The unreasonable effectiveness of mathematics

[With apologies to Eugene Wigner.]

I was noodling around with some graphics code the other day to try to produce some schematic representations of water waves for a book that I'm working on.  I wanted to produce a little animation of what happens when you throw a stone into a pond.  It didn't have to be very flashy, I just wanted it to be qualitatively correct, that is, I wanted to produce a drawing of a wave that spread out from a central source and decreased in amplitude with time and distance from the source.  So I started out with the venerable sin(x)/x function:

That's a good start, but now I wanted to animate it, so I changed it to sin(x+t)/(x+t) and varied the time t from zero up to some positive value.  The result was this:

That was kind of what I was after, but time seemed to be running backwards.  So I changed the sign on my time parameter, i.e. sin(x-t)/(x-t), which yielded this:

Now my waves were moving in the direction I wanted them to, but they weren't being damped out.  A bit of reflection revealed the reason: because I changed the sign of my time parameter in both the numerator and the denominator of my function, I had reversed the not only the time direction, but also the damping influence of time, which I had gotten right the first time.  So the function I wanted was (apparently) sin(x-t)/(x+t).  When I tried that, I got this as my first frame:

That looked promising.  The graph had flipped itself upside down, but that actually seemed closer to the Right Answer, because when you throw a stone into a pond the first thing it does it to make a "hole" in the water.  So I advanced the time a bit, and got this:

WTF?  Where did that spike come from?  I didn't want a spike.  Water doesn't do that.  Water is always nice and round, not pointy.  This couldn't be right.  And yet, the rest of the animation actually looked pretty reasonable:

I spent several hours fiddling with it trying to tweak the function so that it did the same thing but without that annoying spike.  I tried changing signs, using a cosine function instead of a sine, you name it.  Nothing looked right [1].  And then it occurred to me (duh!) to take another look at what water actually does when you drop something into it.

There, right in the center of an actual physical water wave, was my spike!  It didn't have a pointy end: surface tension had made the point shrink up into a sphere, but the spike was unmistakable.  It was as if the math was trying to take me by the throat and tell me, "No, water really does work this way."

In retrospect it is actually obvious why water has to work this way.  You drop a stone into a pond and the stone makes a hole in the water.  The stone keeps falling through the water (because the stone is denser), and as soon as it has moved out of the way, water rushes back in from all sides to fill the hole.  All that water rushing in meets at the center of the hole, and because of inertia and the fact that water is not compresible, it has to keep moving, so it has to go somewhere.  The only place left for it to go is up.

In 1960 Eugene Wigner published a famous paper entitled "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" which first pointed out this phenomenon, that math often "takes you by the throat" and forces you towards the correct answer even if it sometimes takes people a while to realize that this is what is going on.  I thought it was cool to experience this phenomenon firsthand.

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[1]  The reason the spike is there, mathematically speaking, is that the function sin(x-t)/(x+t) must be zero when x=t and t>0, but the limit of the function as x->t from above is -1.  So at t=0 it has to look like -sin(x)/x, but at t=epsilon it has to have two zero-crossings at x = +/- epsilon.  The only way to satisfy that condition, along with continuity constraints, is to have a spike.  It is might even be possible to prove that no mathematical function can possibly produce all the desired qualitative characteristics of water waves (damping, forward motion in time, conservation of mass) without a spike, but that's above my pay grade.

Looking under the hood of the scientific process

TJ Radcliffe pops open the hood on the scientific process and lets you peer inside to see the inner workings in unusual detail.  He also has a pretty good description of what science actually is:

Science is the discipline of publicly testing ideas by systematic observation, controlled experiment and Bayesian inference. As such, it is fundamentally about exploration. We have ideas, we test them, we let the results of those tests guide where we go next. In the end, we publish, because if not made public it is not science. People were investigating reality long before the Proceedings of the Royal Society saw the light of day, but they didn’t accumulate knowledge because they didn’t publish. Science is both intensely individualistic and profoundly communal.

(Compare and contrast the level of detail and self-criticism to, say, this.)

He also offers up this brilliant little gem:

When someone lectures you on the importance of being open minded, try responding with something along the lines of, “I’m open to any idea that we can figure out how to test, because if it can’t be tested it probably can’t explain anything. If it can explain a phenomenon, then it can act as a cause on other things, so it can be tested, because we can make predictions of other things that it is likely to cause. If it can’t cause anything other than what it’s being invoked to explain, then it really doesn’t have any meaning beyond ‘the thing that causes that’, and that’s pretty boring. So give me an idea–one idea, not ten–and let’s talk about how to test it, what other consequences it would have that we can look into. I’m totally open to any idea like that.” 

The practice of science is very much about learning where to look for plausible ideas, and focusing on looking rather than imagining as the first step on any search for a more plausible proposition. This is difficult because it requires us to accept that we don’t know what the problem is and we might not be able to find the actual source. Imagination is much more comforting than reality at times like this. But we should learn to trust ourselves, and look to the world to guide us. That’s the only way we’ll find more plausible propositions. People were imagining answers to hard questions for thousands of years before we learned the discipline of science, and we have precious little besides some decent poetry to show for it. We certainly never cured disease or ended hunger that way.

Lyft is even more evil than Uber

Yes, I get it.  Uber is evil.  But Lyft is worse.

Today I got a text message spam from Lyft.  I don't like getting text message spam, so I tried to log in to my Lyft account to update my contact preferences so I could opt out of future spam.

It turns out that it is not possible.  I tried everything I could think of: the Lyft web site, the app, the help center.  Nothing.  If you go to the Lyft help center and search for "cancel" or "opt-out" the only thing that comes up is how to cancel a ride request.

So, Lyft folks: I understand that you are under intense pressure from Uber and you need to do something.  But this ain't it.

Talk about missing the point

PETA, that is, the organization that calls itself People for the Ethical Treatment of Animals, kidnapped and killed a pet chihuahua.

I am not one to be easily rendered speechless, but that did it.

This is why prominent atheists should not critique religion

BioLogos has an an interview with Bill Nye on the occasion of the publication of his new book.  It is nearly as painful to read as his infamous debate with Ken Ham was painful to watch [1].  The level of ignorance and tone-deafness he displays with regards to religion in general and Christianity in particular is equivalent to YECs who stand on the street corner and ask if your grandpappy was a monkey.

BioLogos: While you say your book has little to do with religion, you write in the book that it’s unreasonable to see any sort of divine “plan” in nature (p. 78). Paired with strong endorsements from many prominent atheists and agnostics on the back cover, can you see how many Christians would feel your book has an anti-religious agenda? 

Nye: Put briefly, no; I don’t perceive an anti-religious agenda, especially with regard to Christians and Christianity. The issue being debated was creationism, the idea that the Earth is 6,000 years old. As I understand it, this involves the Bible’s Old Testament exclusively. As I understand it, Jesus of Nazareth and his worldview did not come to be until the New Testament times.

Oh.  My.  God.  How can anyone not know that Christian theology holds that Jesus was a fulfillment of Old Testament prophecies, that the Old and New Testaments form a seamless whole, that Jesus and Yahweh are the same deity?  There are all kinds of reasons one might be a Christian without being a YEC, but the idea that Christianity has nothing to do with the Old Testament is not one of them.

If you're going to critique something you should at least take the time to learn the basics of the thing you are critiquing.  This goes for scientists as well as everyone else.

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[1] The reason the Nye-Ham debate was painful to watch was that Bill completely missed the most basic and fundamental point: Ken Ham, by his own admission, is not doing science.  Ken, again by his own admission multiple times during the debate, starts from the premise that the Bible is the inerrant Word of God.  Ham gave away the game in his opening statement:

"I assert that the word “science” has been hijacked by secularists in teaching evolution, to force the religion of naturalism on generations of kids."

No, it is not that the word has been hijacked.  The word "science" is completely irrelevant.  You could call it fnorbage instead of science, it wouldn't make a clingleblat of difference.  What matters is that if you choose to use evidence, experience and reason rather than divine revelation as the ultimate arbiters of truth, you get better results, at least by certain quality metrics that most people care about.  And the evidence is overwhelmingly against the theory that the earth is 6000 years old.  Whether you call that science or fnorbage or squibbs and crackers matters not at all.

