Archive for November, 2012

Einstein circa 1905

There are a lot of people who, to this day, deny the truth of Einstein’s special relativity (SR).  I’m not even referring to the OPERA superluminal neutrino debacle—an anomaly that was eventually found to be caused by a misconnected fiber optic cable.  No, I’m referring to laymen who deny SR because it goes against common sense.

A Google search will find such people readily.  Most of the time, their arguments aren’t even worth refutation, since it’s obvious in most cases that they haven’t mastered even the simplest algebra, much less sophomore-level physics.  (I am planning to use this gem in my Modern Physics class in the spring as a homework problem: for 20 pts., find the elementary flaw in this person’s logic.)  However, as a working physicist, I sometimes find myself dismissing such people too readily: it is easy, and self-gratifying, to call such people cranks.

A person who doubts SR is not necessarily a crank.  After all, relativity is very counter-intuitive, and our brains have been exquisitely fine-tuned by natural selection to perceive the world as inherently classical.  In fact I will go so far as to say that if you accept SR whole-cloth, without any mathematical or scientific background, then you’re basically showing a blind faith in science in the same way that Iotians have a blind faith in “The Book”.  I would rather beginning physics students showed some skepticism; it makes their final “conversion” that much more intellectually pleasing.

I think the main problem with perceptions of SR is the way it is normally presented.  My thesis is this: most physicists are teaching it wrong.  And as a consequence, many people who have studied SR come away with a misguided notion of what SR is all about.

The old way to teach SR begins with Einstein’s two postulates.  The first is that the laws of physics should be the same, in any inertial reference frame.  The second is that the speed of light is the same for all inertial observers.  There is then an obligatory picture of a train and lightning bolts, and talk about how simultaneity isn’t preserved in SR.  This leads (usually after a lengthy derivation) to time dilation and length contraction.  And then, out of the blue, there might be talk of the twin paradox and the obligatory pole vaulter in the barn.

Shudder.  Such a pedagogically confusing approach!  No wonder very few first-time SR students “get it” at all.

The original train picture from Einstein’s 1916 book

This approach has a long history.  In Relativity: The Special and General Theory (1916), by Einstein himself (!) the discussion begins with the two postulates, and there is then a diagram of a train and a discussion of simultaneity (see above).  Seriously?  I’m not blaming Einstein, mind you; I’m blaming the textbook authors today who can’t let go of that stupid train.  It’s been almost 96 years.  Get over it.  Hop off that train, please.  There are more intuitive approaches that are easier for the layman to grasp.

Here’s the approach I use in my classes.  This is not the only approach, of course, nor do I claim it is the best approach.  However in my experience (admittedly, just one data point) this approach is a better way to get students to gradually accept SR.  The trick is to present information one plausible chunk at a time, and then only gradually derive all the weird stuff.  Thus, without realizing it, the students have been convinced of the truth of SR despite themselves.  If you start with simultaneity and time dilation and length contraction then half of the students will get turned off immediately (because their common-sense alarms will be blaring full-force).

  1. Talk about classical (Galilean) relativity.  That is, discuss how the laws of physics should be the same in any (inertial) reference frame you choose.
  2. Talk about coordinate transforms: how you can take the spatial coordinates of an object (x,y,z) and find what the coordinates (x’,y’,z’) would be in a different coordinate system.
  3. Talk about how some coordinate transforms are “good” and some are “bad”.  For example, a translation in space such as x’ = x – L preserves distance, but a rescaling transform like x’ = ax does not.
  4. Mention how the good ol’ Pythagorean theorem s2 = x2 + y2 + z2 gives you an invariant quantity (s2) that is preserved under “good” transforms.
  5. Mention that the (experimental) behavior of light throws a monkey wrench into this analysis.  For whatever reason, all observers measure the same speed c for light, and this actually makes things a little harder.  (Don’t do any math at this point!)
  6. Here you should start talking about time as being a 4th dimension.  The earlier you introduce the idea of an event P as a point P=(x,y,z,ct) in space-time, the better.
  7. State Einstein’s postulate about the speed of light.
  8. Show that the light postulate implies that s2 = x2 + y2 + z2 is no longer an invariant quantity, when talking about transforms as applied to space-time.
  9. If s2 = x2 + y2 + z2 is no longer invariant, can we modify the formula in any way so as to make s2 invariant, while still preserving the light postulate?  The answer is yes; and so you should derive the 4D version of the distance formula, s2 = x2 + y2 + z2c2t2.

