Untangling Cognition/Power Behind Science
Suppose that one day, a sorcerer, wearing black robes inscribed with mystic symbols, walked through the corridors of a major hospital and healed more than a hundred inoperable patients by chanting arcane syllables. Suppose that this happened in front of the TV cameras, despite all the anti-cheating precautions that could be mustered by scientists and professional magicians. Suppose we had blatant, undeniable evidence of true magic. If you don't think the scenario described is sufficiently blatant and undeniable, substitute whatever scenario you like. If you don't like the word "magic", substitute the phrase "something we don't quite understand" - this substitution would probably be a good idea in any case. But suppose that the sorcerer chanted and the patients were healed.
Some would say: "I wonder how it works?" Some would say: "I want to do that!" Some, no matter what you showed them, would say: "I'm sorry, but this has to be a clever lie." Others would give in after being presented with sufficiently blatant evidence - more blatant evidence than a truly fair reasoner would require, perhaps, but nonetheless giving in eventually. Some people would try and explain the operation of sorcery in terms of laws they already knew about, while others would point out that sorcery is really not the sort of thing that you'd expect presently known laws to successfully explain. Some people would sigh and say: "Magic already existed. You already had enough evidence to know that magic existed. The only thing that's changed is that you've finally run out of excuses."
Different people would have different reasons for calling this "a turning point in human history", but not many people would shrug and walk away. Or would they? It doesn't seem likely, does it?
What would make magic so important? It might turn out that magic wasn't all that powerful, and that it was cheaper to grow food on farms then to conjure it. Medical uses might prove too dangerous. There might be little or no commercial market aside from entertainment. The discovery of magic would still be one of the most important moments in the history of the human species. Why? Because so many people have dreamed of doing magic? No; dreams come true every day. Promotions are granted, marriage proposals are accepted. Humans dreamed of flight for millennia, and while the first hot-air balloon and the Wright Brothers' first airplane were interesting moments in history, neither begins to compare with what the discovery of magic would mean. Magic would be important because it would be so utterly unexpected - because we knew so little about it that we didn't even know why, specifically, it might be important. We might not know what we had discovered until decades or centuries later. If I don't know something, I can't know how much I need to know it - it's a gap in my mind, a hole in my picture of the world. Anything at all could come out of that gap. Beautiful things, terrible things; there's no way to guess in advance. That's the value of general curiosity. I would find out why I had needed to investigate after I had investigated.
If, as in the stories, I found myself waking up one morning in a world where magic worked - a world where a few people could, by virtue of their eldritch knowledge, heal the sick or build castles floating in the air - I would study sorcery. It seems like such an obvious thing to do! Finding themselves in this world, why do so few people study science? Why is healing the sick any less impressive if the sorcerer is wearing a white laboratory coat instead of robes?
Maybe the secrets of science aren't exciting if just any random yahoo is allowed to know. It's not that everyone does know. Most scientists know only the small handful of secrets that pertain to their particular fields. No one knows them all; a human lifetime is not long enough. And many people around the world don't know any. So it's not that the secret is cheapened by everyone knowing, because people don't know. But somehow, just being allowed to know takes the fun out. A secret can't be interesting if they'll go around telling just anyone. And yet... should we really stop being curious, just because someone else knows the answer? Does that make the mystery any less mysterious? If you see that other people affect disinterest, being too jaded and sophisticated to care about a truth that no one is trying to conceal... does that make the answer less valuable to you?
If magic worked reliably, no one would care about it. If magic existed, any suggestion that magic was somehow unusual would be met with the puzzled reply, "Oh, but that's just magic."
Centuries ago, humanity caught on to something - we discovered a mode of thinking that unlocked secrets. In the relative blink of an eye, humanity went from swords and plowshares to guns and combine harvesters, from tending campfires to wielding the vast energies that burn in the heart of the sun. We have shouted our voice into the interstellar night and set our footprints upon the moon.
I say this, not as a cheerleader, but to point out that something strange is happening. Why do our eyes and senses of mystery pass over such bizarre events just because we're told that "science" is at work? Why is healing the sick front-page news if "magic" is at work, and yet utterly unremarkable if the cure is "a new medical therapy"? Why are people so easily bamboozled into ignoring the elephant in their living room, just by being told that someone, somewhere understands it? How can we get a peek past the curtains of reality, and ignore it? Why does science work? The question shouldn't become any less mysterious if we're told that someone else knows the answer.