A public service announcement regarding 650-780-9288

If you call the number in the headline (650-780-9288) you will find that it has been disconnected.  The reason it is disconnected is because it used to be our home phone number, and we were getting so overwhelmed by robocalls (despite -- or perhaps because of -- being on the federal do-not-call list) that we finally threw in the towel and got an unlisted number.  At some point in the future, this phone number will be recycled, and some other poor unfortunate sod will probably end up getting the same deluge of marketing calls that we got.  But that is not the reason for this PSA.

The reason I'm putting up a PSA is that before this number was our number it (apparently) belonged to one Julian Carrillo and an associate of his named Maria.  The reason I believe this to be the case is that in addition to marketing robocalls we also often got calls for Mr. and Ms. Carrillo, mostly from collection agencies, but occasionally also from car rental companies and insurance companies.  On the off chance that anyone trying to contact the Carrillos tries to Google their phone number, I wanted them to find this: the phone number 650-780-9288 was assigned to me in June of 2010.  If anyone named Carrillo (or any other hispanic name) provided you with that phone number as theirs between June of 2010 and January of 2015, they were providing false information.  It is hard to imagine how this could be an honest mistake, as we have evidence that the Carrillos were still giving out this phone number more than four years after it was assigned to us.

As long as I'm on this topic, I will also mention this: the most egregious robocall offender was a company called (as best I can determine) Energy Upgrade California.  Their robocaller is very distinctive in that it opens with a woman's voice saying, "Due to the constant rise in energy costs..."  We heard this line on our answering machine so many times that I long ago lost count.  I tried everything to get them to stop calling, but they were relentless.  They are the cinder block that broke the camel's back and motivated us to get a new number.

I don't know if the company calling us was in any way affiliated with this web site.  I suspect not, because the web site seems kinda legit [1] while the phone version felt like a pretty shady boiler-room operation.  On several occasions I actually talked to one of their CSRs trying to find out who they were and what they were selling (and how to get them to stop calling!) but as soon as it became apparent that I was not a rube they hung up on me.

If you happen to be one of their victims, you have my deepest sympathies, and if there's anything I can do to help get them shut down I would be thrilled to do whatever I can to contribute to their demise.

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[1] The reason I say "kinda legit" is that they claim to be affiliated with the California Public Utilities Commission.  If this isn't true, then this is a transparent fraud and I would think the attorney general would be all over their ass.  On the other hand, the site does not provide any traceable contact information, so that seems a tad fishy to me.  On the other other hand, the site does seem to be chock-full of real content, so if it's a scam someone put an awful lot of effort into making it look real.

The pope backpedals (sort of) on limits to offensive speech

Two days ago Pope Francis issued a clarification (which I would characterize more as a wishy-washy retraction) of his implicit endorsement of physical violence as an appropriate response to free speech that he made last week.  I enthusiastically endorse the excellent analysis by Jacob Sullum (thanks to regular commenter Luke for pointing me to that link!) and I encourage everyone to go read it in its entirety.

I want to reiterate the nature of my disagreement with the pope: it is not about human nature.  I agree, of course, that many humans instinctively want to respond to insults with violence.  That is not the point.

My disagreement with the pope is two-fold.  First, the pope strongly implied in his original remarks that the human instinct to respond to insults with violence is a fundamental fact of life to which we must (perhaps even should) simply resign ourselves.  I disagree, and so does Jesus (hence my leveling a charge of hypocrisy against the pope).  This aspect of human nature is not a feature, it's a bug, and the pope should have said so.  He should have said, "Insults make us angry.  We want to respond to anger with violence.  I get that.  But Jesus teaches that we should respond to anger not with violence but with compassion and forgiveness, because anger is usually a result of emotional pain.  This is the thing that those who insult religion need to understand: their insults cause pain to their fellow human beings.  And while they have the absolute right to say whatever they want, we all have a moral responsibility to temper our actions with compassion."

That's what the pope should have said.  (And, Frankie, if you want to hire me as a PR consultant, I'm available.)

But the second aspect of my disagreement with the pope is that he singled out insults against religion for special treatment.  The problem with offensive speech is that offense exists only in the mind of the offended.  In the case of physical violence there is no disagreement about the harm: the life is lost, the bone is broken, the nose is bloodied.  But offense is subjective, a matter of taste.  I, for example, do not find the Charlie Hebdo cartoons at all offensive.  In fact, I think they are well within the bounds of reasonable socio-political satire (unlike, for example, "The Innocence of Muslims" which I did think was offensive.)  This raises the same unanswerable question that all matters of faith inevitably lead to: on what basis do decide who is right?  Are Muslims "legitimately" offended or are they being hypersensitive pussies?  (And, of course, if someone takes offense at my use of the (deliberately provocative) phrase "hypersensitive pussies" the same question applies recursively.)

Personally, in the Charlie Hebdo case I come down on the hypersensitive-pussy side.  This idea that creating an image of the Prophet is a grievous sin is a relatively recent invention.  Muslims used to create images of Mohammed themselves.  But it doesn't matter if I'm right or wrong about that (there is no way to tell, that is the whole point).  If we give in to the offense of Muslims, what about other people's offense?  What about my offense?  I am deeply offended by many things the pope says (like the garbage he continues to spew about homosexuality being sinful, women not being suitable for the priesthood, the unacceptability of birth control, yada yada yada).  Should the pope stop saying those things because they offend me?  Of course not.  Why should Muslims be entitled to more consideration than anyone else?

The elephant in the room is that the actual answer to this question is: because there are a billion Muslims, and some of them riot in the streets and blow shit up when they get offended.  But the correct response to terrorism is never to capitulate to the terrorists.  That simply emboldens them.  The correct response to terrorists, as it is to any bully, is to stand up to them, to say fuck you, no, you do not get special treatment simply because some of you are willing to violate the social contract.

Open mic night on Rondam Ramblings

Whew, I have just spent an inordinate amount of time responding to various dangling comment threads.  Despite my best efforts, I fear I may have left some points or questions unanswered.  If I did, I apologize.  If there's anything you'd like me to respond to that I haven't, please post it in the comments section of this post.  (If you're picking up a thread from another post, please include a link.)

My thanks to Luke and Publius for ongoing lively discussions!

Apparently the Pope needs to read the Bible more carefully

Pope Francis showed his true colors the other day:

“If my good friend Dr Gasparri says a curse word against my mother, he can expect a punch,” Francis said while pretending to throw a punch in his direction. 

He added: “It’s normal. You cannot provoke. You cannot insult the faith of others. You cannot make fun of the faith of others.”

So... the pope just endorsed the use of violence against those who "insult the faith of others."  Well, you know what, Frankie?  Fuck you.  After taking the cardinals to task for developing spiritual alzheimers I thought you might be cool, but apparently you're just another in a long line of walking talking hypocrites.  It is you who seem to have the spiritual alzheimers, as you have obviously forgotten Matthew 5:39.  Or don't they teach that one in seminary any more?

[Beat.]

Yes, I really did just tell the pope to go fuck himself, I'm that pissed off.  You know what you don't do if you want to advance yourself as an advocate of peace?  You don't fucking endorse violence as an acceptable response to speech, no matter how fucking offensive it is!  So fuck you, pope Francis, and the horse you rode in on.  Think of all the suicide bombers who will hear your words and conclude from them that they are on the righteous path.  The blood of their victims will be on your hands and your tongue.

God damn what is the world coming to when an atheist has to school the pope on his own scriptures?

My parents neglected me when I was a child

I wasn't aware of this until today, but my parents apparently neglected me when I was a child.  Every week day from the age of six until ten I walked to school by myself. And back.  0.8 miles each way according to Google Maps.  I even walked in the rain and the snow (though I have to confess it was not uphill both ways).

Well, OK, I wasn't actually alone.  There were lots of other kids walking to school, and usually I would walk in the company of some of fellow neglected waifs.  Oh, and there was the crossing guard near the school.  But no parents hovering over us.  That was just the way things were done back in the day.

