There is no problem of free will, just a lot of really confused people

Jan 15, JDN 2457769

I was hoping for some sort of news item to use as a segue, but none in particular emerged, so I decided to go on with it anyway. I haven’t done any cognitive science posts in awhile, and this is one I’ve been meaning to write for a long time—actually it’s the sort of thing that even a remarkable number of cognitive scientists frequently get wrong, perhaps because the structure of human personality makes cognitive science inherently difficult.

Do we have free will?

The question has been asked so many times by so many people it is now a whole topic in philosophy. The Stanford Encyclopedia of Philosophy has an entire article on free will. The Information Philosopher has a gateway page “The Problem of Free Will” linking to a variety of subpages. There are even YouTube videos about “the problem of free will”.

The constant arguing back and forth about this would be problematic enough, but what really grates me are the many, many people who write “bold” articles and books about how “free will does not exist”. Examples include Sam Harris and Jerry Coyne, and have been published in everything from Psychology Today to the Chronicle of Higher Education. There’s even a TED talk.

The worst ones are those that follow with “but you should believe in it anyway”. In The Atlantic we have “Free will does not exist. But we’re better off believing in it anyway.” Scientific American offers a similar view, “Scientists say free will probably doesn’t exist, but urge: “Don’t stop believing!””

This is a mind-bogglingly stupid approach. First of all, if you want someone to believe in something, you don’t tell them it doesn’t exist. Second, if something doesn’t exist, that is generally considered a pretty compelling reason not to believe in it. You’d need a really compelling counter-argument, and frankly I’m not even sure the whole idea is logically coherent. How can I believe in something if I know it doesn’t exist? Am I supposed to delude myself somehow?

But the really sad part is that it’s totally unnecessary. There is no problem of free will. There are just an awful lot of really, really confused people. (Fortunately not everyone is confused; there are those, such as Daniel Dennett, who actually understand what’s going on.)

The most important confusion is over what you mean by the phrase “free will”. There are really two core meanings here, and the conflation of them is about 90% of the problem.

1. Moral responsibility: We have “free will” if and only if we are morally responsible for our actions.

2. Noncausality: We have “free will” if and only if our actions are not caused by the laws of nature.

Basically, every debate over “free will” boils down to someone pointing out that noncausality doesn’t exist, and then arguing that this means that moral responsibility doesn’t exist. Then someone comes back and says that moral responsibility does exist, and then infers that this means noncausality must exist. Or someone points out that noncausality doesn’t exist, and then they realize how horrible it would be if moral responsibility didn’t exist, and then tells people they should go on believing in noncausality so that they don’t have to give up moral responsibility.

Let me be absolutely clear here: Noncausality could not possibly exist.

Noncausality isn’t even a coherent concept. Actions, insofar as they are actions, must, necessarily, by definition, be caused by the laws of nature.

I can sort of imagine an event not being caused; perhaps virtual electron-positron pairs can really pop into existence without ever being caused. (Even then I’m not entirely convinced; I think quantum mechanics might actually be deterministic at the most fundamental level.)

But an action isn’t just a particle popping into existence. It requires the coordinated behavior of some 10^26 or more particles, all in a precisely organized, unified way, structured so as to move some other similarly large quantity of particles through space in a precise way so as to change the universe from one state to another state according to some system of objectives. Typically, it involves human muscles intervening on human beings or inanimate objects. (Recently it has come to mean specifically human fingers on computer keyboards a rather large segment of the time!) If what you do is an action—not a muscle spasm, not a seizure, not a slip or a trip, but something you did on purpose—then it must be caused. And if something is caused, it must be caused according to the laws of nature, because the laws of nature are the laws underlying all causality in the universe!

And once you realize that, the “problem of free will” should strike you as one of the stupidest “problems” ever proposed. Of course our actions are caused by the laws of nature! Why in the world would you think otherwise?

If you think that noncausality is necessary—or even useful—for free will, what kind of universe do you think you live in? What kind of universe could someone live in, that would fit your idea of what free will is supposed to be?

It’s like I said in that much earlier post about The Basic Fact of Cognitive Science (we are our brains): If you don’t think a mind can be made of matter, what do you think minds are made of? What sort of magical invisible fairy dust would satisfy you? If you can’t even imagine something that would satisfy the constraints you’ve imposed, did it maybe occur to you that your constraints are too strong?

Noncausality isn’t worth fretting over for the same reason that you shouldn’t fret over the fact that pi is irrational and you can’t make a square circle. There is no possible universe in which that isn’t true. So if it bothers you, it’s not that there’s something wrong with the universe—it’s clearly that there’s something wrong with you. Your thinking on the matter must be too confused, too dependent on unquestioned intuitions, if you think that murder can’t be wrong unless 2+2=5.

In philosophical jargon I am called a “compatibilist” because I maintain that free will and determinism are “compatible”. But this is much too weak a term. I much prefer Eleizer Yudkowsky’s “requiredism”, which he explains in one of the greatest blog posts of all time (seriously, read it immediately if you haven’t before—I’m okay with you cutting off my blog post here and reading his instead, because it truly is that brilliant), entitled simply “Thou Art Physics”. This quote sums it up briefly:

My position might perhaps be called “Requiredism.” When agency, choice, control, and moral responsibility are cashed out in a sensible way, they require determinism—at least some patches of determinism within the universe. If you choose, and plan, and act, and bring some future into being, in accordance with your desire, then all this requires a lawful sort of reality; you cannot do it amid utter chaos. There must be order over at least over those parts of reality that are being controlled by you. You are within physics, and so you/physics have determined the future. If it were not determined by physics, it could not be determined by you.

Free will requires a certain minimum level of determinism in the universe, because the universe must be orderly enough that actions make sense and there isn’t simply an endless succession of random events. Call me a “requiredist” if you need to call me something. I’d prefer you just realize the whole debate is silly because moral responsibility exists and noncausality couldn’t possibly.

We could of course use different terms besides “free will”. “Moral responsibility” is certainly a good one, but it is missing one key piece, which is the issue of why we can assign moral responsibility to human beings and a few other entities (animals, perhaps robots) and not to the vast majority of entities (trees, rocks, planets, tables), and why we are sometimes willing to say that even a human being does not have moral responsibility (infancy, duress, impairment).

This is why my favored term is actually “rational volition”. The characteristic that human beings have (at least most of us, most of the time), which also many animals and possibly some robots share (if not now, then soon enough), which justifies our moral responsibility is precisely our capacity to reason. Things don’t just happen to us the way they do to some 99.999,999,999% of the universe; we do things. We experience the world through our senses, have goals we want to achieve, and act in ways that are planned to make the world move closer to achieving those goals. We have causes, sure enough; but not just any causes. We have a specific class of causes, which are related to our desires and intentions—we call these causes reasons.

So if you want to say that we don’t have “free will” because that implies some mysterious nonsensical noncausality, sure; that’s fine. But then don’t go telling us that this means we don’t have moral responsibility, or that we should somehow try to delude ourselves into believing otherwise in order to preserve moral responsibility. Just recognize that we do have rational volition.

How do I know we have rational volition? That’s the best part, really: Experiments. While you’re off in la-la land imagining fanciful universes where somehow causes aren’t really causes even though they are, I can point to not only centuries of human experience but decades of direct, controlled experiments in operant conditioning. Human beings and most other animals behave quite differently in behavioral experiments than, say, plants or coffee tables. Indeed, it is precisely because of this radical difference that it seems foolish to even speak of a “behavioral experiment” about coffee tables—because coffee tables don’t behave, they just are. Coffee tables don’t learn. They don’t decide. They don’t plan or consider or hope or seek.

Japanese, as it turns out, may be a uniquely good language for cognitive science, because it has two fundamentally different verbs for “to be” depending on whether an entity is sentient. Humans and animals imasu, while inanimate objects merely arimasu. We have free will because and insofar as we imasu.

Once you get past that most basic confusion of moral responsibility with noncausality, there are a few other confusions you might run into as well. Another one is two senses of “reductionism”, which Dennett refers to as “ordinary” and “greedy”:

1. Ordinary reductionism: All systems in the universe are ultimately made up of components that always and everywhere obey the laws of nature.

2. Greedy reductionism: All systems in the universe just are their components, and have no existence, structure, or meaning aside from those components.

