Singularitarian

Is Singularitarianism a religion?

pnrj ethics, futurism , , , , , , ,

 

Nov 17 JDN 2458805

I said in last week’s post that Pascal’s Mugging provides some deep insights into both Singularitarianism and religion. In particular, it explains why Singularitarianism seems so much like a religion.

This has been previously remarked, of course. I think Eric Steinhart makes the best case for Singularitarianism as a religion:

I think singularitarianism is a new religious movement. I might add that I think Clifford Geertz had a pretty nice (though very abstract) definition of religion. And I think singularitarianism fits Geertz’s definition (but that’s for another time).

My main interest is this: if singularitarianism is a new religious movement, then what should we make of it? Will it mainly be a good thing? A kind of enlightenment religion? It might be an excellent alternative to old-fashioned Abrahamic religion. Or would it degenerate into the well-known tragic pattern of coercive authority? Time will tell; but I think it’s worth thinking about this in much more detail.

To be clear: Singularitarianism is probably not a religion. It is certainly not a cult, as it has been even worse accused; the behaviors it prescribes are largely normative, pro-social behaviors, and therefore it would at worst be a mainstream religion. Really, if every religion only inspired people to do things like donate to famine relief and work on AI research (as opposed to, say, beheading gay people), I wouldn’t have much of a problem with religion.

In fact, Singularitarianism has one vital advantage over religion: Evidence. While the evidence in favor of it is not overwhelming, there is enough evidential support to lend plausibility to at least a broad concept of Singularitarianism: Technology will continue rapidly advancing, achieving accomplishments currently only in our wildest imaginings; artificial intelligence surpassing human intelligence will arise, sooner than many people think; human beings will change ourselves into something new and broadly superior; these posthumans will go on to colonize the galaxy and build a grander civilization than we can imagine. I don’t know that these things are true, but I hope they are, and I think it’s at least reasonably likely. All I’m really doing is extrapolating based on what human civilization has done so far and what we are currently trying to do now. Of course, we could well blow ourselves up before then, or regress to a lower level of technology, or be wiped out by some external force. But there’s at least a decent chance that we will continue to thrive for another million years to come.

But yes, Singularitarianism does in many ways resemble a religion: It offers a rich, emotionally fulfilling ontology combined with ethical prescriptions that require particular behaviors. It promises us a chance at immortality. It inspires us to work toward something much larger than ourselves. More importantly, it makes us special—we are among the unique few (millions?) who have the power to influence the direction of human and posthuman civilization for a million years. The stronger forms of Singularitarianism even have a flavor of apocalypse: When the AI comes, sooner than you think, it will immediately reshape everything at effectively infinite speed, so that from one year—or even one moment—to the next, our whole civilization will be changed. (These forms of Singularitarianism are substantially less plausible than the broader concept I outlined above.)

It’s this sense of specialness that Pascal’s Mugging provides some insight into. When it is suggested that we are so special, we should be inherently skeptical, not least because it feels good to hear that. (As Less Wrong would put it, we need to avoid a Happy Death Spiral.) Human beings like to feel special; we want to feel special. Our brains are configured to seek out evidence that we are special and reject evidence that we are not. This is true even to the point of absurdity: One cannot be mathematically coherent without admitting that the compliment “You’re one in a million.” is equivalent to the statement “There are seven thousand people as good or better than you.”—and yet, the latter seems much worse, because it does not make us sound special.

Indeed, the connection between Pascal’s Mugging and Pascal’s Wager is quite deep: Each argument takes a tiny probability and multiplies it by a huge impact in order to get a large expected utility. This often seems to be the way that religions defend themselves: Well, yes, the probability is small; but can you take the chance? Can you afford to take that bet if it’s really your immortal soul on the line?

And Singularitarianism has a similar case to make, even aside from the paradox of Pascal’s Mugging itself. The chief argument for why we should be focusing all of our time and energy on existential risk is that the potential payoff is just so huge that even a tiny probability of making a difference is enough to make it the only thing that matters. We should be especially suspicious of that; anything that says it is the only thing that matters is to be doubted with utmost care. The really dangerous religion has always been the fanatical kind that says it is the only thing that matters. That’s the kind of religion that makes you crash airliners into buildings.

I think some people may well have become Singularitarians because it made them feel special. It is exhilarating to be one of these lone few—and in the scheme of things, even a few million is a small fraction of all past and future humanity—with the power to effect some shift, however small, in the probability of a far grander, far brighter future.

