there are other possibilities for this reality, which still live side by side to ‘our’ reality, since – hey – it’s all in our minds!

Doesn’t make sense to you? I can’t blame you. Consider though: many would say that quantum mechanics doesn’t make sense either.

My ‘collapsing mind’ theory has clear drawbacks, but suppose it were true, just imagine the possibilities! It could explain many mysterious phenomena around us. As a first example: The web is full of rumors of people with multiple personalities losing some scar or tumor, as they transition between personalites…* aha! I know what’s wrong – their mind is not ‘collapsing correctly’! The multiple personalities are easily explained as the same personality, just reacting to a quantum reality which is different than the one that the rest of us agree on. By a little. What about Schizophrenia? You guessed it! Hallucinations might just be interpreting sensory stimulus from a different part of the collective wavefunction. In fact, this approach could start a whole new field: “Quantum archeology”. A hallucination might be an exploration of an alternative quantum reality that could have happened – well – happened, but had split off from our common reality some time in the past. Contrasting alternative realities with ours may possibly allow us to interpolate and reconstruct the critical junctures of the evolution of our reality. You see orange men all around? Maybe in a different branch of evolution we did actually turn orange.

As you can hopefully tell, this was not a serious candidate I was proposing to replace the Copenhagen interpretation. At best, I thought of making it into a science fiction story (“mind collapse?”, “Quantumphrenia?”). But then, years later, at the recommendation of my wife, I read a book by the German writer Juli Zeh, “Schilf”. In English it was published under the name ‘In Free Fall’. The book is a detective story which focuses on two physics frenemies. One is an experimentalist who is an ardent believer of the many-worlds interpretation. The other, a CERN theorist, is a complete many-worlds skeptic. One of them commits a nasty murder.

Before the murder, however, the book describes a televised quantum-measurement showdown, and there it appeared out of nowhere – Dieter Zeh and his many-minds interpretation. This caught me by complete surprise, as I thought that at least my science fiction was original, not to mention that I never heard of Zeh before. Wikipedia to the rescue: Dieter Zeh, unrelated to the krimi** author, has indeed proposed the so called ‘many-minds’*** interpretation back in 1970′s. Not only that, he reproduced a 1981 paper from the ‘Epistemological letters’ in the preprint arxiv in 1999 as quant-ph/9908084. There it was, my crazy science fiction idea, come to life! And proven to be consistent – actually, the only consistent – interpretation of quantum mechanics and the many-worlds theory.

Usually I’m upset about being scooped, but somehow I let this one go without too much agony. I sat back and finished reading the book. At least my college quantum measurement escapade turned into a good detective story, even if I didn’t win a Nebula award in the process. The book was the most quantum-physics piece of literature that both me and my wife (a Germanist) could equally enjoy. Quantum measurement was all over the plot. Even the detective that solves the case has a girlfriend which may or may not exist and is constantly fretting about calling her, concerned about collapsing the wavefunction to a reality where she does not exist.

It seems that (J) Zeh, despite being a lawyer by training, hit on something that I thought only us quantum physicists really knew: quantum-measurement theory is nothing less than a matter of life and death and not necessarily only for cats!

* Some examples I found by light googling:
http://answers.yahoo.com/question/index?qid=20110624221813AAKTvpy

http://www.powerfulintentions.org/forum/topics/undeniable-unescapeable?commentId=1335877%3AComment%3A2726033

** Criminal novel in German slang

*** Initially the many-consciousness interpretation

Alicia Hardesty: full-time fashion designer, part-time nerd.

Have you seen the movie Frankenweenie? It’s a black and white cartoon (an experiment in itself these days) with a very important message:

Don’t be afraid to do what you love and don’t be afraid to be good at it.

The main character is a smart, sensitive kid who is ostracized for his science experiments. Like the teacher says, people don’t understand science so they are afraid of it. Ironically, artists often deal with the same kind of misunderstandings from the public.

I’m not technically a scientist, but I do love to experiment and try stuff. I’m a fashion designer, which requires it’s own level of scientific conviction. I create, combine unlikely variables, hypothesize, and work within my own scientific method throughout my process.

How does this relate to you?

