In Philosophical Investigations (translated by G. E. M. Anscombe), Ludwig Wittgenstein argues that something strange occurs when we learn a language. As an example, he cites the problems that could arise when you point at something and describe what you see:
The definition of the number two, “That is called ‘two’ “ – pointing to two nuts – is perfectly exact. But how can two be defined like that? The person one gives the definition to doesn’t know what one wants to call “two”; he will suppose that “two” is the name given to this group of nuts!
I laughed aloud when I read this statement. I borrowed Philosophical Investigations a few months after the birth of our second child, and I had spent most of his first day pointing at various objects in the hospital maternity ward and saying to him, “This is red.” “This is red.”
“This is red.”
Of course, the little guy didn’t understand language yet, so he probably just thought, the warm carry-me object is babbling again.
Over time, though, this is how humans learn. Wittgenstein’s mistake here is to compress the experience of learning a language into a single interaction (philosophers have a bad habit of forgetting about the passage of time – a similar fallacy explains Zeno’s paradox). Instead of pointing only at two nuts, a parent will point to two blocks – “This is two!” and two pillows – “See the pillows? There are two!” – and so on.
As a child begins to speak, it becomes even easier to learn – the kid can ask “Is this two?”, which is an incredibly powerful tool for people sufficiently comfortable making mistakes that they can dodge confirmation bias.
(When we read the children’s story “In a Dark Dark Room,” I tried to add levity to the ending by making a silly blulululu sound to accompany the ghost, shown to the left of the door on this cover. Then our youngest began pointing to other ghost-like things and asking, “blulululu?” Is that skeleton a ghost? What about this possum?)
When people first programmed computers, they provided definitions for everything. A ghost is an object with a rounded head that has a face and looks very pale. This was a very arduous process – my definition of a ghost, for instance, is leaving out a lot of important features. A rigorous definition might require pages of text.
Now, programmers are letting computers learn the same way we do. To teach a computer about ghosts, we provide it with many pictures and say, “Each of these pictures has a ghost.” Just like a child, the computer decides for itself what features qualify something for ghost-hood.
In the beginning, this process was inscrutable. A trained algorithm could say “This is a ghost!”, but it couldn’t explain why it thought so.
From Philosophical Investigations:
And what does ‘pointing to the shape’, ‘pointing to the color’ consist in? Point to a piece of paper. – And now point to its shape – now to its color – now to its number (that sounds queer). – How did you do it? – You will say that you ‘meant’ a different thing each time you pointed. And if I ask how that is done, you will say you concentrated your attention on the color, the shape, etc. But I ask again: how is that done?
After this passage, Wittgenstein speculates on what might be going through a person’s head when pointing at different features of an object. A team at Google working on automated image analysis asked the same question of their algorithm, and made an output for the algorithm to show what it did when it “concentrated its attention.”
Here’s a beautiful image from a recent New York Times article about the project, “Google Researchers Are Learning How Machines Learn.” When the algorithm is specifically instructed to “point to its shape,” it generates a bizarre image of an upward-facing fish flanked by human eyes (shown bottom center, just below the purple rectangle). That is what the algorithm is thinking of when it “concentrates its attention” on the vase’s shape.
At this point, we humans could quibble. We might disagree that the fish face really represents the platonic ideal of a vase. But at least we know what the algorithm is basing its decision on.
Usually, that’s not the case. After all, it took a lot of work for Google’s team to make their algorithm spit out images showing what it was thinking about. With most self-trained neural networks, we know only its success rate – even the designers will have no idea why or how it works.
It’s possible to create images that most humans recognize as one thing, and that an image-analysis algorithm recognizes as something else. This is a rather scary opportunity for terrorism in a world of self-driving cars; street signs could be defaced in such a way that most human onlookers would find the graffiti unremarkable, but an autonomous car would interpret in a totally new way.
In the world of criminal justice, inscrutable algorithms are already used to determine where police officers should patrol. The initial hope was that this system would be less biased – except that the algorithm was trained on data that came from years of racially-motivated enforcement. Minorities are still more likely to be apprehended for equivalent infractions.
When an algorithm thinks that the shape of a vase is a fish flanked by human eyes, it’s funny. But it’s a little less comedic when an algorithm’s mistake ruins somebody’s life – if an incident is designated as a “gang-related crime”, prison sentences can be egregiously long, or send someone to solitary for long enough to cause “anxiety, depression, and hallucinations until their personality is completely destroyed.”
A deep undercurrent of misogyny courses through much of the world’s mythology. In the Mahabharata (the Indian epic that includes the Bhagavad Gita), the hero’s wife is gambled away by her husband as just another possession after he’d lost his jewels, money, and chariot. She is forced to strip in the middle of the casino; happily, divine intervention provides her with endless layers of garments.
In the Ramayana, the hero’s wife is banished by her husband because her misery in exile is preferable to the townsfolk’s malicious rumors. She’d been kidnapped, so the townsfolk assumed she’d been raped and was therefore tarnished.
In Emily Wilson’s translation of The Odyssey, a woman asks a visiting bard to sing something else when he launches into a description of the calamitous escapade that whisked away her husband. But the woman’s son intervenes:
There is something faintly ridiculous about this wet-behind-the-ears lad shutting up the savvy, middle-aged Penelope. But it is a nice demonstration that right where written evidence for Western culture starts, women’s voices are not being heard in the public sphere. More than that, as Homer has it, an integral part of growing up, as a man, is learning to take control of public utterance and to silence the female of the species.
Belief in women’s inferiority is a long and disheartening part of each [Abrahamic] tradition’s story. For almost all of Jewish history, no woman could become a rabbi. For almost all of Christian history, no woman could become a priest. For almost all of Muslim history, no woman could become a prophet (though scores of men did) or an imam (thousands of men did).
Call in two men as witnesses. If two men are not there, then call one man and two women out of those you approve as witnesses, so that if one of the two women should forget the other can remind her. Let the witnesses not refuse when they are summoned.
