# Computability

Just a quick link here. Rich Terrile is a scientist at NASA (of course, “scientist” is an unbearably broad word, but that’s all he’s identified as in this article) with an interesting theory that, according to VICE webmag, “every college student with a gravity bong and The Matrix on DVD has thought of before.”

The idea is this: we are a computer simulation of reality. No, really.

The idea has more merit, actually, than you might suspect. I’ve given it some thought before myself, and no, I own neither a gravity bong nor The Matrix on DVD. The thought is that quantum mechanics is just too weird to be explained by anything else. Consider the parallels:

• Matter is ultimately discrete: as far as we know, there are such things as elementary particles that cannot be broken into constituents. They can transmute from one to another, but you never get, say, half an electron. Compare to a computer which has discrete bits of storage: a transistor is either on or off.
• Matter’s measurable properties– that is, the information it contains– are also discrete, which is perhaps more surprising than the bare fact that there are particles. The simplest example, and one that contains most of the basic principles of quantum weirdness, is that of spin. The electron has some intrinsic angular momentum; the principal effect of this is to give it a magnetic moment, which means it acts just like a little bar magnet. (The electron is always charged; moving charges make magnets.) The axis of rotation, you’d think, can point whichever direction it happens to be pointing. Except that when we measure it by sticking it in a magnetic field, it turns out to be always pointing parallel or antiparallel to the field. Always. It’s never at some angle. Ever. All of quantum mechanics has basically been created to explain this fact, which there doesn’t seem to be any classical reason for.
• Matter’s properties don’t seem to exist until we measure them. That electron in the field– is its spin up or down? Until we look, there’s only a probability of each. As far as we can tell, the actual direction gets decided when we look. (You might ask how we could possibly know whether or not it’s decided before we look when the very point is that we don’t know yet. There is, in fact, an absolutely beautiful proof of this fact by John Bell that would almost certainly have won him the Nobel Prize had he not died after being nominated but before winners were announced. It’s simple enough to be taught in undergraduate physics classes, but probably too involved for here.)

Terrile argues that this means we basically live in the Matrix. Why? Well, a computer program seems to fit the bill for all of quantum weirdness: values aren’t computed until they’re needed, and then can take only a discrete set of values, consistent with binary storage. Spin up and spin down literally translate to one and zero.

How can we be conscious, then, in this computer program? If I’m a simulation, why does it feel like I’m not– why can I even ask these questions? Well, some people think that consciousness isn’t a physical thing but a pattern, one that can be instantiated by any complex enough structure, which in practice is usually human brains. But the pattern could just as easily be instantiated in a computer chip simulating a brain.

Of course, if the Universe is a simulation, we exist at a pretty high level of abstraction. In this view, the atoms and stars of which we are made are just high-level concepts isomorphic to patterns of electric impulses in a computer chip. And then you, my friend, are just high-level concepts isomorphic to patterns of high-level concepts isomorphic to patterns on a computer chip. Gives a lot of meaning to “what the fuck am I going to do with my life after college,” no? Pass the gravity bong, Rich.

# Hot Pans and Pretty Girls

When a man sits with a pretty girl for an hour, it seems like a minute. But let him sit on a hot stove for a minute — then it’s longer than any hour. That’s relativity!

Albert Einstein.

You may be familiar with the above quote by Einstein. It’s all over the Internet. Google “einstein hot pan” and you will find countless websites printing it– in some form or another. Quotes tend to do this: they get mangled over time. The “definitive version” is, of course, the version originally penned or spoken or typed by the quotee, but how do you know? It’s like a giant game of “Telephone,” and the person who started off the circle died decades ago, his manuscripts disintegrated, his brain in some jar in New Jersey.

Personally, I’ve never had occasion to question which arrangement of “let him sit” versus “if he sits” was the Original Intent. My first encounter with this quote, as I remember it, was in a magazine in my grandparents’ house, an indeterminate number of years ago, in Valley Stream. It was before Grandma got sick, that was for sure. We were probably there for Chanukah. I read a lot when I was a kid, anything I could get my hands on, any free time I had: in the car, while the adults were finishing dinner, on the couch with Zayda doing the crossword. At some point I discovered the magazine in Mom’s old room, the room we always slept in. I never questioned why anything was where it was, in the house in Valley Stream: it was always there, and it always would be there, and if the magazine was here instead of downstairs with the rest of them then that was where it was supposed to be. Anyway– I read the magazine, and it had that quote in it somewhere, and it was funny. That is my memory.

Since then I have seen the quote several times– many times. I’ve seen it on websites intending to lighten the mood of its relativity-learning readers. I can’t remember if I’ve seen it in print, but I’ve heard people say it. It has never really drawn much thought, except that I couldn’t help but wonder at its– well, its sheer absurdity. Einstein had a sense of humor, no doubt, but he was a subtle man, and a scientific one. It wasn’t the tone of the quote that didn’t sit right, but its having nothing to do with the actual theory of relativity, which says that time (as measured by a clock) passes at different rates for observers moving relative to each other. There is nothing about mental states. Einstein may have said this as a joke, but I’d expect something much more clever out of him that plays on how the theory actually works.