I actually had trouble formulating greedy reductionism as a coherent statement, because it’s such a nonsensical notion. Does anyone really think that a pile of two-by-fours is the same thing as a house? But people do speak as though they think this about human brains, when they say that “love is just dopamine” or “happiness is just serotonin”. But dopamine in a petri dish isn’t love, any more than a pile of two-by-fours is a house; and what I really can’t quite grok is why anyone would think otherwise.

Maybe they’re simply too baffled by the fact that love is made of dopamine (among other things)? They can’t quite visualize how that would work (nor can I, nor, I think, can anyone in the world at this level of scientific knowledge). You can see how the two-by-fours get nailed together and assembled into the house, but you can’t see how dopamine and action potentials would somehow combine into love.

But isn’t that a reason to say that love isn’t the same thing as dopamine, rather than that it is? I can understand why some people are still dualists who think that consciousness is somehow separate from the functioning of the brain. That’s wrong—totally, utterly, ridiculously wrong—but I can at least appreciate the intuition that underlies it. What I can’t quite grasp is why someone would go so far the other way and say that the consciousness they are currently experiencing does not exist.

Another thing that might confuse people is the fact that minds, as far as we know, are platform independentthat is, your mind could most likely be created out of a variety of different materials, from the gelatinous brain it currently is to some sort of silicon supercomputer, to perhaps something even more exotic. This independence follows from the widely-believed Church-Turing thesis, which essentially says that all computation is computation, regardless of how it is done. This may not actually be right, but I see many reasons to think that it is, and if so, this means that minds aren’t really what they are made of at all—they could be made of lots of things. What makes a mind a mind is how it is structured and above all what it does.

If this is baffling to you, let me show you how platform-independence works on a much simpler concept: Tables. Tables are also in fact platform-independent. You can make a table out of wood, or steel, or plastic, or ice, or bone. You could take out literally every single atom of a table and replace it will a completely different atom of a completely different element—carbon for iron, for example—and still end up with a table. You could conceivably even do so without changing the table’s weight, strength, size, etc., though that would be considerably more difficult.
Does this mean that tables somehow exist “beyond” their constituent matter? In some very basic sense, I suppose so—they are, again, platform-independent. But not in any deep, mysterious sense. Start with a wooden table, take away all the wood, and you no longer have a table. Take apart the table and you have a bunch of wood, which you could use to build something else. There is no “essence” comprising the table. There is no “table soul” that would persist when the table is deconstructed.

And—now for the hard part—so it is with minds. Your mind is your brain. The constituent atoms of your brain are gradually being replaced, day by day, but your mind is the same, because it exists in the arrangement and behavior, not the atoms themselves. Yet there is nothing “extra” or “beyond” that makes up your mind. You have no “soul” that lies beyond your brain. If your brain is destroyed, your mind will also be destroyed. If your brain could be copied, your mind would also be copied. And one day it may even be possible to construct your mind in some other medium—some complex computer made of silicon and tantalum, most likely—and it would still be a mind, and in all its thoughts, feelings and behaviors your mind, if not numerically identical to you.

Thus, when we engage in rational volition—when we use our “free will” if you like that term—there is no special “extra” process beyond what’s going on in our brains, but there doesn’t have to be. Those particular configurations of action potentials and neurotransmitters are our thoughts, desires, plans, intentions, hopes, fears, goals, beliefs. These mental concepts are not in addition to the physical material; they are made of that physical material. Your soul is made of gelatin.

Again, this is not some deep mystery. There is no “paradox” here. We don’t actually know the details of how it works, but that makes this no different from a Homo erectus who doesn’t know how fire works. Maybe he thinks there needs to be some extra “fire soul” that makes it burn, but we know better; and in far fewer centuries than separate that Homo erectus from us, our descendants will know precisely how the brain creates the mind.

Until then, simply remember that any mystery here lies in us—in our ignorance—and not in the universe. And take heart that the kind of “free will” that matters—moral responsibility—has absolutely no need for the kind of “free will” that doesn’t exist—noncausality. They’re totally different things.

Debunking the Simulation Argument

Oct 23, JDN 2457685

Every subculture of humans has words, attitudes, and ideas that hold it together. The obvious example is religions, but the same is true of sports fandoms, towns, and even scientific disciplines. (I would estimate that 40-60% of scientific jargon, depending on discipline, is not actually useful, but simply a way of exhibiting membership in the tribe. Even physicists do this: “quantum entanglement” is useful jargon, but “p-brane” surely isn’t. Statisticians too: Why say the clear and understandable “unequal variance” when you could show off by saying “heteroskedasticity”? In certain disciplines of the humanities this figure can rise as high as 90%: “imaginary” as a noun leaps to mind.)

One particularly odd idea that seems to define certain subcultures of very intelligent and rational people is the Simulation Argument, originally (and probably best) propounded by Nick Bostrom:

This paper argues that at least one of the following propositions is true: (1) the human species is very likely to go extinct before reaching a “posthuman” stage; (2) any posthuman civilization is extremely unlikely to run a significant number of simulations of their evolutionary history (or variations thereof); (3) we are almost certainly living in a computer simulation.

In this original formulation by Bostrom, the argument actually makes some sense. It can be escaped, because it makes some subtle anthropic assumptions that need to be considered more carefully (in short, there could be ancestor-simulations but we could still know we aren’t in one); but it deserves to be taken seriously. Indeed, I think proposition (2) is almost certainly true, and proposition (1) might be as well; thus I have no problem accepting the disjunction.

Of course, the typical form of the argument isn’t nearly so cogent. In popular outlets as prestigious as the New York Times, Scientific American and the New Yorker, the idea is simply presented as “We are living in a simulation.” The only major outlet I could find that properly presented Bostrom’s disjunction was PBS. Indeed, there are now some Silicon Valley billionaires who believe the argument, or at least think it merits enough attention to be worth funding research into how we might escape the simulation we are in. (Frankly, even if we were inside a simulation, it’s not clear that “escaping” would be something worthwhile or even possible.)

Yet most people, when presented with this idea, think it is profoundly silly and a waste of time.

I believe this is the correct response. I am 99.9% sure we are not living in a simulation.

But it’s one thing to know that an argument is wrong, and quite another to actually show why; in that respect the Simulation Argument is a lot like the Ontological Argument for God:

However, as Bertrand Russell observed, it is much easier to be persuaded that ontological arguments are no good than it is to say exactly what is wrong with them.

To resolve this problem, I am writing this post (at the behest of my Patreons) to provide you now with a concise and persuasive argument directly against the Simulation Argument. No longer will you have to rely on your intuition that it can’t be right; you actually will have compelling logical reasons to reject it.

Note that I will not deny the core principle of cognitive science that minds are computational and therefore in principle could be simulated in such a way that the “simulations” would be actual minds. That’s usually what defenders of the Simulation Argument assume you’re denying, and perhaps in many cases it is; but that’s not what I’m denying. Yeah, sure, minds are computational (probably). There’s still no reason to think we’re living in a simulation.

To make this refutation, I should definitely address the strongest form of the argument, which is Nick Bostrom’s original disjunction. As I already noted, I believe that the disjunction is in fact true; at least one of those propositions is almost certainly correct, and perhaps two of them.

Indeed, I can tell you which one: Proposition (2). That is, I see no reason whatsoever why an advanced “posthuman” species would want to create simulated universes remotely resembling our own.


First of all, let’s assume that we do make it that far and posthumans do come into existence. I really don’t have sufficient evidence to say this is so, and the combination of millions of racists and thousands of nuclear weapons does not bode particularly well for that probability. But I think there is at least some good chance that this will happen—perhaps 10%?—so, let’s concede that point for now, and say that yes, posthumans will one day exist.

To be fair, I am not a posthuman, and cannot say for certain what beings of vastly greater intelligence and knowledge than I might choose to do. But since we are assuming that they exist as the result of our descendants more or less achieving everything we ever hoped for—peace, prosperity, immortality, vast knowledge—one thing I think I can safely extrapolate is that they will be moral. They will have a sense of ethics and morality not too dissimilar from our own. It will probably not agree in every detail—certainly not with what ordinary people believe, but very likely not with what even our greatest philosophers believe. It will most likely be better than our current best morality—closer to the objective moral truth that underlies reality.