Clearly, this is derogatory toward women. But the phrase “if one of the women should forget, the other can remind her” made me think about why disrespectful attitudes toward women were rampant in so many cultures.
I think that, in the society where the Qur’an was composed, women would be more likely to forget the details of a contract. But the problem isn’t biological – I would argue that attentive parents of young children are more forgetful than other people. The parent’s gender is irrelevant here. My own memory was always excellent – during college I was often enrolled in time and a half the standard number of courses, never took notes, and received almost all A’s – but when I’m taking care of my kids, it’s a miracle if I can hold a complex thought in mind for more than a few seconds.
People talk to me, I half-listen while also answering my kids’ questions, doling out snacks, saying no, no book now, wait till we get home, and then my conversation with the grown-up will end and I’ll realize that I have no idea what we just talked about.
Hopefully it wasn’t important.
Parenting obliterates my short-term memory, even though I have it easy. I rarely worry about other parents intentionally poisoning my children, for instance. In The Anthropology of Childhood, David Lancy discusses
… the prevalence of discord within families – especially those that practice polygyny. [Polygyny is one man marrying several women, as was practiced by the people who composed the Qur’an.] This atmosphere can be poisonous for children – literally.
It was widely assumed that co-wives often fatally poisoned each other’s children. I witnessed special dance rituals intended by husbands to deter this behavior. Co-wife aggression is documented in … court cases with confessions and convictions for poisoning … sorcery might have a measurable demographic impact – [given] the extraordinarily high mortality of males compared with females. Males are said to be the preferred targets because daughters marry out of patrilineage whereas sons remain to compete for land. Even if women do not poison each other’s children, widespread hostility of the mother’s co-wife must be a source of stress.
Even when we don’t have to ward off sorcery or murder, parents of young children have shorter attention spans than other people. A kid is often grabbing my leg, or tugging on my hand, or yelling fthhhaaaddda until I turn to look and watch him bellyflop onto a cardboard box.
Once my two children grow up, I should regain my memory. But during most of human evolution, mortality rates were so high that families always had small children. And, unfortunately, our species often established misogynistic patriarchies that believed women alone should do all the work of parenting.
There are a few species, like penguins, in which males and females contribute almost equally to the task of caring for young. But it’s more common for a single parent to get stuck doing most of the work. According to game theory, this makes sense – as soon as one party has put in a little bit more effort than the other, that party has more to lose, and so the other has an increased incentive to shirk. Drawn out over many generations, this can produce creatures like us primates, in which males are often shabby parents.
This is bad for children (in an aside, Lancy writes “I’m tempted to argue that any society with conspicuous gender parity is likely to be a paradise for children.”), bad for women, and bad for men. Inequality hurts everyone – men in patriarchies get to skimp on parental contribution, but they have to live in a less happy, less productive world.
It’s reasonable for the Qur’an to imply that women are less attentive and less able to understand the intricacies of contracts, given that their husbands weren’t helping with the kids. Caring for young children can be like a straitjacket on the brain.
… if what we mean by “human nature” is the Homo sapiens physique, and the “fundamental pattern … [of] social organization” which apparently prevailed when that physique first took shape, then human nature involves the females in a strange bind:
Like the male, she is equipped with a large brain, competent hands, and upright posture. She belongs to an intelligent, playful, exploratory species, inhabiting an expanding environment which it makes for itself and then adapts to. She is the only female, so far as we know, capable of thinking up and bringing about a world wider than the one she sees around her (and her subversive tendency to keep trying to use this capacity is recorded, resentfully, in Eve and Pandora myths).
She thus seems, of all females, the one least fitted to live in a world narrower than the one she sees around her. And yet, for reasons inherent in her evolutionary history, she has been, of all females, the one most fated to do so. Her young are born less mature than those of related mammals; they require more physical care for a relatively longer time; they have much more to learn before they can function without adult supervision.
It hurts to have talents that the world won’t let you use. What good is a massive brain when your kid is just yelling for more Cheerios?
Maybe I’m not doing a good job of selling the idea that “you should pitch in and help with the children” to any potential new fathers out there. It really does make a wreckage of your brain – but I’ve heard that this is temporary, and I’ve met plenty of parents of older children who seem perfectly un-addled.
And it doesn’t have to be fun to be worth doing.
Experiences during early development have ramifications for somebody’s wellbeing. As children grow, they’ll forget narrative details from almost everything that happened during their first few years – but this time establishes the emotional pallet that colors the rest of their life.
It’s strange. After all, most of the work of parenting is just doling out cereal, or answering questions about what life would be like if we stayed at the playground forever, or trying to guess how many different types of birds are chirping during the walk to school. And yet a parent’s attitudes while doing those small things help shape a person.
When most older people look back on their lives, they’ll tell you that their happiest and most rewarding moments were spent interacting with their families. By caring for your children when they’re young, you help determine the sort of person who’ll be in your family. If you’re lucky enough to be so wealthy that you’ll still have food and shelter, parenting decisions matter more for future happiness than a few years’ salary.
The costs are high. But equality, happiness, and establishing a culture of respect should matter to men as well as women.
The best way to show that you value something is to pitch in and do it.
When I turn on my computer, I don’t consider what my computer wants. It seems relatively empty of desire. I click on an icon to open a text document and begin to type: letters appear on the screen.
If anything, the computer seems completely servile. It wants to be of service! I type, and it rearranges little magnets to mirror my desires.
When our family travels and turns on the GPS, though, we discuss the system’s wants more readily.
“It wants you to turn left here,” K says.
“Pfft,” I say. “That road looks bland.” I keep driving straight and the machine starts flashing make the next available u-turn until eventually it gives in and calculates a new route to accommodate my whim.
The GPS wants our car to travel along the fastest available route. I want to look at pretty leaves and avoid those hilly median-less highways where death seems imminent at every crest. Sometimes the machine’s desires and mine align, sometimes they do not.
The GPS is relatively powerless, though. It can only accomplish its goals by persuading me to follow its advice. If it says turn left and I feel wary, we go straight.