But apparently, letting your kids walk by themselves is child neglect.  Who knew?  I sure didn't.

It was a one-mile walk home from a Silver Spring park on Georgia Avenue on a Saturday afternoon. But what the parents saw as a moment of independence for their 10-year-old son and 6-year-old daughter, they say authorities viewed much differently. 

Danielle and Alexander Meitiv say they are being investigated for neglect for the Dec. 20 trek — in a case they say reflects a clash of ideas about how safe the world is and whether parents are free to make their own choices about raising their children.

The one question faith cannot answer

Sometimes things don't go as planned.  My Parable of the Free Beer seems to have landed with a resounding thud, so perhaps a word of explanation is in order.

First, in case it wasn't obvious: yes, it was intended to be an allegory about theology, and Christian theology in particular.  Replace "free beer" with "God's grace" and you have an almost verbatim transcript of sermons I have heard street evangelists deliver.  In fact, I remember one street preacher in Santa Monica back when I was making my movie literally take a five dollar bill out of his wallet and ask, "Who would like five dollars?" and then go on to say that God's grace was infinitely more valuable and "all you have to do is take it."  It wasn't literally free beer, but in those days you could still get a beer for five dollars.  (Maybe you still can.  I don't actually much care for beer.)

Second, it was supposed to be funny.  If you didn't think it was, well, go get yourself a sense of humor.  You can order one from Amazon nowadays.

Last but not least, the Parable was intended to make a serious point, namely, that without an independent standard (like evidence) how is an honest Seeker of the Truth supposed to choose from among the many religions on offer in today's market?  You've got Christianity, which comes in so many flavors it is like the Baskin-Robbins of theology.  Islam comes in two major varieties and handful of minor ones (like Sufism).  Then you've got yer Buddhists and yer Hindus rounding out the world's major religions.  But wait, as they say in the trade, there's more: there's Jews, Jains, Mormons, Scientologists, Raelians, Bahais, Satanists, Wiccans, and good old fashioned neo-pagans.  (Give me that old time religion!  It was good enough for grandpa so it's good enough for me.)

This is the question faith cannot answer: on what basis should one choose where to put one's faith?

The Parable of the Free Beer

There is a classic logic problem that goes like this: you are on an island where some of the natives always lie and others always tell the truth.  You find yourself at a fork in the road where one branch leads to the village, the other into the jungle, and you wish to determine which branch is which.  There is a native standing at the fork, of whom you may ask one yes-no question.  What do you ask?

The usual, nerdy answer goes something like, "If I were to ask you if the left path is the way to the village, would you say yes?"  The problem with this answer is that the native may as well decide that by the time he sorts out the hypotheticals, the cannibals will have emerged from the jungle and had both of you for lunch.  So in the real world (and I may as well warn you now, this post will require a certain level of suspension of disbelief) he is as likely to say, "Bugger off" or "WTF?" as he is to say yes or no.

Martin Gardner suggested a brilliant, practical solution: you should ask, "Did you know they are serving free beer in the village?"  Then you ignore the answer, and just follow the villager whichever way he goes.

This solution is cute, but not without its issues.  It assumes, for example, that your interlocutor likes beer, that he doesn't have urgent business in the jungle, that he is not an "artful deceiver" willing to forego a shot at free beer in order to mislead a foreigner, etc.  Furthermore, it assumes that the native is not considering the possibility that you might be a deceiver, and that you are asking the question not because there is, in point of fact, free beer in the village, but that you have (as indeed you do) some hidden agenda that has nothing at all to do with beer.

In this post I want to consider the inverse problem: suppose you know the way to the village and a native comes up to you and says, "Did you know they are serving free beer in the village?"  How would you respond?  Assume for the sake of argument that you like beer, and all else being equal you'd rather pay less than more.  But in this case all else is not equal.  To act on the information that is (apparently) being provided to you, you have to walk to the village.  If you get there and discover that they are not, in fact, serving free beer then you have incurred, at the very least, an opportunity cost.  Since you are wise in the ways of wily natives, you decide to make further inquiries, and the following conversation ensues:

You: No, I did not know they are serving free beer in the village.  Are they in fact serving free beer in the village, or are you trying to trick me into showing you the way to the village?  Because if it's the latter, all you have to do is ask.  This isn't a logic puzzle.

Native: Oh no, I assure you, there is no trickery, and I have no hidden agenda.  They are indeed serving free beer in the village.  Do you like beer?

You: Indeed I do.

Native: Then why are you not at this very moment rushing off to the village?  It's right over there.

You: It's because I'm a little skeptical.  It seems odd that they should be serving free beer.  As far as I know, there is no reason for them to be doing so.  Is there a festival going on that I didn't hear about?  Or maybe the beer company is running a promotion?

Native: No, nothing like that.  The barkeep is just a particularly generous fellow.

You: I see.  So he sometimes serves free beer just out of the goodness of his heart, does he?

Native: Not sometimes.  Always.  Twenty-four by seven.  All you have to do is walk into the pub and ask.

You: That seems a tad implausible.  How does he stay in business?

Native: Tips.

You: You'll have to pardon me if I'm not convinced.

Native: Oh, it's true.  Ask anyone.  Say, Fred, come over here a second?

Fred: What can I do for you?

Native: This foreigner here doesn't believe that they serve free beer in the village.

Fred: Oh, they do.  I've availed myself of it many times.

[So you go to the village and enter the bar.]

Barkeep: Welcome, stranger!  What can I get for you?

You: I hear you're serving free beer.

Barkeep: Indeed we are.  And not just any old beer.  It's the best beer you've ever had.

You: Can't wait to try it.

Barkeep: Well, as soon as you're dead, you can.

You: What?!

Barkeep:  Oh yeah, didn't they tell you?  You can only have this beer in the afterlife.

You: I knew there had to be a catch.

Barkeep: It's not a catch.  This beer is so good that if you had it while you were alive your head would explode.

You: Do you have any idea how ridiculous that sounds?

Barkeep: Yeah, I know, but it's true.

You: What makes you think so?

Barkeep: Oh, the evidence is overwhelming.  People have written books about the beer.  2000 years ago people were actually able to try it.  And even today, while you can't actually drink it until after you're dead, you can experience it.

You: How?  (And what does it even mean to experience beer without drinking it?)

Barkeep: You have to believe in the beer, and then the beer will reveal itself to you.

You: That is the most absurd thing I have ever heard in my life.

Barkeep: Be that as it may, you really want to believe in the beer.

You: Why?

Barkeep: Because if you don't then when you die you will go to the Hostelry of Eternal Liquor Lossage, which is a very bad place.

You: What makes it such a bad place?

Barkeep: No beer.

You: Hm, that does sound unpleasant.  Can I take some time to think about it?

Barkeep: Sure, but don't take too long.  Once you're dead, that's it, no do-overs.  And you never know when you might get hit by a bus.

You: I'll be careful.  Thank you, and good bye.

Barkeep:  Good bye. Oh, before you go, take a copy of the Beer Insider's and Brew Lover's Encyclopedia.  It will tell you all about the beer.  How it was made, what makes it so special, why you can't get it any more except after you're dead...

[He hands you a thick book.]

You: Thank you.

[You exit the bar, making a mental note to be very careful to look both ways before you cross the street.  On the sidewalk outside you encounter another villager.]

Villager: Say, stranger, did you know that they are serving free wine in the next village?

Reframing theodicy

The latest round of my recent interaction with Publius made me realize that there might be a new move in the theological chess game known as theodicy.  The usual opening gambit is, "Why would an all-powerful God allow the existence of evil?"  And the usual reply is that evil is regrettable collateral damage caused by God's granting us free will, which is necessary for our salvation (at least that's the Arminian response.  I actually have no idea how Calvinists deal with the theodicy problem.  If I have any Calvinist readers perhaps you could enlighten me?)