I say this because this is the pattern that has emerged throughout the advancement of civilization thus far, and the whole reason we’re assuming posthumans might exist is that we are projecting this advancement further into the future. Humans have, on average, in the long run, become more intelligent, more rational, more compassionate. We have given up entirely on ancient moral concepts that we now recognize to be fundamentally defective, such as “witchcraft” and “heresy”; we are in the process of abandoning others for which some of us see the flaws but others don’t, such as “blasphemy” and “apostasy”. We have dramatically expanded the rights of women and various minority groups. Indeed, we have expanded our concept of which beings are morally relevant, our “circle of concern”, from only those in our tribe on outward to whole nations, whole races of people—and for some of us, as far as all humans or even all vertebrates. Therefore I expect us to continue to expand this moral circle, until it encompasses all sentient beings in the universe. Indeed, on some level I already believe that, though I know I don’t actually live in accordance with that theory—blame me if you will for my weakness of will, but can you really doubt the theory? Does it not seem likely that this it the theory to which our posthuman descendants will ultimately converge?

If that is the case, then posthumans would never make a simulation remotely resembling the universe I live in.

Maybe not me in particular, for I live relatively well—though I must ask why the migraines were really necessary. But among humans in general, there are many millions who live in conditions of such abject squalor and suffering that to create a universe containing them can only be counted as the gravest of crimes, morally akin to the Holocaust.

Indeed, creating this universe must, by construction, literally include the Holocaust. Because the Holocaust happened in this universe, you know.

So unless you think that our posthuman descendants are monstersdemons really, immortal beings of vast knowledge and power who thrive on the death and suffering of other sentient beings, you cannot think that they would create our universe. They might create a universe of some sort—but they would not create this one. You may consider this a corollary of the Problem of Evil, which has always been one of the (many) knockdown arguments against the existence of God as depicted in any major religion.

To deny this, you must twist the simulation argument quite substantially, and say that only some of us are actual people, sentient beings instantiated by the simulation, while the vast majority are, for lack of a better word, NPCs. The millions of children starving in southeast Asia and central Africa aren’t real, they’re just simulated, so that the handful of us who are real have a convincing environment for the purposes of this experiment. Even then, it seems monstrous to deceive us in this way, to make us think that millions of children are starving just to see if we’ll try to save them.

Bostrom presents it as obvious that any species of posthumans would want to create ancestor-simulations, and to make this seem plausible he compares to the many simulations we already create with our current technology, which we call “video games”. But this is such a severe equivocation on the word “simulation” that it frankly seems disingenuous (or for the pun perhaps I should say dissimulation).

This universe can’t possibly be a simulation in the sense that Halo 4 is a simulation. Indeed, this is something that I know with near-perfect certainty, for I am a sentient being (“Cogito ergo sum” and all that). There is at least one actual sentient person here—me—and based on my observations of your behavior, I know with quite high probability that there are many others as well—all of you.

Whereas, if I thought for even a moment there was even a slight probability that Halo 4 contains actual sentient beings that I am murdering, I would never play the game again; indeed I think I would smash the machine, and launch upon a global argumentative crusade to convince everyone to stop playing violent video games forevermore. If I thought that these video game characters that I explode with virtual plasma grenades were actual sentient people—or even had a non-negligible chance of being such—then what I am doing would be literally murder.

So whatever else the posthumans would be doing by creating our universe inside some vast computer, it is not “simulation” in the sense of a video game. If they are doing this for amusement, they are monsters. Even if they are doing it for some higher purpose such as scientific research, I strongly doubt that it can be justified; and I even more strongly doubt that it could be justified frequently. Perhaps once or twice in the whole history of the civilization, as a last resort to achieve some vital scientific objective when all other methods have been thoroughly exhausted. Furthermore it would have to be toward some truly cosmic objective, such as forestalling the heat death of the universe. Anything less would not justify literally replicating thousands of genocides.

But the way Bostrom generates a nontrivial probability of us living in a simulation is by assuming that each posthuman civilization will create many simulations similar to our own, so that the prior probability of being in a simulation is so high that it overwhelms the much higher likelihood that we are in the real universe. (This a deeply Bayesian argument; of that part, I approve. In Bayesian reasoning, the likelihood is the probability that we would observe the evidence we do given that the theory is true, while the prior is the probability that the theory is true, before we’ve seen any evidence. The probability of the theory actually being true is proportional to the likelihood multiplied by the prior.) But if the Foundation IRB will only approve the construction of a Synthetic Universe in order to achieve some cosmic objective, then the prior probability is something like 2/3, or 9/10; and thus it is no match whatsoever for the some 10^12 evidence in favor of this being actual reality.

Just what is this so compelling likelihood? That brings me to my next point, which is a bit more technical, but important because it’s really where the Simulation Argument truly collapses.

How do I know we aren’t in a simulation?

The fundamental equations of the laws of nature do not have closed-form solutions.

Take a look at the Schrodinger Equation, the Einstein field equations, the Navier-Stokes Equations, even Maxwell’s Equations (which are relatively well-behaved all things considered). These are second-order partial differential equations all, extremely complex to solve. They are all defined over continuous time and space, which has uncountably many points in every interval (though there are some physicists who believe that spacetime may be discrete on the order of 10^-44 seconds.) Not one of them has a general closed-form solution, by which I mean a formula that you could just plug in numbers for the parameters on one side of the equation and output an answer on the other. (x^3 + y^3 = 3 is not a closed-form solution, but y = (3 – x^3)^(1/3) is.) They have such exact solutions in certain special cases, but in general we can only solve them approximately, if at all.

This is not particularly surprising if you assume we’re in the actual universe. I have no particular reason to think that the fundamental laws underlying reality should be of a form that is exactly solvable to minds like my own, or even solvable at all in any but a trivial sense. (They must be “solvable” in the sense of actually resulting in something in particular happening at any given time, but that’s all.)

But it is extremely surprising if you assume we’re in a universe that is simulated by posthumans. If posthumans are similar to us, but… more so I guess, then when they set about to simulate a universe, they should do so in a fashion not too dissimilar from how we would do it. And how would we do it? We’d code in a bunch of laws into a computer in discrete time (and definitely not with time-steps of 10^-44 seconds either!), and those laws would have to be encoded as functions, not equations. There could be many inputs in many different forms, perhaps even involving mathematical operations we haven’t invented yet—but each configuration of inputs would have to yield precisely one output, if the computer program is to run at all.

Indeed, if they are really like us, then their computers will probably only be capable of one core operation—conditional bit flipping, 1 to 0 or 0 to 1 depending on some state—and the rest will be successive applications of that operation. Bit shifts are many bit flips, addition is many bit shifts, multiplication is many additions, exponentiation is many multiplications. We would therefore expect the fundamental equations of the simulated universe to have an extremely simple functional form, literally something that can be written out as many successive steps of “if A, flip X to 1” and “if B, flip Y to 0”. It could be a lot of such steps mind you—existing programs require billions or trillions of such operations—but one thing it could never be is a partial differential equation that cannot be solved exactly.

What fans of the Simulation Argument seem to forget is that while this simple set of operations is extremely general, capable of generating quite literally any possible computable function (Turing proved that), it is not capable of generating any function that isn’t computable, much less any equation that can’t be solved into a function. So unless the laws of the universe can actually be reduced to computable functions, it’s not even possible for us to be inside a computer simulation.

What is the probability that all the fundamental equations of the universe can be reduced to computable functions? Well, it’s difficult to assign a precise figure of course. I have no idea what new discoveries might be made in science or mathematics in the next thousand years (if I did, I would make a few and win the Nobel Prize). But given that we have been trying to get closed-form solutions for the fundamental equations of the universe and failing miserably since at least Isaac Newton, I think that probability is quite small.