Project X Squared. Where art, science, and technology meet fashion to create a clothing line, much like an experiment, with the underlying hypothesis being that a quantum physicist, a neuroscientist and a fashion designer can create something tangible together.

We are not creating a fashion line to change the world. This is just a proof of concept, an example if you will, of what is possible when we step outside of our box. After all, Crystal, Spiros and I just wanted to hang out and learn from each other; we weren’t planning to start a company. Still, a first step was necessary…

We had to be open. Open to the uncertainty facing every explorer. Open to becoming masters of our domain – using that mastery to create surprising things in unlikely places. Open to a life of passionate pursuit of things that have real, tangible value. We don’t know what the highest ideals are in this world, but whatever they are (if such things exist), it is the journey that drives us to attain new heights so that we may get a better glimpse of this world’s infinite possibilities.

And so, like the movie Frankenweenie, this project carries its own message:

Find your passion. Become a master. Go out and play!

I have a feeling that there are others like us out there. Scientists and engineers, dancers and musicians, builders and innovators, young and old. Drawn to science, art and technology because of an insatiable curiosity about the world around us. I would love to hear from you in the comments – what would you like to see in our collection? what elements do you find interesting? where should we go from here? And, of course, if you like what we are doing, support our project and share it with your friends. Now sit back, relax and enjoy our Kickstarter video.

Editor’s Note: Alicia Hardesty, a full-time fashion designer and part-time nerd, is the founder of Original Tomboy. A Project Runway favorite, she brings her unique style to this out-of-the-box collaboration. You can follow her on Twitter and Instagram @originaltomboy.

This number, the product of all prime numbers known so far plus one, is so large that I can’t even write it down on this blog post. But it is certainly (proof left as an exercise…!) a prime number (see Problem 4 in The allure of elegance) and definitely larger than the one getting all the hype. Finally, I will be getting published in Nature!

In the meantime, if you are looking for a real challenge, calculate how many digits my prime number has in base 10. Whoever gets it right (within an order of magnitude), will be my co-author in the shortest Nature paper ever written.

Update 2: I read somewhere that in order to get attention to your blog posts, you should sprinkle them with grammatical errors and let the commenters do the rest for you. I wish I was mastermind-y enough to engineer this post in this fashion. Instead, I get the feeling that someone will run a primality test on just to prove me wrong. Well, what are you waiting for? In the meantime, another challenge: What is the smallest number (ballpark it using Prime Number Theorem) of primes we need to multiply together before adding one, in order to have a number with a larger prime factor than ?

Update: The number given above may not be prime itself, as pointed out quickly by Steve Flammia, Georg and Graeme Smith. But, it does contain within it the new largest prime number ever known, which may be the number itself. Now, if only we had a quantum computer to factor numbers quickly…Wait, wasn’t there a polynomial time primality test?

Note: The number mentioned is the largest known Mersenne prime. That Mersenne primes are crazy hard to find is an awesome problem in number theory.

Ron Rivest

What is public-key cryptography (PKC)? The basic notion is due to Ralph Merkle in 1974 and (in a stronger form) to Whitfield Diffie and Martin Hellman in 1976. Their remarkable proposal was that two parties, “Alice” and “Bob”, could cooperate in cryptographic protocols, even if they had never met before. All prior cryptography, from the ancients up through and after the cryptographic adventures of WWII, had relied on the cooperating parties sharing in advance some “secret key” that gave them an edge over any eavesdropper “Eve”.

How can the Merkle-Diffie-Hellman idea be possible? Alice and Bob wish to share a secret, but they have never met or communicated previously, and Eve can read every message they send each other. How, then, can they learn anything from the communication that she does not?

The crux is computational complexity. It is true that Alice and Bob do not learn any more information than Eve does. But, because they get to “frame” the message exchange, they learn the information in a readily-digestible form, whereas Eve learns the information in a form that requires, apparently, exponential time to be converted to useful information. By then the information will be too stale to be useful, or the sun will have gone nova, whichever comes first.

For their elegant cryptosystem carrying out this idea, Rivest, Shamir and Adleman shared the Turing Award in 2002. This is fitting, because Turing was a leader in the very successful cryptanalytic efforts in Great Britain during WWII. It is sad that (among other things) Turing did not live to see, and maybe be part of, these modern developments in cryptography—born in 1912, he should still have been vigorous and active when PKC came on the scene.