To me, this is the core idea of SR.  Everything else follows from the invariant interval s2.  One should no longer think of our existence as being 3D; time represents another “direction”.  And it turns out that the time you perceive depends upon your vantage point (time is “relative”), just like position.

For example, suppose you are looking at a row of trees.  From one location, the trees are lined up in front of you (they all share the same x-coordinate).  From another vantage point, they are separated by 1 m each (x=0, 1m, 2m, 3m, etc.)  No one, not even Galileo, would find this controversial.

But now imagine that you think of time as just another “direction”.  Why is it so hard to believe that your time coordinate could have one value in one reference frame, and another value in a different frame?  Why is it so hard to believe that events that are simultaneous in one frame are not simultaneous in another?

Time dilation and length contraction follow from this in a straightforward way.  And they are much easier to visualize if you buy into the paradigm (I’ll say it again) that time is another “direction”, and therefore relative just like position.

[Caveat: I do know that time is special, in the sense that there’s a minus sign in the s2 = x2 + y2 + z2c2t2 formula.  That minus sign is crucial.  But discussing its importance should be deferred to a later (pun-intended) time.]

If you’re interested, here’s the rest of my SR program:

10.  Discuss space-like, time-like, and light-like intervals, and the ideas of proper length and proper time.
11.   Show how the Galilean boost (which is a “good” transform in classical relativity) must be modified into the Lorentz boost in order to preserve s2.
12.   Show how the Lorentz boost implies length contraction and time dilation.
13.   Discuss relative velocity in SR.
14.   Discuss so-called paradoxes like the twin paradox and the pole vaulter paradox.

The discussion can then go into advanced topics: momentum, energy, E=mc2, forces, etc.  However, with the foundation I have described, I believe these topics are much easier to present.

I’m sure there are some great professors out there who have had great success with the “traditional” program of SR instruction.  I’m sure Feynman could teach circles around me, even with the train and lightning bolts.  But I prefer this different approach, as I have presented it, and I hope others will realize that there’s more than one way to explain special relativity.


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Please don’t be offended!

A Socratic dialogue

[Inside PASCAL’s home.  SOCRATES is watching television, while PASCAL is kneeling in the corner, praying.]

SOCRATES: They just bleeped a word on my favorite show!

PASCAL: Well, there are certain words you can’t say on TV.

SOCRATES: Like “fuck”, apparently.

PASCAL: Dear Lord!

SOCRATES: What, you don’t like hearing that word?

PASCAL: Heavens, no!

SOCRATES: And I bet you think that we shouldn’t be able to say “fuck” on television?

PASCAL: Certainly not!

SOCRATES: But why not?  The word simply means “sex” or “intercourse” and you can say those words on the air.

PASCAL: The word f—, uh, the word you mentioned, is obscene.  It is vulgar.

SOCRATES: What exactly does that mean?  Would the word, if heard, harm the listeners in some way?

PASCAL: Of course.  People’s sensibilities would be harmed.  Decent people would hate to hear such rubbish.

SOCRATES: But why?  Does the sound of a voiceless labiodental fricative preceding a mid-back, unrounded vowel and followed then by a voiceless velar stop somehow produce a dangerous resonance pattern that could damage the eardrums of unsuspecting people?

PASCAL: You mock me.

SOCRATES: Not at all.  I am simply at a loss to understand how any word, any single morpheme, could possibly harm anyone, apart from the word being delivered at a dangerous volume level.

PASCAL: You misunderstand.  It is not physical harm that such language can cause, but mental harm.  Distress, if you will.

SOCRATES: But how does such distress come about?  Do the concepts cause distress?

PASCAL: Why, yes.

SOCRATES: So the word “sex” offends you.


SOCRATES: Let me rephrase.  Would the word “sex” offend an ordinary person, a person that…perhaps…had not written the Pensées?

PASCAL: I would think not.  No.

SOCRATES: So the content of a word like “fuck” is not what offends, after all.

PASCAL: OK then, it is not the content of the word that offends, but the word itself.  The word is offensive.