Then there’s the fact that (again unless you believe some humans in our universe are NPCs) there are 7.3 billion minds (and counting) that you have to simulate at once, even assuming that the simulation only includes this planet and yet somehow perfectly generates an apparent cosmos that even behaves as we would expect under things like parallax and redshift. There’s the fact that whenever we try to study the fundamental laws of our universe, we are able to do so, and never run into any problems of insufficient resolution; so apparently at least this planet and its environs are being simulated at the scale of nanometers and femtoseconds. This is a ludicrously huge amount of data, and while I cannot rule out the possibility of some larger universe existing that would allow a computer large enough to contain it, you have a very steep uphill battle if you want to argue that this is somehow what our posthuman descendants will consider the best use of their time and resources. Bostrom uses the video game comparison to make it sound like they are just cranking out copies of Halo 917 (“Plasma rifles? How quaint!”) when in fact it amounts to assuming that our descendants will just casually create universes of 10^50 particles running over space intervals of 10^-9 meters and time-steps of 10^-15 seconds that contain billions of actual sentient beings and thousands of genocides, and furthermore do so in a way that somehow manages to make the apparent fundamental equations inside those universes unsolvable.

Indeed, I think it’s conservative to say that the likelihood ratio is 10^12—observing what we do is a trillion times more likely if this is the real universe than if it’s a simulation. Therefore, unless you believe that our posthuman descendants would have reason to create at least a billion simulations of universes like our own, you can assign a probability that we are in the actual universe of at least 99.9%.

As indeed I do.

How personality makes cognitive science hard

August 13, JDN 2457614

Why is cognitive science so difficult? First of all, let’s acknowledge that it is difficult—that even those of us who understand it better than most are still quite baffled by it in quite fundamental ways. The Hard Problem still looms large over us all, and while I know that the Chinese Room Argument is wrong, I cannot precisely pin down why.

The recursive, reflexive character of cognitive science is part of the problem; can a thing understand itself without understanding understanding itself, understanding understanding understanding itself, and on in an infinite regress? But this recursiveness applies just as much to economics and sociology, and honestly to physics and biology as well. We are physical biological systems in an economic and social system, yet most people at least understand these sciences at the most basic level—which is simply not true of cognitive science.

One of the most basic facts of cognitive science (indeed I am fond of calling it The Basic Fact of Cognitive Science) is that we are our brains, that everything human consciousness does is done by and within the brain. Yet the majority of humans believe in souls (including the majority of Americans and even the majority of Brits), and just yesterday I saw a news anchor say “Based on a new study, that feeling may originate in your brain!” He seriously said “may”. “may”? Why, next you’ll tell me that when my arms lift things, maybe they do it with muscles! Other scientists are often annoyed by how many misconceptions the general public has about science, but this is roughly the equivalent of a news anchor saying, “Based on a new study, human bodies may be made of cells!” or “Based on a new study, diamonds may be made of carbon atoms!” The misunderstanding of many sciences is widespread, but the misunderstanding of cognitive science is fundamental.

So what makes cognitive science so much harder? I have come to realize that there is a deep feature of human personality that makes cognitive science inherently difficult in a way other sciences are not.

Decades of research have uncovered a number of consistent patterns in human personality, where people’s traits tend to lie along a continuum from one extreme to another, and usually cluster near either end. Most people are familiar with a few of these, such as introversion/extraversion and optimism/pessimism; but the one that turns out to be important here is empathizing/systematizing.

Empathizers view the world as composed of sentient beings, living agents with thoughts, feelings, and desires. They are good at understanding other people and providing social support. Poets are typically empathizers.

Systematizers view the world as composed of interacting parts, interlocking components that have complex inner workings which can be analyzed and understood. They are good at solving math problems and tinkering with machines. Engineers are typically systematizers.

Most people cluster near one end of the continuum or the other; they are either strong empathizers or strong systematizers. (If you’re curious, there’s an online test you can take to find out which you are.)

But a rare few of us, perhaps as little as 2% and no more than 10%, are both; we are empathizer-systematizers, strong on both traits (showing that it’s not really a continuum between two extremes after all, and only seemed to be because the two traits are negatively correlated). A comparable number are also low on both traits, which must quite frankly make the world a baffling place in general.

Empathizer-systematizers understand the world as it truly is: Composed of sentient beings that are made of interacting parts.

The very title of this blog shows I am among this group: “human” for the empathizer, “economics” for the systematizer!

We empathizer-systematizers can intuitively grasp that there is no contradiction in saying that a person is sad because he lost his job and he is sad because serotonin levels in his cingulate gyrus are low—because it was losing his job that triggered other thoughts and memories that lowered serotonin levels in his cingulate gyrus and thereby made him sad. No one fully understands the details of how low serotonin feels like sadness—hence, the Hard Problem—but most people can’t even seem to grasp the connection at all. How can something as complex and beautiful as a human mind be made of… sparking gelatin?

Well, what would you prefer it to be made of? Silicon chips? We’re working on that. Something else? Magical fairy dust, perhaps? Pray tell, what material could the human mind be constructed from that wouldn’t bother you on a deep level?

No, what really seems to bother people is the very idea that a human mind can be constructed from material, that thoughts and feelings can be divisible into their constituent parts.

This leads people to adopt one of two extreme positions on cognitive science, both of which are quite absurd—frankly I’m not sure they are even coherent.

Pure empathizers often become dualists, saying that the mind cannot be divisible, cannot be made of material, but must be… something else, somehow, outside the material universe—whatever that means.

Pure systematizers instead often become eliminativists, acknowledging the functioning of the brain and then declaring proudly that the mind does not exist—that consciousness, emotion, and experience are all simply illusions that advanced science will one day dispense with—again, whatever that means.

I can at least imagine what a universe would be like if eliminativism were true and there were no such thing as consciousness—just a vast expanse of stars and rocks and dust, lifeless and empty. Of course, I know that I’m not in such a universe, because I am experiencing consciousness right now, and the illusion of consciousness is… consciousness. (You are not experiencing what you are experiencing right now, I say!) But I can at least visualize what such a universe would be like, and indeed it probably was our universe (or at least our solar system) up until about a billion years ago when the first sentient animals began to evolve.

Dualists, on the other hand, are speaking words, structured into grammatical sentences, but I’m not even sure they are forming coherent assertions. Sure, you can sort of imagine our souls being floating wisps of light and energy (ala the “ascended beings”, my least-favorite part of the Stargate series, which I otherwise love), but ultimately those have to be made of something, because nothing can be both fundamental and complex. Moreover, the fact that they interact with ordinary matter strongly suggests that they are made of ordinary matter (and to be fair to Stargate, at one point in the series Rodney with his already-great intelligence vastly increased declares confidently that ascended beings are indeed nothing more than “protons and electrons, protons and electrons”). Even if they were made of some different kind of matter like dark matter, they would need to obey a common system of physical laws, and ultimately we would come to think of them as matter. Otherwise, how do the two interact? If we are made of soul-stuff which is fundamentally different from other stuff, then how do we even know that other stuff exists? If we are not our bodies, then how do we experience pain when they are damaged and control them with our volition? The most coherent theory of dualism is probably Malebranche’s, which is quite literally “God did it”. Epiphenomenalism, which says that thoughts are just sort of an extra thing that also happens but has no effect (an “epiphenomenon”) on the physical brain, is also quite popular for some reason. People don’t quite seem to understand that the Law of Conservation of Energy directly forbids an “epiphenomenon” in this sense, because anything that happens involves energy, and that energy (unlike, say, money) can’t be created out of nothing; it has to come from somewhere. Analogies are often used: The whistle of a train, the smoke of a flame. But the whistle of a train is a pressure wave that vibrates the train; the smoke from a flame is made of particulates that could be used to smother the flame. At best, there are some phenomena that don’t affect each other very much—but any causal interaction at all makes dualism break down.

How can highly intelligent, highly educated philosophers and scientists make such basic errors? I think it has to be personality. They have deep, built-in (quite likely genetic) intuitions about the structure of the universe, and they just can’t shake them.

And I confess, it’s very hard for me to figure out what to say in order to break those intuitions, because my deep intuitions are so different. Just as it seems obvious to them that the world cannot be this way, it seems obvious to me that it is. It’s a bit like living in a world where 45% of people can see red but not blue and insist the American Flag is red and white, another 45% of people can see blue but not red and insist the flag is blue and white, and I’m here in the 10% who can see all colors and I’m trying to explain that the flag is red, white, and blue.

The best I can come up with is to use analogies, and computers make for quite good analogies, not least because their functioning is modeled on our thinking.