From time to time I've encountered people who believe, as their personal philosophies, that reality is subjective; that we each create our own universes. Or that science is only one belief system, among many possible ones. I shall have more to say on this later. But let's suppose this were true; wouldn't that make the puzzle even more mysterious? Why then would science appear to work? Why does a digital wristwatch, unlike a voodoo doll, go on working even if we stop believing in it? People sometimes speculate that the whole world is only a figment of their own imaginations - or rather, I should say, some of the so-called "people" you invented to populate your private universe have appeared to make such speculations, though, of course, it is only your own mind trying to communicate with itself. Still, aren't you at least a little interested in finding out what kind of world you invented? It's very beautiful, and speaking as a figment of your own imagination, I think you should be proud. If I thought I was dreaming, and in my dream I found a book called "How Everything Works In Your Dream", then I would read it.
You don't have to agree with the philosophy of science, you don't have to like science, you don't have to believe science, to wonder why science works - or why science appears to work, or why so many people think science works, or why you dreamed a dream where science works.
In the late eighteenth century, the French chemist Antoine-Laurent de Lavoisier discovered fire. Today, when fire is routinely used in industry and even around the home, this no longer seems remarkable; but in those days Lavoisier's discovery came as a tremendous surprise. "What?", you say. "Hasn't the use of fire been dated back for hundreds of thousands of years?" Well, yes; people used fire. Fire was very hot, bright, sort of orangey-colored, and you could use it to cook things. People practiced making fires, and developed greater or lesser skills at handling fires. Perhaps a few exceptional folk became known as tribal experts on fire. But nobody had any idea how fire worked. The Greek alchemists and medieval alchemists thought that fire was a basic thing. They held all matter to be composed of the Four Elements: Earth, Water, Air, and Fire. In Lavoisier's time the alchemical paradigm had been gradually amended and greatly complicated, but fire was still held to be basic - in the form of "phlogiston", a rather mysterious substance which explained fire, and just about every other phenomenon in alchemy.
Here in brief is the story of the discovery of fire. Lavoisier's great innovation as a chemist was to painstakingly weigh all the pieces of the chemical puzzle he was studying, both before and after the chemical reaction. Previously, chemists had thought that there were chemical (or alchemical) transformations that decreased or increased the weight of the total material involved. If you subjected finely ground antimony to the focused sunlight of a burning glass, the antimony would be reduced to ashes after one hour, and the ashes would weigh one-tenth more than the original antimony - even though the burning had been accompanied by the loss of a thick white smoke. Lavoisier weighed all the components of such reactions, including the air in which the reaction took place, and discovered that matter was neither being created nor destroyed. If the burnt ashes increased in weight, there was a corresponding decrease in the weight of the air.
At this point it becomes complicated to assign credit, owing to the work of Lavoisier's contemporaries such as Joseph Priestley. Here is what they found: A burning fire, such as a candle, diminished the amount of one kind of gas, vital air, and produced another gas, fixed air. Today we would call them oxygen and carbon dioxide. When the vital air was exhausted, the fire went out. One might guess, perhaps, that the fire was transforming vital air into fixed air along with the transformation of fuel to ash, and that the ability of this transformation to continue was limited by the amount of vital air available. Lavoisier generalized, correctly, that fire was "the combination of fuel with oxygen" - as we would put it today.
Lavoisier's proposal directly contradicted the then-current phlogiston theory. That alone would have been shocking enough, but it also turned out...
To appreciate what comes next requires putting oneself into an eighteenth-century frame of mind. Forget the discovery of DNA, which occurred only in 1953. Unlearn the cell theory of biology, which was formulated in 1839. Imagine looking at your hand, flexing your fingers... and having absolutely no idea how it worked. The anatomy of muscle and bone was known, but no one had any notion of "what makes it go" - why a muscle moves and flexes, while clay molded into a similar shape just sits there. Imagine being composed of mysterious, incomprehensible gloop. And then, imagine discovering...