But it occurred to me that evil is actually a red-herring.  The real question is: how can there be unsaved souls in the presence of an all-powerful all-loving God?  To put this in the starkest possible terms:

1.  Either it is God's will that I be saved, or it is not.

2.  If it is not, then God is not all-loving.

3.  If it is, and I can thwart God's will (by e.g. not believing in Him) then God is not all-powerful.

I think this formulation is more powerful than the usual one because it prevents playing evil off against salvation as the greater good.  Unsaved souls in the presence of an all-loving all-powerful god are simply a logical impossibility.  Hence, if I (or anyone else for that matter) reject God, then that rejection in and of itself is proof that God cannot be all-loving and all-powerful.

(Note that this argument does not depend on free will.  It doesn't matter why someone rejects God, only that someone does.)

Take that, Descartes!

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Note: this argument does have one tacit (i.e. unstated) assumption.  See if you can figure out what it is.

Why I believe in the Michelson-Morley experiment

Despite the fact that I haven't been writing much lately, I'm still getting a few hundred pageviews a day according to Google, and I also picked up a few new subscribers over the holidays.  Whoever you are, welcome, and thanks for reading.

Regular commenter Publius and I have been mixing it up in the comments section of an old post about being an AI in a box.  In it, Publius asked:

Even Michelson & Morley looked for the Luminiferous Ether. You replicated that, right? Just didn't read about it in a book?

The answer, of course, is that no, I have not personally tried to replicate the Michelson-Morley experiment.  And yet, I believe the extraordinary claim that the speed of light is the same for all observers (with a few caveats).  So why do I believe that even though I "just read about it in a book" but I don't believe in Jesus despite the fact that I can read about him in a book too?

The glib answer is that I don't believe in Harry Potter either, despite the fact that I read about him in a book too.  But the real answer is much deeper than that.  It's "obvious" that Harry Potter is fiction and the Michelson Morley experiment is not.  But the reason this is obvious is not at all obvious.

The first-hand evidence I have for Harry Potter's existence is actually much, much stronger than what I have for Michelson-Morley.  I have seen actual photos of Harry Potter.  Not just still photos, but high-definition video.  Hours and hours of it.  And all of it is consistent with the written accounts, of which there are seven volumes written in my native language (so no concerns over mistranslations).  By way of contrast, I have no idea what Michelson or Morley looked like.  I wouldn't even know their first names if I hadn't looked them up.  I have never read their original paper, only second-hand accounts in text books and Wikipedia.  I have no idea whether the people who wrote the accounts upon which I rely ever knew Michelson or Morley (I suspect they didn't) or even read their original paper (I suspect they did, though I would not be totally shocked to learn that they didn't).

So it would seem that the actual evidence I have in hand even for the existence of Michelson and Morley is pretty thin, let alone that they actually performed the experiment they are purported to have performed, or that it had the outcome it is purported to have had.  After all, special relativity at first blush seems to border on the miraculous, and my acceptance of it on such thin evidence does indeed appear to be a leap of faith.

But it's not.

To see why, let's go back to Harry Potter.  I reject the proposition that Harry really exists (or existed) despite the overwhelming evidence that he does (or did) because there is a theory that explains the (apparent) evidence for Harry's existence better than Harry's actual existence.  That theory is: Harry Potter is a work of fiction.  It was originally written by J.K. Rowling, and then turned into films as a commercial venture.

Why is the Harry-is-fiction theory better than the Harry-is/was-real theory?  Let me start with a bad argument: Harry is fiction because there is no evidence of the wizarding world outside of the books and the movies.  The reason this is a bad argument is that this lack of evidence is actually explained by the Harry-is-real theory: the wizarding world takes great pains to keep itself concealed from the muggle world, so it is not at all surprising that there is very little evidence of it in day-to-day life.  Moreover, the reason that the wizarding world conceals itself has a plausible explanation: if the muggle world were to learn of the reality of the wizarding world, social order would collapse.

A better argument for the Harry-is-fiction theory is that it's consistent with our current understanding of the laws of physics.  If Harry Potter really exist(s/ed) that means that magic really exists, and all of our understanding of physics goes out the window.  This is a stronger argument, but it is still weak because it is in fact possible for our understanding of physics to be wrong.  But the ways in which it can be wrong are not open-ended.  For example, the odds that even the most radical revolution in physics would permit a violation of the law of conservation of energy are indistinguishable from zero.  And yet, that is exactly the sort of change that the reality of magic would require.  In every nook and cranny of Harry's world there are vast quantities of energy being employed with no apparent source.  (Indeed, that is almost the defining characteristic of magic.)  But even that is not really the slam-dunk argument.

The slam-dunk argument for the Harry-is-fiction theory is that it explains a lot of additional observations that the Harry-is-real theory does not.  It explains the fact that everyone -- including J.K. Rowling, her publishers, the filmmakers, the booksellers -- all of these people insist that Harry Potter is fiction.  It explains the fact that all known photos of Harry Potter bear a striking resemblance to the actor Daniel Radcliffe.  It explains why none of the Harry Potter films were ever nominated for an oscar in the "best documentary" category.  It explains why no university in the world has a department of wizardry.   It explains why even on the fringiest fringes of tinfoil hattery you will not find anyone who seriously advances the theory that Harry is/was real.  The scale of conspiracy you would have to envision to explain all that in the face of the proposition that Harry Potter is/was real surely boggles even the most credulous mind.

The situation with Michelson-Morley is exactly the opposite.  We have a huge community of scientists all insisting that Michelson and Morley were real people, that they really did the experiment they are purported to have done, and that it really did have the result that it was purported to have had.  Moreover (and this is crucial) this community insists that Michelson and Morley's results have been replicated many times since the original.  How many times?  I have no idea.  Can I name even a single person who has ever replicated the M&M result?  No, I can't.  So why do I believe it?

It's because I have a GPS in my phone.

What does GPS have to do with the Michelson-Morley experiment?  It's because of the way GPS works.  The receiver in your phone listens for signals transmitted by a few dozen satellites orbiting the earth.  By measuring the timing of those signals and comparing that with the known orbits of those satellites, a GPS receiver can figure out its location.  To be accurate, the math has to take the results of not only the Michelson-Morley experiment into account (which demonstrates special relativity) but also has to make corrections for general relativity, because clocks on the surface of the earth run more slowly than clocks in orbit.  If Michelson-Morley were not true, GPS could not possibly work in the way that it is purported to work.

The fact that my GPS does in fact work is something I can directly observe every single day.  I can walk around my block or drive around town or even travel to distant lands and see that my GPS at all times reflects exactly where I am to an astonishing degree of accuracy.  There are only three possible ways to account for this:

1.  GPS works exactly as advertised, and is therefore direct, firsthand evidence available to me (and everyone else) of the correctness of the theory of relativity

2.  GPS works some other way, and there is a vast conspiracy afoot to promulgate a false story of how GPS works for some nefarious reason that I cannot even begin to imagine

3.  GPS does not actually work at all, and the fact that it seems to work is some kind of freakish coincidence

I leave it as an exercise for you, dear reader, to work out which of these is most likely to be true.

Now, applying this sort of analysis to God is not nearly as straightforward as most people (on both sides of the debate) seem to think.  The situation is not nearly as cut-and-dried as it is in the case of Harry Potter and Michelson-Morley, where the overwhelming consensus aligns with all of the available evidence.  The reason God is problematic is precisely that the majority view does not align with the scientific evidence.  The result is two bad arguments, one on each side of the debate.

On the atheist side, the bad argument against God is exactly the same as the bad argument against Harry: God is not real because there is no evidence that He is real.  There are two reasons this is a bad argument.  First, most theories of God account for the fact that the scientific evidence for Him is thin: God doesn't want to beat you over the head with proof of His existence.  He wants you to come to Him of your own free will, and you can't do that in the face of incontrovertible proof of His existence.  And second, it's simply wrong.  There is overwhelming evidence, even more accessible to you as a human than the GPS evidence for relativity, that there is something crucial missing from the scientific account of reality.  That evidence is: the laws of physics are symmetric with respect to space and time, but you have a privileged reference frame that you call "here" and "now".  The laws of physics cannot account for that.  Most atheists deal with this by sweeping it under the rug and deciding it's not important.  But if you choose to attach cosmic significance to your own experiences (and, ultimately, your own experiences are all you have, so it is not at all unreasonable to choose to attach cosmic significance to them) then you have no choice but to go beyond (our current understanding of) physics.