Is this word processor program (LibreOffice Writer, as it turns out) really here, or is it merely an illusion? Clearly it’s really here, right? I’m using it. It’s doing things right now. Parts of it are sort of illusions—it looks like a blank page, but it’s actually an LCD screen lit up all the way; it looks like ink, but it’s actually where the LCD turns off. But there is clearly something here, an actual entity worth talking about which has properties that are usefully described without trying to reduce them to the constituent interactions of subatomic particles.

On the other hand, can it be reduced to the interactions of subatomic particles? Absolutely. A brief sketch is something like this: It’s a software program, running on an operating system, and these in turn are represented in the physical hardware as long binary sequences, stored by ever-so-slightly higher or lower voltages in particular hardware components, which in turn are due to electrons being moved from one valence to another. Those electrons move in precise accordance with the laws of quantum mechanics, I assure you; yet this in no way changes the fact that I’m typing a blog post on a word processor.

Indeed, it’s not even particularly useful to know that the electrons are obeying the laws of quantum mechanics, and quite literally no possible computer that could be constructed in our universe could ever be large enough to fully simulate all these quantum interactions within the amount of time since the dawn of the universe. If we are to understand it at all, it must be at a much higher level—and the “software program” level really seems to be the best one for most circumstances. The vast majority of problems I’m likely to encounter are either at the software level or the macro hardware level; it’s conceivable that a race condition could emerge in the processor cache or the voltage could suddenly spike or even that a cosmic ray could randomly ionize a single vital electron, but these scenarios are far less likely to affect my life than, say, I accidentally deleted the wrong file or the battery ran out of charge because I forgot to plug it in.

Likewise, when dealing with a relationship problem, or mediating a conflict between two friends, it’s rarely relevant that some particular neuron is firing in someone’s nucleus accumbens, or that one of my friends is very low on dopamine in his mesolimbic system today. It could be, particularly if some sort of mental or neurological illness in involved, but in most cases the real issues are better understood as higher level phenomena—people being angry, or tired, or sad. These emotions are ultimately constructed of axon potentials and neurotransmitters, but that doesn’t make them any less real, nor does it change the fact that it is at the emotional level that most human matters are best understood.

Perhaps part of the problem is that human emotions take on moral significance, which other higher-level entities generally do not? But they sort of do, really, in a more indirect way. It matters a great deal morally whether or not climate change is a real phenomenon caused by carbon emissions (it is). Ultimately this moral significance can be tied to human experiences, so everything rests upon human experiences being real; but they are real, in much the same way that rocks and trees and carbon emissions are real. No amount of neuroscience will ever change that, just as no amount of biological science would disprove the existence of trees.

Indeed, some of the world’s greatest moral problems could be better solved if people were better empathizer-systematizers, and thus more willing to do cost-benefit analysis.

What is the processing power of the human brain?

JDN 2457485

Futurists have been predicting that AI will “surpass humans” any day now for something like 50 years. Eventually they’ll be right, but it will be more or less purely by chance, since they’ve been making the same prediction longer than I’ve been alive. (Similarity, whenever someone projects the date at which immortality will be invented, it always seems to coincide with just slightly before the end of the author’s projected life expectancy.) Any technology that is “20 years away” will be so indefinitely.

There are a lot of reasons why this prediction keeps failing so miserably. One is an apparent failure to grasp the limitations of exponential growth. I actually think the most important is that a lot of AI fans don’t seem to understand how human cognition actually works—that it is primarily social cognition, where most of the processing has already been done and given to us as cached results, some of them derived centuries before we were born. We are smart enough to run a civilization with airplanes and the Internet not because any individual human is so much smarter than any other animal, but because all humans together are—and other animals haven’t quite figured out how to unite their cognition in the same way. We’re about 3 times smarter than any other animal as individuals—and several billion times smarter when we put our heads together.

A third reason is that even if you have sufficient computing power, that is surprisingly unimportant; what you really need are good heuristics to make use of your computing power efficiently. Any nontrivial problem is too complex to brute-force by any conceivable computer, so simply increasing computing power without improving your heuristics will get you nowhere. Conversely, if you have really good heuristics like the human brain does, you don’t even need all that much computing power. A chess grandmaster was once asked how many moves ahead he can see on the board, and he replied: “I only see one move ahead. The right one.” In cognitive science terms, people asked him how much computing power he was using, expecting him to say something far beyond normal human capacity, and he replied that he was using hardly any—it was all baked into the heuristics he had learned from years of training and practice.

Making an AI capable of human thought—a true artificial person—will require a level of computing power we can already reach (as long as we use huge supercomputers), but that is like having the right material. To really create the being we will need to embed the proper heuristics. We are trying to make David, and we have finally mined enough marble—now all we need is Michelangelo.

But another reason why so many futurists have failed in their projections is that they have wildly underestimated the computing power of the human brain. Reading 1980s cyberpunk is hilarious in hindsight; Neuromancer actually quite accurately projected the number of megabytes that would flow through the Internet at any given moment, but somehow thought that a few hundred megaflops would be enough to copy human consciousness. The processing power of the human brain is actually on the order of a few petaflops. So, you know, Gibson was only off by a factor of a few million.

We can now match petaflops—the world’s fastest supercomputer is actually about 30 petaflops. Of course, it cost half a month of China’s GDP to build, and requires 24 megawatts to run and cool, which is about the output of a mid-sized solar power station. The human brain consumes only about 400 kcal per day, which is about 20 watts—roughly the consumption of a typical CFL lightbulb. Even if you count the rest of the human body as necessary to run the human brain (which I guess is sort of true), we’re still clocking in at about 100 watts—so even though supercomputers can now process at the same speed, our brains are almost a million times as energy-efficient.

How do I know it’s a few petaflops?

Earlier this year a study was published showing that a conservative lower bound for the total capacity of human memory is about 4 bits per synapse, where previously some scientists thought that each synapse might carry only 1 bit (I’ve always suspected it was more like 10 myself).

So then we need to figure out how many synapses we have… which turns out to be really difficult actually. They are in a constant state of flux, growing, shrinking, and moving all the time; and when we die they fade away almost immediately (reason #3 I’m skeptical of cryonics). We know that we have about 100 billion neurons, and each one can have anywhere between 100 and 15,000 synapses with other neurons. The average seems to be something like 5,000 (but highly skewed in a power-law distribution), so that’s about 500 trillion synapses. If each one is carrying 4 bits to be as conservative as possible, that’s a total storage capacity of about 2 quadrillion bits, which is about 0.2 petabytes.

Of course, that’s assuming that our brains store information the same way as a computer—every bit flipped independently, each bit stored forever. Not even close. Human memory is constantly compressing and decompressing data, using a compression scheme that’s lossy enough that we not only forget things, we can systematically misremember and even be implanted with false memories. That may seem like a bad thing, and in a sense it is; but if the compression scheme is that lossy, it must be because it’s also that efficient—that our brains are compressing away the vast majority of the data to make room for more. Our best lossy compression algorithms for video are about 100:1; but the human brain is clearly much better than that. Our core data format for long-term memory appears to be narrative; more or less we store everything not as audio or video (that’s short-term memory, and quite literally so), but as stories.

How much compression can you get by storing things as narrative? Think about The Lord of the Rings. The extended edition of the films runs to 6 discs of movie (9 discs of other stuff), where a Blu-Ray disc can store about 50 GB. So that’s 300 GB. Compressed into narrative form, we have the books (which, if you’ve read them, are clearly not optimally compressed—no, we do not need five paragraphs about the trees, and I’m gonna say it, Tom Bombadil is totally superfluous and Peter Jackson was right to remove him), which run about 500,000 words altogether. If the average word is 10 letters (normally it’s less than that, but this is Tolkien we’re talking about), each word will take up about 10 bytes (because in ASCII or Unicode a letter is a byte). So altogether the total content of the entire trilogy, compressed into narrative, can be stored in about 5 million bytes, that is, 5 MB. So the compression from HD video to narrative takes us all the way from 300 GB to 5 MB, which is a factor of 60,000. Sixty thousand. I believe that this is the proper order of magnitude for the compression capability of the human brain.