Nonetheless, I was surprised to see a friend of a friend posting on Facebook what I thought was Einstein and attributing it to– “I like LL Cool J’s explanation,” she said. “When a man sits with a pretty girl…”

I started, reflexively, to type a correction to a perfect stranger: “Actually, that one is Einstein too!” Then I stopped. Am I sure? I thought. I was pretty sure that it wasn’t LL Cool J. But where does the quote actually come from? I thought I’d investigate.

I Googled “einstein hot stove” and came up with a lot of quote websites. You know the type. They have names like notablequotes and quotationspage and brainyquote and so on and so forth: typically pages and pages of agglomerated phrases and pithy statements and witticisms, all organized by author, with no citation, no source, nothing but a sentence with a name next to it. Not exactly a help in figuring out the veracity of the quote. Wouldn’t it be easy, I thought, to fabricate a quote entirely?

Wouldn’t it? I started to get interested. I scrolled through the trash until I found something that looked promising. A paper by a Russian, Z.K. Silagadze, referring to the paper “On the Eﬀects of External Sensory Input on Time Dilation” by Einstein. I searched again, new reference in hand, but couldn’t find the original. In fact, the journal it was from– the Journal of Exothermic Science and Technology– was particularly hard to locate! Something was fishy. Finally I found a reprint in a newer medium.

An article from 2002. My jaw dropped. It was that same article. It was here at Scientific American (you need subscriber access; here is a free version.) The goddamn picture was the same; it was from 2002, and all of a sudden I was eleven again, somehow. And it faded.

The article in Scientific American was called “Einstein’s Hot Time” by Steve Mirsky. It had the full text of the “Sensory Input” paper; in fact, the quote was the abstract of the paper. The abstract of the paper? No. No, it couldn’t be; no journal that could possible call itself a journal would take an abstract like that. And then it hit me: Journal of Exothermic Science and Technology: JEST.

I read the paper, which I had only scanned. It was a joke. (Read it!) Of course. Of course, it made sense now. It hadn’t made sense when I was eleven. I was told that this was a fact, and I believed it was a fact, why shouldn’t I believe? But now I know better. I searched Mirsky: he is a humor columnist! For Scientific American! The paper Silagadze had cited as his source, indeed based his whole paper on, wasn’t real! I did a little cursory, non-creeper research on him: he works at the Budker Institute in Russia and last published a paper in 2010. I was surprised that he could have taken the Mirsky (not Einstein) paper for the real thing– I realize the language barrier makes telling the difference between satire and straightface hard, but this is on arXiv!

But that wasn’t all. Silagadze shouldn’t feel bad, because he’s not the only one taken in by the telephonic tweeting and re-tweeting of quotes on the Internet. In fact, the volume of online sources quoting the JEST paper as official would be enough to confuse a lot of people. The Library of Alexandria has it listed in Einstein’s complete works, under 1938. A fairly serious paper published on PLOS, “an open-access journal,” reports an experiment on rats apparently inspired by “Einstein’s” idea. All over the place there are citations to this ENTIRELY FICTITIOUS journal article! In fact– and here is where I got quite excited– I couldn’t find any evidence of the quote existing before 2002 at all. It seemed, briefly, possible that Mirsky at Scientific American had invented a quote out of thin air, and gotten it attributed to the Great Man Himself, quite accidentally creating a piece of past.

Now it gets good.

I searched and searched and searched for references to the quote before 2002. Finally, I found one. It was from the movie “Deep Blue Sea.” A character named Preacher says it; I couldn’t find the context. Preacher is played by LL Cool J. Deep Blue Sea is from 1999.

I really wish I could stop here, because it could make such a damn good story, but perpetuating myths is exactly what I am trying not to do, so let’s put all the facts in one place. Because after all, that story (LL Cool J quote misattributed to Einstein!) is a little too good to be true. Continued searching finally found one source that seemed to merit a little respect: the Yale Book of Quotations, page 230. This, too, was post-Mirsky– from 2006– but provided an earlier reference: James B. Simpson, “Best Quotes of ’54, ’55, ’56,” published 1957, as well as Alice Calaprice’s “The Expanded Quotable Einstein” (2005).

The former is available at Bobst; it in turn quoted another book by Sayer, call number QC16.E5.S285.1985. I  could not find this book online, so I went to the library. (By this point, I was committed.) No citation is quoted: the quote is there, neither in quotation marks nor followed by footnotes. It is attributed to Einstein, speaking to his secretary Helen Dukas, but while the rest of the book is heavily footnoted, that paragraph has no superscripted numbers. I was unable to find the Simpson book, which itself is just a book of quotes I do not expect to have further sourcing.