...that humans, in the course of breathing, consumed vital air and breathed out fixed air. People also ran on combustion! Lavoisier measured the amount of heat that animals (and Lavoisier's assistant, Seguin) produced when exercising, the amount of vital air consumed, and the fixed air breathed out. When animals produced more heat, they consumed more vital air and exhaled more fixed air. People, like fire, consumed fuel and oxygen; people, like fire, produced heat and carbon dioxide. Deprive people of oxygen, or fuel, and the light goes out.
For hundreds of thousands of years, fire was humanity's friend and occasional enemy. We used fire as a tool to cook meat, or create light. We made tools to create fires, such as bowdrills. We made tools, such as fire arrows and torches, that used fire as part of the artifact. We used fire to make tools, charring the points of spears, and later, smelting metals. Fire, in its form as an orangey-bright hot thing, has been tamed for millennia. We used it, but we didn't really comprehend it. It was only after Lavoisier's discovery of combustion that we realized what it was we had discovered and called by the name, "fire". If you go by surface appearances, a human being and a campfire look different. It was only after we understood combustion, the phenomenon behind fire, that we could pierce past surface appearances to see fire and breath as two special cases of a general rule. It was only after we understood fire that we realized that every human being contained within themselves the flame - that what we had been calling "fire" was just a more concentrated version of something that everyone had been doing their whole lives, all unaware, as easily as we breathe.
So what underlying force does science draw upon? And is this deeper force something that anyone can wield, or only a chosen few? It takes effort and special knowledge to start a science and keep it going; only a few people are acknowledged as expert science-tenders. Is the deeper force behind science something that we wield effortlessly, inherently, without ever being aware of it?
Since I've gone to all the trouble to ask the question, you can guess that I think the answer is Yes. But the deeper phenomenon behind science is something which takes work to explain, or even introduce. Giving the power a name, at this point, would not help. You can say that the secret of fire is "combustion", but unless there is something new and surprising to say about "combustion", the renaming is of no use. New discoveries are sometimes given old names - for example, "combustion" to describe the combination of fuel with oxygen - but that comes at the end of the problem; shuffling names, alone, can never help. In the case of fire, people spent millennia recombining old words such as "fire", and new words such as "phlogiston", and never did get anywhere. The enigma was only transferred, not solved. The mystery becomes a small, hard, opaque ball, batted around from one word to another. It's a common error made during the early days of problems. As when early chemists explained fire by reference to "phlogiston", or when vitalists explained biology by reference to "elan vital".
Eventually someone makes an observation that cracks open the mystery, creates a handhold, and gives us a firm grip with which to unfold the rest of the problem. In the case of fire, the first crack showed when Priestley and Lavoisier observed the behavior of vital air and fixed air in the presence of fire. This is one reason why fire was not understood earlier; oxygen and carbon dioxide are both transparent gases, and it takes some cleverness to separate them and weigh them. If I were dropped into the seventeenth century and stripped of my anachronistic knowledge of chemistry, I would not be able to figure out the answer just by staring at the flames. Vital air and fixed air had been discovered not much earlier, and their existence was known primarily to a handful of specialists. So the clues were hidden, and the final answer was not psychologically obvious - not the sort of story you'd make up while sitting around a campfire.
And Lavoisier did not finish understanding fire, did not live to see the day when chemistry became physics; that took more than a century, to see combustion as a special case of chemical reactions, which in turn are a special case of those universal laws which govern all interactions between molecules, both stable configurations and chemical reactions - the laws of quantum electrodynamics.
Today, centuries after the discovery of fire, it is possible to explain fire quickly and easily, using widely known concepts. Oxygen, combining with carbon, yields carbon dioxide - why, when you put it that way, you wonder why no one stumbled across it before. You'd think the names would have been a hint, right? But instead they insisted on obscure technical terms - calling oxygen "vital air" and carbon dioxide "fixed air" - thus making the problem needlessly obscure...