SOCRATES: For what reason?  Is there some intrinsic property of the word that offends you…perhaps the way the word rolls off one’s tongue?  Or perhaps you hate the word because it scores 13 points in a game of Scrabble, and 13 is an unlucky number?

PASCAL: The word is offensive.  Everyone knows that.

SOCRATES:  But do you mean that literally?  Everyone?  Would a person who speaks no English be offended?

PASCAL: Of course not.

SOCRATES: But why not?

PASCAL: They wouldn’t know what the word means.

SOCRATES: But we agreed that being offended doesn’t come from the meaning of the word.

PASCAL: Oh, uh…well, they don’t know it’s a vulgar word.  They haven’t been raised in an English-speaking culture, so they don’t know that the word isn’t proper.

SOCRATES: So being offended by “fuck” must be learned.

PASCAL: Of course.  One must learn correct etiquette, the right manners.  Why should language be different?

SOCRATES: So you would agree, would you not, that being offended by a word like “fuck” is a completely arbitrary, learned behavior?

PASCAL: I would not say arbitrary.  After all, that particular word denigrates what is actually a solemn bond between man and wife.  That word cheapens the act itself.  That can’t be tolerated.

SOCRATES: It can’t be tolerated?  How come?  What would happen if you did show tolerance?

PASCAL:  The foundations of society rest on certain conventions, certain morals.  If we allow vulgarities, the whole framework is weakened significantly.

SOCRATES: And then what would happen?

PASCAL: Society would become unraveled; in its place would be—

SOCRATES: A better society?

PASCAL: —anarchy.

SOCRATES: Can you really believe that allowing certain words to become less vulgar would mean that all society would crumble?

PASCAL: But there is nothing we can do.  There are always words that will be vulgar; you cannot make them less so.

SOCRATES: Why not?  We’ve already shown that a word like “fuck” offends only because society arbitrarily says so.  Well, we are society, all of us, are we not?  What if we simply said that “fuck” is hereby no longer a “dirty” word.  It means, simply, “sexual intercourse”—if taken as a verb—or “I am very displeased” if taken as an interjection.  How could such an action harm society?  Wouldn’t it help, in the sense that no one will ever again feel mental distress when that particular word is pronounced within earshot?

PASCAL: Such a thing could never happen.  Proper people will always be aghast at the mentioning of obscenities.

SOCRATES: Ah, but there’s the rub: how will they know which words are obscenities and which are not?  What if society refuses to sort this out for them?

PASCAL:  You propose an end to all that’s decent!

SOCRATES: Not at all, my bridge-dangling friend.  I propose to remove an arbitrary system of “word regulation” from our society, because doing so will make our society that much better.  No one will ever be offended by “dirty” words again, because there will be no dirty words!  We would have a society in which censorship would be nonexistent, and in which freedom of expression would reach new, unexplored levels.

PASCAL: You are persuasive, but servants of the Devil often are.  But now I think I see what you are doing.  In grand Orwellian fashion, you propose to make odious words acceptable by simply indoctrinating people.  Brainwashing them.

SOCRATES:  No, that’s your jurisdiction.  Look at it this way: I am not trying to make murder more acceptable, simply by calling “murder” by another name such as “wexelflugen”.  You cannot change concepts by switching their labels around.  “A rose by any other name…”  But you can change the connotations a given word has, if you want, because words are just placeholders for concepts around us.  Why not take all the so-called vulgarities and throw them out the window?  Who says that our language has to have any vulgarities at all?  Why don’t we all just agree that no word will ever again bother us, ever offend us?  Don’t people have enough control of their own minds to make such a decision…a decision that would benefit everyone?

PASCAL: Well, be that as it may, some concepts would remain offensive.  There’s nothing you can do about that.

SOCRATES: There isn’t?  Give me an example of something—not a word—that offends you.

PASCAL: OK.  Violence offends me.  Surely you will not try to tell me that we should all just agree that violence is acceptable, and that we should all live with violence happily.

SOCRATES:  You are right, I will not.  I abhor violence; the very idea of murder sickens me.

PASCAL:  A ha!  Then you agree with me.

SOCRATES: Well, yes and no.  “Violence” does not offend me, but violence does.