So, to wit, I’ve found the following:

• The primary (that is, heaviest-cited) source on the Internet for Einstein’s quote is fictitious. It was not deliberately meant to be misleading, but was written as a humor column and misinterpreted.
• If I trace back the quote through the ages, the earliest reference I can actually find is from 1985 (Sayer), itself unsourced. “Deep Blue Sea,” however, was probably referring to what the writer believed to be a quip by Einstein.
• There is a reference to the quote saying it was cited in 1957; I was unable to find an actual copy, and thus to verify the quote is older than 1985.

As of right now, I can say the following two things: 1) At least a few people have quoted Steve Mirsky’s fictitious paper as if it were real; 2) I personally can neither verify nor disprove the original quote by Einstein. A person with some experience in this sort of thing might be able to. Key to doing so would be to get my hands on a copy of Simpson’s quotations, but to be perfectly honest, my interest has started to sputter. In any case, I myself would hesitate to cite this as by Einstein.

I hope you enjoyed the products of a night’s and a day’s worth of research: for this is what I do with my nights, and sometimes with my days.

A postscript: it really is like a game of telephone, isn’t it? Words get passed from the past and sometimes new ones appear out of nowhere. How do you know what history really was? You can’t go back and look at it. Who controls the present controls the past, they told Winston. To what extent is that true? To what extent does the physical state of the past depend on our knowledge of the present? After all, the relationship between our knowledge and the future is an open question.

# Powers of Ten

There are, for everyone I assume, a few films or books or songs or what have you, that have a disproportionate effect on your life. One of those films for me is Charles and Ray Eames’ 1977 short piece, Powers of Ten. It is nine minutes long, and those nine minutes in all likelihood pushed me more towards being a physicist than any other single factor, except of course my grandmother, who insisted that I understand the concepts of special relativity by the time I was twelve.

Powers of Ten is a delightful little short that begins with some picknickers at Soldiers’ Field in Chicago. Keeping the same point at its center, the camera zooms out at an exponential pace, ten times faster every ten seconds, out through the atmosphere, to the reaches of the Solar System, to the stars and galaxies and out to the blackest voids. It then returns home and travels on to just as alien a world, inside the nucleus of a carbon atom inside a picknicker’s hand. It is fitting that the carbon should be inside his DNA.

I cannot remember not having seen this movie; it is older than language. The music brings me back. The ticking of the percussive clock upon entering the skin; the strange, airy tinny picnic music by an instrument I have no name for. “A line extends, at the true speed of light!” Philip Morrison’s narration: how excited he still is after all these years!

# Coffee, and rain.

I have been reading Portnoy’s Complaint. I understand why it was banned in Australia. On the L into Manhattan this morning I sat down at the end of the car, across from the handicapped seats, to read. At Graham a convoy of kindergarteners entered the train, wearing green school uniforms, following like ducks. One sat to my right; one stood to my left, her head up to my seated shoulder. I pulled the book closer to my face. I don’t know if they can read, but if they can, no one is going to accuse me of corrupting the youth.

I had lunch with Padmini at which we bemoaned Paul Ryan. We ate at Chelsea Market; I got an avocado sandwich. I missed easy vegetarian food, I told her. I’ve been eating a lot of meat, just because that’s all there is there. I’m looking forward to being able to get some good soy.

“Yeah,” she said, “I think I could probably find a way to survive.”

“You’ve been a vegetarian your whole life,” I reminded her, though I wasn’t sure why. Maybe if my convictions are more recent that makes them easier to violate. Maybe? I suppose it did. A fait accompli.

We parted ways at two; I had two hours before coffee with Jane at four in the West Village. I wandered, briefly, giving Denny a call and silently reminiscing last year’s walks on the West Side with a phone to my ear even as it froze off. It started to rain and I located Minerva Café. “I love this place,” Jane had said, “because you can get a cup of coffee and they will let you sit there all afternoon.” The waiter handed me a rather fancy-looking menu and wine list. I nervously informed him I would be getting only coffee. No problem, he told me, and brought it. And back into Portnoy’s perversions I dove.

In between pages I sipped on my coffee. I watched the ripples that formed when I set the cup down on the table: slow, quarter-wave oscillations, one side then the other rising and falling, and quick little short-lived circular waves going inwards and outwards when you tap on the rim. I thought about the pool at Brandon’s house and the reflections of the underwater light: all the refraction takes place at the surface. The dancing, intricate patterns that appear to be on the floor of the pool are nothing, nothing but the dancing, intricate patterns that actually exist on the wavy interface with the air.

I closed my right eye, then my left. With the right eye open I saw the fire escape reflected in the cup; with the left eye, trees. The cup, of course, did not move. It was prepared for any way I could look at it, any way I could tilt my head or shift my eyes or get up and walk around it and look from the other side. Here is a fun little fact: light does not “bounce” off a mirror the way a ball bounces off a wall. It hits the mirror, is absorbed by the atoms in the glass, or the coffee, and is re-emitted in another direction. It’s not possible to say that this photon came from the fire escape and that one came from the tree, for as David Griffiths would say, there is no such thing as this photon or that photon: there is only a photon, or two or none. Your definite articles are things for the classical world.