Other machines get their way more often. For instance, the program that chooses what to display on people’s Facebook pages. This program wants to make money. To do this, it must choose which advertisers receive screen time, and to curate an audience that will look at those screens often. It wants for the people looking at advertisements to enjoy their experience.
Luckily for this program, it receives a huge amount of feedback on how well it’s doing. When it makes a mistake, it will realize promptly and correct itself. For instance, it gathers data on how much time the target audience spends looking at the site. It knows how often advertisements are clicked on by someone curious to learn more about whatever is being shilled. It knows how often those clicks lead to sales for the companies giving it money (which will make those companies more eager to give it money in the future).
Of course, this program’s desire for money doesn’t always coincide with my desires. I want to live in a country with a broadly informed citizenry. I want people to engage with nuanced political and philosophical discourse. I want people to spend less time staring at their telephones and more time engaging with the world around them. I want people to spend less money.
But we, as a people, have given this program more power than a GPS. If you look at Facebook, it controls what you see – and few people seem upset enough to stop looking at Facebook.
With enough power, does a machine become a moral actor? The program choosing what to display on Facebook doesn’t seem to consider the ethics of its decisions … but shouldit?
Bad human actors don’t pose the only problem; a machine-learning algorithm, left unchecked, can misbehave and compound inequality on its own, no help from humans needed. The same mechanism that decides that 30-something women who like yoga disproportionately buy Lululemon tights – and shows them ads for more yoga wear – would also show more junk-food ads to impoverished populations rife with diabetes and obesity.
If a machine designed to want money becomes sufficiently powerful, it will do things that we humans find unpleasant. (This isn’t solely a problem with machines – consider the ethical decisions of the Koch brothers, for instance – but contemporary machines tend to be much more single-minded than any human.)
I would argue that even if a programmer tried to include ethical precepts into a machine’s goals, problems would arise. If a sufficiently powerful machine had the mandate “end human suffering,” for instance, it might decide to simultaneously snuff all Homo sapiens from the planet.
One virtue of video games over other art forms is how well games can create empathy. It’s easy to read about Guantanamo prison guards torturing inmates and think, I would never do that. The game Grand Theft Auto 5 does something more subtle. It asks players – after they have sunk a significant time investment into the game – to torture. You, the player, become like a prison guard, having put years of your life toward a career. You’re asked to do something immoral. Will you do it?
Most players do. Put into that position, we lapse.
In Frank Lantz’s game, Paperclips, players are helped to empathize with a machine. Just like the program choosing what to display on people’s Facebook pages, players are given several controls to tweak in order to maximize a resource. That program wanted money; you, in the game, want paperclips. Click a button to cut some wire and, voila, you’ve made one!
But what if there were more?
A machine designed to make as many paperclips as possible (for which it needs money, which it gets by selling paperclips) would want more. While playing the game (surprisingly compelling given that it’s a text-only window filled with flickering numbers), we become that machine. And we slip into folly. Oops. Goodbye, Earth.
There are dangers inherent in giving too much power to anyone or anything with such clearly articulated wants. A machine might destroy us. But: we would probably do it, too.
From the beginning, artists understood that time travel either denies humans free will or else creates absurd paradoxes.
This conundrum arises whenever an object or information is allowed to travel backward through time. Traveling forward is perfectly logical – after all, it’s little different from a big sleep, or being shunted into an isolation cell. The world moves on but you do not… except for the steady depredations of age and the neurological damage that solitary confinement inevitably causes.
A lurch forward is no big deal.
Consider one of the earlier time travel stories, the myth of Oedipus. King Laius receives a prophecy foretelling doom. He strives to create a paradox – using information from the future to prevent that future, in this case by offing his son – but fails. This story falls into the “time travel denies humans free will” category. Try as they might, the characters cannot help but create their tragic future.
James Gleick puts this succinctly in his recent New York Review essay discussing Denis Villeneuve’s Arrival and Ted Chiang’s “Story of Your Life.” Gleick posits the existence of a “Book of Ages,” a tome describing every moment of the past, present, and future. Could a reader flip to a page describing the current moment and choose to evade the dictates of the book? In Gleick’s words,
Can you do that? Logically, no. If you accept the premise, the story is unchanging. Knowledge of the future trumps free will.
(I’m typing this essay on January 18th, and can’t help but note how crappy it is that the final verb in that sentence looks wrong with a lowercase “t.” Sorry, ‘merica. I hope you get better soon.)
Gleick is the author of Time Travel: A History, in which he presents a broad survey of the various tales (primarily literature and film) that feature time travel. In each tale Gleick discusses, time travel either saps free will (a la Oedipus) or else introduces inexplicable paradox (Marty slowly fading in Back to the Future as his parents’ relationship becomes less likely; scraps of the Terminator being used to invent the Terminator; a time-traveling escapee melting into a haggard cripple as his younger self is tortured in Looper.)
It’s not just artists who have fun worrying over these puzzles; over the years, more and more physicists and philosophers have gotten into the act. Sadly, their ideas are often less well-reasoned than the filmmakers’. Time Travel includes a long quotation from philosopher John Hospers (“We’re still in a textbook about analytical philosphy, but you can almost hear the author shouting,” Gleick interjects), in which Hospers argues that you can’t travel back in time to build the pyramids because you already know that they were built by someone else, followed by with the brief summary:
Admit it: you didn’t help build the pyramids. That’s a fact, but is it a logical fact? Not every logician finds these syllogisms self-evident. Some things cannot be proved or disproved by logic.
Gleick uses this moment to introduce Godel’s Incompleteness Theorem (the idea that, in any formal system, we must include unprovable assumptions), whose author, Kurt Godel, also speculated about time travel (from Gleick: If the attention paid to CTCs [closed timelike curve] is disproportionate to their importance or plausibility, Stephen Hawkins knows why: “Scientists working in this field have to disguise their real interest by using technical terms like ‘closed timelike curves’ that are code for time travel.” And time travel is sexy. Even for a pathologically shy, borderline paranoid Austrian logician).