Yet, in fact this is very likely the circumstance in which we are. We could have been born in the Neolithic, struggling to survive, utterly unaware of what would come a few millennia hence; we could have been born in the posthuman era, one of a trillion other artist/gamer/philosophers living in a world where all the hard work that needed to be done is already done. In the long S-curve of human development, we could have been born in the flat part on the left or the flat part on the right—and by all probability, we should have been; most people were. But instead we happened to be born in that tiny middle slice, where the curve slopes upward at its fastest. I suppose somebody had to be, and it might as well be us.

Sigmoid curve labeled

A priori, we should doubt that we were born so special. And when forming our beliefs, we should compensate for the fact that we want to believe we are special. But we do in fact have evidence, lots of evidence. We live in a time of astonishing scientific and technological progress.

My lifetime has included the progression from Deep Thought first beating David Levy to the creation of a computer one millimeter across that runs on a few nanowatts and nevertheless has ten times as much computing power as the 80-pound computer that ran the Saturn V. (The human brain runs on about 100 watts, and has a processing power of about 1 petaflop, so we can say that our energy efficiency is about 10 TFLOPS/W. The M3 runs on about 10 nanowatts and has a processing power of about 0.1 megaflops, so its energy efficiency is also about 10 TFLOPS/W. We did it! We finally made a computer as energy-efficient as the human brain! But we have still not matched the brain in terms of space-efficiency: The volume of the human brain is about 1000 cm^3, so our space efficiency is about 1 TFLOPS/cm^3. The volume of the M3 is about 1 mm^3, so its space efficiency is only about 100 MFLOPS/cm^3. The brain still wins by a factor of 10,000.)

My mother saw us go from the first jet airliners to landing on the Moon to the International Space Station and robots on Mars. She grew up before the polio vaccine and is still alive to see the first 3D-printed human heart. When I was a child, smartphones didn’t even exist; now more people have smartphones than have toilets. I may yet live to see the first human beings set foot on Mars. The pace of change is utterly staggering.

Without a doubt, this is sufficient evidence to believe that we, as a civilization, are living in a very special time. The real question is: Are we, as individuals, special enough to make a difference? And if we are, what weight of responsibility does this put upon us?

If you are reading this, odds are the answer to the first question is yes: You are definitely literate, and most likely educated, probably middle- or upper-middle-class in a First World country. Countries are something I can track, and I do get some readers from non-First-World countries; and of course I don’t observe your education or socioeconomic status. But at an educated guess, this is surely my primary reading demographic. Even if you don’t have the faintest idea what I’m talking about when I use Bayesian logic or calculus, you’re already quite exceptional. (And if you do? All the more so.)

That means the second question must apply: What do we owe these future generations who may come to exist if we play our cards right? What can we, as individuals, hope to do to bring about this brighter future?

The Singularitarian community will generally tell you that the best thing to do with your time is to work on AI research, or, failing that, the best thing to do with your money is to give it to people working on artificial intelligence research. I’m not going to tell you not to work on AI research or donate to AI research, as I do think it is among the most important things humanity needs to be doing right now, but I’m also not going to tell you that it is the one single thing you must be doing.

You should almost certainly be donating somewhere, but I’m not so sure it should be to AI research. Maybe it should be famine relief, or malaria prevention, or medical research, or human rights, or environmental sustainability. If you’re in the United States (as I know most of you are), the best thing to do with your money may well be to support political campaigns, because US political, economic, and military hegemony means that as goes America, so goes the world. Stop and think for a moment how different the prospects of global warming might have been—how many millions of lives might have been saved!—if Al Gore had become President in 2001. For lack of a few million dollars in Tampa twenty years ago, Miami may be gone in fifty. If you’re not sure which cause is most important, just pick one; or better yet, donate to a diversified portfolio of charities and political campaigns. Diversified investment isn’t just about monetary return.

And you should think carefully about what you’re doing with the rest of your life. This can be hard to do; we can easily get so caught up in just getting through the day, getting through the week, just getting by, that we lose sight of having a broader mission in life. Of course, I don’t know what your situation is; it’s possible things really are so desperate for you that you have no choice but to keep your head down and muddle through. But you should also consider the possibility that this is not the case: You may not be as desperate as you feel. You may have more options than you know. Most “starving artists” don’t actually starve. More people regret staying in their dead-end jobs than regret quitting to follow their dreams. I guess if you stay in a high-paying job in order to earn to give, that might really be ethically optimal; but I doubt it will make you happy. And in fact some of the most important fields are constrained by a lack of good people doing good work, and not by a simple lack of funding.