Even more interesting is the fact that the human brain is almost certainly in some sense holographic storage; damage to a small part of your brain does not produce highly selective memory loss as if you had some bad sectors of your hard drive, but rather an overall degradation of your total memory processing as if you in some sense stored everything everywhere—that is, holographically. How exactly this is accomplished by the brain is still very much an open question; it’s probably not literally a hologram in the quantum sense, but it definitely seems to function like a hologram. (Although… if the human brain is a quantum computer that would explain an awful lot—it especially helps with the binding problem. The problem is explaining how a biological system at 37 C can possibly maintain the necessary quantum coherences.) The data storage capacity of holograms is substantially larger than what can be achieved by conventional means—and furthermore has similar properties to human memory in that you can more or less always add more, but then what you had before gradually gets degraded. Since neural nets are much closer to the actual mechanics of the brain as we know them, understanding human memory will probably involve finding ways to simulate holographic storage with neural nets.

With these facts in mind, the amount of information we can usefully take in and store is probably not 0.2 petabytes—it’s probably more like 10 exabytes. The human brain can probably hold just about as much as the NSA’s National Cybersecurity Initiative Data Center in Utah, which is itself more or less designed to contain the Internet. (The NSA is at once awesome and terrifying.)

But okay, maybe that’s not fair if we’re comparing human brains to computers; even if you can compress all your data by a factor of 100,000, that isn’t the same thing as having 100,000 times as much storage.

So let’s use that smaller figure, 0.2 petabytes. That’s how much we can store; how much can we process?

The next thing to understand is that our processing architecture is fundamentally difference from that of computers.

Computers generally have far more storage than they have processing power, because they are bottlenecked through a CPU that can only process 1 thing at once (okay, like 8 things at once with a hyperthreaded quad-core; as you’ll see in a moment this is a trivial difference). So it’s typical for a new computer these days to have processing power in gigaflops (It’s usually reported in gigahertz, but that’s kind of silly; hertz just tells you clock cycles, while what you really wanted to know is calculations—and that you get from flops. They’re generally pretty comparable numbers though.), while they have storage in terabytes—meaning that it would take about 1000 seconds (about 17 minutes) for the computer to process everything in its entire storage once. In fact it would take a good deal longer than that, because there are further bottlenecks in terms of memory access, especially from hard-disk drives (RAM and solid-state drives are faster, but would still slow it down to a couple of hours).

The human brain, by contrast, integrates processing and memory into the same system. There is no clear distinction between “memory synapses” and “processing synapses”, and no single CPU bottleneck that everything has to go through. There is however something like a “clock cycle” as it turns out; synaptic firings are synchronized across several different “rhythms”, the fastest of which is about 30 Hz. No, not 30 GHz, not 30 MHz, not even 30 kHz; 30 hertz. Compared to the blazing speed of billions of cycles per second that goes on in our computers, the 30 cycles per second our brains are capable of may seem bafflingly slow. (Even more bafflingly slow is the speed of nerve conduction, which is not limited by the speed of light as you might expect, but is actually less than the speed of sound. When you trigger the knee-jerk reflex doctors often test, it takes about a tenth of a second for the reflex to happen—not because your body is waiting for anything, but because it simply takes that long for the signal to travel to your spinal cord and back.)

The reason we can function at all is because of our much more efficient architecture; instead of passing everything through a single bottleneck, we do all of our processing in parallel. All of those 100 billion neurons with 500 trillion synapses storing 2 quadrillion bits work simultaneously. So whereas a computer does 8 things at a time, 3 billion times per second, a human brain does 2 quadrillion things at a time, 30 times per second. Provided that the tasks can be fully parallelized (vision, yes; arithmetic, no), a human brain can therefore process 60 quadrillion bits per second—which turns out to be just over 6 petaflops, somewhere around 6,000,000,000,000,000 calculations per second.

So, like I said, a few petaflops.

Why is there a “corporate ladder”?

JDN 2457482

We take this concept for granted; there are “entry-level” jobs, and then you can get “promoted”, until perhaps you’re lucky enough or talented enough to rise to the “top”. Jobs that are “higher” on this “ladder” pay better, offer superior benefits, and also typically involve more pleasant work environments and more autonomy, though they also typically require greater skill and more responsibility.

But I contend that an alien lifeform encountering our planet for the first time, even one that somehow knew all about neoclassical economic theory (admittedly weird, but bear with me here), would be quite baffled by this arrangement.

The classic “rags to riches” story always involves starting work in some menial job like working in the mailroom, from which you then more or less magically rise to the position of CEO. (The intermediate steps are rarely told in the story, probably because they undermine the narrative; successful entrepreneurs usually make their first successful business using funds from their wealthy relatives, and if you haven’t got any wealthy relatives, that’s just too bad for you.)

Even despite its dubious accuracy, the story is bizarre in another way: There’s no reason to think that being really good at working in the mail room has anything at all to do with being good at managing a successful business. They’re totally orthogonal skills. They may even be contrary in personality terms; the kind of person who makes a good entrepreneur is innovative, decisive, and independent—and those are exactly the kind of personality traits that will make you miserable in a menial job where you’re constantly following orders.

Yet in almost every profession, we have this process where you must first “earn” your way to “higher” positions by doing menial and at best tangentially-related tasks.

This even happens in science, where we ought to know better! There’s really no reason to think that being good at taking multiple-choice tests strongly predicts your ability to do scientific research, nor that being good at grading multiple-choice tests does either; and yet to become a scientific researcher you must pass a great many multiple-choice tests (at bare minimum the SAT and GRE), and probably as a grad student you’ll end up grading some as well.

This process is frankly bizarre; worldwide, we are probably leaving tens of trillions of dollars of productivity on the table by instituting these arbitrary selection barriers that have nothing to do with actual skills. Simply optimizing our process of CEO selection alone would probably add a trillion dollars to US GDP.

If neoclassical economics were right, we should assign jobs solely based on marginal productivity; there should be some sort of assessment of your ability at each task you might perform, and whichever you’re best at (in the sense of comparative advantage) is what you end up doing, because that’s what you’ll be paid the most to do. Actually for this to really work the selection process would have to be extremely cheap, extremely reliable, and extremely fast, lest the friction of the selection system itself introduce enormous inefficiencies. (The fact that this never even seems to work even in SF stories with superintelligent sorting AIs, let alone in real life, is just so much the worse for neoclassical economics. The last book I read in which it actually seemed to work was Harry Potter and the Sorceror’s Stone—so it was literally just magic.)

The hope seems to be that competition will somehow iron out this problem, but in order for that to work, we must all be competing on a level playing field, and furthermore the mode of competition must accurately assess our real ability. The reason Olympic sports do a pretty good job of selecting the best athletes in the world is that they obey these criteria; the reason corporations do a terrible job of selecting the best CEOs is that they do not.

I’m quite certain I could do better than the former CEO of the late Lehman Brothers (and, to be fair, there are others who could do better still than I), but I’ll likely never get the chance to own a major financial firm—and I’m a lot closer than most people. I get to tick most of the boxes you need to be in that kind of position: White, male, American, mostly able-bodied, intelligent, hard-working, with a graduate degree in economics. Alas, I was only born in the top 10% of the US income distribution, not the top 1% or 0.01%, so my odds are considerably reduced. (That and I’m pretty sure that working for a company as evil as the late Lehman Brothers would destroy my soul.) Somewhere in Sudan there is a little girl who would be the best CEO of an investment bank the world has ever seen, but she is dying of malaria. Somewhere in India there is a little boy who would have been a greater physicist than Einstein, but no one ever taught him to read.

Competition may help reduce the inefficiency of this hierarchical arrangement—but it cannot explain why we use a hierarchy in the first place. Some people may be especially good at leadership and coordination; but in an efficient system they wouldn’t be seen as “above” other people, but as useful coordinators and advisors that people consult to ensure they are allocating tasks efficiently. You wouldn’t do things because “your boss told you to”, but because those things were the most efficient use of your time, given what everyone else in the group was doing. You’d consult your coordinator often, and usually take their advice; but you wouldn’t see them as orders you were required to follow.

Moreover, coordinators would probably not be paid much better than those they coordinate; what they were paid would depend on how much the success of the tasks depends upon efficient coordination, as well as how skilled other people are at coordination. It’s true that if having you there really does make a company with $1 billion in revenue 1% more efficient, that is in fact worth $10 million; but that isn’t how we set the pay of managers. It’s simply obvious to most people that managers should be paid more than their subordinates—that with a “promotion” comes more leadership and more pay. You’re “moving up the corporate ladder” Your pay reflects your higher status, not your marginal productivity.

