I Saw a Cat Who Wasn't There...

One of the many mysteries of quantum mechanics is why things that are very small act so weirdly, compared to everyday, normal-sized things. After all, everyday, normal-sized things are made up of the very small things, so we might expect them to behave like they are groups of the very small things. But they don't, and physicists have long scratched their collective heads as to why that is.

Strike a Superpose

One of those weird things very small objects do is called "quantum superposition." Physical systems, like the incredibly tiny subatomic particles we call electrons, can exist in a bunch of different states. They have different properties, like their electrical charge or energy level, which is called "spin." Each of these properties can show up in different ways: Electrons have a negative electrical charge, but they can have different energy levels. The combination of a certain energy level and the negative charge is a state.

Lots of different experiments, both physical and "thought-experiments," have shown that electrons and many other very tiny subatomic particles show up in one state or another depending on which experiment is being done. An experiment designed to show electrons exist in state A, for example, whatever that state is, will find electrons are in state A. But an experiment on the same electrons that's supposed to show they're in state B will show they are indeed in state B. The electrons seem to hang out in some kind of in-between condition that collapses into one state or another when they are measured.

A physicist named Edwin Schrödinger devised a thought-experiment that showed just how wacky a situation superposition was (it's a thought-experiment because doing it for real would be mean and get you arrested). Suppose, he said, there was a cat inside a closed box. Without opening the lid, you can't see the cat. Now suppose there is a mechanism that would release poison gas into the box and ice poor Whiskers, depending on whether a specific nuclear particle decayed or not. That decay is completely random; it may happen but it isn't guaranteed to happen.

This means, Schrödinger said, that Whiskers is either alive or he's dead, depending on whether the nuclear decay has happened. But the observer doesn't know which until the box opens, meaning that for all practical purposes, to all outside observers Whiskers is both dead and alive at the same time and won't "collapse" into one state or another until someone opens the box lid and looks. One purpose of Schrödingers' experiment was to try to illustrate how superposition works, of course. But another was to establish how different the quantum subatomic world was from the world we experience through our senses and measurements. Measurement and experimentation force the electron into one state or another as the wave function of its superposition collapses. The state really does depend on the measurement. But Whiskers is really alive or really toast, no matter whether we look in the box or not. We don't know which one he is, but that doesn't change that he is one or the other. But on the quantum scale, the electron really isn't one or the other until we look at it.

So one might expect these macroscopic things to behave like an aggregation of quantum-scale things, because that's what they are. Only they don't: superposition doesn't occur on the macroscopic scale. We do not need the wave function of a tuna fish sandwich to collapse in order to detect or experience it. Scientists have never really been able to explain very well why this is.

Super-solving?

Schrödinger did more than imagine experiments to tick off PETA. He also developed Schrödinger's Equation, which can be solved to describe quantum behavior for limited systems, such as a single particle. Particle physicist and retired Anglican priest John Polkinghorne has described it as a matter of language -- what can't be expressed with words can be expressed with equations. So while everyday language (and everyday heads) can't get clear on something being both a particle and a wave at the same time, mathematical language can. This is what Schrödinger's Equation does.

In principle, the equation should be able to describe not simply one particle but larger groups of particles, such as cats or people. Even though we never see larger objects demonstrate superposition or quantum indeterminancy, the equation should be able to describe them in that way. But even the top supercomputers balk at trying to solve Schrödinger's Equation for anything larger than a few thousand subatomic particles. You can see why. The equation for one electron suggests one of two solutions; one state or another, particle or wave. The equation for two electrons has four solutions: A is a particle and B is a wave, A is a particle and B is a particle, A is a wave and B is a particle or A is a wave and B is a wave. It only gets worse, from the point of view of those solving the equations. Three electrons means eight possible solutions, four electrons would mean 24 possible solutions, and so on. When we realize that everyday objects like cats, people and Twinkies consist of billions of atoms, each with its own number of electrons being quantumly uncertain, it becomes pretty clear why it would be difficult for is to figure out superposition for those everyday objects. The math is too complex and like a juggler working one too many things into the pattern, even a computer loses track of what it's doing.