I see this especially in economics: As a field, economics is really not focused on the right kind of questions. There’s far too much prestige for incrementally adjusting some overcomplicated unfalsifiable mess of macroeconomic algebra, and not nearly enough for trying to figure out how to mitigate global warming, how to turn back the tide of rising wealth inequality, or what happens to human society once robots take all the middle-class jobs. Good work is being done in devising measures to fight poverty directly, but not in devising means to undermine the authoritarian regimes that are responsible for maintaining poverty. Formal mathematical sophistication is prized, and deep thought about hard questions is eschewed. We are carefully arranging the pebbles on our sandcastle in front of the oncoming tidal wave. I won’t tell you that it’s easy to change this—it certainly hasn’t been easy for me—but I have to imagine it’d be easier with more of us trying rather than with fewer. Nobody needs to donate money to economics departments, but we definitely do need better economists running those departments.

You should ask yourself what it is that you are really good at, what you—you yourself, not anyone else—might do to make a mark on the world. This is not an easy question: I have not quite answered for myself whether I would make more difference as an academic researcher, a policy analyst, a nonfiction author, or even a science fiction author. (If you scoff at the latter: Who would have any concept of AI, space colonization, or transhumanism, if not for science fiction authors? The people who most tilted the dial of human civilization toward this brighter future may well be Clarke, Roddenberry, and Asimov.) It is not impossible to be some combination or even all of these, but the more I try to take on the more difficult my life becomes.

Your own path will look different than mine, different, indeed, than anyone else’s. But you must choose it wisely. For we are very special individuals, living in a very special time.

Pascal’s Mugging

pnrj cognitive science, heuristics and biases , , , , , , , , , ,

Nov 10 JDN 2458798

In the Singularitarian community there is a paradox known as “Pascal’s Mugging”. The name is an intentional reference to Pascal’s Wager (and the link is quite apt, for reasons I’ll discuss in a later post.)

There are a few different versions of the argument; Yudkowsky’s original argument in which he came up with the name “Pascal’s Mugging” relies upon the concept of the universe as a simulation and an understanding of esoteric mathematical notation. So here is a more intuitive version:

A strange man in a dark hood comes up to you on the street. “Give me five dollars,” he says, “or I will destroy an entire planet filled with ten billion innocent people. I cannot prove to you that I have this power, but how much is an innocent life worth to you? Even if it is as little as $5,000, are you really willing to bet on ten trillion to one odds that I am lying?”

Do you give him the five dollars? I suspect that you do not. Indeed, I suspect that you’d be less likely to give him the five dollars than if he had merely said he was homeless and asked for five dollars to help pay for food. (Also, you may have objected that you value innocent lives, even faraway strangers you’ll never meet, at more than $5,000 each—but if that’s the case, you should probably be donating more, because the world’s best charities can save a live for about $3,000.)

But therein lies the paradox: Are you really willing to bet on ten trillion to one odds?

This argument gives me much the same feeling as the Ontological Argument; as Russell said of the latter, “it is much easier to be persuaded that ontological arguments are no good than it is to say exactly what is wrong with them.” It wasn’t until I read this post on GiveWell that I could really formulate the answer clearly enough to explain it.

The apparent force of Pascal’s Mugging comes from the idea of expected utility: Even if the probability of an event is very small, if it has a sufficiently great impact, the expected utility can still be large.

The problem with this argument is that extraordinary claims require extraordinary evidence. If a man held a gun to your head and said he’d shoot you if you didn’t give him five dollars, you’d give him five dollars. This is a plausible claim and he has provided ample evidence. If he were instead wearing a bomb vest (or even just really puffy clothing that could conceal a bomb vest), and he threatened to blow up a building unless you gave him five dollars, you’d probably do the same. This is less plausible (what kind of terrorist only demands five dollars?), but it’s not worth taking the chance.

But when he claims to have a Death Star parked in orbit of some distant planet, primed to make another Alderaan, you are right to be extremely skeptical. And if he claims to be a being from beyond our universe, primed to destroy so many lives that we couldn’t even write the number down with all the atoms in our universe (which was actually Yudkowsky’s original argument), to say that you are extremely skeptical seems a grievous understatement.

That GiveWell post provides a way to make this intuition mathematically precise in terms of Bayesian logic. If you have a normal prior with mean 0 and standard deviation 1, and you are presented with a likelihood with mean X and standard deviation X, what should you make your posterior distribution?