No matter how I look at the cup, the atoms in the coffee are re-emitting reflected light in the right amounts in the right frequencies in the right direction: each atom contains in its motion, in its states, anything that could possibly be reflected into my eye. “I contain multitudes:” how right you were.

Jane arrived and we drank a ridiculous amount of French press and talked about Douglas Hofstadter, who might or might not indirectly be the reason we have become friends. I am reading her copy of “I Am a Strange Loop,” which Hofstadter insists is not only a rehashing of his classic Gödel, Escher, Bach but also the combined wisdom of the intermediary thirty years. It was a wonderful afternoon. There is little I like better than the combination of caffeine and the mind-body problem. The chemical’s effect on my thoughts about the relationship between brain’s chemistry and thought is a little too self-referential to print in a family newspaper.

After leaving Jane to meet a friend of hers I called Oliver to see if he wanted to meet for dinner. On my way southeast (down and right) it began to pour torrentially. The streets looked ready to overflow. I bought an umbrella so as not to get Portnoy any wetter than he already was. Upon my arrival we sat in Oliver’s room and watched the rain for a little while. I explained time dilation. When you are sitting still, you are in reality moving at the speed of light through time; when you do what we normally think of as “speeding up”, your overall speed doesn’t change, so you go a little slower in time to make up for your movement through space.

“It’s crazy,” said Oliver, “that there’s that constant for everything– everything is going at the same speed? Can that be right?”

“I think so,” I admitted, “it’s been a few months since I took a class in it.” We sat a while longer and watched the streets fill with water.

# Presenting

“Do not be surprised if there is nobody there,” she had said. “People may get up and leave before your talk. It is nothing personal, but you understand, if people are busy they may not want to hear a summer student speak.”

“I hope the room’s not totally empty,” I had said. “At least one person should stay.”

“That will be me,” she said, laughing.

The room had not been packed for the prior talk, which was presenting a draft of a paper for review by the top group. There were maybe a dozen people there. When it was over, the meeting convener, who was not physically present but was introducing people via EVO (a physicist’s version of Skype, basically), called me to the stand.

“Now Ben Burdick will present some preliminary results on the top mass at 8 TeV,” he said. I walked to the front of the room, trying to look calm, but my mind was racing. That’s it? I thought. He doesn’t say I’m a summer student? Do I say I’m a summer student? Here is the thing: in eight weeks, I have managed to get together what is, in my mind, a respectable summer project. It is not by any stretch of the imagination presentable as official science. My error analysis is on par with what you do in a freshman lab course; my fits to histograms are just Gaussians in a range I picked pretty ad hoc to get the best fits. I have no citable systematic errors and I frankly admit that some of the code I use I was given to use as a blackbox. If the people in this room were expecting anything like what they had just seen, they had another thing coming.

Luckily, Stephanie came to my rescue. “I just want to briefly introduce Ben,” she said, grabbing the mic from me. I breathed an internal sigh of relief. I looked around as she informed everyone that I was a summer student, that this was a learning experience, etcetera. Nobody got up and left. People looked at me with about the same level of interest as they had for the last speaker. It is standard practice, at CERN, for people to be on their laptops during meetings, and my talk was no exception, but people did not look particularly bored. When she was done explaining, essentially, that they should not ask me hard questions, there were still a dozen people in the room.

“Thanks, Stephanie,” I said, and launched into my talk, which I had rehearsed all morning in the cafeteria, reading my slides over and over, thinking about how to phrase things, avoiding “ums” to the best of my ability, which was not much. I stumbled once or twice but did not spontaneously burst into flames and consume the entire building, which I gave thanks for. When it was over, I got a question or two from EVO. One I could answer; one I didn’t hear. “I’m sorry, I didn’t hear–” “Say yes,” Stephanie mouthed at me. “Um, yes,” I said into the mic.

“So there are no further questions? Then we will give the room over to the next group,” the convener said, and only then did people get up and leave.

On the way back up to the office, Stephanie told me she had a meeting to go to right now. “So I’ll probably just see you tomorrow,” I said. “Sure,” she said, “but you are done now, are you not? You only have your paper to write?”

“Yeah,” I said, it only then sinking in to me. “I guess that’s true.” She left and I worked on my paper/Facebook in the office for a bit. It hit me that I was essentially done. My talk on Thursday is a distilled version of the one I gave yesterday; my paper is essentially a transcript of it. There is no more work for me.

At 7, I went to R1 to say goodbye to Brandyn, who left this morning before I woke up. He has been one of my better friends here and hopefully will come visit me in the city this fall or winter. It is strange, everybody leaving, and to think I will be in New York in just three days; in three days from this moment I will be on a plane, flying over Paris in the great circle. Time is not real.