On the religious side, there are a whole host of bad arguments.  Most prominent among them is the argument that God must be real because He has revealed Himself through the Bible.  Or the Quran.  Or the Book of Mormon.  Or the writings of L. Ron Hubbard.  That's the thing, there are so many versions of God's Word available, and they contradict each other, so they can't all be right.

Even if you just take the Bible and ignore all the others, it just doesn't hang together, and it particularly doesn't hang together with what most Christians seem to believe: that there is one God (though somehow made of three parts), that this God is all-powerful, all-knowing, all-good, all-loving, that the OT and NT describe the same God.  Frankly, I don't understand how anyone who has read Leviticus or Joshua can believe that gentle Jesus, meek and mild, is the same deity.

In fact, the whole idea of an omniscient, omnipotent deity who requires blind faith to avoid eternal damnation makes no sense to me at all.  Omnipotence and omniscience are logically incompatible with free will, but free will is a pre-requisite for moral culpability.  So either God punishes people for things over which they have no control, or man has the power to thwart the will of God (and hence God is not omnipotent).  I see no other possibilities.

Another bad argument for God is that He must be real because the idea of a world without God leads inexorably to unbearable existential despair.  That's a bad argument because the truth doesn't care what you want.  The truth is the truth, and there's no reason to believe a priori that the truth doesn't suck.  Even if there is a God, there's no logical reason He has to be all-knowing all-powerful all-loving.  There isn't even any logical reason there has to be only one of Him.  Maybe the truth is not that there is a God, but that there are many gods.  Or maybe there is one God, but he's a trickster (or a spoiled brat), more like Loki or Trelane than Jesus.

An only slightly better argument is: I know God is real because I have personally experienced Him.  I've never heard anyone give an adequate account of how they know that what they have experienced is (say) Jesus and not Loki.  Somehow they Just Know.  And again, people claim that God tells them things that are mutually inconsistent.  Some people claim that God tells them to love thy enemies, others say God tells them to engage in jihad.  They can't all be right.  Since God has not seen fit not to reveal Himself to me in this way, I have no basis for separating the true claims from the false ones.

This same credit-assignment problem exists for ontological and cosmological arguments as well. Even if these were good arguments for some god (they aren't, but it's a moot point because...) they are not at all arguments for any particular god.  Fine-tuning could be achieved as well by a super-intelligent alien as by the God of Abraham.

A final bad argument is: look at all the sacrifices made by believers for their beliefs.  People would not endure such suffering if their beliefs were not true.  This argument is plainly false, because people sacrifice themselves for mutually-incompatible beliefs.  Early Christians martyred themselves for Jesus.  Today, Muslims martyr themselves for Allah.  In 1978, over 900 people died for Jim Jones and gave rise to the popular aphorism "drinking the Kool-Aid."

So there might be a good argument out there for believing in God, but I haven't found one, and it's not for lack of trying.  I've read the Bible (and the Quran, and the Book of Mormon, and the Bhagwan Bible, and a few others).  I've talked to Christians and Muslims and Jews.  (I've even talked to a few Scientologists, though frankly they scare the shit out of me.)  The theory that makes the most sense to me is that there are no gods, and people believe (or pretend to believe) because of a mixture of indoctrination, social pressure, and as a palliative against existential despair.

This theory explains most of the observed data, but not all of it.  In particular, Luke is still an unexplained anomaly, and that keeps me a little humble.

Happy new year, everyone!

A cheesy warning label

So... does this mean that other food products are OK?

The terrorists have won

Sony Pictures has cancelled the release of "The Interview".  :-(

[UPDATE] They've uncancelled the release!  Woohoo!

Take it from me: all dogs go to heaven

Apparently garments are being rent (by journalists if not by pet owners) over the revelation that Pope Francis never said pets go to heaven.  Maybe the pope won't say it, but you can take it from me: if you should ever find yourself in heaven in the afterlife, I promise that your beloved fido will be there too.  So sleep soundly.

The cure for ebola

Remember, you heard it here first, folks.  The cure for ebola is described in this paper, published in the World Journal of Critical Care Medicine last May.

So why hasn't anybody noticed?  Well, for starters, it's not just a cure for ebola, but a host of other conditions that kill a lot more people than ebola, including septic shock.  That puts is squarely in the too-good-to-be-true category that would make anyone hearing this news for the first time rightfully skeptical.  But I've looked into it, and it seems plausible.  The theory is that it is not the infections that do the damage, it's the metabolic by-products of your immune system fighting the infections, and specifically a buildup of hydrogen peroxide.  If you intervene to get rid of the peroxide then you can keep the patient alive long enough for the body to finish fighting off the infection.  And there is a drug already on the market that does exactly that, though it is currently used for a different purpose.  (I've been asked by Jay Pravda, the author of the paper not to reveal what this drug is.)

If anyone reading this happens to know someone doing field work with ebola victims in Africa and would be willing to put me in touch with them please drop me a line.  There's a fairly straightforward experiment that could be done to test Dr. Pravda's theory (check ebola victims for elevated levels of hydrogen peroxide in their bloodstreams) and I'd like to do what I can to get this experiment done sooner rather than later.  The situation is too urgent to just let the usual processes run their course.

Yet another reason never to fly Korean Air

Aside from the fact that Korean pilots are incompetent, a KAL executive today ordered a flight to return to the gate because she didn't like how her macadamia nut were served.

Freaking out about how your nuts are served is bad enough, but delaying an entire planeload of passengers simply because you can is way beyond the pale.

The AP (via ABC news) reports:

[The executive in question] is the oldest child of Korean Air's chairman, tycoon Cho Yang-ho. Her two siblings are also executives at South Korea's largest airline.

As the mechanic who opened the hood of the car to find the engine missing said, "Well, there's yer problem right there."  And the way things are going at KAL it would hardly surprise me to see that scene actually played out there.

Quantum teleportation demystified

About a week ago, NASA's Jet Propulsion Lab, where I used to work, published this news item about an advance in quantum Teleportation.  The progress reported in the story is real, but the description of quantum teleportation presented in the article is misleading at best.  Yes, there are certain compromises that you have to make when describing quantum mechanics to a lay audience, but you don't have to actually lie to them, which is what the cartoon at the beginning of the article does.

Here's a recap of the description of QT in the cartoon:

1. Alice has a yellow photon
2. Charlie has a pair of blue photons that are entangled
3. Charlie sends one to Alice
4. And one to Bob who stores it in his crystal memory bank
5. Alice and Bobs relationship is cordial but somewhat distant
6. As the blue photon Alice received collides with her yellow photon she measures the event and learns that the state of her photon has been teleported to Bob's
7. Alice's measuring of the event affects Bob's far-away photon, changing its state
8. However, Bob can't determine that his photon has been changed
9. until Alice sends him two bits of information over an optical fiber
10. And Bob learns his photon has changed from blue to yellow too!

There are so many problems with this description that it's hard to know where to begin, but the most egregious is the last step.  It is not true that Bob "learns" that his photon has changed state from Alice's bits.  Bob has to manipulate his photon in order to make its state the same as Alice's original photon.  The two bits that Alice sends to Bob are instructions on how Bob should manipulate the state of his photon.  In the parlance of the cartoon, Alice measures her photon and discovers that it's yellow.  She then sends a message to Bob: "Make your photon yellow."  Bob does this, and lo and behold, Bob's photon, which used to be blue, is now yellow, just like Alice's original photon.

Of course, when you add this step, the whole process seems a whole lot less mysterious and newsworthy.  In fact, it seems completely mundane.  Why even bother with the entangled photons in the first place?  Well, it's because photons are weird.  They are not either blue or yellow.  That is too simple of a model.  Photons can be blue and yellow (in the parlance of the cartoon) at the same time.  But even that doesn't really capture the truth.