Alternatively, Hospers’ strange pyramid argument could’ve been followed by a discussion of Timecrimes [http://www.imdb.com/title/tt0480669/], the one paradox-less film in which a character travels backward through time but still has free will (at least, as much free will as you or I have).
But James Gleick’s Time Travel: A History doesn’t mention Timecrimes. Obviously there are so many stories incorporating time travel that it’d be impossible to discuss them all, but leaving out Timecrimes is a tragedy! This is the best time travel movie (of the past and present. I can’t figure out how to make any torrent clients download the time travel movies of the future).
Timecrimes is great. It provides the best analysis of free will inside a sci-fi world of time travel. But it’s not just for sci-fi nerds – the same ideas help us understand strange-seeming human activities like temporally-incongruous prayer (e.g., praying for the safety of a friend after you’ve already seen on TV that several unidentified people died when her apartment building caught fire. By the time you kneel, she should either be dead or not. And yet, we pray).
Timecrimes progresses through three distinct movements. In the first, the protagonist believes himself to be in a world of time travel as paradox: a physicist has convinced him that with any deviation from the known timeline he might cause himself to cease to exist. And so he mimics as best he can events that he remembers. A masked man chased him with a knife, and so he chases his past self.
In the second movement, the protagonist realizes that the physicist was wrong. There are no paradoxes, but he seems powerless to change anything. He watched his wife fall to her death at the end of his first jaunt through time, so he is striving to alter the future… but his every effort fails. Perhaps he has no free will, no real agency. After all, he already remembers her death. His memory exists in the form of a specific pattern of neural connections in his brain, and those neurons will not spontaneously rearrange. His memory is real. The future seems set.
But then there is a third movement: this is the reason Timecrimes surpasses all other time travel tales. The protagonist regains a sense of free will within the constraints imposed by physics.
Yes, he saw his wife die. How can he make his memory wrong?
Similarly, you’ve already learned that the Egyptians built the pyramids. I’m pretty confident that none of the history books you’ve perused included a smiling picture of you with the caption “… but they couldn’t have done it without her.” And yet, if you were to travel back to Egypt, would it really be impossible to help in such a way that no history books (which will be written in the future, but which your past self has already seen) ever report your contributions.
Indeed, an analogous puzzle is set before us every time we act. Our brains are nothing more than gooey messes of molecules, constrained by the same laws of physics as everything else, so we shouldn’t have free will. And yet: can we still act as though we do?
We must. It’s either that or sit around waiting to die.
Because the universe sprung senselessly into existence, birthed by chance fluctuations during the long march of eternity… and then we appeared, billions of years later, through the valueless vagaries of evolution… our actions shouldn’t matter. But: can we pretend they do?
With two credits left to finish his degree, a friend switched his major from philosophy to computer science. One of his first assignments: build a website for a local business. Rather than find someone needing this service, he decided to fabricate an empire.
I never knew whether he thought this would be easier. In any case, he resolved to create the simulacrum of a small publishing company and asked me for help. We wrote short biographies for approximately a dozen authors on the company’s roster, drafted excerpts from several books for each, designed book covers, and used Photoshop to paste our creations into conference halls, speaking at podiums and being applauded for their achievements.
This was in the fall of 2003, so we assumed that aspiring artists would also pursue a social media presence. We created profiles for the authors on Myspace (the original incarnation of Facebook, loathe to admit fakery, would only let users register for an account using a university email address; the email accounts we’d made for our authors were all hosted through Hotmail and Yahoo). My friend put profiles for several on dating websites. He arranged trysts that the (imaginary) authors cancelled at the last minute.
My apologies to the men and women who were stood up by our creations. I’d like to think that most real-world authors are less fickle.
Several years later, when my family began recording holiday albums in lieu of a photograph to mail to our friends and relatives, we named the project after the most successful of these authors… “success” here referring solely to popularity on the dating sites. We figured that, because these entities were all constructs of our imaginations, this was the closest we’d ever come to a controlled experiment comparing the allure of different names.
Eventually, my friend submitted his project. By this time he’d kept up the profiles of our creations for about two months. At first the authors were only friends with each other, but by then they’d begun to branch out, each participating in different online discussion groups, making a different set of connections to the world…
My friend received a failing grade. None of the links to buy the authors’ books were functional. He had thought this was a reasonable omission, since the full texts did not exist, but his professor was a stickler.
Still, I have to admit: faking is fun.
Profitable, too. Not in my friend’s case, where he devoted prodigious quantities of effort toward a project that earned exceptionally low marks (he gave up on computer science at the end of that semester, and indeed changed his major thrice more before resigning himself to a philosophy degree and completing those last two credits). But, for others?
From William Gaddis’s The Recognitions:
Long since, of course, in the spirit of that noblesse oblige which she personified, Paris had withdrawn from any legitimate connection with works of art, and directly increased her entourage of those living for Art’s sake. One of these, finding himself on trial just two or three years ago, had made the reasonable point that a typical study of a Barbizon peasant signed with his own name brought but a few hundred francs, but signed Millet, ten thousand dollars; and the excellent defense that this subterfuge had not been practiced on Frenchmen, but on English and Americans “to whom you can sell anything” . . . here, in France, where everything was for sale.
Or, put more explicitly by Jean de la Bruyêre (& translated by Jean Stewart):
It is harder to make one’s name by means of a perfect work than to win praise for a second-rate one by means of a name one has already acquired.
Our world is saturated in information and art – to garner attention, it might seem necessary to pose as a trusted brand.
Or, it seems, to peddle untruths so outlandish that they stand distinct from run-on-the-mill reality, which might be found anywhere. This, it seems, was a profitable moneymaking scheme during the 2016 U.S. elections. With a sufficiently catchy fabrication, anyone anywhere could dupe Facebook users and reap Google advertising dollars.
Which is frustrating, sure. Networks created by ostensibly socially-conscious left-leaning Silicon Valley companies enabled a far-right political campaign built on lies.