Normal priors are quite convenient; they conjugate nicely. The precision (inverse variance) of the posterior distribution is the sum of the two precisions, and the mean is a weighted average of the two means, weighted by their precision.

So the posterior variance is 1/(1 + 1/X^2).

The posterior mean is 1/(1+1/X^2)*(0) + (1/X^2)/(1+1/X^2)*(X) = X/(X^2+1).

That is, the mean of the posterior distribution is just barely higher than zero—and in fact, it is decreasing in X, if X > 1.

For those who don’t speak Bayesian: If someone says he’s going to have an effect of magnitude X, you should be less likely to believe him the larger that X is. And indeed this is precisely what our intuition said before: If he says he’s going to kill one person, believe him. If he says he’s going to destroy a planet, don’t believe him, unless he provides some really extraordinary evidence.

What sort of extraordinary evidence? To his credit, Yudkowsky imagined the sort of evidence that might actually be convincing:

If a poorly-dressed street person offers to save 10(10^100) lives (googolplex lives) for $5 using their Matrix Lord powers, and you claim to assign this scenario less than 10-(10^100) probability, then apparently you should continue to believe absolutely that their offer is bogus even after they snap their fingers and cause a giant silhouette of themselves to appear in the sky.

This post he called “Pascal’s Muggle”, after the term from the Harry Potter series, since some of the solutions that had been proposed for dealing with Pascal’s Mugging had resulted in a situation almost as absurd, in which the mugger could exhibit powers beyond our imagining and yet nevertheless we’d never have sufficient evidence to believe him.

So, let me go on record as saying this: Yes, if someone snaps his fingers and causes the sky to rip open and reveal a silhouette of himself, I’ll do whatever that person says. The odds are still higher that I’m dreaming or hallucinating than that this is really a being from beyond our universe, but if I’m dreaming, it makes no difference, and if someone can make me hallucinate that vividly he can probably cajole the money out of me in other ways. And there might be just enough chance that this could be real that I’m willing to give up that five bucks.

These seem like really strange thought experiments, because they are. But like many good thought experiments, they can provide us with some important insights. In this case, I think they are telling us something about the way human reasoning can fail when faced with impacts beyond our normal experience: We are in danger of both over-estimating and under-estimating their effects, because our brains aren’t equipped to deal with magnitudes and probabilities on that scale. This has made me realize something rather important about both Singularitarianism and religion, but I’ll save that for next week’s post.

The real Existential Risk we should be concerned about

pnrj ethics, futurism, public policy , , , , , , , , , , , , , , , , , , , , ,

JDN 2457458

There is a rather large subgroup within the rationalist community (loosely defined because organizing freethinkers is like herding cats) that focuses on existential risks, also called global catastrophic risks. Prominent examples include Nick Bostrom and Eliezer Yudkowsky.

Their stated goal in life is to save humanity from destruction. And when you put it that way, it sounds pretty darn important. How can you disagree with wanting to save humanity from destruction?

Well, there are actually people who do (the Voluntary Human Extinction movement), but they are profoundly silly. It should be obvious to anyone with even a basic moral compass that saving humanity from destruction is a good thing.

It’s not the goal of fighting existential risk that bothers me. It’s the approach. Specifically, they almost all seem to focus on exotic existential risks, vivid and compelling existential risks that are the stuff of great science fiction stories. In particular, they have a rather odd obsession with AI.

Maybe it’s the overlap with Singularitarians, and their inability to understand that exponentials are not arbitrarily fast; if you just keep projecting the growth in computing power as growing forever, surely eventually we’ll have a computer powerful enough to solve all the world’s problems, right? Well, yeah, I guess… if we can actually maintain the progress that long, which we almost certainly can’t, and if the problems turn out to be computationally tractable at all (the fastest possible computer that could fit inside the observable universe could not brute-force solve the game of Go, though a heuristic AI did just beat one of the world’s best players), and/or if we find really good heuristic methods of narrowing down the solution space… but that’s an awful lot of “if”s.

But AI isn’t what we need to worry about in terms of saving humanity from destruction. Nor is it asteroid impacts; NASA has been doing a good job watching for asteroids lately, and estimates the current risk of a serious impact (by which I mean something like a city-destroyer or global climate shock, not even a global killer) at around 1/10,000 per year. Alien invasion is right out; we can’t even find clear evidence of bacteria on Mars, and the skies are so empty of voices it has been called a paradox. Gamma ray bursts could kill us, and we aren’t sure about the probability of that (we think it’s small?), but much like brain aneurysms, there really isn’t a whole lot we can do to prevent them.