A better model of a photon is a coin: there's a heads side and a tails side, but you can only ever see one or the other.  You can't look at both sides at the same time.  These photon-coins are like vampires: they don't cast reflections in mirrors.  And if you try to enlist the help of an accomplice to look at the tails side while you look at the head side, the coin vanishes.  Try as you might, you can never see both sides at once.

So you look at the heads side and it's yellow.  You turn the coin over to look at the tails side and it's red.  You turn the coin over to look at the heads side again and suddenly it has changed from yellow to blue!  You turn it over again, and the tails side, which was red, is now green.

You do this a zillion times and you discover that the coin behaves in the following way:

1. Every time you look at the heads side, it is either blue or yellow.
2. Every time you look at the tails side, it is either red or green.
3. Every time you turn the coin over, the color you see bears no relationship to the color you saw on that side the last time you looked.  As far as you can tell, the color of the newly revealed side is always completely random.
4. However, you never actually see the coin change color.  Whatever side you are looking at stays the same color until you turn it over to look at the other side.

You also have a magic coin vending machine: you put one coin in, and two coins come out.  (Let us call this Vending Machine D for Duplicator).  Each one is half the size of the original, and they come out of the machine edge-on so that you can't see either side.  But each of these smaller coins behaves exactly like the larger coins did: the heads side is always blue or yellow, the tails side is always red or green.  But here's the kicker: if you take a pair of coins that just came out of Vending Machine D and turn them both over the same way (i.e. both heads or both tails) the colors on the two coins will always be the same.  But this is true only the first time you look at any given pair of coins.  After that the coins lose their magical connection and their colors are just random when you turn the over again.

What quantum teleportation does is allow you to transfer the magic connection from a pair of half-size coins from Vending Machine D to a pair of (previously unconnected) full-size coins [1].  It uses two additional vending machines, which I will call Vending Machines A and B.  Vending Machine A is on Alice's side, and Vending Machine B is on Bob's side.

Vending machine A has two coin slots, one for a full-size coin and one for a half-size coin.  It also has a display that flashes a number between 1 and 4.  Alice inserts her coins and notes what number the machine flashes.  She then calls Bob on the phone and tells him what the number was.

Vending machine B has a single half-size coin slot, and a knob with four settings numbered, as you might expect, from 1 to 4.  Bob sets the knob to the setting corresponding to the number that Alice told him on the phone.  He then inserts his half-sized coin, which the machine spits right back out.  (Whether or not this is the "same coin" turns out to be a Very Deep Question which we will ignore here.)  Like Vending Machine D, this half-size coin comes out edge-on, so Bob can choose whether to look at the heads side or tails side first.  Whichever he chooses, the color will be the same as that on the corresponding side of the full-size coin that Alice inserted into Vending Machine A.

That is a much more accurate description of quantum teleportation, and I think it's one that a layman is capable of grasping.  So why didn't NASA describe it that way?  Well, I asked them.  I sent an email to the contact person listed on the article, and here is the response I got:

Hi Ron, I very much appreciate your feedback. I took it back to the
scientists and they explained while the photon would not be initially blue
per se, we made this choice ‹ to say that the photon is initially blue ‹
to communicate the broad idea for the public. The question of at which
moment the photon is ³changed² cannot be answered with quantum mechanics
and is too subtle a point for our purpose, which is to give the public a
general sense of this experiment.

To which I responded:

> The question of at which moment the photon is ³changed² cannot be answered with quantum mechanics 

Yes, it can. And actually, this points out another problem with your presentation: when Bob receives Alice’s bits, he uses that information to apply one of four transformations to his photon. It is Bob’s action that changes his photon’s state into the state of Alice’s original photon. And that is the *only* time that Bob’s photon changes state. 

> and is too subtle a point for our purpose, which is to give the public a general sense of this experiment.

I think you underestimate your readers, and do them (and NASA) a grave disservice by not telling them the truth, particularly since this particular non-truth makes quantum teleportation seem much more mysterious than it really is. At the very least you should explicitly say that your presentation is an oversimplification, and give your readers a pointer to where they can get a more accurate explanation. I would be happy to write up a more accurate (but still accessible) description of quantum teleportation if you don’t have the time to do it yourself.

I never got a reply to that, which is what motivated me to publish this explanation here.

It frustrates me to no end that the popular press continues to publish false and misleading information about quantum mechanics in general, and about entanglement in particular.  There is no legitimate reason for it.  So why do they do it?  Well, the description in the NASA article is certainly more dramatic and mysterious.  For starters, it sounds a lot more like "real" teleportation than the more accurate description.  The fact that Alice has to send Bob instructions on how to set the dial on Vending Machine B takes a lot of the charm out of it.  In fact, you have to think pretty deeply about the behavior of the coins in order to see why quantum teleportation is interesting at all.  After all, why can't the four settings of the machine simply be an encoding of the colors on the two sides of the coin?  To answer that question you have to get into a discussion of the Bell inequalities, but that can also be done in a way that is accessible to laymen.

So why does the popular press so consistently get this wrong?  And why does the physics community let them get away with it?  Quite simply (I conjecture) because physicists think that it's good for business for the public to perceive what they do as indistinguishable from magic.  But for scientists to allow misinformation to promulgate is hypocritical, and fraught with all manner of peril.  When physicists endorse nonsense like "Alice's measuring of the event affects Bob's far-away photon, changing its state" on the grounds that it's a harmless white lie, it makes it that much harder to combat the not-so-white lies.  In a world where rejecting science can pose existential threats, deliberately obfuscating the truth is not a trivial transgression.  The fact of the matter is that quantum mechanics is not the intractable mystery that it has been made out to be, and allowing this perception to persist for the sake of grant money is making a deal with the devil.

---
[1] Since I just got finished ranting about the evils of allowing scientific misinformation to promulgate I should point out that this is slightly inaccurate.  Quantum teleportation does not transfer the magic connection to a pair of previously unconnected coins, it transfers it from one member of a pair of connected coins to one previously unconnected coin.  Of course, you can do this process twice in order to produce the effect as I describe it, so I submit that this really is a white lie.  But I will let you, gentle reader, be the judge of that.

Yet another reason to despise Groupon

Aside from being parasites, they are now brazenly trying to steal the GNOME Foundation's GNOME trademark.

Assholes.

[UPDATE:] Groupon backed down in the face of public pressure.

The coolest thing ever, again

I thought this photo of Saturn from above was the coolest thing ever until I saw this:

That is a picture of a comet.  Not in the background, mind you, the foreground.  It was taken by the Rosetta spacecraft, which is currently in orbit around said comet (which is burdened by the unwieldy name of 67P/ Churyumov-Gerasimenko).  The scale is just under a meter per pixel.  If there was a human walking around down there, you could see her (just barely).  The photo is about 800 meters (half a mile) from side to side.

In the next few days, a lander will detach from the spacecraft and, if all goes well, will actually land on the surface of the comet.  This will be only the fifth place in the universe from which we will have photos from the surface, the other four being the moon, Mars, Venus, Titan (one photo), and of course, Earth.

My nominee for second-coolest-thing-ever is this awe-inspiring backlit shot of Saturn:

You can find more of these at the Cassini images hall of fame.

It is truly an amazing universe we live in.  (Too bad we're blithely destroying the best part of it.)

Harris, Aflek, Dawkins, oh my!

It's been a busy couple of days for people who like to opine on the evils of Islam and Islamophobia.  Sam Harris and Ben Affleck kicked things off with a segment on Bill Maher's show where they had quite the scuffle over whether or not Harris was justified in his anti-Islamic rhetoric, or whether Affleck was trying to deny the truth in the name of political correctness.

Lots and lots and lots of people weighed in after that, and there are so many logical fallacies being brandished on both sides that it's hard to know where to begin.  For example, from Reza Aslan we have an argument from authority:

Sam Harris, to me, gives atheism a bad name because he comes from a tradition of atheism that is really disconnected from the titans of intellectual, philosophical atheism who gave birth to the modern world. These were experts in religion who, from a position of expertise, criticized religion. Sam Harris is a neuroscientist; he knows as much about religion as I do about neuroscience. The difference is that I don’t go around writing books about neuroscience.

