# “Nature, you instruct me.”

“Settle thy studies.”

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 Feynman flower

Since I met Sean Carroll about a year ago, my life has changed for the better. In particular, I started following his wife @JenLucPiquant on Twitter and began reading her Scientific American blog, Cocktail Party Physics, a great place to get the latest news on physics – with a twist. Today, through one of Mrs. Ouellette’s RTs (re-tweets), I came across a fascinating article on Feynman, titled `Richard Feynman: Life, the universe and everything.

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?

# A Public Lecture on Quantum Information

Sooner or later, most scientists are asked to deliver a public lecture about their research specialties. When successful, lecturing about science to the lay public can give one a feeling of deep satisfaction. But preparing the lecture is a lot of work!

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.”

# An unlikely love affair

Most readers of this blog already know that when it comes to physics, I am faking it. I am a mathematician, after all, and even that is a bit of a stretch. So, what force of nature could convince me to take graduate level Quantum Mechanics during my years of pursuing a doctorate in Applied Mathematics?

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+.

# Quantum mechanics – it’s all in our mind!

Last week was the final week of classes, and I brought my ph12b class, aka baby-quantum, to conclusion. Just like the last time I taught the class, I concluded with what should make the students honor the quantum gods – the EPR paradox and Bell’s inequality. Even before these common conundrums of quantum mechanics, the students had already picked up on the trouble with measurement theory and had started hammering me with questions on the “many-worlds interpretation”. The many-worlds interpretation, pioneered by Everett, stipulates that whenever a quantum measurement is made of a state in a quantum superposition, the universe will split into several copies where each possible result will be realized in one of the copies. All results come to pass, but if we are cats, in some universes, we won’t survive to meaow about it.

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!

# Project X Squared

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.

# Largest prime number found?

Over the past few months, I have been inundated with tweets about the largest prime number ever found. That number, according to Nature News, is $2^{57,885,161}-1$. This is certainly a very large prime number and one would think that we would need a supercomputer to find a prime number larger than this one. In fact, Nature mentions that there are infinitely many prime numbers, but the powerful prime number theorem doesn’t tell us how to find them!
Well, I am here to tell you of the discovery of the new largest prime number ever found, which I will call $P_{euclid}$. Here it is:

$P_{euclid} = 2\cdot 3\cdot 5\cdot 7\cdot 11 \cdot \cdots \cdot (2^{57,885,161}-1) +1.$

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 $P_{euclid}$ 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 $2^{57,885,161}-1$?

Update: The number $P_{euclid}$ 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.