But I would argue that the real problem with Facebook, in terms of distorting political discourse, isn’t the platform’s propensity for spreading lies. The problem is Facebook itself, the working-as-properly attention waster. Even when the material is real-ish – pointless lists, celebrity updates, and the like – it degrades the power to think. The site is designed to be distracting. After all, Facebook makes money through advertising. Humans are most persuadable when harried & distracted – it’s while I’m in the grocery store holding a screaming toddler that I’m most likely to grab whatever item has a brightly-colored tag announcing its SALE! price instead of checking to see which offers the best value. All the dopamine-releasing pings and pokes on Facebook keep users susceptible.
Consider that the ability to concentrate without distraction on hard tasks is becoming increasingly valuable in an increasingly complicated economy. Social media weakens this skill because it’s engineered to be addictive. The more you use social media in the way it’s designed to be used – persistently throughout your waking hours – the more your brain learns to crave a quick hit of stimulus at the slightest hint of boredom.
Once this Pavlovian connection is solidified, it becomes hard to give difficult tasks the unbroken concentration they require, and your brain simply won’t tolerate such a long period without a fix.
Big ideas take time. And so we have a conundrum: how, in our world, can we devote the time and energy necessary to gain deep understanding?
Or becoming a place populated by people who hate Donald Trump but think that their hate alone – or, excuse me, their impassioned hate plustheir ironic Twitter posts – without getting off their asses to actually do something about all the suffering in the world, is enough. There are very clear actions you could take to push back against climate change and massincarceration.
For several months, a friend and I have volleyed emails about a sprawling essay on consciousness, free will, and literature.
The essay will explore the idea that humans feel we have free will because our conscious mind grafts narrative explanations (“I did this because…”) onto our actions. It seems quite clear that our conscious minds do not originate all the choices that we then take credit for. With an electroencephalogram, you could predict when someone is about to raise an arm, for instance, before the person has even consciously decided to do so.
Which is still free will, of course. If we are choosing an action, it hardly matters whether our conscious or subconscious mind makes the choice. But then again, we might not be “free.” If an outside observer were able to scan a person’s brain to sufficient detail, all of that person’s future choices could probably be predicted (as long as our poor study subject is imprisoned in an isolation chamber). Our brains dictate our thoughts and choices, but these brains are composed of salts and such that follow the same laws of physics as all other matter.
That’s okay. It is almost certainly impossible that any outside observer could (non-destructively) scan a brain to sufficient detail. If quantum mechanical detail is implicated in the workings of our brains, it is definitely impossible: quantum mechanical information can’t be duplicated. Wikipedia has a proof of this “no cloning theorem” involving lots of bras and kets, but this is probably unreadable for anyone who hasn’t done much matrix math. An easier way to reason through it might be this: if you agree with the Heisenberg uncertainty principle, the idea that certain pairs of variables cannot be simultaneously measured to arbitrary precision, the no cloning theorem has to be true. Otherwise you could simply make many copies of a system and measure one variable precisely for each copy.
So, no one will ever be able to prove to me that I am not free. But let’s just postulate, for a moment, that the laws of physics that, so far, have correctly described the behavior of all matter outside my brain also correctly describe the movement of matter inside my brain. In which case, those inviolable laws of physics are dictating my actions as I type this essay. And yet, I feel free. Each word I type feels like a choice. My brain is constantly concocting a story that explains why I am choosing each word.
Does the same neural circuitry that deludes me into feeling free – that has evolved, it seems, to constantly sculpt narratives that make sense of our actions, the same way our dreams often burgeon to include details like a too hot room or a ringing telephone – also give me the ability to write fiction?
In other words, did free will spawn The Iliad?
The essay is obviously rather speculative. I’m incorporating relevant findings from neuroscience, but, as I’ve mentioned, it’s quite likely that no feasible experiments could ever test some of these ideas.
The essay is also unfinished. No laws of physics forbid me from finishing it. I’m just slow because K & I have two young kids. At the end of each day, once our 2.5 year old and our 3 month old are finally asleep, we exhaustedly glance at each other and murmur, “Where did the time go?”
But I am very fortunate to have a collaborator always ready to nudge me back into action. My friend recently sent me an article by Tim Christiaens on the philosophy of financial markets. He sent it because the author argues – correctly, in my opinion – that for many stock market actions it’s sensible to consider the Homo sapiens trader + the nearby multi-monitor computer as a single decision-making entity. Tool-wielding is known to change our brains – even something as simple as a pointing stick alters our self-perception of our reach. And the algorithms churned through by stock traders’ computers are incredibly complex. There’s not a good way for the human to check a computer’s results; the numbers it spits out have to be trusted. So it seems reasonable to consider the two together as a single super-entity that collaborates in choosing when to buy or sell. If something in the room has free will, it would be the tools & trader together.
Which isn’t as weird as it might initially sound. After all, each Homo sapiens shell is already a multi-species super-entity. As I type this essay, the choice of which word to write next is made inside my brain, then signals are sent through my nervous system to my hands and fingers commanding them to tap the appropriate keys. The choice is influenced by all the hormones and signaling molecules inside my brain. It so happens that bacteria and other organisms living in my body excrete signaling molecules that can cross the blood-brain barrier and influence my choice.
The milieu of intestinal bacteria living inside each of us gets to vote on our moods and actions. People with depression seem to harbor noticeably different sets of bacteria than people without. And it seems quite possible that parasites like Toxoplasma gondii can have major influences on our personalities.
Indeed, in his article on stock markets, Christiaens mentions the influence of small molecules on financial behavior, reporting that “some researchers study the trader’s body through the prism of testosterone levels as an indicator of performance. It turns out that traders who regularly visit prostitutes consequently have higher testosterone levels and outperform other traders.”
Now, I could harp on the fact that we designed these markets. That they could have been designed in many different ways. And that it seems pretty rotten to have designed a system in which higher testosterone (and the attendant impulsiveness and risky decision-making) would correlate with success. Indeed, a better, more equitable market design would probably quell the performance boost of testosterone.