It is not an accident that PKC was invented in the first few years after computational complexity was born as a field and it was conjectured that “P is not equal to NP”. Public-key cryptography relies not only on this, the most famous conjecture in computer science, but on even stronger conjectures. Most of these seem very solid—for forty or more years now, mathematicians and computer scientists and others have worked hard at developing algorithms of all sorts, and progress on any of a multitude of fronts would have been a viable threat to the conjectures—with nothing to show for it. That is not enough to make the conjectures true but (just as Laplace calculated odds that the sun will rise tomorrow), a reasonable basis for planning.

Not all conjectures live quietly to old age, however. The security of the RSA cryptosystem relies on the very particular conjecture that it is hard to factor large numbers. This conjecture received a rude, but exciting, surprise in 1994.

But let’s first roll back to 1981. That was when Richard Feynman—one of our favorite figures here at Caltech—first contemplated that a computer taking advantage of quantum mechanical effects might have significant computational advantages over a computer taking advantage only of classical mechanics. Feynman had won the Nobel Prize way back in 1965 for work on completely different topics, but this late-career one-off article is one of his greatest insights. (In case you don’t follow these things, the Nobel Prize is a well-known award that is given for spectacular work in fields that are not eligible for the Turing Award.)

In 1993, Umesh Vazirani and Ethan Bernstein read Feynman’s paper, understood the implications for complexity theory, and kicked off the field of quantum computation. Within a year, Peter Shor had shown that quantum computers can factor numbers efficiently.

Well, there goes the RSA cryptosystem! (And other popular ones, especially ECC.) If, of course, you can build quantum computers. Which we still can’t. But my physicist colleagues, both here at the IQIM and around the world, assure me that they’re working on it, “day and night, honest”. Meanwhile most of us, living on the edge, still use RSA and ECC, but we have to prepare for a transition.

Is there a cryptosystem we can use if and when someone does build a quantum computer? The first machine might be built in secrecy, so we have to be ready to transition to new methods whenever the lab work starts looking too promising.

Fortunately, yes, there are several promising candidates for what is fashionably called “post-quantum cryptography”. I’ll give a little list here. In all of these methods there is a parameter “” that measures the size of the messages or other information being manipulated. In order that a cryptosystem merit the title “post-quantum”, I’ll require that it maintain the following two properties as grows:

(a) The processing time required by the honest parties (Alice and Bob in our little story) is no more than for some finite constant . The honest parties only need to use a classical computer, such as those we use today.

(b) The processing time required by the attacker (Eve) is no less than for some positive constant , even if she has access to a full-strength -qubit quantum computer.

Ultimately we care about the values of and also other parameters, but today let’s keep it simple. Here is a list of some candidates, with a few notes on each.

Bob McEliece

(1) The McEliece cryptosystem (and variants), due to Caltech’s very own Bob McEliece in 1978. This is the first “code-based” cryptosystem: it relies on the hardness of decoding random linear error-correcting codes. Interestingly, a weakened version of the method was compromised in the late 90′s by an algorithm of Sendrier. But the full-strength cryptosystem is still secure against all known attacks.

(2) Lattice cryptosystems: these come in various flavors, due to works by Ajtai and Dwork, Regev and others. They rely on the hardness of basis reduction and related problems in random—and even adversarially chosen!—lattices. In some ways these cryptosystems are the most likely replacements for RSA/ECC. However, we have a nontrivial quantum algorithm, due to Kuperberg, that is fairly good at solving a problem that is, in turn, uncomfortably similar to cracking these cryptosystems. I’m glossing over key distinctions—all I want to say, here, is that it will take some time before we can gain conviction whether these distinctions are sufficient to ensure security.

(3) Multivariate quadratic (MQ) cryptosystems such as HFEv-, based on a method introduced by Patarin. The security of these systems relies on the hardness of solving systems of polynomial (but nonlinear) equations. This is a problem that we have absolutely no quantum-over-classical edge on, which is a great research topic.

(4) Since I started thinking about this subject I came up with another candidate. Cryptanalysts haven’t had much chance to look at it yet, so it hasn’t yet acquired any credibility; time will tell. Also, it is slow, but this may improve if a certain open question in coding theory can be solved. It is an MQ cryptosystem and also code-based, and it seems to be more secure than McEliece’s system against the main kinds of attack.

