I, Probability

Physicists tell us the universe is random. The laws of quantum mechanics demand it. When we say (or I should say when they say, as I'm certainly no authority, on quantum mechanics or anything really) that, say, the position of an electron is described by a probability, that's as far as it goes. Full stop. Physics is not merely throwing up its hands and saying this is the best we can do. Rather, they mean to say this is all there is. There are no hidden variables, nothing deeper. There is no wizard pulling levers behind the curtain they are currently seeking to uncover.

Such a worldview is hard to accept. Everyone who has confronted quantum mechanics, from lay reader to learned professional, has recoiled at the thought of abandoning determinism. God does not play dice, Einstein famously recoiled. Albert went to his grave in 1955 believing determinism would return. Determinism went to its grave in 1964, Bell's Theorem establishing once and for all there is nothing beyond a shell game.

The mind reels. Yet, your mind has no business reeling. It, too, is built on probability and I don't mean in the sense that everything is. There is a much larger probability at work inside your noggin that has nothing to do with quantum mechanics. What you call thinking, what you call Self, is really just a cosmic game of roulette. A spin of the well-figured wheel. A dance on a volcano.

God might not play dice, but your brain does.

It's playing right now.

---

The Two Towers

Neuroscience has invented a mythology about how the brain works which goes something like this: Neurons collect excitatory and inhibitory inputs and if the algebraic sum exceeds some threshold then an action potential is generated. I've discovered the degree to which a person believes this story is inversely proportional to the amount of time they've spent poking around real actual squishy brains. It's easy to pontificate about Hodgkin-Huxley equations and Boltzmann machines and renewal processes when the only neurons you've ever wrestled came out of a computer. Well, you're in my house now Neo, so put on an apron and pick up that bone saw and remember if you're going to barf lift up your face shield. (Also, don't put your fingers in the DMSO -- it's a carcinogen.)

For a proper telling of the story we must go back to the beginning, and at the beginning nobody had much of a clue about anything. It is the waning of the 19th century, and the great scientific debate of the day concerns the fundamental structure of the brain. In one camp are those who propose the brain is a syncytium -- one continuous network with all parts connected into a single computational organ. Opposing them are those who claim the brain comprises a vast collection of interacting computational units. What those units computed or how they interacted was not understood. First it was necessary to prove they existed.

Such debate may seem quaint to us Heutzutage, but this was not a time of fluorescent proteins and in situ hybridization and electron microscopy and intracellular recording. Histology was in its infancy, and most labs didn't have electricity, let alone use it for experiments.

The light microscope was the cutting edge technology of the day. To study the microscopic structure of the brain it is necessary to make thin slices of the tissue (chunks of brain are just nondescript blobs under the microscope) and then stain the tissue to reveal its components (unstained thin tissue is approximately transparent -- this is why photoreceptors work even though they're behind the rest of the retinal circuitry). Then, as now, staining is both art and science. The stains used in microscopy generally exhibit a fondness for a specific cellular structure -- the ribosomes or the cytoskeleton or whatever -- but because of the oppressive complexity of neural tissue, applying almost any stain results in nothing but a colorful thicket of incomprehensibility. What was needed was a way to stain something while not staining everything.

The breakthrough comes from Camillo Golgi, who stumbles across a silver impregnation technique while working in his laboratory at the University of Pavia. This stains entire neurons (he did not yet know to call them that) but only a choice few, creating a surreal landscape of intense cellular objects dotting a pristine landscape. (Aside: Last time I checked, we still don't know why the Golgi method stains some cells and not others. The answer is not exactly Nobel worthy, but it would be nice to know.)

Golgi views these discrete stained thingys staring back at him from under his microscope. The debate was over. To him, there could be no doubt: The brain was a continuous syncytium.

I'm telling ya, you can't make this stuff up.

Presumably, the thought process which led Golgi to exactly the wrong interpretation of his results is rather more complicated than we have time to delve into presently. Fortunately for us, Golgi has a nemesis. The El Cid to his Sancho, the Don Quixote to his Sally. This is the great Spanish neuroanatomist Santiago Ramón y Cajal.

Cajal took the Golgi method out for a spin (more like a marathon, as anyone who has faced Cajal's imposing two volume set on human neuroanatomy can attest) and because we still have quite a ways to go let me just skip to the end of the first act: Cajal provides convincing evidence that the syncytium model is wrong. Rather, the brain is a collection of cells -- he (or somebody) christened them "neurons" -- of multiple shapes and sizes, and in vast numbers.

Cajal puts neurons on the map. But how they communicate, how information goes from one to the next is still a mystery. Cajal takes down his vast library of Golgi-stained sections and does what he always does. He squints.