I could rant about all that. But I won’t. Instead I’ll simply mention that Toxoplasma seems to boost testosterone. Instead of popping into brothels after work, traders could snack on cat shit.
On the topic of market design, Christiaens also includes a lovely description of the interplay between the structure of our economy and the ways that people are compelled to live:
The reason why financial markets are able to determine the viability of lifestyles is because most individuals and governments are indebted and therefore need a ‘creditworthy’ reputation. As the [U.S.] welfare state declined during the 1980s, access to credit was facilitated in order to sustain high consumption, avoid overproduction and stimulate economic growth. For Lazzarato [a referenced writer], debt is not an obligation emerging from a contract between free and equal individuals, but is from the start an unequal power relation where the creditor can assert his force over the debtor. As long as he is indebted, the latter’s rights are virtually suspended. For instance, a debtor’s property rights can be superseded when he fails to reimburse the creditor by evicting him from his home or selling his property at a public auction. State violence is called upon to force non-creditworthy individuals to comply. We [need] not even jump to these extreme cases of state enforcement to see that debt entails a disequilibrium of power. Even the peaceful house loan harbors a concentration of risk on the side of the debtor. When I take a $100,000 loan for a house that, during an economic crisis, loses its value, I still have to pay $100,000 plus interests to the bank. The risk of a housing crash is shifted to the debtor’s side of the bargain. During a financial crisis this risk concentration makes it possible for the creditors to demand a change of lifestyle from the debtor, without the former having to reform themselves.
Several of my prioressays have touched upon the benefits of a guaranteed basic income for all people, but I think this paragraph is a good lead-in for a reprise. As Christiaens implies, there is violence behind all loans – both the violence that led to initial ownership claims and the threat of state violence that compels repayment. Not that I’m against the threat of state violence to compel people to follow rules in general – without this threat we would have anarchy, in which case actual violence tends to predominate over the threat of incipient enforcement.
We all need wealth to live. After all, land holdings are wealth, and at the very least each human needs access to a place to collect fresh water, a place to grow food, a place to stand and sleep. But no one is born wealthy. A fortunate few people receive gifts of wealth soon after birth, but many people foolishly choose to be born to less well-off parents.
The need for wealth curtails the choices people can make. They need to maintain their “creditworthiness,” as in Christiaens’s passage, or their hire-ability. Wealth has to come from somewhere, and, starting from zero, we rely on others choosing to give it to us. Yes, often in recompense for labor, but just because you are willing and able to do a form of work does not mean that anyone will pay you for it.
Unless people are already wealthy enough to survive, they are at the mercy of others choosing to give them things. Employers are not forced to trade money for salaried working hours. And there isn’t wealth simply waiting around to be claimed. It all starts from something – I’d argue that all wealth stems originally from land holdings – but the world’s finite allotment of land was claimed long ago through violence.
A guaranteed basic income would serve to acknowledge the brutal baselessness of those initial land grabs. It is an imperfect solution, I know. It doesn’t make sense to me that everyone’s expenses should rise whenever a new child is born. But a world where people received a guaranteed basic income would be better than one without. The unluckily-born populace would be less compelled to enter into subjugating financial arrangements. We’d have less misery – feeling poor causes a lot of stress. We’d presumably have less crime and drug abuse, too, for similar reasons.
And, of course, less hypocrisy. It’s worth acknowledging that our good fortune comes from somewhere. No one among us created the world.
Reading about the uncertainty principle in popular literature almost always sets my teeth on edge.
I assume most people have a few qualms like that, things they often see done incorrectly that infuriate them. After a few pointed interactions with our thesis advisor, a friend of mine started going berserk whenever he saw “it’s” and “its” misused on signs. My middle school algebra teacher fumed whenever he saw store prices marked “.25% off!” when they meant you’d pay three quarters of the standard price, not 99.75%. A violinist friend with perfect pitch called me (much too early) on a Sunday morning to complain that the birds on her windowsill were out of tune… how could she sleep when they couldn’t hit an F#??
“Ha,” I say. “That’s silly… they should just let it go.” But then I start frowning and sputtering when I read about the uncertainty principle. Anytime somebody writes a line to the effect of, we’ve learned from quantum mechanics that measurement obscures the world, so we will always be uncertain what reality might have been had we not measured it.
My ire is risible in part because the idea isn’t so bad. It even holds in some fields. Like social psychology, I’d say. If a research group identifies a peculiarity of the human mind and then widely publicizes their findings, that particularity might go away. There was a study published shortly before I got my first driver’s license concluding that the rightmost lanes of toll booths were almost always fastest. Now that’s no longer true. Humans can correct their mistakes, but first they have to realize they’re mistaken.
That’s not the uncertainty principle, though.
And, silly me, I’d always thought that this misconception was due to liberal arts professors wanting to cite some fancy-sounding physics they didn’t understand. I didn’t realize the original misconception was due to Heisenberg himself. In The Physical Principles of Quantum Theory. he wrote (and please note that this is not the correct explanation for the uncertainty principle):
Thus suppose that the velocity of a free electron is precisely known, while the position is completely unknown. Then the principle states that every subsequent observation of the position will alter the momentum by an unknown and undeterminable amount such that after carrying out the experiment our knowledge of the electronic motion is restricted by the uncertainty relation. This may be expressed in concise and general terms by saying that every experiment destroys some of the knowledge of the system which was obtained by previous experiments.
Most of this isn’t so bad, despite not being the uncertainty principle. The next line is worse, if what you’re hoping for is an accurate translation of quantum mechanics into English.
This formulation makes it clear that the uncertainty relation does not refer to the past; if the velocity of the electron is at first known and the position then exactly measured, the position for times previous to the measurement may be calculated. Then for these past times ∆p∆q [“p” stands for momentum and “q” stands for position in most mathematical expressions of quantum mechanics] is smaller than the usual limiting value, but this knowledge of the past is of a purely speculative character, since it can never (because of the unknown change in momentum caused by the position measurement) be used as an initial condition in any calculation of the future progress of the electron and thus cannot be subjected to experimental verification.