It might seem like the answer is just to wait for better, faster computers. Schrödinger's Equation is not an inherently unsolvable problem like computing the last digit of pi. It has a solution, but like many solvable equations it gets pretty tough to work when the terms get really big. A + B = C, for example, is a solvable equation: Given any two of the terms, the third can be computed. If I know A=1 and C=3, then I can figure out that B=2. Now, as the terms get larger and larger, the solving takes more and more time. But today's computers can solve equations and make calculations that would have locked up a TRS-80 in a heartbeat, so more powerful computers could be the answer. That would work, except for one reality: Even the simplest math computation takes time and energy.

Because we can almost intuitively solve something like "1+1=2" faster than we can say it, we may overlook this, but a finite amount of time elapsed between when I started to say the equation and when I solved it. We could obviously see that a complex equation would take more time, but even a simple equation takes more time as the terms get larger. Simple addition of two single digit numbers takes next to no time at all, but make those even two-digit numbers and it takes an extra beat. More digits will involve still more time. Computers work much much faster than we do, but they still require measurable time to figure answers. It's possible to imagine a fairly simple equation that uses terms so large it could take a computer a very long time to solve it. In fact, there are some equations that would take more time to solve than the universe may have left. The so-called "heat death" of the universe is immensely far into the future, but if current cosmology has it right, there will come a time when the universe has used up all its energy and will be for all intents and purposes "dead." The equation may have a solution, but the universe has said we are out of time and have to put our pencils down even though we are not finished.

If I use a pencil and paper to work a problem, my body uses energy to physically move my hand around the sheet of paper. Even if I solve it "in my head," energy is expended, since the brain cells that do the calculations work by electrical impulses (albeit somewhat slowly, in some cases). Calculators solve math problems more quickly, but they use more energy to do it. Computers work even more quickly than calculators, but only at the cost of a still higher energy use. That energy produces heat, which is why computer towers have fans in them to cool off the processors. A supercomputer can do millions of operations in an eyeblink, but requires huge air-conditioning units to keep it cooled because its operations require -- you guessed it -- even more energy.

The universe has a finite amount of energy. The first law of thermodynamics says that energy can't be created or destroyed, only transformed from one form to another. The second law says that at each transformation, the energy involved is less and less useful for work, meaning more and more energy on hand that can't be used to do things -- like mathematical calculations. This non-usable energy is called "entropy," and in every closed system, entropy increases over time. This is how the universe winds down in the manner mentioned above. And so our solvable equation with the too-large terms in it goes unsolved because the universe runs out of time to solve it and energy to perform the calculations -- in fact, the energy used in the attempt to solve it speeds up the process of dying! Had I known about entropy while a student I might have tried to point out that math homework hastened the death of the universe but I suspect I would not have been heeded.

So, is Schrödinger's Equation potentially solvable for a macroscopic object? It would seem, given infinite energy and time, the answer would be yes. But the universe contains finite energy and will exist for only a finite time, meaning that Schrödinger's Equation won't be solved for a macroscopic object even if it could be.

And in this case, the lack of a solution means that macroscopic objects don't exhibit quantum behavior and they're particles or they're waves, period. Schrödinger's Equation is not just a blackboard decorator -- it describes things that actually happen. If it can't be solved that means what it's supposed to describe can't happen.

Invoking a Deity

But suppose there was infinite energy -- call it "omnipotence." And suppose there was infinite time -- call it "eternity." That's not precisely what eternity is, but in this instance we can use that word. And suppose there was a being that possessed omnipotence and existed in eternity...but you see where I'm going. Macroscopic objects, like, say, people, and systems that contain them like, say, universes, don't show quantum behavior in situations with finite energy and time, giving them a sense of determinancy. Smack one billiard ball with another and it will carom off in a predictable direction rather than disappear and materialize on Neptune. The chance that it would do so exists, but it's so small that the universe is almost certainly too limited to contain that particular outcome. But if an omnipotent being in eternity sees that same action, then such a being could indeed see the interplanetary outcome, or ones even weirder than that.