PASCAL:  Um.  I’m confused.  You just said—

SOCRATES: I said that I abhor violence.  But “violence” doesn’t bother me.

PASCAL: What is this, semantic trickery?

SOCRATES: I do not like violence; I dislike seeing graphic pictures of murder victims; I become nauseated at the thought of war; the sight of blood often makes me sick.

PASCAL: Then violence offends your soul.

SOCRATES: I suppose.  But talk of violence doesn’t bother me at all.

PASCAL: What do you mean?

SOCRATES: I experience certain physiological symptoms when exposed to violence, but if someone says “murder” or “rioting” or “rape” or “you may eat the flesh of kings” then I am not offended.  And what I mean by that is this: I do not like to see or hear violence as it is committed, nor do I enjoy thinking about violent acts, and I certainly am very angry that certain forms of violence still exist in this world.  However, the concept of violence, the abstraction, can’t “offend” me any more than the concept of volcanoes or tsunamis or great white sharks.  Maybe I don’t want to be near them, but how can they “offend” me?  And if you talk about them, why should that bother me?

PASCAL: Let me understand.  The word “murder” is not offensive.  And a discussion of murder is not offensive.  But if someone commits murder—

SOCRATES: Then yes, that would bother me.  Look: concepts like murder are too important as issues for people to ignore just because they’re afraid their sensibilities might be punctured.  And this applies to other concepts I dislike as well: bigotry, deception, subjugation—these words do not offend me, because I do not let them.  But the acts themselves very well might piss me off.

PASCAL: But if a word is used in a hateful way, such as a racial epithet…

SOCRATES: Again, don’t blame the word.  What I find offensive in such a case is the insensitivity (or downright malice) of the speaker, their intent to harm.  So saying “fuck you!” might be offensive not because that particular phrase was uttered, but because of the intent of the speaker.

PASCAL: But then it would be too hard to sort out what was offensive and what was not!  If you always had to check the context—

SOCRATES: Sorry, but you have to do that anyway.  “Pain” means one thing to us, and quite another thing to the French.

PASCAL: I am at a loss for words.

SOCRATES: Here is my manifesto.  Many people, when encountering an idea they find distasteful, turn up their noses and say they are offended.  I, however, cannot be offended by ideas—that is, by abstract words devoid of context.  Nothing in the abstract can offend me at all, and I am very proud of this fact.  Sure, there are things I don’t like to see (like rotting corpses) or hear (like fingernails on a blackboard) or smell (like a diaper full of shrimp) but these things don’t offend me.  Why should I hold a grudge against such phenomena?  I don’t like them, but that’s not a problem: I can shut my eyes or cover my ears or pinch my nose shut.  I choose not to participate in these sensory experiences—choose—and for quite understandable reasons.  My aversion to such things is instinctual, biological, untainted by arbitrary sociological constraints.  Now, in certain cases, I cannot choose to avoid something, in which case I am offended by the selfishness of the perpetrator.  If you smoke in an elevator with me, I will be offended because I have no choice but to breathe your noxious detritus.  If you commit murder or cheat on your taxes or beat your wife, I will be offended because you have committed a crime, and betrayed an implied covenant between you and the rest of society.  But I emphasize again that the words “murder” or “cheating” or “beating” can’t offend me, as they’re just words.  And so too, the word “fuck” cannot have any effect on me at all.

PASCAL: Well then.

SOCRATES: Being offended is a learned skill.  There is no evolutionary gain to having people grimace when they hear a collection of phonemes such as “clusterfuck”.  People are offended by such a word because they choose to be offended, but do not even realize that they have a choice.  The content of the word is irrelevant…else “group sex” would offend just as much.  But it does not.

PASCAL: Speak for yourself.

SOCRATES: You don’t look convinced.

PASCAL: Well, your discourse has offended me.


PASCAL: And I would wager that some part of you is offended, as well.  You just can’t admit it.

SOCRATES: You and your wagers.

PASCAL: Anyway, I’ve made some tea out of Queen Anne’s Lace.  Would you like some?

SOCRATES: Not really.  There’s something about that plant that offends me—

PASCAL: No matter.  I have to catch the carriage to Neuilly anyway.

SOCRATES:  And I must kill a rooster for Asclepius.  So long.