This is not an optimal economic system by any means. And yet it seems perfectly natural to us to do this, and most people have trouble thinking any other way—which gives us a hint of where it’s probably coming from.

Perfectly natural. That is, instinctual. That is, evolutionary.

I believe that the corporate ladder, like most forms of hierarchy that humans use, is actually a recapitulation of our primate instincts to form a mating hierarchy with an alpha male.

First of all, the person in charge is indeed almost always male—over 90% of all high-level business executives are men. This is clearly discrimination, because women executives are paid less and yet show higher competence. Rare, underpaid, and highly competent is exactly the pattern we would expect in the presence of discrimination. If it were instead a lack of innate ability, we would expect that women executives would be much less competent on average, though they would still be rare and paid less. If there were no discrimination and no difference in ability, we would see equal pay, equal competence, and equal prevalence (this happens almost nowhere—the closest I think we get is in undergraduate admissions). Executives are also usually tall, healthy, and middle-aged—just like alpha males among chimpanzees and gorillas. (You can make excuses for why: Height is correlated with IQ, health makes you more productive, middle age is when you’re old enough to have experience but young enough to have vigor and stamina—but the fact remains, you’re matching the gorillas.)

Second, many otherwise-baffling economic decisions make sense in light of this hypothesis.

When a large company is floundering, why do we cut 20,000 laborers instead of simply reducing the CEO’s stock option package by half to save the same amount of money? Think back to the alpha male: Would he give himself less in a time of scarcity? Of course not. Nor would he remove his immediate subordinates, unless they had done something to offend him. If resources are scarce, the “obvious” answer is to take them from those at the bottom of the hierarchy—resource conservation is always accomplished at the expense of the lowest-status individuals.

Why are the very same poor people who would most stand to gain from redistribution of wealth often those who are most fiercely opposed to it? Because, deep down, they just instinctually “know” that alpha males are supposed to get the bananas, and if they are of low status it is their deserved lot in life. That is how people who depend on TANF and Medicaid to survive can nonetheless vote for Donald Trump. (As for how they can convince themselves that they “don’t get anything from the government”, that I’m not sure. “Keep your government hands off my Medicare!”)

Why is power an aphrodisiac, as well as for many an apparent excuse for bad behavior? I’ll let Cameron Anderson (a psychologist at UC Berkeley) give you the answer: “powerful people act with great daring and sometimes behave rather like gorillas”. With higher status comes a surge in testosterone (makes sense if you’re going to have more mates, and maybe even if you’re commanding an army—but running an investment bank?), which is directly linked to dominance behavior.

These attitudes may well have been adaptive for surviving in the African savannah 2 million years ago. In a world red in tooth and claw, having the biggest, strongest male be in charge of the tribe might have been the most efficient means of ensuring the success of the tribe—or rather I should say, the genes of the tribe, since the only reason we have a tribal instinct is that tribal instinct genes were highly successful at propagating themselves.

I’m actually sort of agnostic on the question of whether our evolutionary heuristics were optimal for ancient survival, or simply the best our brains could manage; but one thing is certain: They are not optimal today. The uninhibited dominance behavior associated with high status may work well enough for a tribal chieftain, but it could be literally apocalyptic when exhibited by the head of state of a nuclear superpower. Allocation of resources by status hierarchy may be fine for hunter-gatherers, but it is disastrously inefficient in an information technology economy.

From now on, whenever you hear “corporate ladder” and similar turns of phrase, I want you to substitute “primate status hierarchy”. You’ll quickly see how well it fits; and hopefully once enough people realize this, together we can all find a way to change to a better system.

Bet five dollars for maximum performance

JDN 2457433

One of the more surprising findings from the study of human behavior under stress is the Yerkes-Dodson curve:

OriginalYerkesDodson
This curve shows how well humans perform at a given task, as a function of how high the stakes are on whether or not they do it properly.

For simple tasks, it says what most people intuitively expect—and what neoclassical economists appear to believe: As the stakes rise, the more highly incentivized you are to do it, and the better you do it.

But for complex tasks, it says something quite different: While increased stakes do raise performance to a point—with nothing at stake at all, people hardly work at all—it is possible to become too incentivized. Formally we say the curve is not monotonic; it has a local maximum.

This is one of many reasons why it’s ridiculous to say that top CEOs should make tens of millions of dollars a year on the rise and fall of their company’s stock price (as a great many economists do in fact say). Even if I believed that stock prices accurately reflect the company’s viability (they do not), and believed that the CEO has a great deal to do with the company’s success, it would still be a case of overincentivizing. When a million dollars rides on a decision, that decision is going to be worse than if the stakes had only been $100. With this in mind, it’s really not surprising that higher CEO pay is correlated with worse company performance. Stock options are terrible motivators, but do offer a subtle way of making wages adjust to the business cycle.

The reason for this is that as the stakes get higher, we become stressed, and that stress response inhibits our ability to use higher cognitive functions. The sympathetic nervous system evolved to make us very good at fighting or running away in the face of danger, which works well should you ever be attacked by a tiger. It did not evolve to make us good at complex tasks under high stakes, the sort of skill we’d need when calculating the trajectory of an errant spacecraft or disarming a nuclear warhead.

To be fair, most of us never have to worry about piloting errant spacecraft or disarming nuclear warheads—indeed, you’re about as likely to get attacked by a tiger even in today’s world. (The rate of tiger attacks in the US is just under 2 per year, and the rate of manned space launches in the US was about 5 per year until the Space Shuttle was terminated.)

There are certain professions, such as pilots and surgeons, where performing complex tasks under life-or-death pressure is commonplace, but only a small fraction of people take such professions for precisely that reason. And if you’ve ever wondered why we use checklists for pilots and there is discussion of also using checklists for surgeons, this is why—checklists convert a single complex task into many simple tasks, allowing high performance even at extreme stakes.

But we do have to do a fair number of quite complex tasks with stakes that are, if not urgent life-or-death scenarios, then at least actions that affect our long-term life prospects substantially. In my tutoring business I encounter one in particular quite frequently: Standardized tests.

Tests like the SAT, ACT, GRE, LSAT, GMAT, and other assorted acronyms are not literally life-or-death, but they often feel that way to students because they really do have a powerful impact on where you’ll end up in life. Will you get into a good college? Will you get into grad school? Will you get the job you want? Even subtle deviations from the path of optimal academic success can make it much harder to achieve career success in the future.

Of course, these are hardly the only examples. Many jobs require us to complete tasks properly on tight deadlines, or else risk being fired. Working in academia infamously requires publishing in journals in time to rise up the tenure track, or else falling off the track entirely. (This incentivizes the production of huge numbers of papers, whether they’re worth writing or not; yes, the number of papers published goes down after tenure, but is that a bad thing? What we need to know is whether the number of good papers goes down. My suspicion is that most if not all of the reduction in publications is due to not publishing things that weren’t worth publishing.)

So if you are faced with this sort of task, what can you do? If you realize that you are faced with a high-stakes complex task, you know your performance will be bad—which only makes your stress worse!

My advice is to pretend you’re betting five dollars on the outcome.

Ignore all other stakes, and pretend you’re betting five dollars. $5.00 USD. Do it right and you get a Lincoln; do it wrong and you lose one.
What this does is ensures that you care enough—you don’t want to lose $5 for no reason—but not too much—if you do lose $5, you don’t feel like your life is ending. We want to put you near that peak of the Yerkes-Dodson curve.

The great irony here is that you most want to do this when it is most untrue. If you actually do have a task for which you’ve bet $5 and nothing else rides on it, you don’t need this technique, and any technique to improve your performance is not particularly worthwhile. It’s when you have a standardized test to pass that you really want to use this—and part of me even hopes that people know to do this whenever they have nuclear warheads to disarm. It is precisely when the stakes are highest that you must put those stakes out of your mind.