A lot of times our talk of God suggests that God knows the future before it happens. Such a view is implied if we claim God is all-knowing or omniscient. This leaves us with questions, though, such as why God would have created human beings with free will knowing that we would abuse it and cause others to suffer. But the omniscient God would also know of possible futures in which an individual chose to use his or her free will to not harm someone else. And, in fact, of all possible futures, deriving from all possible choices and all possible combinations of matter and every possible solution to Schrödinger's Equation. The omniscient God could know this because God's perspective is not limited by entropy or time, and thus equations unsolvable in our universe would be solvable for God.

So we don't say that God knows the future; God actually knows all possible futures.

The thought-experiment Schrödinger created is not technically an example of a macroscopic object showing quantum behavior. Remember, the poison gas was released or contained based on the actions of a single atom. The cat's survival is affected by quantum behavior, but the cat itself remains non-quantum, whether it has passed on from poison or not. Schrödinger said that because of the weirdness of quantum indeterminancy, an observer could not know if the cat was alive or dead before the box opened. Macroscopic quantum behavior leads to an even weirder question than Schrödinger's. He only asked if the cat was alive or dead. The macroscopic question is, "Is the cat even inside the box?"

And it would seem that the answer, in the fullest sense, is "God only knows."


(This piece came after some reflection on reading this paper at The Physics arXiv Blog at medium.com. Although it deals more with one of the mathematical features of macroscopic quantum indeterminancy, the P≠NP problem, this wound up headed a different way. Thanks for reading, if you have!)

Quis Custodiet?

It's a sin to spoil a book without warning, just as it is to kill a mockingbird. So here's your warning; spoilers below!

Every great story needs a villain and in the story of how Go Set a Watchman came into being, the villain is most probably HarperCollins Publishing Company.

Harper Lee. of course, wrote one of the nation's most beloved novels, To Kill a Mockingbird. It was made into one of the nation's most beloved movies, with that love owing no small debt to the fact that one of the nation's most beloved actors, Gregory Peck, considered his portrayal of small-town lawyer and paragon of decency Atticus Finch his finest role. Mockingbird's telling of how Atticus defended a black man accused of raping a white woman in 1930s Alabama is a frequent school assignment read, with the novel adding layers of Jean Louise "Scout" Finch's awakening to the realities of the world around her that the movie sets aside to focus on the trial. Several generations of middle-schoolers have made Mockingbird one of their first acquaintances with the experience of novels being as much about ideas as they are about plots and characters, and for many of them that first association has been a lasting one.

Mockingbird was published in 1960 and remained Lee's only novel. Whether or not she had ever even finished another full-length manuscript was open to question, until her representatives announced in late 2014 that the manuscript of Watchman had been discovered in a safe-deposit box. According to the story, it was the original novel that the J. B. Lippincott publishing company purchased, and it was over the course of working with editor Tay Hohoff that the idea of building an entire novel from one of the flashback sequences that Lee developed Mockingbird.