# Hubble Deep Field

The Hubble Deep Field is a picture of the dark night sky at intense magnification. NASA pointed the telescope’s lens towards a segment of the sky that had no visible foreground stars and zoomed in as much as they could. The whole image is 2.5 arc minutes across, less than one-tenth the width of the Moon as seen from Earth. What they found was an unimaginable, unexpected richness and density of galaxies. The Universe is teeming with them. They are far from one another, and from us, but the place is so big that when we look straight out we are almost bound to see one.

This image was shown in lectures today and I was struck by a beautiful symmetry between the large and the small. The Universe is teeming with galaxies just as the Earth is teeming with life. Look around and you are almost bound to have some bacterium or other in your direct line of sight. Have you ever put a random piece of non-disinfected glass under a microscope? Try it sometime.

It’s this kind of coincidental connections, this sort of accidental mirroring, that makes life worth living, that makes me stop and think and get up out of lecture to go hunt for pictures of petri dishes.

# Determinism

This is going to be a fairly mathematical post; feel free to skim or skip as your will tells you.

Today, I got a section of my program working that has been giving me errors for fully a week now; I was quite pleased with myself, as it looks like a number for the top mass, with statistically meaningful error bars and all, might (knock on wood) magically pop out of my computer before I leave, if I am lucky. Right now I am waiting for the code to run, which takes about an hour, and hopefully not produce output (knock again) that makes me eat these words. Waiting for code to run is the best time, of course, to think about determinism. The streams of numbers flying by on my terminal are completely determined by the code I’ve typed in and the data it’s running over; there is no room for the computer to choose to say one thing or another. Also, it’s damn boring just watching it go.

I wrote, a while ago, about analytic continuation- the idea that if you know what a function is doing at this point, and you know it’s smooth (in the right, rigorously mathematically defined way), you can extrapolate what it’s doing everywhere. Of course, not all curves are like this. If I give you some jagged line, knowing what it does here doesn’t tell you anything about what it’s doing down the road– it can do whatever it pleases.

Last year, taking Chaos and Dynamical Systems in Courant with James, we began the semester studying maps and only after the midterm moved on to differential equations.A differential equation is an equation that has, as its unknowns, not numbers (like in x2 – 4 = 0) but functions. They show up all the time in physics; I was surprised the math majors had used them so little. Most people’s first introduction is the harmonic oscillator equation, mx”(t) + kx(t) = 0. x” here is the acceleration, i.e., the second time derivative; x is the position; the goal is to get x(t), the position over time. The general solution is a sine wave, which means that if you put a mass on a spring and kick it, it’ll oscillate: duh. Also, the frequency of the oscillation is determined (it’s sqrt(k/m), though I imagine if you care you already know.)

The interesting thing here is how you go from a general solution to a specific solution, that is, how you go from saying “the mass oscillates” to saying “the mass oscillates with this amplitude and phase.” You need initial conditions, that is, the position and velocity at t=0. There’s a famous theorem, I forget which (it’s not important) that says that for properly well-behaved differential equations, you need to specify as many initial conditions as the number of the leading order derivative (in this case, two, for the second derivative: initial position and velocity). And then you will have a uniquely defined solution.

This is if the equation is linear, which means neither the function you’re looking for or any of its derivatives are squared or cubed or whatnot; nonlinear systems are much more complicated. Take my favorite example: x‘(t) –  √x(t) = 0. This was the example the professor wrote on the board at the beginning of the class. Dismissively, he said that this equation was not deterministic, and so was not interesting as a model of dynamical systems, which in mathematics are deterministic by definition. That chaos can emerge from a totally deterministic system is a beautiful idea, more beautiful because it’s provably true, but that is not my focus today: my focus is that how could I possibly pass up bait like that?

Let’s symmetrize (always, always symmetrize) and take either root: x'(t)2 -x(t) = 0.  I won’t prove it here (because, again, if you have some basic experience with these things you can do it yourself, and if you don’t then the details will be uninteresting), but given any initial condition x(0), except x(0) = 0, there are two solutions: the unique two parabolae that pass through the point you want, are tangent to the x-axis, and have leading coefficient 1/4. Like this:

But what if your initial condition is x(0) = 0? Well, there’s still a solution that’s a parabola:

What happened to the other one? Mathematica is failing us here. There is another solution: a flat line. If x = 0 always, then x’ = 0 always too; the equation is satisfied. Why can’t Mathematica get this? Don’t ask me; computers are weird.

Now here comes the beautiful part: remember that all possible solutions of this equation, for any initial conditions, are tangent to the t-axis. What this means is, take those parabolae that were solutions before, but cut them off where they’re tangent to the t-axis and just make them zero there: they’re defined piecewise. This new half-function, that is a parabola on one side and zero on the other side, is also a solution of the equation.