Hemant Mehta follows up with some ad hominems:

Aslan seems to suffer from a mix of neediness (brought on by insecurity) and outright hubris. It might be a defect of his imagination ...

Guy Harrison offers up a straw man:

Reading the Koran and being aware of its potential to inspire some people to violence do not lead me to fear every Muslim on Earth

Surprisingly, Richard Dawkins starts out by being the voice of reason:

“Religion itself is not responsible for this… It’s also this feeling of political involvement. It’s a feeling that it’s ‘us against them.’ And I think that quite a large number of young Muslims feel kind of beleaguered against the rest of the world. [Emphasis added.]

Indeed.  Alas, he does not go on to ask the obvious question: how much of this beleaguerment might be attributable to the kinds of blanket statements that are made by the likes of Harris and Dawkins?  Instead he jumps straight to affirming the consequent:

And so religion in some sense might be just an excuse, but I do think that a dominant part of the motivation for these young men has to be religion.”

For a community supposedly dedicated to reason, the amount of unreasonableness being un-self-reflectedly bandied about is truly disheartening.

Utterly lost in the confusion is this central claim raised by Aslan:

There is a fundamental misunderstanding among these critics of religion in that they believe, first and foremost, that people get their values, their morals from their scripture, when in reality the exact opposite is true. You bring your morals and your values to the scriptures; you don’t extract them from them.

I don't want to take a side here on whether or not this claim is true.  I believe it is, but that's not the point.  The point is no one is talking about this despite the fact that it's the most important thing that got said in the entire discussion.  Why?  Because if it's true then Harris & co. are wrong, and if it's false then Aflek & co. are wrong.  So why is so much ink being spilled slinging logical fallacies around and absolutely no effort is going into determining the truth or falsity of a crucial empirical claim that could actually inform the debate?  Perhaps atheists, too, bring their prejudices to the scriptures (or the data) rather than the other way around.

So to lead by example, I'd like to offer up an actual data point.  That link goes to the Wikipedia page on the application of Sharia law by country.  I don't have time to slice-and-dice the numbers, but even a cursory glance will show that although there are major populations of Muslims all over the globe, those countries where Sharia law is in full effect are overwhelmingly found in the Middle East.  Last I checked, the Quran is the same all over the world, so this seems to me to be very strong evidence that the violence and barbarism often associated with Islam (and, to be sure, that's a very real problem) cannot be accounted for merely by the words in the Quran.

But I don't have a Ph.D. in religious studies, so what do I know?

Parallel universes and the arrow of time

In a previous post about quantum mechanics and parallel universes I ended with a puzzle:

All measurements are in principle reversible. Imagine that we could actually carry out this program of undoing the myriad entanglements that constitute your making a particular observation. What would be the subjective sensation, i.e. what would it "feel like" if this were done to you?

If you haven't read the previous post, please do before you read the rest of this one, otherwise this won't make any sense.  The point of this puzzle is not the answer, but the process by which one arrives at the answer.  Knowing the answer and understanding why it is the right answer are not the same thing, and in this case the latter is much more important than the former.

The intuitive answer to the question is that it would feel something like having time run backwards, but this is wrong.  The reason it is wrong goes to the very heart of the nature of reality.  To prime your mind to accept that the answer I am going to give is in fact correct I'm going to start by giving you the answer to what seems like it should be a completely different problem but is in fact almost exactly the same problem.  It is a classic problem first contemplated by Albert Einstein: what would it feel like to travel at the speed of light?

The intuitive answer to this question is that it would feel like a thrill ride, like zipping through the universe really, really fast.  Pluto is about four light-hours away, so if you headed towards it at the speed of light you'd get there four hours later, right?  How could it possibly be otherwise?

The unintuitive but undeniable fact of the matter is that the speed of light is the same in all reference frames.  This was shown experimentally in 1887 by the Michelson-Morley experiment, but it was actually predicted by James Clerk Maxwell 23 years earlier, in 1864.  Maxwell's equations for electromagnetic fields predicted the existence of electromagnetic waves that propagated at the (already well known) speed of light, but the equations made this prediction without any mention of a frame of reference.  The significance of this was not understood except in retrospect: it was forty years before Einstein first took the mathematical prediction and the experimental verification seriously and derived the theory of relativity, which can be summed up in the following pithy slogan: the speed of light is the universal reference.  Everything is always moving at the speed of light through space-time.  When you move faster through space you move slower through time.  When you move through space at the speed of light, time stops.  So what it would "feel like" to travel to Pluto at the speed of light is not that it would take four hours, but that you would get there instantaneously.  In other words, you would arrive at the same time that you left.

Now, an interesting thing happens if you arrive at the same time you left, and that is that you can no longer distinguish between leaving and arriving.  A trip from earth to pluto at the speed of light is indistinguishable (to the traveller) from a trip from pluto to earth at the speed of light.  Both consist simply of being at earth and pluto (and everywhere in between) at the same time (in the traveler's reference frame).  How do we reconcile this with the fact that an observer back on earth can easily tell the difference between a beam of light traveling in one direction rather than the other?

Here's a clue: the solutions of Maxwell's equations that predict electromagnetic waves are time-symmetric, that is, they predict the existence not only of waves traveling at the speed of light c, but they also predict waves traveling at speed minus c, that is, waves that move backwards in time.  These solutions are usually discarded out of hand as being "unphysical", but if Einstein teaches us anything it is that discarding mathematical results just because they don't "feel right" can blind us to deep truths.  (And indeed, if we take seriously the idea that there are electromagnetic waves moving backwards in time what we end up with is a completely self-consistent theory called the transactional interpretation of quantum mechanics.)

So what happens in QM if we really take the math seriously?  Well, we end up with a deeply unintuitive but nonetheless self-consistent description of the universe (except near a black hole -- physics is still working on that).  The math tells us that our classical reality is merely an approximation of the underlying metaphysical truth, just as Galilean relativity (where space and time are separate things) is.  The reason we think particles exist is not because they really exist, but because when you slice-and-dice the wavefunction in a certain way you end up with something that acts like (but isn't really) a bunch of classical entities all of which agree on a set of measurements (i.e. are in classical correlation with each other).

But, like Maxwell's equations, the Schroedinger equation is time-symmetric.  You can run it backwards as well as forwards.  And if you throw relativity into the mix then space and time are equivalent, and you can't distinguish forwards versus backwards any more than you can left versus right or up versus down.  In other words, the wave function is a static four-dimensional "thing" (for want of a more general noun) out of which space, time, and classical reality "emerge" when you slice it up in certain ways.  But there is nothing in the math that says that the slice that we are living in (what we call classical reality) is in any way special.  You can slice up the wave function in a different way and get a different universe.  All of this seems to be very much at odds with the (apparently) undeniable truth that our universe is special (at least to us), and that time only moves in one direction.

But again we must be very careful about trusting our intuitions, which have been proven wrong time and time again (the pun being a quantum superposition of intended and not :-)  The math says time doesn't "flow", just as it says particles aren't real.  So why does it appear to flow?

Again, we will approach the issue of time obliquely by drawing an analogy with particles.  Why do we think particles exist?  Because we can measure them.  But QM tells us that the results of our measurements indicate the presence of particles despite the fact that there are in fact no particles (or, if you're a multiple-worlder, that there must be other universes).  Let us go through the exact same mental exercise with respect to time: why do we think that time moves in one direction?  Because there is this manifest asymmetry: we can remember the past, but we can't remember the future.  And it's not just us: the universe "remembers" the past but not the future, which is to say, the universe contains information about the past (in books, for example) but not about the future.