So the situation is encouraging, in that we have diverse options for the future. What this list cannot reveal, though, is how much trust we should place in the security of these proposals. Computer science today has no techniques to prove in absolute terms the security of any PKC. Even the best security proofs, such as for lattice methods, say merely that “cracking system A is at least as hard as solving some other problem B” where B is, a priori, more general or more adversarial. So trust in a cryptosystem is, like trust in people, mainly a function of the intensity and duration of our acquaintance; except that in the case of cryptosystems, we measure this acquaintance by how many people, and how smart and how dedicated and over how many years, have tried to attack the system. Come to think of it, trust in cryptosystems is simply trust in people.

And trust in post-quantum cryptosystems is trust in the people who study quantum algorithms. There are rather few of that species, and they have not been at work for very long. So we don’t understand quantum algorithms very well. Which means that we cannot yet put much trust in the post-quantum security of any cryptosystem.

I want to wrap up but I cannot resist filling you in a little on Alice and Bob. Remember Alice and Bob?—all of our efforts are dedicated to protecting their communications. Who are they? What have they to hide? I don’t know them, but fortunately, I can refer you to an unauthorized but definitive biography.

Arthur Wightman

Arthur Wightman passed away this past January, at age 90. He was one of the great mathematical physicists of the past century.

Two of Arthur’s most renowned students, Arthur Jaffe and Barry Simon, wrote an affectionate obituary. I thought I would add some reminiscences of my own — Wightman was my undergraduate thesis advisor at Princeton.

I loved math in high school, and like many high school students before and since, I became convinced that Gödel’s incompleteness theorem is the coolest insight ever produced by the human mind. I resolved to devote my life to set theory and logic, and somehow I also became convinced that Princeton would be the best place in the world to study the subject. So there I went. I had a plan.

As a freshman, I talked my way into a graduate level course on Advanced Logic taught by Dana Scott. (I cleared the biggest obstacle by writing an essay to pass out of the freshman English requirement.) The course was wonderful, but by the end of it I was starting to accept what I had already sensed while in high school — I lack the talent to be a great mathematician.

A door was closing, but meanwhile another was opening. I was also taking a course on Electricity and Magnetism, based on the extraordinary book by Ed Purcell, taught by the charismatic Val Fitch. Chapter 5 contains an unforgettable argument explaining how electrostatic forces combined with special relativity imply magnetic forces. Meanwhile, while learning advanced calculus from the lovely (but challenging) little book by Michael Spivak, I realized that the Maxwell field is actually a two-form! Physics can be almost as cool as logic, so I would be a physics major! I had a new plan.

By the end of my junior year, I was feeling some dissatisfaction with the paucity of rigor in much of theoretical physics. In those days I liked to browse the physics books in the Princeton U-Store, and occasionally I would treat myself by buying one. One day a book by Streater and Wightman caught my eye, with the charming title PCT, Spin and Statistics, and All That. The content of the book was equally charming, starting with the first sentence of the brief preface: “The idea of this book arose in a conversation with H. A. Bethe, who remarked that a little book about modern field theory which contained only Memorable Results would be a Good Thing.” Ever since, I have been unable to resist capitalizing Good Thing when the situation seemed to call for it.

I didn’t understand everything in the book, but the point was that it was a mathematically rigorous book about Quantum Field Theory! Having learned just that year that an unbounded operator in Hilbert space should be defined on a dense subspace (the operator’s domain), I felt relieved that Streater and Wightman (unlike, say, Bjorken and Drell) were keenly aware of this indispensable mathematical fact.

Every Princeton undergrad writes a Senior Thesis. As I plowed through Streater and Wightman in my spare time during the summer before senior year, I resolved that Arthur Wightman would be my thesis advisor, which led to an acutely embarrassing moment. At the university’s opening exercises that fall, I received an award from President Bowen, and we chatted for a while beforehand. He asked about my thesis, and I told him of my plan to work with Wightman, failing to mention that Wightman and I had never met. Sure enough, when I caught Arthur after his class a week later to introduce myself, he immediately responded that he had “already heard about you from a surprising source,” meaning President Bowen. While Prof. Wightman seemed unfazed by this incident, I was somewhat mortified.