Why does this matter for determinism? Because you can reason the other way too. Say x is the position of some particle, and t is the time. Let’s say that the particle starts out at x=0. It can start moving right away on the parabola x = t2/4, but it doesn’t have to. It can sit at the origin for a bit. And then it can start moving after any amount of time it likes, and it will still satisfy our nonlinear differential equation. Piecewise, we’d say a solution for x=0 is: {x = 0, t < a}, {x = (t-a)2/4, t > a} for any a.

I said “when it likes;” if I can’t anthropomorphize flies I certainly can’t do it to functions, but what the hell. You might be wondering how this funny formula fits in to what I said earlier about analytic continuation. Well, the function I’ve just written down isn’t “smooth” in the right mathematical sense. Its first derivative is a ramp function, its second is a step function, and its third is a Dirac delta; basically, it doesn’t have all derivatives well defined and finite. But it doesn’t matter: the equation only wants the first.

Classical E&M contained “advanced waves” that went inwards from infinitely far away to start a particle vibrating, just like the time-reversed situation is how normal radiation works: that solution was always discarded as the “secondary aphysical” solution. General relativity is a nonlinear theory. There’s no indication that I know of that it contains anything noncausal like this– things starting to move of their own accord– but there is a lot of research to be done still on the subject. “Naked singularities,” essentially visible black holes (brushing over a huge amount of substance there), have a lot of potentially interesting properties but are usually considered aphysical; I’m thinking, as of now, about working towards writing some kind of senior thesis on that topic, but no promises. I don’t know enough about the subject to talk about it yet; maybe one day.

Or maybe not, isn’t that the point?

# Physicalism and Materialism

Several recent and not-so-recent conversations with friends and family– as well as the entire Philosophy of Mind class I took last year– have made me realize that my views on the mind-body problem are somewhat nonstandard. Having finally accomplished something at work today, however minor (I ran my code on a much larger data set than I had been using, about 2.5/fb, for those of you that care, and got non-ridiculous results), I thought I’d take a little time and try to lay them out. Forgive me if it winds up a little jumbled; it’s a hard problem, and recall that this blog is as much for me to figure out what I think as it is for you to read about it. (The allusion to Chalmers, by the way, was accidental.)

Philosophy is something most physicists don’t concern themselves with much, and yet because they get quoted in the relevant discussions all the time, I wish more of them would pay attention to it. Hard Laplacean determinism– the view that the universe consists of atoms moving according to differential equations, and nothing more– took Newton as its patron saint for hundreds of years. The early quantum physicists– Bohr, Einstein, Schrödinger, Dirac, they all thought about the meaning of the thing, but it seems now that that’s not what physics is for, and laymen quote and misquote them all the time since besides Bell not much has happened on the interpretations front in seventy years. “A particle is a wave until a person observes it;” yes, we all know. But the stunned incomprehension of the initiate is not misguided, he does not learn the answers, he learns to ask more specific questions.

I am not here going to talk about interpretations of quantum mechanics, though I find it fascinating, and highly relevant to the mind-body problem. (When does an amplitude turn into a result? What is an observer? Does it follow the laws of quantum mechanics too?) I want to talk a little bit more generally about something that came up the other day, about the difference I see between physicalism and materialism. When I first started thinking about this in Nagel’s class last year, I thought of it as a subtle but important distinction: the possibility of non-material entities that could be described by physics somehow. But the more I reflect on it, it’s not subtle at all; it goes at the root of how we think about science.

Normally, answers to the mind-body problem get divided up into two categories. Dualists say that the mind and body both exist, but are fundamentally distinct in that their most basic constituents are fundamentally distinct. Usually, the mind is thought of as an ontological primitive, indivisible even if describable; it is not made of atoms, or fields, or any other physical object, but just is, its own thing, separate from all the rest. The body, of course, is made of normal stuff: in a physical sense, the same stuff rocks are made of, protons and neutrons and electrons and all the rest. Descartes was a fan of this view.

The opposing standpoint, physicalism or materialism, argues that this is ridiculous, that the world must be ontologically unified, that even if there are different kinds of things (a quark is not a photon) they have to fit together in the same physical framework, and that therefore we need to figure out a way in which the mind is a physical thing. People have tried to say that beliefs are patterns of behavior, that sensations are electrical currents in the brain, all sorts of things. This was the most popular philosophical viewpoint for all of the last century, but it always struck me as just plain wrong. “How,” I asked Robert once in class, “can so many intelligent men deny their own existence?” It seemed to me that my thoughts and sensations are just different kinds of things than could be made of electrical currents in my brain. I didn’t see how it was possible. But the dualist standpoint was too close to positing an immaterial, immortal soul (well, that’s exactly what it does, actually) for my taste.