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An Oulipo poem

Ouvroir de littérature potentielle (Oulipo for short) is a group of mainly French writers and mathematicians who create works with rigid constraints, in order to spark creativity and celebrate wordplay in general.  My favorite example is the extraordinary sonnet “Washington Crossing the Delaware” by David Shulman, in which every line is an exact anagram of the title.  Shulman wasn’t French and neither am I, but c’est la vie.

Here is my attempt at an Oulipo poem.  See if you can determine the rigid constraint at play.


An Oulipo Poem

Aim your arrows carefully, and

Be careful not to miss your target.  Do you

See how important the

Demarcation of the boundary is?

Even the best archers miss, in

Effect piercing the innocent, like

Jesus and His stigmata; “on target” is the

“A” choice, and off the bloody circle is the “B”.

I, myself, prefer to think my fletching’s made of

Jade, mined from whatever Byzantine

Cave my heart carves out; full of

Elements and isotopes and

Empathy for the Devil.  You, there, conscience,

Enter that cave:

Open its mossy portals, discern its shadowy

People, and, on

Cue, whistle to the bats and darkness within.

Are you with me, there, inside that cave?  In

Essence, the arrows and the cave are but metaphors; each a

Tease, exotic, exigent, taunting


Vehemently as you try to count your blessings.  You

Double, you triple, you quadruple your count but nothing

Extra remains: the cave is empty, the arrow has missed its target, the darkness descends—

Why?  Because your pain has reached a



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It may seem odd that this blog is called “Many Worlds Theory” and yet I have not yet blogged about, well, many worlds theory.  Well, I am doing so now.

The arguments that lead a sizable portion of theoretical physicists to postulate a multiverse are subtle and complicated.  I hope to eventually cover these arguments, but I’d like to start with a discussion of what many worlds is not.  Therefore, with much fanfare, I present to you:

The Top 5 Misconceptions About the Many-worlds Interpretation (MWI) of Quantum Mechanics

1.      Every time you do a quantum experiment, the universe branches into multiple universes.

This is a popular notion, as seen in TV shows like Nova and as presented by Martin Gardner.  Unfortunately, it is the wrong way to look at things.  It is much better to imagine that all of the possible universes already exist, and that doing an experiment just tells you (the experimenter) which universe you happen to be in.

Suppose you’re watching Star Wars.  You have no idea whether you are watching the original, or the retconned 1997 version.  You finally realize which version you’re watching when you see Han shoot and kill Greedo without Greedo ever getting a shot off.  You conclude you’re watching the original version.

Of course, up until that point, the movies are exactly the same. (Rather, let’s just say they are the same.  I haven’t actually checked this.) You wouldn’t conclude, when you got to that scene, that two movies were created from one, would you?  There were two movies all along; watching Han shoot first just told you which movie you were watching.  A physicist who performs a Stern-Gerlach experiment doesn’t split the universe in two; doesn’t create a whole universe; instead she has gained some new information: “Oh, so that’s what universe I am in.”  No new physics of universe-creation is needed, and we need not violate conservation of energy.

2.      The existence of a multiverse is a postulate of a strange kind of quantum mechanics.

There is a formulation of quantum mechanics often called universally valid quantum mechanics, which was first described by Hugh Everett III in 1957.  It involves (see this for details) just one postulate: isolated systems evolve according to the Schrödinger equation.  That’s it.  A multiverse is a prediction of this postulate, not a postulate in and of itself.  So if you believe that isolated systems evolve according to the Schrödinger equation, you will be led to the MWI, unless you invent new postulates to make yourself feel better (see #3).

3.      The Many-worlds Interpretation has a lot of baggage.

This obviously depends upon what you mean by baggage, but the claim is often made that the MWI is horribly antithetical to Occam’s razor.  That is, how could anyone seriously believe that countless billions upon billions of universes exist, when believing in one universe is much, much simpler?

If you feel this way, I have two responses.

One: how can you believe that countless billions upon billions of stars exist, when believing in just one star is much, much simpler?  Shouldn’t you be Earth-centric, and call for Galileo’s excommunication?  Or what about the integers?  Mathematicians claim that there are an infinite number of them, but infinity is too hard to fathom, so why don’t you just say that there are a lot of integers, but that there is only a finite number of them?  There.  I bet you feel better.