In front of Princeton’s Jadwin Hall during senior year.

My sense of humiliation melted away as it became clear that Prof. Wightman was actually quite receptive to supervising my thesis. Not long earlier, Osterwalder and Schrader had discovered the axioms satisfied by a quantum field theory in imaginary time (most notably, reflection positivity) which correspond to the famous Wightman axioms for a relativistic quantum field theory in real time, thus transforming the task of constructing quantum field theories into a problem in classical statistical mechanics. Wightman was very enthusiastic about these new Euclidean methods, and suggested that I use them to prove there is a phase transition in the pseudoscalar Yukawa theory in two spacetime dimensions. This problem was way too hard for me (it was solved years later by Balaban and Gawedzki), and I didn’t make much headway, but I learned a lot under Arthur’s tutelage.

Though I did not sufficiently appreciate it at the time, Arthur was incredibly generous with his time. He decided I should start by studying Barry Simon’s book The Euclidean (Quantum) Field Theory, so I worked through it, taking full advantage of Arthur’s willingness to instruct me where my background was lacking. A few times, Barry spotted me carrying the book and shot a curious glance my way, but I never asked him any questions about it — he was far too intimidating! (Even now, though we have been colleagues on the Caltech faculty for 30 years, and I realize that Barry is actually a very nice man with an engaging sense of humor, I’m still a little bit scared of him.)

Arthur Wightman was not intimidating; he was avuncular. I made frequent appointments with Arthur, which he would record in the pocket-size little black book that professors used to carry in those days. But sometimes I would find him alone in his office when I passed by, and with an undergraduate’s sense of entitlement (particularly pronounced at Princeton, at least according to the graduate students), I would barge in to ask a question. He almost always received me amiably, and these impromptu visits sometimes turned into long meetings. I sometimes felt uncomfortable, sensing that graduate students and postdocs, who may have had more compelling reasons to claim some of Arthur’s time, were a bit annoyed: That kid is talking to Arthur again! I kept coming back because Arthur always made me feel like he genuinely enjoyed my company. Maybe he made everyone feel that way.

Although our meetings would typically begin with a particular well-honed question I wanted to pose, they would often meander in unexpected directions, with Arthur glad for the opening to tell an ancedote or muse on a related issue in physics or mathematics. After each meeting I would scramble to the library and make copious notes, trying to reconstruct the substance of our discussion. Over the course of the year these notes filled four spiral ring notebooks, which I still have.

There was a memorable moment during my oral thesis defense. I had derived the one-loop effective potential for the Yukawa theory by a laborious method, and Sam Treiman was skeptical of both the method and the result. Arthur made a suggestion: “Maybe we should ask one of the whiz-bang kids?” As if on cue, David Gross went rushing by the open door of the conference room, and Arthur called him in. David, after looking at the formula I had written on the board for just a few seconds, confidently announced that not only was the formula correct, it was obviously correct. It would take another year and a half for me to realize that David was right: the formula was obvious.

The opening paragraph of the Preface to my thesis reads: “I am surely not the first student to discover that seven months is not enough time to write a senior thesis. My ambition to choose a thesis problem that would be both “non-trivial” and “important” forced me to devote more than half of that time to learning the background material that made the statement of the problem intelligible. Even that task might have been impossible if not for the constant guidance of my advisor, Professor Arthur Wightman. Our frequent conversations were the major source of this paper; it would be impossible to acknowledge his influence on every thought expressed here. His lucid explanations, extraordinary patience with my stupidity, and sense of humor made our meetings thoroughly delightful for me. I have never known a better teacher.”

I guess it sounds like I was laying it on pretty thick, yet I was really sincere. Arthur’s example made me want to inspire others as he had inspired me, but I know I will always fall short of that standard.

So, we began with touring some of the labs of the agreeing advisors in the IQIM division, who were fine with a huge camera, a dolly track for movement and a couple of non-science strangers, namely our film crew, in their sensitive, experiment-running labs. I started meeting with the postdocs and grad students and not surprisingly, they inspired me. We realized that we wanted to celebrate the people behind the science and not the science, in this video.  The science is known and celebrated in so many other avenues. It was about the scientists and how they did all these amazing things in addition to their scientific pursuits and oh, by the way, they did do some serious science too. To me, it was about making a more 3-D vision of the “nerdspace” out there in media for science and engineers. Breaking the identity that if you are a scientist, you are boring and all you do is work in the lab. What could have been the most risqué representation I thought… bingo: High Fashion! And then came the convincing…

Emma Wollman, with her drill and black gown.