But the completed Watchman manuscript, or at least one of its revisions, still existed and it was that which HarperCollins, which now owns Lippincott's copyrights and other assets, began hyping in 2014 and publicizing until publishing it this month. What makes the company villainous instead of heroic is just how much of a disservice to Lee, Mockingbird and their legacy Watchman is. A number of reviewers have pointed out that without Mockingbird, no one would publish Watchman as is. Lee's own advanced age and health left her unable to contribute to preparing the manuscript for publication, and what rests between the enticingly retro covers of Watchman shows that clearly. It's a set of barely-connected episodes as an adult Jean Louise, on her annual visit to Maycomb from where she now lives in New York City, encounters up close and personally the effects of the civil rights movement and the racism that makes it necessary. That racism is in her own family, in her prospective fiance and in her hero, Atticus himself. While not a sheet-wearing cross-burner, Atticus is a member of one of the citizens groups that opposes federal court rulings forcing integration in the South. In one of the many long and overwrought dialogues that make Watchman a chore to read, he explains that he believes the African-Americans of the South have yet not enough exposure to "white civilization" to be entrusted with full citizenship and all its rights. Jean Louise, remembering only his teaching from earlier in her life about loving all equally and his defense of a black man accused of raping a white woman, is devastated by learning what Atticus thinks and breaks with him, vowing to leave Maycomb and never return. She partially reconciles with him by finally removing him from the pedestal where she had placed him and allowing him to be a flawed human being instead of an infallible deity.

As a part of its fairly brilliant publicity campaign, HarperCollins teased first the idea of the book, then the cover, and finally a preview chapter that featured Atticus's backward views on full display. Buzz, of course, was inevitable. I lost count of the clickbait headlines along the lines of "Atticus is now a racist!" The campaign, plus the deeply-felt sentiment for Mockingbird, made Watchman review-proof, which is good thing for it. Although it features several wonderful scenes of the adult Jean Louise recalling her iconoclastic upbringing, written with the combination of youthful worldview filtered through adult language of which Lee is a master, it is in many places curiously lifeless. The temptation is to see the difference sorting out as the dull scenes being those not yet edited when Watchman was abandoned for Mockingbird, but there's probably no way of knowing.

It's not as though Watchman couldn't have been revised to make a proper sequel to Mockingbird. Atticus's seemingly divided character could have been an examination of how someone who has privately awful thoughts may publicly do noble things -- how could the two tendencies be reconciled? How could a man who believed in saying, "Be patient," to a group of people still oppressed almost a hundred years after they were supposed to be have been freed also put his profession and even his personal safety on the line to try to fight an unjust accusation against one of those same people? Jean Louise the adult white woman has an encounter with Calpurnia, the African-American woman who mostly raised her and was almost a surrogate mother to Scout, that is cold and correct and suspicious, an incident that shows how important Martin Luther King's message of ending segregation by preaching love really was, as well as what a tightrope walk it was to try to maintain. The actual arc of the novel -- Jean Louise discovers her sainted father is actually a flawed human being -- is almost trivial, and becomes even more so if you read Watchman without giving it the context and resonance lent it by Mockingbird.

Did Hohoff and Lee spend time trying to work Watchman into such a form, to address and handle those ideas the way that Mockingbird tried to handle its subjects?  An executive who worked at Lippincott when Mockingbird was published says they probably didn't, but we don't really know, and even if they did, that version of the manuscript was not the one in the safe deposit box. And it's probable that HarperCollins didn't concern themselves with that paper once they realized what a truckload of negotiable paper it represented. They were at least right about that, as Amazon reported pre-sales as big as Harry Potter and the Deathly Hallows.

I've read lots of theories. Some suggest Watchman helps deflate a concept that Mockingbird promotes, that of the "white savior" figure of Atticus aiding the poor helpless people of color. Others say it "exposes the dark side of Atticus Finch." All of these are basically silly ideas. Atticus is a fictional character, and he has whatever thoughts, beliefs, habits and words his creator wishes to give him. If, as the public history of Watchman says, it was written first, then it's far more likely that Lee developed him from a man committed to justice and the law -- even for those he considered backwards and uncivilized -- to a man committed to equality and love. The supposedly more realistic Atticus of Watchman became the compassionate and decent vested and spectacled paladin of Mockingbird, not the other way around.

Watchman, once discovered, should not have stayed hidden. Gregory Peck's son Stephen believes his father, who became good friends with Harper Lee, would have counseled her against publishing it but would definitely approved of its preservation with her papers for use by literature scholars. Stephen also believes that, had this version of Watchman appeared during his father's lifetime and someone suggested filming it, his father would have taken a pass on its version of Atticus.