That’s not correct. Because the uncertainty principle is not about measurement, it’s about the world and what states the world itself can possibly adopt. We can’t trace the position & momentum both backward through time to know where & how fast an electron was earlier because the interactions that define a measurement create discrete properties, i.e. they are not revealing crisp properties that pre-existed the measurement.
Heisenberg was a brilliant man, but he made two major mistakes (that I know of, at least. Maybe he had his own running tally of things he wished he’d done differently). One mistake may have saved us all, as was depicted beautifully in Michael Frayn’s Copenhagen (also… they made a film of this? I was lucky enough to see the play in person, but I’ll have to watch it again!) — who knows what would’ve happened if Germany had the bomb?
Heisenberg’s other big mistake was his word-based interpretation of the uncertainty principle he discovered.
His misconception is understandable, though. It’s very hard to translate from mathematics into words. I’ll try my best with this essay, but I might botch it too — it’s going to be extra-hard for me because my math is so rusty. I studied quantum mechanics from 2003 to 2007 but since then haven’t had professional reasons to work through any of the equations. Eight years of lassitude is a long time, long enough to forget a lot, especially because my mathematical grounding was never very good. I skipped several prerequisite math courses because I had good intuition for numbers, but this meant that when my study groups solved problem sets together we often divided the labor such that I’d write down the correct answer then they’d work backwards from it and teach me why it was correct.
I solved equations Robert Johnson crossroads style, except I had a Texas Instruments graphing calculator instead of a guitar.
The other major impediment Heisenberg was up against is that the uncertainty principle is most intuitive when expressed in matrix mechanics… and Heisenberg had no formal training in linear algebra. I hadn’t realized this until I read Jagdish Mehra’s The Formulation of Matrix Mechanics and Its Modifications from his Historical Development of Quantum Theory. A charming book, citing many of the letters the researchers sent to one another, providing mini-biographies of everyone who contributed to the theory. The chapter describing Heisenberg’s rush to learn matrices in order to collaborate with Max Born and Pascual Jordan before the former left for a lecture series in the United States has a surprising amount of action for a history book about mathematics… but the outcome seems to be that Heisenberg’s rushed autodidacticism left him with some misconceptions.
Which is too bad. The key idea was Heisenberg’s, the idea that non-commuting variables might underlie quantum behavior.
Commuting? I should probably explain that, at least briefly. My algebra teacher, the same one who turned apoplectic when he saw miswritten grocery store discount signs, taught the subject like it was gym class (which I mean as a compliment, despite hating gym class). Each operation was its own sport with a set of rules. Multiplication, for instance, had rules that let you commute, and distribute, and associate. When you commute, you get to shuffle your players around. 7 • 5 will give you the same answer as 5 • 7.
But just because kicks to the head are legal in MMA doesn’t mean you can do ’em in soccer. You’re allowed to commute when you’re playing multiplication, but you can’t do it in quantum mechanics. You can’t commute matrices either, which was why Born realized that they might be the best way to express quantum phenomena algebraically. If you have a matrix A and another matrix B, then A • B will often not be the same as B • A.
That difference underlies the uncertainty principle.
So, here’s the part of the essay wherein I will try my very best to make the math both comprehensible and accurate. But I might fail at one or the other or both… if so, my apologies!
A matrix is an array of numbers that represents an operation. I think the easiest way to understand matrices is to start by imagining operators that work in two dimensions.
Just like surgeons all dressed up in their scrubs and carrying a gleaming scalpel and peering down the corridors searching for a next victim, every operator needs something to operate on. In the case of surgeons, it’s moneyed sick people. In the case of matrices, it’s “vectors.”
As a first approximation, you can imagine vectors are just coordinate pairs. Dots on a graph. Typically the term “vector” implies something with a starting point, a direction, and a length… but it’s not a big deal to imagine a whole bunch of vectors that all start from the origin, so then all you need to know is the point at which the tip of an arrow might end.
It’ll be easiest to show you some operations if we have a bunch of vectors. So here’s a list of them, always with the x coordinate written above the y coordinate.
3 4 5 2 6 1 7 3 5
0 , 0 , 0 , 1 , 1 , 2 , 2 , 5 , 5
That set of points makes a crude smiley face.
And we can operate on that set points with a matrix in order to change the image in a predictable way. I’ve always thought the way the math works here is cute… you have to imagine a vector leaping out of the water like a dolphin or killer whale and then splashing down horizontally onto the matrix. Then the vector sinks down through the rows.
It won’t be as fun when I depict it statically, but the math works like this:
Does it make sense why I imagine the vector, the (x,y) thing, flopping over sideways?
The simplest matrix is something called an “identity” matrix. It looks like this:
When we multiply a vector by the identity matrix, it isn’t changed. The zeros mean the y term of our initial vector won’t affect the x term of our result, and the x term of our initial vector won’t affect the y term of our result. Here:
And there are a couple other simple matrices we might consider (you’ll only need to learn a little more before I get back to that “matrices don’t commute” idea).
If we want to make our smiling face twice as big, we can use this operator:
Hopefully that matrix makes a little bit of sense. The x and y terms still do not affect each other, which is why we have the zeros on the upward diagonal, and every coordinate must become twice as large to scoot everything farther from the origin, making the entire picture bigger.
We could instead make a mirror image of our picture by reflecting across the y axis:
Or rotate our picture 90º counterclockwise:
The rotation matrix has those terms because the previous Y axis spins down to align with the negative X axis, and the X axis rotates up to become the positive Y axis.
And those last two operators, mirror reflection and rotation, will let us see why the commutative property does not hold in linear algebra. Why A • B is not necessarily equal to B • A if both A & B are matrices.
Here are some nifty pictures showing what happens when we first reflect our smile then rotate, versus first rotating then reflecting. If the matrices did commute, if A • B = B • A, the outcome of the pair of operations would be the same no matter what order they were applied in. And they aren’t! The top row of the image below shows reflection then rotation; the bottom row shows rotating our smile then reflecting it.