But then I hit on this analogy. When we first learned, 150 years ago, that light was an electromagnetic wave, physicists set about to discover what it was that was waving. After all, a sound wave is a wave in air; there has to be actual air there, to move back and forth, that’s what a wave is. The ether, as they called it, had to permeate all space and matter, be so light and thin you could walk right through it without noticing anything, but be under truly enormous pressure to be able to propagate waves so fast. It didn’t make sense. Well, the solution was that there was no ether; the light was a wave in a field that existed in and of itself, it didn’t need to be a field of motion of some other stuff. You might have argued, then, that this solution was non-physical; it postulated something that was simply not in the pantheon of possible physical things, which at that time included exactly one kind of thing: what Newton called “ponderable objects,” like atoms. But we have learned a lot about electric fields, and the better we systematize the knowledge, the more we accept them as physical things in their own right.

Here, then, is the difference between physicalism and materialism. Physicalism is the following argument:

1. Physics is the science that studies the universe and everything in it. If it exists, then physics wants to know about it. We accept the practical importance of specialized sciences, but ultimately all ontological meaning comes from physics: it studies what there is.
2. Minds, and all the things that come along with them like thoughts and sensations, evidently are.
3. Therefore, physics wants to know about minds; they have some place in the world, and we want to know what that is.

Both a physicalist and a materialist accept this argument in full. I don’t see how you can not. Dualism is essentially giving up; it’s saying, we can’t make minds and bodies the same thing with what we know, so it’s impossible. That’s ridiculous. If I say physics is the science that seeks to understand the world, if I don’t understand the world, it’s because I’m not done. The difference, in my view, comes here. A physicalist– I consider myself one– stops. This is all we can say at this point. Some things, say the properties of solids, have to be, and can be, explained in terms of more fundamental concepts. Others, like the properties of quarks, are accepted as basic, but only in the process of systematizing the knowledge we have. I am not suggesting here that minds be accepted as basic ontological entities like quarks and leptons; I’d probably lose my job if I did. What I’m suggesting is that we just don’t know how minds fit into the big picture.

A materialist, on the other hand, adds a fourth claim, which is essentially– and perhaps I am not being kind, but everything I have read by materialists leads me to think this is fair– that we can incorporate minds into the big picture, without changing our current system of knowledge in any particularly radical way.

I think this is the height of hubris. We couldn’t even incorporate atomic spectra without a total overhaul of what we thought the world was; we’re not done doing it yet.

That’s basically it. Two additional points: I think that under my definition of physics, it’s true that physicalism follows. Some people might disagree; some people might limit the scope of physics to studying a particular kind of phenomena, specifically excluding minds. I think this is silly, especially with everything we’ve learned about quantum mechanics begging the question; I’d love to argue it if you’re interested. Secondly, you might think there’s another premise implicit in my understanding of physics, which is that it is possible (in principle) for humans to form a system of knowledge that encompasses the entire world, including minds. Of course, it might not be. I think that’s right; I think that there is no proof of this premise, and I think if you believe it, you accept it on faith. I also think it is possible to be a physicalist, and a fulfilled one at that, without believing this. All you have to think is that there is truth, and that we can get closer to it than we are.

# Parity

“When I was learning Newton in high school,” Cameron said, “my teacher used to tell us to imagine that behind mirrors, the images were actually part of some real mirror-world; that behind every mirror, there’s another universe, exactly like ours, but flipped. The forces cancel at the boundary, and that’s how actions and reactions work.”

“That’s pretty funny,” I replied. We were walking by the Jet d’Eau downtown, by the lake, on the way to a beach party that Salvatore had heard about. That Salvatore had heard about it was the sum total of our knowledge regarding this party. The conversation quickly turned to something else. I zoned out for a bit and watched the Jet, thinking about the water pressure, and the mirrors.

“You know,” I said, “that’s ridiculous, but it’d be pretty hard to empirically disprove.”

“What?” I realized a few minutes had passed, and no one was thinking about the mirrors anymore.

“The mirror thing. Let’s say that there’s another universe exactly like ours in every way, down to the quantum states of individual particles, but parity reversed.” (That just means swap left for right, front for back, but not up for down- literally the mirror image.) “And let’s say that our two universes exist in different spaces, joined only at a flat boundary. Your teacher was being facetious, but it’s true, isn’t it? The forces would cancel at the boundary. Whenever you push on the mirror, your double pushes back, and he thinks you’re doing the same. Neither one of you thinks it’s anything but a mirror.”

“True.” Cameron thought for a few seconds. “What about the weak force?”

“It violates parity symmetry. The mirror image of our universe isn’t physically the same. Beta decay would happen differently. You’d think it wouldn’t matter on a human scale, but if we’re made out of atoms that act differently, there’s no way you could maintain the symmetry. They’d grow apart and the forces would stop canceling.”

“Oh. Right.” I paused. “Still, I like the idea.”

“Yeah, it’s a cool idea, but it couldn’t happen.”

We arrived at where the party supposedly was and nothing was going on except for some high schoolers drinking on the beach. We had not acted on overwhelming experimental or theoretical evidence. It was OK, though, because it was a nice night, and a nice walk. We bused back to Cornavin and got drinks at a pub near there.