It would have been nice if HarperCollins had done the same.

Maybe You Will Leave Harlan Alive

Spoilers appear here, but this episode aired a week ago. So I imagine you, O Patient Reader, already know how the show ended. If you don't, then exercise your lauded patience yet again and wait and watch before reading. ;-)

Last week saw the end of the modern-day western Justified, which was based on the Elmore Leonard short story "Fire in the Hole." The six-year confrontation between criminal Boyd Crowder (Walton Goggins) and U.S. Deputy Marshal Raylan Givens (Timothy Olyphant) was finally on tap, and the fate of Ava Crowder (Joelle Carter), who had been in love with both men and married (and shot) Boyd's brother Bowman, would be revealed.

The episode was a good conclusion for the series, and interestingly its construction probably mirrored the series' uneven final season. Justified came out of the gate with a lot of potential but a loose first season; a show finding its way. The second season, with main villain Mags Bennett (Emmy-winner Margo Martindale), got next to everything right as Raylan fought against Mags and her more-or-less competent but completely evil sons and their scheme to enrich themselves at the expense of their neighbors. The third season was also uneven, meandering around in the middle with too much filler and wasting the potential of Neal McDonough as Detroit-based mobster Bobby Quarles.

Season Four, featuring a 30-year-old mystery and the hunt for the elusive Drew Thompson, came in just a notch under the second. It offered some great character development in the form of the former hooker Ellen May and a fascinating sub-plot with the conflict between Deputy Marshall Tim Gutterson and Boyd's henchman Colton Rhodes. It exposed how Ava's greed and resentment about her poor childhood would lead her to embrace too much of Boyd's criminal enterprise. It took religion -- a fixture of life in rural Kentucky that most shows probably would ignore -- seriously as Ellen May's religious awakening brought her to make decisions she might never have otherwise made, and showed her as a much stronger person than the woman we met in season 2 fellating a crooked doctor for oxycontin. But it lacked a real heavyweight villain, which made it just a little less satisfying than Season Two. And it ended with Ava's arrest, which set up much of the time-wasting nonsense of Season Five. Five spent much of its time in what I've seen called "fan service," meaning giving fans what they clamor and ask for. Fans hated Raylan's ex-wife and current baby mama Winona, so Raylan chased everything in a skirt. Boyd was criminal genius mastermind, so he criminally masterminded all kinds of plots to manipulate Ava out of prison and build his drug empire and outsmart everyone else because he was smart. Loretta McReady had a sassy mouth and Kaitlyn Dever is a great actress, so let's shoehorn Loretta back into the plot for no good reason whatsoever. None of it rang true and very little of it was all that interesting, as it mainly marked time until we could finish things out in Season Six.

The final season began strongly, with Raylan running Ava as his confidential informant spying on Boyd. The Marshals sought evidence to put Boyd away on racketeering and other serious charges, and the race was on to see if she would learn anything of value and keep herself out of prison before Boyd discovered her treachery. Although the criminal enterprise that Boyd undertook was dressed up with a couple too many complications -- the presence of Mary Steenburgen as Katherine Hale and her sometimes beau, sometimes foe Avery Markham (Sam Elliot) being the main culprits. Along about mid-season, we began spending way too much time on Katherine and Avery; the skill of both actors couldn't overshadow that these two were not the people we had been watching this show to see. It was almost as though producer Graham Yost thought he was shooting a ten-episode final season only to learn somewhere around episode eight or nine that he was actually doing thirteen episodes and he'd better start stretching. There aren't too many other reasons that Wynn Duffy (Jere Burns)'s Mikey the goombah bodyguard gets his own death scene. Nor for Loretta to return again and set up a confrontation with Markham and alliance with Boyd that never goes anywhere before the show runs out.