Why five dollars? Well, the exact amount is arbitrary, but this is at least about the right order of magnitude for most First World individuals. If you really want to get precise, I think the optimal stakes level for maximum performance is something like 100 microQALY per task, and assuming logarithmic utility of wealth, $5 at the US median household income of $53,600 is approximately 100 microQALY. If you have a particularly low or high income, feel free to adjust accordingly. Literally you should be prepared to bet about an hour of your life; but we are not accustomed to thinking that way, so use $5. (I think most people, if asked outright, would radically overestimate what an hour of life is worth to them. “I wouldn’t give up an hour of my life for $1,000!” Then why do you work at $20 an hour?)

It’s a simple heuristic, easy to remember, and sometimes effective. Give it a try.

The power of exponential growth

JDN 2457390

There’s a famous riddle: If the water in a lakebed doubles in volume every day, and the lakebed started filling on January 1, and is half full on June 17, when will it be full?

The answer is of course June 18—if it doubles every day, it will go from half full to full in a single day.

But most people assume that half the work takes about half the time, so they usually give answers in December. Others try to correct, but don’t go far enough, and say something like October.

Human brains are programmed to understand linear processes. We expect things to come in direct proportion: If you work twice as hard, you expect to get twice as much done. If you study twice as long, you expect to learn twice as much. If you pay twice as much, you expect to get twice as much stuff.

We tend to apply this same intuition to situations where it does not belong, processes that are not actually linear but exponential. As a result, when we extrapolate the slow growth early in the process, we wildly underestimate the total growth in the long run.

For example, suppose we have two countries. Arcadia has a GDP of $100 billion per year, and they grow at 4% per year. Berkland has a GDP of $200 billion, and they grow at 2% per year. Assuming that they maintain these growth rates, how long will it take for Arcadia’s GDP to exceed Berkland’s?

If we do this intuitively, we might sort of guess that at 4% you’d add 100% in 25 years, and at 2% you’d add 100% in 50 years; so it should be something like 75 years, because then Arcadia will have added $300 million while Berkland added $200 million. You might even just fudge the numbers in your head and say “about a century”.

In fact, it is only 35 years. You could solve this exactly by setting (100)(1.04^x) = (200)(1.02^x); but I have an intuitive method that I think may help you to estimate exponential processes in the future.

Divide the percentage into 69. (For some numbers it’s easier to use 70 or 72; remember, these are just to be approximate. The exact figure is 100*ln(2) = 69.3147… and then it wouldn’t be the percentage p but 100*ln(1+p/100); try plotting those and you’ll see why using p works.) This is the time it will take to double.

So at 4%, Arcadia will double in about 17.5 years, quadrupling in 35 years. At 2%, Berkland will double in about 35 years. Thus, in 35 years, Arcadia will quadruple and Berkland will double, so their GDPs will be equal.

Economics is full of exponential processes: Compound interest is exponential, and over moderately long periods GDP and population both tend to grow exponentially. (In fact they grow logistically, which is similar to exponential until it gets very large and begins to slow down. If you smooth out our recessions, you can get a sense that since the 1940s, US GDP growth has slowed down from about 4% per year to about 2% per year.) It is therefore quite important to understand how exponential growth works.

Let’s try another one. If one account has $1 million, growing at 5% per year, and another has $1,000, growing at 10% per year, how long will it take for the second account to have more money in it?

69/5 is about 14, so the first account doubles in 14 years. 69/10 is about 7, so the second account doubles in 7 years. A factor of 1000 is about 10 doublings (2^10 = 1024), so the second account needs to have doubled 10 times more than the first account. Since it doubles twice as often, this means that it must have doubled 20 times while the other doubled 10 times. Therefore, it will take about 140 years.

In fact, it takes 141—so our quick approximation is actually remarkably good.

This example is instructive in another way; 141 years is a pretty long time, isn’t it? You can’t just assume that exponential growth is “as fast as you want it to be”. Once people realize that exponential growth is very fast, they often overcorrect, assuming that exponential growth automatically means growth that is absurdly—or arbitrarily—fast. (XKCD made a similar point in this comic.)

I think the worst examples of this mistake are among Singularitarians. They—correctly—note that computing power has become exponentially greater and cheaper over time, doubling about every 18 months, which has been dubbed Moore’s Law. They assume that this will continue into the indefinite future (this is already problematic; the growth rate seems to be already slowing down). And therefore they conclude there will be a sudden moment, a technological singularity, at which computers will suddenly outstrip humans in every way and bring about a new world order of artificial intelligence basically overnight. They call it a “hard takeoff”; here’s a direct quote:

But many thinkers in this field including Nick Bostrom and Eliezer Yudkowsky worry that AI won’t work like this at all. Instead there could be a “hard takeoff”, a huge subjective discontinuity in the function mapping AI research progress to intelligence as measured in ability-to-get-things-done. If on January 1 you have a toy AI as smart as a cow, one which can identify certain objects in pictures and navigate a complex environment, and on February 1 it’s proved the Riemann hypothesis and started building a ring around the sun, that was a hard takeoff.

Wait… what? For someone like me who understands exponential growth, the last part is a baffling non sequitur. If computers start half as smart as us and double every 18 months, in 18 months, they will be as smart as us. In 36 months, they will be twice as smart as us. Twice as smart as us literally means that two people working together perfectly can match them—certainly a few dozen working realistically can. We’re not in danger of total AI domination from that. With millions of people working against the AI, we should be able to keep up with it for at least another 30 years. So are you assuming that this trend is continuing or not? (Oh, and by the way, we’ve had AIs that can identify objects and navigate complex environments for a couple years now, and so far, no ringworld around the Sun.)

That same essay make a biological argument, which misunderstands human evolution in a way that is surprisingly subtle yet ultimately fundamental:

If you were to come up with a sort of objective zoological IQ based on amount of evolutionary work required to reach a certain level, complexity of brain structures, etc, you might put nematodes at 1, cows at 90, chimps at 99, homo erectus at 99.9, and modern humans at 100. The difference between 99.9 and 100 is the difference between “frequently eaten by lions” and “has to pass anti-poaching laws to prevent all lions from being wiped out”.

No, actually, what makes humans what we are is not that we are 1% smarter than chimpanzees.

First of all, we’re actually more like 200% smarter than chimpanzees, measured by encephalization quotient; they clock in at 2.49 while we hit 7.44. If you simply measure by raw volume, they have about 400 mL to our 1300 mL, so again roughly 3 times as big. But that’s relatively unimportant; with Moore’s Law, tripling only takes about 2.5 years.

But even having triple the brain power is not what makes humans different. It was a necessary condition, but not a sufficient one. Indeed, it was so insufficient that for about 200,000 years we had brains just as powerful as we do now and yet we did basically nothing in technological or economic terms—total, complete stagnation on a global scale. This is a conservative estimate of when we had brains of the same size and structure as we do today.

What makes humans what we are? Cooperation. We are what we are because we are together.
The capacity of human intelligence today is not 1300 mL of brain. It’s more like 1.3 gigaliters of brain, where a gigaliter, a billion liters, is about the volume of the Empire State Building. We have the intellectual capacity we do not because we are individually geniuses, but because we have built institutions of research and education that combine, synthesize, and share the knowledge of billions of people who came before us. Isaac Newton didn’t understand the world as well as the average third-grader in the 21st century does today. Does the third-grader have more brain? Of course not. But they absolutely do have more knowledge.

(I recently finished my first playthrough of Legacy of the Void, in which a central point concerns whether the Protoss should detach themselves from the Khala, a psychic union which combines all their knowledge and experience into one. I won’t spoil the ending, but let me say this: I can understand their hesitation, for it is basically our equivalent of the Khala—first literacy, and now the Internet—that has made us what we are. It would no doubt be the Khala that made them what they are as well.)

Is AI still dangerous? Absolutely. There are all sorts of damaging effects AI could have, culturally, economically, militarily—and some of them are already beginning to happen. I even agree with the basic conclusion of that essay that OpenAI is a bad idea because the cost of making AI available to people who will abuse it or create one that is dangerous is higher than the benefit of making AI available to everyone. But exponential growth not only isn’t the same thing as instantaneous takeoff, it isn’t even compatible with it.

The next time you encounter an example of exponential growth, try this. Don’t just fudge it in your head, don’t overcorrect and assume everything will be fast—just divide the percentage into 69 to see how long it will take to double.