Protoplasmic Kiss

Those protoplasmic kisses, the intercellular articulations ... seem to constitute the final ecstasy of an epic love story.

Thus did Cajal describe the synapse, the meeting place between the output of one neuron and the input of the next.

Which is odd because Cajal never saw a synapse in his life (they're too small to be resolved by light microscopy). There is a leap of faith here, or at least a leap of intuition; Cajal tracing a long tenuous process given off by a neuron, barely visible in a Golgi stain, to where it terminates, examining sample after sample until serendipity smiles and he finds a sample where the axon of one stained cell terminates on the stained dendrite of another. There must be something going on at the junction, Cajal surmises, although the details of his protoplasmic kiss would take some decades to suss.

Footnote: I think that quote is from Cajal's acceptance speech for the Nobel Prize, which he shared with Golgi in 1906. It's easy to imagine Cajal being somewhat peeved at sharing the prize -- one of these guys was, well, wrong -- and I like to think Cajal's little ode is just him twisting the knife in Camillo standing next to him on the rostrum. Yeah, stand there and stew in your wrongness, ya big stupid baby. If you think Nobel laureates are above this sort of thing, you really don't understand academics.

Call Cajal intuitive, call him lucky, just don't call him late for dinner. A small gap indeed exists* between where the axon of one neuron ends and the cell membrane where the next neuron begins (*usually). Something is happening in there, but this is a riddle Cajal will not solve. Visualization of the synapse requires the electron microscope, a tool which would not be in widespread use in neuroscience until decades after Cajal had died.

But we're getting ahead of ourselves. If our tale is to be told properly, there are other fish we must first fry. Or frogs, as it were.

Stuff of Dreams

Meanwhile in Bavaria, Otto Loewi is suffering restless sleep. He is tortured by a strange dream, and not the good kind like Kari Byron dressed as an ice cream cone. One fateful night he is shaken awake by a thunderclap echoing through the cavernous hallways of his secret laboratory fortress high above the Alps, which may have actually been his modest house outside the University of Graz but no matter. A thought has arrived, inspiration via the subconscious conduit. Legend has it Loewi feverishly scribbles in a bedside journal, then falls back to sleep.

The next morning he cannot read his handwriting. Somewhere the Muse folds her arms across her chest and glares.

Later that week Loewi again wakens from the same dream. This time he takes no chances. Donning a nightshirt and candelabra he rushes downstairs to his basement laboratory, there rousting a hunchbacked assistant (or graduate student, in some tellings of the tale). They prepare two frogs, stimulate the vagus nerve of the first to increase its cardiac function, then extract the vital juices from the pericardial sac and inject those into the heart of the second frog. It's cardiac function, too, increases (unfortunately, this is the sort of random cruelty scientific progress seems to require).

Loewi has demonstrated the world's first neurotransmitter. A substance was released by nerve stimulation (later shown to be acetylcholine) that effects change in cells of the targeted organ. Here, that organ was the heart, but it was quickly recognized the same mechanism was at work in all organs, and more generally between neurons.

Combining Loewi's experiment, and Cajal's histology, and much else besides that we're going to gloss over, a picture emerges: The brain is a collection of neurons of multiple shapes and sizes, and in vast numbers, separated by a little gap called a synapse, which communicate by spitting chemicals at one another. Pfft. Pfft. Pfft. The neurotransmitter crosses the synapse and does something to the next cell in line.

The neuroanatomy and neurochemistry ducks were aligned, but there was still a missing piece of the puzzle: Just what did a neurotransmitter do to a neuron?

The Final Duck

It was known electricity and brain function were related -- the "stimulation" in Loewi's experiment was "galvanic" (i.e., electrical). But it was recognized early on the brain also produced electricity of its own. Hans Berger first recorded the electroencephalogram from dogs around the turn of the century, and if that conjures up a visage of Berger's experimental subjects wearing doggy EEG shower caps I will not disabuse you of that family-friendly re-imagining (we should really be speaking of ECoG not EEG, if you know what I mean).

Whatever was the source and meaning of these wiggly traces, the fluctuations of the electric field* that coursed within the brain? (* the EEG actually measures current in a volume conductor, not an electric field, but that distinction need not concern us). Down, down, they went, using ever smaller electrodes and ever more-sensitive recording equipment looking for the fount. Crude silver balls were jettisoned for sharp tungsten microelectrodes, these in turn replaced by tiny glass capillaries heated and extruded to a fine point. Until, finally -- a breakthrough. Literally. Someone (I believe it was John Eccles, or Sir John Eccles to us serfs) made an electrode so tiny that it poked inside a neuron and recorded one neuron's innermost electrical thoughts. Here was an entirely new milieu, a rich country ripe for exploitation no less than Columbus stumbling upon the coast of the Americas.