In the twenty-first century, we think in concepts that render the nature of fire psychologically obvious, and it is difficult to think back to a time when everything was just... stuff. Even if you've managed to go your whole life without hearing about oxygen and carbon dioxide, growing up today renders it hard to sympathize with the eighteenth century. Here I am, telling you about these two invisible substances, which nobody can see, which can only be isolated by some obscure procedure I haven't even described to you, which can supposedly be weighed despite floating in the air, and which allegedly prove that a person is like a campfire in some obscure way, although the two don't seem at all alike. Now you might feel some skepticism, you might go and search on Google to see whether I'm making it all up, but you wouldn't think I was insane. You wouldn't slowly back away, or have me committed to a lunatic asylum, or set me on fire. You've heard similar-sounding words on television and in the newspaper, so the explanation sounds socially acceptable and normal. Even if the statements were wrong, they wouldn't be, by public standards, crazy.
And the phlogiston theory is dead. For most people today, in First World countries, with respect to the particular question of fire, there is no vast cloud of mistakes and misconceptions and illusions and plausible-sounding stories to get in the way. It is the best kind of ignorance, an absence of knowledge rather than false knowledge. That, above all, is what makes it easier to explain fire today than in the eighteenth century. If someone didn't learn about fire in school, you can just walk up and explain it; you don't have to painstakingly pry the person away from an elaborate mistaken explanation that forms a seamless part of their integrated philosophical worldview. Discoveries that crack open a problem are rare and prized, but they only begin the story of a scientific revolution; the heartbreakingly difficult effort lies in clearing away past mistakes.
When a problem has been cracked open, it is not unusual for the "problem", as we see it, to change. First we ask the question, then we find the answer, then we realize that we got the question wrong. Some incorrect ways to phrase the question of fire are "Why do some substances emit phlogiston and others absorb it?" or "Can the Element of Fire be isolated from the Elements of Earth and Air?" Today we know the question is about chemical transformations - molecules, arrangements of atoms, recombining to form other arrangements of atoms. When first approaching an unsolved problem, it's best to begin with the most intuitive, concrete question available: "What is this orangey-bright hot stuff over here, and how does it work?"
Sometimes, in the course of arriving at a deeper understanding, you find out that you phrased the problem too generally, and bit off too much phenomenon in your question. The Sun looks fiery, but it runs on nuclear reactions rather than chemical reactions. If you try to explain the Sun without nuclear reactions, you run into a problem: the Sun cannot have been burning for very long! Lord Kelvin was a prestigious nineteenth-century physicist who did decent work in his early days, but later had the misfortune to pick the wrong side of rather a lot of arguments, so that today Lord Kelvin is remembered chiefly for statements such as "Radio has no future", "I can state flatly that heavier-than-air flying machines are impossible", "There is nothing new to be discovered in physics now; all that remains is more and more precise measurement", and "X-rays will prove to be a hoax." In the case of sunlight, Lord Kelvin calculated that chemical and gravitational energy combined could not have kept the Sun alight for more than 40 million years, proving (as was then thought) an upper bound on the age of the Earth. The evolutionists and geologists of the nineteenth century, whose theories invoked processes that required hundreds of millions of years in which to operate, had to stand up and say "The physicists are wrong." Not a comfortable position, but oh, the glory when they turned out to be right! At any rate the fire of the Sun is not fire; or if I wished to call it fire, I would distinguish between nuclear fire and chemical fire. If you ask that any theory which describes a blazing campfire also account for the blazing Sun, under the common banner of "explaining orangey-bright hot things", you must wait another hundred years and deal with a much more difficult theory than would suffice to explain chemical fire alone.
And sunlight was not the only questionable flame. Phlogiston was invoked to explain the properties of metals and acids and gases, and earlier the Element of Fire was invoked to explain pretty much everything, including the existence of time. Heraclitus of Ephesus, in the sixth century BC, stated "all is fire"; a theory can't be asked to explain more phenomena than that! Or consider Franz Mesmer, of the eighteenth century, who described as "animal magnetism" the phenomenon we today call "hypnosis". It would have taken rather longer to come up with a unifying theory of electromagnetism if we included hypnosis on the list of phenomena to explain. We only learn the question after finding the answer.
I sometimes hear it said that the definitions of words are arbitrary. Admittedly, I can choose to define a word in a wide variety of ways - just like I can choose to eat nothing but cheese, or choose to drive on the other side of the road. But the choice has consequences. The way I define a word affects the way I think. I can decide that "fire" by definition refers to campfires and sunlight but not breath. I can decide that "fire" is an arbitrarily defined set which includes the phenomenon of a campfire and the phenomenon of sunlight, but excludes the phenomenon of respiration. I can arbitrarily decide to exclude flames built with charcoal, and arbitrarily decide to include microwave ovens. But if I inflict this definition on myself, the consequence is that I will have an excruciatingly hard time understanding "fire". I can't call this choice arbitrary if it has consequences I care about.