We had a meeting where we asked people to wear tuxes and gowns and pick the one item that they would take with them if Earth was to be evacuated; the one hobby, the one piece of identity. Initially there was paranoia, nerves and resistance, but then I cut a pitch tape to give an idea of my theme and style. They were getting convinced, but still not too sold on being so high fashion. So we met halfway. It was not the initial black, formal event attire, but it was still clean cut whilst being real, and frankly, a lot more personal in the end. People came up with very interesting stuff, whether it was Emma Wollman who held a drill and wore a gorgeous draped black gown she made herself (!), or Chen-Lung Hung, who played a violin in the Kimble lab, or Erik Henriksen with his long, lightsaber-looking device, or John Preskill with his baseball glove!

John Preskill really likes baseball.

By putting them in the labs and their environments of science, but having a fashionable look, where they were lit especially to create distance from their environment thanks to the talented cinematography of Anthony C. Kuhnz, the shots became about the person more than the science in the labs, without completely separating them. It was their identity, but not all of it.

Another segment of the video that celebrates the power of “imagination and inspiration” is the inter-cutting of archival imagery of nature and science. Whether it is a ballerina’s spin bringing to life the spin of an atom, the probabilistic nature of the casino roulette metaphorizing the inherent indeterminism of nature, or water waves moving like a sine wave display in an oscilloscope, making the viewer aware that Physics is around us in ways that we might not even notice, is important. These juxtapositions with work that is being done here at Caltech may capture the eye of a new viewer who would initially react and say, “wait a minute…what does this have to do with science?” The video is supposed to be the hook, to  intrigue and confuse and question and answer and I hope it does all this and, maybe, a little more.

A ballerina swiftly turns, hinting at quantum “spin”.

Of course, the punch to it all is the incredibly exciting and goose-bumping score by British composer, Andrew T. Mackay, part of the award-winning duo of Bombay Dub Orchestra, who, within a week, scored the video remotely from his Sunshine Desserts studio in London. Having worked with him on my feature film, we had developed a short-hand of what I like and it worked, within 9 days.

And all this crazy coordination and handling was thanks to Mrs. Marcia Brown who was always far too understanding and giving. She knows how to get us absent minded scientists and artists with our quirky moods and creative withdrawals, in line and on time to get the job done.

Lastly, I leave you with a few highlights of the video to urge you to click and watch and share. My favorite part of the video now, apart from Emma Wollman’s unbelievably attractive drill shot, is the beginning text that was a complete collaboration between me, Spiros and John Preskill with emails back and forth over a Wednesday in sunny Pasadena. Preskill’s genius tagline “nature is subtle” completely summarized my vision and the vision of IQIM and its scientists. The genius, the inspiration, the movement is all too important, yet subtle…and just purely “hot” in whatever sense of the word you want to take it!

Chen-Lung Hung with his violin. The text written in collaboration with John Preskill.

Here is the intro text in the video:

There is mind
There is matter
There is motion
There is interaction
There is the universe
To understand
To change
There is you…and your imagination.

IQIM

Nature is subtle.

And now, without further ado, I present to you, the IQIM Promotional Film. Sit back, relax, enjoy and share!

Editor’s Note: Pakistani filmmaker, Iram Parveen Bilal is the CEO and Founder of Parveen Shah Productions, a film production company with offices in Pakistan and Los Angeles. Having made and distributed a few short films, she is currently touring with her noted first feature length film, JOSH (English title: Against the Grain). Bilal is a Caltech alum, BS ’04 with honors, in Environmental Science Engineering and has an MFA from the USC School of Cinematic Arts in Filmmaking. Recent awards and fellowships include the 2012 Women In Film Award, the USC Stark Special Project Award, the Thomas J. Watson Fellowship, the Paul Studenski Fellowship, the Caltech Mabel Beckman Leadership Award and the Caltech Dean’s Cup.