Correlation is not causation, but it is causation's calling card. Electrical stimulation, the kind Loewi used to release acetylcholine, was correlated with electrical fluctuations in the intracellular recording. A post-synaptic potential, as it came to be called, since stimulation was presumed to create a signal on that side of the synapse just as the recorded cell was on this. Two kinds of PSP were observed. Sometimes the PSP was inhibitory, driving the cell membrane potential more negative. Sometimes the PSP was excitatory, and if one or more made the membrane potential sufficiently less negative it coaxed the neuron to produce an axon potential, which then presumably sped off to create PSPs in neurons downstream. And so on and so on.

A picture emerged: The brain is a collection of neurons of multiple shapes and sizes, and in vast numbers, separated by a little gap called a synapse, which communicate by spitting chemicals at one another. Pfft. Pfft. Pfft. The neurotransmitter crosses the synapse and does something to the next cell in line. That something is to flip a switch that lets current flow into cell and create electrical fluctuations, the PSPs they were watching on their oscilloscopes attached to a microelectrode currently impaling the neuron in question.

The brain was circuitry, a cousin of the very equipment electrophysiologists were using to study it. Resistors and capacitors and wires and switches -- vastly complicated, yes, and moist, certainly, but understandable. Perhaps never fully. But understandable in principle, this wet Babbage engine. The brain a symphony; exquisite but orderly. Operating according to the same laws at work in more mundane electronics.

Break out the whiskey and hookers! a call was heard. For it is only a matter of time before we know all there is to know of this thing called brain! All gear work, it is! As predictable as the seasons! Soon there will be nothing left to discover! Exclamation points!

And then something terrible happened.

Alea Iacta Est

Play with the settings on the laboratory gizmo that fabricates your recording pipettes and eventually you can produce a pipette having a tip so small that you can record from individual ion channels that carry the synaptic current. The electrical switch cum pores in the cell membrane that literally let in the juice.

There are wholesome motivations for doing such a thing. For one, it allows you to investigate the action of various chemicals on neural signaling right were the rubber meets the road. This may lead you to discover new drugs for various neural afflictions. It also provides a gander at the primordial signaling mechanism which can be put into various computational models. This provides employment to math majors who want to be neuroscientists but don't have the stomach for a transcardial perfusion.

There were wholesome motivations for building the Event Horizon, too. But instead of interstellar travel, it opened a portal to hell.

Any reasonable person, and LabKitty, would assume an ion channel works as follows: When there is no neurotransmitter present, it is closed. When neurotransmitter arrives, it opens. Easy peasy.

Instead, what you observe is this: When there is no neurotransmitter present, the channel opens and closes at random. When neurotransmitter arrives, the channel also opens and closes at random, but a different kind of random.

Since those words are no doubt clawing at your sanity, I shall attempt an artist's rendition. Suppose we repeatedly observe the state of a single ion channel -- say, once every microsecond -- over some interval and note whether the channel is closed (c) or open (O). Furthermore, suppose we can spritz some neurotransmitter onto the channel while we observe (this is a routine experiment in neuroscience laboratories these days; one wonders what Cajal would think of such magic).

You might expect we would observe this:

---------xxxxxxxx---------
ccccccccOOOOOOOOccccccccc

The top trace is a record of the spritzer (the x's indicate when it's spritzing). The bottom trace is the state of the ion channel we're recording from. It is closed; it is open; it is closed again, correlated with the absence or presence of the neurotransmitter.

Alas, this is not what you observe. Instead, you see something like this:

---------xxxxxxxx---------
cOcOccccOcOOOcOcOcccccOOcc

Ion channels are constantly opening and closing, is the point. Open (and closed) when there is no neurotransmitter present. Closed (and open) when there is. At random. Full stop. Clearly, there is a difference in the overall behavior when the neurotransmitter is present -- the ion channel is trying to do the right thing but it is cursed to chatter. Like my relatives at a Lutheran potluck. Like David Thewlis in Naked who just can't stop himself from making wiseass comments no matter how inappropriate (which eventually earns him a beating).

The Dwarfs drilled too deep into Moria and the Balrog came. Physics drilled too deep into the bedrock of the universe and found only uncertainty. Now Neuroscience has its turn. Electrophysiology upset the apple cart, eventually coaxing randomness out of the brain like Constantine pulling a demon from the possessed (the Keanu Reeves one, not the Roman emperor).