I should like to do is define "fire" in such a way that it corresponds to some deep regularity of the world, so that all the things I call a "fire" share a single underlying cause and structure. It would make the problem so much easier to solve, if I were trying to explain all those things, and only those things, that do indeed have one common explanation. Unfortunately, you can only build this perfect mystery after you know the solution. Defining the problem correctly is part of the victory celebration, when you look back at the history of the question and slap yourself on the forehead and say: "Oh, that's why I had such a hard time inventing a theory of fire that included the Sun."
Much of the work of finding an explanation consists of figuring out which questions are a proper part of the problem. Much of the psychological difficulty of solving a problem comes from implicit assumptions hidden in definitions; if I define phlogiston as "the substance whose release explains fire", I am presuming that fire has that particular kind of explanation. The psychological effects of words are subtle, and dictionary definitions usually fail to list all the connotations.
The word scientist has started to bother me. Not the actual people, but the word, "scientist". It reminds me of the word sorcerer, subtly implying that only a few people are born with the power to use science. "Scientist" is a distancing label, both for the labeled and the labelers. Like so many of the terms that humans apply to each other, it emphasizes differences rather than the things we have in common. So what word should we use? Maybe we shouldn't have a word at all. Maybe sorting people into categories and labeling them is just asking for trouble. If there's one word - "human", "person", "sentient" - you have one tribe. Two words create two tribes.
Even the word science may be problematic - it may skew the way people think about the universe, creating a false divide, like the word scientist. The author L. Sprague de Camp once wrote a story called The Incomplete Enchanter, dealing with a person from our world transported into a world of magic. Naturally, since it is a world of magic rather then technology, when the main character tries to light a fire using a match brought along from Earth, the match fails to strike.
I realize it was only a short story, but... how do I put this...
No.
Matches catch fire because of phosphorus in the match heads, or, more commonly, phosphorus in the strip on which we strike the matches. (Most matches sold today are safety matches; they can only be struck on the match strip. Strike-anywhere matches have phosphorus in the match heads.) Why use phosphorus? Because it's very, very flammable. Pure phosphorus glows in the dark and may even spontaneously catch fire. Henning Brand, who first purified phosphorus in 1669, had a simple explanation for this; he announced that he had discovered Elemental Fire.
Phosphorus is also a component of adenosine triphosphate, ATP, the rechargeable battery of biology. ATP is a compound your body uses to store and provide energy - ATP is the transport mechanism for chemical energy, the "biological unit of currency". Almost every biological process is powered by ATP, from contracting muscles to firing neurons to manufacturing proteins. In plants, ATP is created during photosynthesis; in the animal kingdom, the energy to make ATP comes from the combustion process of respiration.
So it's not just that a campfire is a more concentrated version of a process, combustion, that is inherent in every human. Breathing - respiration - isn't just a coincidental function tacked on to the rest of the human body. The flame inside us provides the power that makes everything else go.
And phosphorus isn't just a convenient way to strike a match and create a campfire. Biology relies on the chemical properties of phosphorus to keep the internal flame alight. If a match stops working, so do you. You can't change just one thing.
One of the most surprising properties of the universe is its inseparability. It's not quite true that everything connects to everything else, but everything connects to something else. We unwrap packages of wildly different shapes and colors and find the same contents inside. Again and again in the history of science it happens, the astonishing reunifications, the meeting of the twins separated at birth. Fire and breath; a falling apple and an orbiting planet; a bolt of lightning and a compass needle.
Human thinking tends to create classes where none exist; we impose artificial divisions on the universe. Words slice the universe into pieces; "light" and "dark", "night" and "day", "electricity" and "magnetism". Often the universe seems to dislike being sliced, and forces us to put it back together again. And the word "science", in particular, is a strange place to make a division. Is fire science? Is breathing science? What about apples, or sunlight, or the mating song of a lark? Can you buy six pounds of science at the supermarket? Here's our word, finely sharpened, but where do we cut?