There is another way to describe this asymmetry: we can "travel" forwards through time but we can't travel backwards.  Except that we actually can (in principle) "travel backwards in time" by "rewinding the universe" i.e. undoing all the entanglements that led to the present situation.  So let us go back and consider the opening puzzle: what would it feel like to "travel backwards in time" this way, to have yourself "reversed"?  Picture the scene: you would have to go into a sealed chamber of the sort that houses Shroedinger's cats.  Once safely ensconced inside, you would make some kind of measurement.  It doesn't really matter what kind, but let's suppose you made a quantum measurement just to keep things simple.  So there is some particle in the box with you, and you arrange for that particle to become entangled with some measurement apparatus and thence with your brain.  Your brain is now, by virtue of having become entangled with the particle in the having-observed-the-particle state.  You can remember making the measurement.  You know what the result of the measurement was.  All of the atoms in your brain are now acting together to make you appear like a classical system in classical correlation with itself and the measuring device.  This is what makes you think you know the state of the particle (even though in reality there is no particle).

Now we turn on the magic reverse-o-matic ray.  One by one, all of the entanglements that led you to be in the having-observed-the-particle state are undone.  This involves reversing the entanglements in your brain, the measuring device, and everything else inside the box (including the magic revers-o-matic ray, but since this is a thought experiment we can ignore the obvious difficulties that entails).  When this process is over, what mental state are you in?  Well, you are in exactly the same mental state that you were in before the whole process began.  You have no memory of having measured the particle.  You would have no memory of having the reverse-o-matic ray turned on.  And since completing the erasure involved undoing all of the entanglements in the box resulting from the initial measurement, you would not be able to find any evidence anywhere inside the box that any of this had happened.

In other words, the subjective sensation of undergoing a macroscopic quantum erasure is exactly the same as the subjective sensation of having nothing happen to you at all!  In fact, the only evidence that you would have that you had in fact undergone a quantum erasure is that when you emerged from the box after the experiment, you would find that more time had elapsed there than could be accounted for by what you experienced.  (Note the similarity to relativistic time-dilation.  Exercise: what would happen if you took a clock inside the box with you?)

So this is an unsatisfying sort of time-travel because it is experimentally indistinguishable from the normal state of affairs.  What we really mean when we fantasize about time travel is moving into the past with the information contained in our brains and bodies intact.  In other words, we're thinking about transporting information about the present into the past, at which point it becomes information about the future.  We think this might be possible because we think we're classical entities, coherent material things that move volitionally through space but are swept inexorably through time by some sort of "flow", and if we could just figure out how to "move through time" the way we move through space that we might be able to swim against the tide.

But we are not classical entities.

To understand the truth you need to adopt a completely different mindset about what you are.  Again, I will approach this obliquely starting with a more familiar concept: you think you're a human being, a physical entity with some coherent identity that remains intact through changes like growing older and learning new things.  (It is this abstract identity that we imagine moving into the past when we fantasize about time travel.)  What does this identity consist of?  It can't be the atoms in your body because those are constantly being swapped out for new atoms.  Maybe it is the arrangement of those atoms, at least at some high level of abstraction.  But the arrangement of your atoms today is radically different from what it was the day you were born.  In what sense, then, are you the "same person"?

The reason we consider ourselves to be in some sense the "same person" throughout our lives is because there is a continuous sequence of "yous" that lead from cradle to grave.  You today may be radically different from when you were born, but in between there is a smooth transition from one to the other.  At any instant in time, the you of that instant is very similar to the you one second previously, and very very similar to the you one Planck time earlier.

Imagine for a moment that you could take a God's-eye view of the universe and see all four dimensions at once.  Consider two different instances of "you" at two different times.  Is there any way you could tell which is the "earlier" you and which is the "later" you?  If the two times are far apart then you could look at which you appears older, but what if the times were just, say, a minute apart?  Well, you could still tell (if you were God) by examining your mental state: the later you would contain information that the earlier you didn't, namely, memories of the events that transpired during the intervening minute.  In fact, if you were presented with an unordered set of all the you's that have ever existed you could easily reassemble them in their proper order simply by looking at which ones contain information about which other ones.  If You-A remembers You-B then You-A must come after You-B.  It can never be the case that You-A remembers You-B and You-B remembers You-A because then one of those you's would be "remembering" the future, and that's not possible.

But the crucial point is not that it is impossible but why it is impossible.  The reason it is impossible is not that time only "flows" one way (that explanation would beg the question).  The reason it is impossible is that memories are entanglements just as measurements are.  In fact, memories are measurements, because every memory is a memory of something.  So it is not that a memory can't be reversed (it can), it is that in order to reverse a memory you have to reverse all the entanglements that comprise that memory.

Now, here's the killer question: given that the observable result of undergoing quantum erasure is indistinguishable from having nothing in particular happen to you at all, how can you be sure that at some point in your life it hasn't happened to you?

The answer is: you can't be sure it hasn't happened to you!  It is possible that you (and the rest of the universe) have undergone quantum erasure at some point.  In fact, it's possible that it happens regularly, that the entire universe is constantly being rolled back and replayed from different points in "time".  In fact, the universe is chock-full of little quantum "isolation boxes" where this happens constantly!  These are called "vacuum fluctuations" or "spontaneous pair generation", where a particle and an anti-particle just materialize out of nothing and almost immediately annihilate each other.  The members of a spontaneously generated pair are entangled.  The annihilation process "undoes" the entanglement and returns the universe to its previous state.

The punch line is this: the statement that we can't time-travel into the past is exactly the same as the statement that we can only remember the past.  It is not the case that one causes the other, it is that the two things are logically equivalent.    Your perception of "traveling through time" emerges from your mental states and not the other way around.  You feel like you are "traveling forward through time" because your mental states have this natural order to them.  You can remember the past and not the future because whatever you remember is your past.  The laws of quantum mechanics (and entanglement in particular) insure that what any given instance of you remembers appears to be a continuous and coherent sequence that behaves according to regularities that we call the laws of physics.  But in fact you do not travel through time, because at root there is no you, and there is no time.  There is only the wavefunction, from which you emerge as an approximation.

It's over

Salon has a pithy summary of the gay marriage scoreboard:

On Monday, the Supreme Court denied review to seven gay-marriage cases, allowing lower-court rulings in favor of marriage equality to stand. In effect, this brought the tally of states recognizing same-sex unions from 19 to 30. Then yesterday, the Ninth Circuit Court of Appeals found gay-marriage bans in Idaho and Nevada unconstitutional; with Alaska, Arizona, and Montana also under the Ninth Circuit’s jurisdiction, gay-marriage bans in those states are expected to fall easily, bringing the tally of states recognizing gay unions to 35.

That is a staggering turnaround.  Two days ago, there were 19 states where gay marriage was legal.  Now that number is 35.  In other words, there are now fewer states that don't allow gay marriage than did allow it two days ago.  If this were a football game, there would still be some time on the clock, but the fans would be leaving the stadium.

While I hesitate to declare victory prematurely, I really can't see any possible way that this could turn around now.  The score in terms of lower court decisions is 40-2, with only lower courts in Louisiana and Tennessee coming down (unsurprisingly) on the side of continuing discrimination against gays.  The worst-case scenario is that the fifth or sixth circuit will uphold a gay marriage ban, at which point SCOTUS will no longer be able to duck the issue the way they did on Monday.  But it is inconceivable that SCOTUS will reverse the overwhelming majority of lower court decisions.  By the time the case comes around to them again (if it does) there will be tens of thousands, maybe hundreds of thousands, of married gay couples all over the U.S.  They will be in California and Massachusetts and Kansas and Utah.  (Utah!)  They will be in Nevada and Oklahoma and Virginia and Illinois and New Mexico.  They will be in Pennsylvania and Maine and Vermont and Rhode Island.  They will be in... well, you get the idea.

They will even be in Texas and Tennessee and Louisiana and the twelve other holdouts for bigotry, because people move in this country.  And not a single one of those states will be able to show any actual harm that has been done to anyone by letting gays get married.  Zero.  Zip.  Nada.  That is, and has always been, the central issue.  All of these chicken-little predictions of the horrible consequences of gay marriage have been -- always have been -- wrong.  And now that wrongness has been removed from the realm of speculation and has become demonstrable.

If there is doubt in anyone's mind that this war is over, they need only look at the latest poll numbers among 18-39 year olds.  In that demographic, support for gay marriage is an overwhelming 72%.  Anti-gay bigotry in the U.S. is, quite literally, dying.

Good riddance.