Dreams of a clockwork mind, organized and comprehensible, were swept away. The brain is built on randomness. Madness baked right in. Yet, it may occur to you that the brain seems to do okay more-or-less. Not just evading predators and leaving offspring, but also reading and writing and 'rithmetic. Building great works. Opera. Mathematics. The aqueduct.

It is a conundrum. A right puzzle. Your waking life is not one prolonged mental cat fight. A tornado of disjoint sound and fury. This very day you are having thoughts which reflect reality, impure though they may be. How is that possible now knowing the defective hardware you are implemented on?

This demands an explanation.

I, Probability

Let's assume ancient peoples told a tale about a blind watchmaker who created everything in the world. The oceans and the land. The sun and the sky. The movement of the firmament against the night and the moon against the firmament. The birds that fly and the fish that swim. All that walks or crawls or slithers.

When it came time to make the brain, legend has it, the watchmaker purchased top quality ion channels from a reputable Amazon seller having many thousands of transactions in the last 12 months and an overall positive rating of 94%. Alas, these were on back order, so the seller substituted the ion channels we have previously discussed, that is to say ones exhibiting all of this random opening and closing business.

How do you expect me to build anything with this crap? the watchmaker emails customer service crossly.

The seller shrugs. You better believe there's some one-star feedback coming his way.

Still, the watchmaker is a cunning creator. Whereas a lesser deity may have let things there stand, moving on to clouds and stuff, the watchmaker is schooled in probability. In particular, the watchmaker is conversant with the Central Limit Theorem, which you might recall as the last sign post in probability before things go off the rails with the sigma algebras and measure theory and whatnot. To wit: The CLT states that the summed effect of a collection of random effects is Gaussian distributed. This provides a way forward.

At any given moment, a neuron senses the summed current passing through all open ion channels. There is a kind of cellular democracy at work. One channel carries such a tiny current that it has no real effect on the system overall. A kind of cellular democracy at work (zing!). As such, let's alter our previous artist's rendition to consider the summed effects of a large number of ion channels responding in concert to a spritz of neurotransmitter:

  ---------xxxxxxxx---------
  cccOcccccOOOOcOcOcccccOccc
+ cOcccOccccOcOcOOOccccccOcc
+ ccccOcccOccOOcOcOccccccccc
+ ccOccOccOcOccccOOcccOccccc
+ cOcccccccOcOOOcOcOccccccOc

= cccccccccOOOOOOOOccccccccc

As before, the top trace indicates the application of the neurotransmitter. Below are shown the random responses of a large number of individual ion channels (assume "5" is a large number). The bottom trace is the summed effect. What I'm attempting to show is that while the individual ion channels are loopy, their summed effect is not. There's a few things that don't make sense in this picture, like why all the O's before and after neurotransmitter application disappeared in the sum, and why we don't get a super crazy big O where a bunch of individual O's occur simultaneously. Even though the summed current is literally a sum of currents, you can view it conceptually as an average; random (we should say uncorrelated) contributions get beat down in an average, correlated effects survive.

The blind watchmaker applies the CLT to convert ion channel mayhem into a usable signal. A single ion channel is unpredictable, like a crazy stripper girlfriend. But a group of them is predictable, like a crazy stripper girlfriend convention. Note carefully: The randomness is not eliminated; it is handled. Dealt with. Corralled. Gotten around. The brain works in randomness in the way some artists work in oil or clay or profanity.

From this, consistent information processing emerges. You do not conclude two plus two equals four today and two plus two equals potato tomorrow. You could; it's just extremely unlikely. But that is not because of the clockwork precision of your timepiece, it's because such a tragic alignment of random openings and closings of your bastard ion channels will not happen in your finite lifetime. Thank goodness for the sweet release of death.

Inside your noggin is a tempest, ion channels flapping erratically. Haphazardly. Randomly. And like physics and its quantum mechanics, neuroscience is not looking for a man behind the curtain; ion channels are truly random. Fundamentally random. Essentially random. Inexorably random.

Your brain plays dice. It's playing right now, as you sit and read this. Yet, from this game emerges a consistent you. A consistent I.

I, Probability.

Synapse Coffee Mug
by LabKitty

Image Credits: Chimpanzee brain in jar from the London Science Museum by Gaetan Lee and appears under the Creative Commons Attribution 2.0 license. Image of Cajal in his laboratory and camera lucida drawing of Golgi-stained Purkinje cells are in the public domain. Still from I, Robot (c) 2004 Twentieth Century Fox Film Corporation and claimed here as fair use as it serves to illustrate a scholarly article and does not in a reasonable person's mind prevent the owner of the copyrighted work from receiving compensation. Images may have been cropped or otherwise modified. Kari the Goddess, and animal self-images by LabKitty.