I’ve been thinking, though. What if in the mirror universe, the weak force itself were also parity reversed– that is, it acted only on right-handed particles instead of left-handed ones? I don’t know the requisite quantum field theory to know how this would work, so I will avoid getting into technical details I will necessarily have to make up, but I think it’s a cool idea.

Would you and your mirror image be different people? Anything that happens to one, happens to the other. You have all the same memories. You have the same past, present and future. You will die at the same time. Presumably, you have all the same thoughts. Can you distinguish the two in any way?

Is there a reason that the guy in the mirror isn’t me? Can the reason really be, fundamentally, the handedness of the W and Z bosons? Does electroweak theory, and no other part of physics, truly cement that I am an individual a unique one, and not one of countless identical copies through the looking glass?

Perhaps you can see why I do what I do.

Edwin Abbott’s Monarch of Pointland was all, was everything; he could not communicate with others outside himself, for they were not just nonexistent but beyond his power to even conceive: “Let us leave this God of Pointland to the ignorant fruition of his omnipresence and omniscience: nothing that you or I can do can rescue him from his self-satisfaction,” said the Sphere, not so much disapprovingly as dripping with pity.

There is a sort of attraction to solipsism, for the logically inclined at least. For as I once told Nathan both solipsism– the denial of minds other than one’s own, and in its extreme form the denial of objects other than one’s own mind– in mental philosophy, and nihilism– the denial of actual moral value or meaning– in ethical philosophy, stand apart from other theories in those fields. They are simple, and they are consistent. Try to come up with a set of general moral rules, an algorithm that applied to any specific situation, will always yield what is right and only what is right; perhaps you can do it, but I can’t. Things always seem gray, if not sui generis at least sui specio, to blatantly fake an understanding of Latin. It is wrong to kill, but what about self-defense? It is right to give to charity, but what of self-preservation? You can add in new ideas, the rights of the individual, but you get an epicyclical regress that would have given Ptolemy conniptions. But nihilism is simple: is it right? Deny all terms. And solipsism is the analogue in ontology.

But, I told Nathan, I reject both, and I hope you do too; and I hope I do not have to explain why. It is rare to catch a scientist saying this, but I would rather be wrong about moral truth than believe there is none; I would rather be wrong about ontology than believe I am alone. Perhaps this is philosophically and logically unsound, but it is a firm conviction. If I believe I am different, at bottom, from the totality of the Universe– I may be a component in it, I may be made of the same stuff as everything else, but I am not the Monarch of Pointland– then I also believe that everyone else has equal status.

This is not a trivial claim, though it may seem one, and in fact I make it conditional on purpose. A thought that has been preoccupying me in recent days is that of analytic continuation. As Douglas Adams put it, “since every piece of matter in the Universe is in someway affected by every other piece of matter in the Universe, it is in theory possible to extrapolate the whole of creation – every Galaxy, every sun, every planet, their orbits, their composition, and their economic and social history from, say, one small piece of fairy cake.” This has some mathematical validity, believe it or not. For those of you who would prefer not to think of functions, feel free to skip, but try to bear with me; I will try to make this make sense, since it is, I think, a pretty beautiful idea.

Consider some smooth curve, describable as a function. We normally think of the curve, it shape, really the information in it, as consisting of the function: for every input value x, we get a number out y, and when we connect the (continuously infinite, cardinality of the reals) set of dots we get a curve. The information is stored in the whole, everywhere. But there is another way to look at it. Pick one point, just one. But also, take its derivative. This is just the slope of the function at that point; what it does is it tells us the function’s value at the next (again, continuously, differentiably close) point. If we take the second derivative, the curvature of the curve, we’ll also know the slope at the next point, and so on down the line.

But now we’ve totally determined everything about the function at the next point, and so we can repeat the procedure ad infinitum to extrapolate the entire function, everywhere. We need an infinite number of derivatives, but only a countably infinite number (this means you can label them, first, second, third, etc., which you can’t do with the original points since there’s another one between any two you pick.) The whole shape, all of the information, is contained in a single point. The whole Universe is in your cake.

Of course, it’s possible to come up with functions for which this doesn’t work; anything with sharp corners will do, for instance. These are called non-analytic. But these are rare in nature. In classical electromagnetism, for instance, the electromagnetic field is only non-analytic right at the single point on top of charges (electrons or protons.) Here is where my math isn’t quite sophisticated enough and I have to speculate, but I am pretty sure that in three dimensions, this doesn’t matter; a singularity can exist without breaking the Total Perspective Vortex, as it were, because you can still extrapolate around it. You could even infer its existence and properties from very far away. I think you can even do this if there are line or sheet discontinuities, as long as they don’t divide spacetime into disconnected regions.

So in smooth, analytic field theories, the whole universe– all of the information, all of the stars and galaxies and people, everything– can be looked at as spread out across space– or truly existing at a single point. Space and time are illusions, fabrications to help us organize things a little better. We are all at the same place; we are all the same thing; separation is illusion.

So why is it so hard to know what other people are thinking?