Garrett Dillahunt's charismatic sociopath Ty Walker, Markham's lead henchman, bows out in episode eight complaining that Raylan shot him in the back -- so the last words he hears on earth are Raylan saying, "If you wanted me to shoot you in the front, you shoulda run towards me." But Avery still needs a henchman and Raylan still needs an antagonist to dance with, so we get the ridiculous collection of performance tics called Boon (Jonathan Tucker). His fascination with Western myths and gunfighting foreshadows a final showdown with Raylan, but I didn't watch seventy-eight episodes of this show to learn what happens to a guy who only shows up when it's 94% over.

Yost also seems to think he needs to remind us of some things so we will expect a proper resolution. Raylan, even though he has shown what Martin Blank once called "a certain 'moral flexibility,'" is the Good Guy. Boyd, even though Walton Goggins' charismatic performance has made him fascinating and often great fun to watch, is the Bad Guy. They may bicker a little like a buddy cop movie that's swallowed William Faulkner's thesaurus, but they are not friends, so Yost must remind us of Boyd's Bad Guyness  in the penultimate episode with a speechy, writerly monologue about being an outlaw. Followed by Boyd shooting his listener in the head, when of course the kind thing to do would be to have reversed the order.

The final episode, though, wraps up the season plotline with about 15 minutes left as we see Ava take off on the run, Boyd head off toward the lengthy prison sentence that awaits him when Raylan doesn't shoot him and Raylan himself head to Florida for a reunion with Winona and their infant daughter Willa. It's muddy but fairly satisfying, but the real resolution comes from the coda, set four years later. Raylan and Winona didn't manage as a couple, but they are sharing custody of Willa and Raylan is an important part of her life. He's settled into the Marshals' office in Florida when he gets a hint about Ava's location. She lives on a pumpkin farm in California and is raising Boyd's son in secret. She asks Raylan not to bring her in but even if he does, to keep the knowledge of his son from Boyd. Raylan leaves her in place, and visits Boyd to tell him that Ava died in a car crash in Texas. When Boyd asks Raylan why he would come to deliver this news in person, Raylan allows there is one thing they shared. "We dug coal together," Boyd says through a plastic window in the prison visiting room. "That's right," Raylan answers.

A lot of internet commentary suggested that Leonard's traditional storytelling sense guided the show in ending this way, with the Good Guy winning, the Bad Guy in jail and the Misguided Woman With a Good Heart turning her life around but still always paying a price for what she has done. Unlike the Darrell Scott song from which this post title takes its name, they do leave Harlan alive, although they have left something behind. Ava has left behind the ability to get through a day free of watching for pursuers, either with badges or without. Raylan left behind his past, for better or worse. Boyd left behind his freedom. Even though the author himself passed in 2013, this is the kind of "old-fashioned" ending that he would have argued for, rather than a more modern ending such as that in a show like Breaking Bad.

My own position that Breaking Bad was a nihilistic flimflam con job may influence my ideas, but I would agree that Justified ended the way it ought to end. The final episode set things right in a season that had lost most of its focus, but it did so with an epilogue that set things right in an episode that had lost most of its focus. It may be that Justified's ingredients were only going to mix right in a couple of ways, and that most of the other possible combinations were always going to be off, either a little like in seasons one and three or a lot like in season five and the last half of six.

Tuesdays won't be as much fun without Raylan's laconic humor, Boyd's hyperkinetic polysyllable-laden snowjobs, Tim's Sahara-arid interjections, Erica Tazel's no-nonsense deadly glare as Deputy Marshall Rachel Brooks, Nick Searcy's I'm-getting-too-old-for-this Chief Deputy Marshall Art Givens or Wynn's World's Fussiest Hitman. But more seasons would probably increase the chances for more misfires like Michael Rapaport's supposed southern accent as Darryl Crowe in season five, so perhaps ending now was not the worst move.

And no matter how much I miss the show, I must confess that not hearing again the mumbled banjo-rap theme song from Gangstagrass instead of the far superior "Harlan County Line" from Dave Alvin will cost me nary a minute of sleep.