If the word "science" denotes anything, it denotes a way humans have of seeing the universe, rather than a division that exists in the universe itself. Apples, sunlight, the mating song of a lark; all of these have complicated stories and people devoted to their study. Knowing the complicated stories behind things; is that science? But there are complicated stories that we don't call "science". "Science", I would say, is a division that we impose in describing our knowledge.
That is the problem with telling a story of a world where a match stops working and a human survives; the division between the two fires is a division we impose on our knowledge, and not a division that exists in the things themselves.
Not all of the images evoked by the word "science" are essential to science, or even related to science. Some of these images are obviously the result of marketing; for example, sellers who use the word "scientific" in advertising copy. "New and improved scientific formula! Buy now!" (Apparently you can buy six pounds of science at the supermarket.) More subtle is the tactic that technology startup companies use to get free publicity; the common confusion between technology and science allows the latest and greatest techietoys to be presented as newsworthy science. Sometimes improvements in technology do have implications for science - it's hard to do astronomy without a telescope. But the overall effect of the companies looking for free publicity is that the word "science" associates to expensive toys. Even the word "technology" shouldn't associate to expensive toys. A telephone or a stove is technology, or manufactured clothing, or a flint handaxe. Associating technology with the most recent and expensive technology contributes to the air of exclusivity. Computers are the famous modern example of a technology that started out rare and expensive and specialized and became ubiquitous... but the automobile also began as an expensive toy, though few now remember those times. And telephones; and wristwatches; and manufactured cloth; and iron tools; and bronze, in its day.
The media also contribute to this effect, reporting only on the latest, most controversial, least settled scientific topics. How often do you see headlines such as "Maxwell's Equations continue to hold" or "Earth still orbiting Sun"? No, these are not the latest, the greatest, the most glamorous and incomprehensible outputs of modern theoretical physics; but once upon a time they were. People spent their lives studying the question; after great efforts, the discoverer finally broke through to the hard-earned answer and exulted in the dazzling beauty; the world was shocked; and the way we saw the universe changed. These discoveries once shone so brightly; why do we value them less today? The discoveries are surely no less beautiful.
There is an advancing frontier, in science, and in technology. Marketing glitz and the media's hunger for "breaking news" make the frontier seem like the whole territory, ignoring the settled lands behind. But the frontier is unlike most of the territory. "Newsworthy" science is controversial, based on a small handful of non-replicated experiments, often ill-understood and confusing, sometimes outright wrong. By the time there's any solid basis for the investigation, the media thinks it's an old story. Newsworthy technology is glitzy, prone to failure, and above all, too expensive for you to afford. But flint handaxes are also technology, as is fire.
Today's world imprints us with a web of associations that surrounds science: glitzy images depicted in movies about science or the future, character traits that form a stereotype of scientists. I'd like to disentangle this cultural image of science from the question of why science works. Our cultural image of science says nothing about what it means to wake up one morning and find yourself in a world where there are footprints on the Moon.
With the permission of the audience, I would speak of the power behind science, which sustains our conscious thoughts and our unconscious cognition. I would speak of the magic that is your birthright, and the birthright of every human being; the strength to shout across continents and walk on the Moon.
The power is called Bayesian decision theory. Humanity first got a firm grip on the problem in the person of Pierre-Simon Laplace, a mathematician and contemporary of Lavoisier. Only recently, however, is humanity understanding what Laplace discovered, a slow dawning realization known as the Bayesian revolution in the Cognitive Sciences.
It is flatly impossible to explain the awesome power of Bayes without math. Fortunately, first entry into the Baysian mysteries requires only that you know how to add, multiply, and divide. If you have never truly wielded math before, never felt the magic burning in your blood, then let this be your initiation. I cannot think of any better first spell for a sorcerer. Bayes' Theorem is the most beautiful of all the Great Equations I know, with the strongest power and the deepest human meaning, and yet of all the Great Equations it is the most accessible to beginners. If you've never thought of yourself as a Math-Wielder until now, give it one more try. For this too is your heritage as a human being.
Please continue with Untangling Cognition/Bayes Theorem.
Bibliography (needs completing):
The Incomplete Enchanter, L. Sprague de Camp
The Age of the Earth as an Abode Fitted for Life, Lord Kelvin