Two: like it or not, Occam’s razor cuts both ways, and can be used to defend MWI.  The idea is whether Occam’s razor applies to the number of universes, or the number of postulates in your physical theory.  As Max Tegmark pointed out, universally valid quantum mechanics leads to a multiverse as a consequence.  In order to get the Copenhagen interpretation (for years, the most popular flavor of quantum mechanics) and rid yourself of those pesky many worlds, you have to take Everett’s quantum mechanics and add one additional postulate: that wave functions collapse according to random and ultimately unknowable criteria.  That is, the MWI is simpler in the number of postulates required.  As Tegmark put it, which way you use Occam’s razor depends upon whether you prefer many worlds, or many words.

4.      The Many-worlds Interpretation is not falsifiable and therefore not science.

The jury’s still out on this one, but many people (including David Deutsch) think that the MWI is misnamed: that it is actually a theory in and of itself, and that it is falsifiable.  I haven’t made up my mind on this.

I tend towards Tegmark’s view that MWI is an untestable prediction of quantum mechanics, which is testable.  Because we take quantum mechanics seriously, we have to take one of its children (MWI) seriously.  As Tegmark says, it’s like black holes.  We can never see inside a black hole, so what goes on in there is never falsifiable; yet we take black holes seriously and call black holes “science” because general relativity (the theory that predicts black holes) is so successful.

5.      The Many-worlds Interpretation is fringe science and only believed by kooks.

These kooks include Stephen Hawking (who said the MWI was “trivially true”), David Deutsch, Bryce DeWitt, and Max Tegmark, among others.  They also include a sizable number of theoretical physicists working today.  In 1995 one poll (published in the French periodical Sciences et Avenir in January 1998) showed that 58% favored MWI; see also this informal 1997 poll.

Maybe we are all kooks.  But there are a lot of us, and the number is growing.

[Note: my book Why Is There Anything? is now available for download on the Kindle!  This book examines the many-worlds interpretation from a philosophical perspective.]

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What if there were a way to increase donations to worthy causes, while at the same time help fight this country’s obesity problem?


I think there is a way, and it would be simple to test.  Suppose fast food restaurants that offer “meal deals” (burger + drink + one side, say) offered a $1 donation to Oxfam (or any other charity) as one of the side dish options?


There are two obvious benefits.  One, I believe that people donate to charities more if they can do so conveniently.  I myself had never given money personally to a hungry family, but when a local grocery store asks me if I want to buy a box of food “for the children” I do so almost automatically.  Convenience allows us to then feel good about ourselves.


Secondly, people who choose this “side dish” are clearly missing out on calories that most don’t need anyway.  How often do people get french fries, even when they don’t want them, just because they “came with the meal”?  And subsequently, how many people eat the fries, because they paid for them–-even if they are no longer hungry?  I’ve done this myself, although it seems irrational in hindsight.


What if instead I order a $5 meal deal and the cashier asks, “What side?” and my response is, “give it to the hungry”, and the restaurant then has some automatic money transfer mechanism in place to make the donation in an instant?  I don’t know which would do society more good: the money raised, or the calories not consumed.  Why isn’t this a win/win?  Or a win/win/win, since the restaurant doesn’t lose anything, and only gains the positive PR?  It would even show evidence that the restaurant has heard the message of “Supersize Me” and taken it to heart.


I think this idea is a good one, and I hope someone reads this post and shares the idea.  All it would take would be one restaurant to start doing this, and before long all of them would be doing it.  I can’t see a single downside at all.


Admittedly, this may have been tried before.  If so: I wonder why it hasn’t caught on?  What are the economics of such institutionalized charity?  I think there are other interesting questions at play here…does charity in fact increase when it is convenient to give?  (I’d love to see the research data on this.)  Would people forgo empty calories in such a scenario?  What would be the economic benefit of millions of calories not being consumed?  Might there even be an adverse effect for, say, the potato industry, if less fries are scarfed down?


Let me know what you think.  And please share this if you think that someone, somewhere, will see it and have the possibility of implementing it.


[Note: this blog post was originally written on Dec. 15, 2010, and emailed to a celebrity who will remain nameless.  Needless to say, there was never a response…not even an automated one.]

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My contribution to the “What I Really Do” meme, back in February 2012.

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