And that, in essence, is where the uncertainty principle comes from. Although there is one more mathematical concept that I should tell you about, the other rationale for using matrices to understand quantum mechanics in the first place.
You can write a matrix that would represent any operation or any set of forces. One important class of matrices are those that use the positions of each relevant object, like the locations of each electron around a nucleus, in order to calculate the total energy of a system. The electrons have kinetic energy based on their momentum (the derivative of their position with respect to time) and potential energy related to their position itself, due to interaction with the protons in the nucleus and, if there are multiple electrons, repulsive forces between each other…
(I assume you’ve heard the term “two-body problem” before, used by couples who are trying to find a pair of jobs in the same city so they can move there together. It’s a big issue in science and medicine, double matching for residencies, internships, post-docs, etc. Well, it turns out that nobody thinks it’s funny to make a math joke out of this and say, “At least two-body problems are solvable. Three-body problems have to be approximated numerically.”)
…but once you have a wavefunction (which is basically just a fancy vector, now with a stack of functions instead of a stack of numbers), you can imagine acting upon it with any matrix you want. Any measurement you make, for instance, can be represented by a matrix. And the cute thing about quantum mechanics, the thing that makes it quantized, is that only a discrete set of answers can come out of most measurements. This is because a measurement causes the system to adopt an eigenfunction of the matrix representing that measurement.
An eigenfunction is a vector that still looks the same after it’s been operated upon by a particular matrix (from the German word “eigen,” which means something like “own” or “self”). If we consider the operator for reflection that I jotted out above, you can see that a vector pointing straight up will still resemble itself after it’s been acted upon.
And a neat property of quantum mechanics is that every operator has a set of eigenfunctions that spans whatever space you’re working with. For instance, the X & Y axes together span all of two-dimensional space… but so do any pair of non-parallel lines. You could pick any pair of lines that cross and use them as a basis set to describe two-dimensional space. Any point you want to reach can indeed be arrived at by moving some distance along your first line and then some distance along your second.
This is relevant to quantum mechanics because any measurement collapses the system into an eigenfunction of its representative matrix, and the probability that it will end up in any one state is determined by the amount of that eigenfunction you need to describe its previous wavefunction in your new basis set.
That is one ugly sentence.
Maybe it’s not so surprising that Heisenberg described this incorrectly in words, because this is somewhat arduous…
Here, I’ll draw another nifty picture. We’ll have to imagine two different operations (you could even get ahead of me and imagine that these represent measuring position and momentum, since that’s the pair of famous variables that don’t commute), and the eigenvectors for these operations are represented by either the blue arrows or the red arrows below.
If we make a measurement with the blue matrix, it’ll collapse the system into one of the two blue eigenvectors. If we decide to measure the same property again, i.e. act upon the system with the blue matrix again, we’re sure to see that same blue eigenvector. We’ll know what we’ll be getting.
But once the system has collapsed into a blue arrow, if we measure with the red matrix the system has to shift to align with one of the red arrows. And our probability of getting each red answer depends upon how similar each red arrow is to the blue arrows… the one that looks more like our current state is more likely to occur, but because neither red arrow matches a blue arrow perfectly, there’s a chance we’ll end up with either answer.
And if we want to make a blue measurement, then red, then blue… the two blue measurements won’t necessarily be the same. After we’re in a state that matches a red eigenvector, we have some probability to flop back to either blue eigenvector, depending, again, on how similar each is to the red eigenvector we land in.
That’s the uncertainty principle. That position is simply not well-defined when momentum is precisely known, and vice versa. The eigenfunctions for one type of measurement do not resemble the eigenfunctions for the other measurement. Which means that the type of measurement you have to make in order to know one or the other property invariably changes the system and gives you an unpredictable result… it’s like you’re rolling dice every time you switch which flavor of measurement you’re making.
But the measurement isn’t causing error. It’s revealing an underlying probability distribution. That is, there is no conceivable “gentle” way of measuring that will give a predictable answer, because the phenomenon itself is probabilistic. Because the mechanics are quantized, because there are no in-between states, the system flops like a landbound fish from eigenvectors of one measurement to eigenvectors of the other.
Which is why it bothers me so much to see the uncertainty principle described as measurement obscuring reality when the idea crops up in philosophy or literature. Those allusions also tend to place too much import on the idea of “observers,” like the old adage about a tree making or not making sound when it falls in an empty forest. Perhaps I did a bad job of this too by writing “measurement” so often. Maybe that word makes it sound as though quantum collapse requires intentional human involvement. It doesn’t. Any interaction between quantum mechanics and a semi-classical system will couple them and can cause the probabilistic distribution of wavefunctions to condense into particle-like behavior.
And I think the biggest difference between the uncertainty principle and the way it’s often portrayed in literature is that, rather than measurements obscuring reality, you could almost say that measurements create reality. There wasn’t a discrete state until the measurement was made. It’s like asking an inebriated collegiate friend who just learned something troubling about his romantic partner, “Well, what are you going to do?” He’ll probably answer. While you’re talking about it, it’ll seem like he’s going to stick to that answer. But if you hadn’t asked he probably would’ve continued to mull things over, continued to exist in that seemingly in-between state where there’s both a chance that he’ll break up or try to work things out. By asking, you learn his plan… but you also forced him to come up with a plan.
And it’s important that our collegian be drunk in this analogy… because making a different measurement has to re-randomize behavior. Even after he resolves to break up, if you ask “Where should we go for our midnight snack,” mulling that over would make him forget what he’d planned to do about the whole dating situation. The next time you ask, he might decide to ride it out. It’s only when allowed to keep the one answer in the forefront of his mind that the answer stays consistent.
The uncertainty principle says that position and momentum can’t both be known precisely not because measurement is difficult, but because elementary particles are too drunk to remember where they are when you ask how fast they’re moving.
And, here, a treat! As a reward for wading through all this, I’ve drawn a cartoon version of Heisenberg’s misconception. Note that this is not, in fact, the correct explanation for the uncertainty principle… but do you really need me to sketch a bunch of besotted electrons?