There is one thing that we really need to worry about destroying humanity, and one other thing that could potentially get close over a much longer timescale. The long-range threat is ecological collapse; as global climate change gets worse and the oceans become more acidic and the aquifers are drained, we could eventually reach the point where humanity cannot survive on Earth, or at least where our population collapses so severely that civilization as we know it is destroyed. This might not seem like such a threat, since we would see this coming decades or centuries in advance—but we are seeing it coming decades or centuries in advance, and yet we can’t seem to get the world’s policymakers to wake up and do something about it. So that’s clearly the second-most important existential risk.

But the most important existential risk, by far, no question, is nuclear weapons.

Nuclear weapons are the only foreseeable, preventable means by which humanity could be destroyed in the next twenty minutes.

Yes, that is approximately the time it takes an ICBM to hit its target after launch. There are almost 4,000 ICBMs currently deployed, mostly by the US and Russia. Once we include submarine-launched missiles and bombers, the total number of global nuclear weapons is over 15,000. I apologize for terrifying you by saying that these weapons could be deployed in a moment’s notice to wipe out most of human civilization within half an hour, followed by a global ecological collapse and fallout that would endanger the future of the entire human race—but it’s the truth. If you’re not terrified, you’re not paying attention.

I’ve intentionally linked the Union of Concerned Scientists as one of those sources. Now they are people who understand existential risk. They don’t talk about AI and asteroids and aliens (how alliterative). They talk about climate change and nuclear weapons.

We must stop this. We must get rid of these weapons. Next to that, literally nothing else matters.

“What if we’re conquered by tyrants?” It won’t matter. “What if there is a genocide?” It won’t matter. “What if there is a global economic collapse?” None of these things will matter, if the human race wipes itself out with nuclear weapons.

To speak like an economist for a moment, the utility of a global nuclear war must be set at negative infinity. Any detectable reduction in the probability of that event must be considered worth paying any cost to achieve. I don’t care if it costs $20 trillion and results in us being taken over by genocidal fascists—we are talking about the destruction of humanity. We can spend $20 trillion (actually the US as a whole does every 14 months!). We can survive genocidal fascists. We cannot survive nuclear war.

The good news is, we shouldn’t actually have to pay that sort of cost. All we have to do is dismantle our nuclear arsenal, and get other countries—particularly Russia—to dismantle theirs. In the long run, we will increase our wealth as our efforts are no longer wasted maintaining doomsday machines.

The main challenge is actually a matter of game theory. The surprisingly-sophisticated 1990s cartoon show the Animaniacs basically got it right when they sang: “We’d beat our swords into liverwurst / Down by the East Riverside / But no one wants to be the first!”

The thinking, anyway, is that this is basically a Prisoner’s Dilemma. If the US disarms and Russia doesn’t, Russia can destroy the US. Conversely, if Russia disarms and the US doesn’t, the US can destroy Russia. If neither disarms, we’re left where we are. Whether or not the other country disarms, you’re always better off not disarming. So neither country disarms.

But I contend that it is not, in fact, a Prisoner’s Dilemma. It could be a Stag Hunt; if that’s the case, then only multilateral disarmament makes sense, because the best outcome is if we both disarm, but the worst outcome is if we disarm and they don’t. Once we expect them to disarm, we have no temptation to renege on the deal ourselves; but if we think there’s a good chance they won’t, we might not want to either. Stag Hunts have two stable Nash equilibria; one is where both arm, the other where both disarm.

But in fact, I think it may be simply the trivial game.

There aren’t actually that many possible symmetric two-player nonzero-sum games (basically it’s a question of ordering 4 possibilities, and it’s symmetric, so 12 possible games), and one that we never talk about (because it’s sort of boring) is the trivial game: If I do the right thing and you do the right thing, we’re both better off. If you do the wrong thing and I do the right thing, I’m better off. If we both do the wrong thing, we’re both worse off. So, obviously, we both do the right thing, because we’d be idiots not to. Formally, we say that cooperation is a strictly dominant strategy. There’s no dilemma, no paradox; the self-interested strategy is the optimal strategy. (I find it kind of amusing that laissez-faire economics basically amounts to assuming that all real-world games are the trivial game.)

That is, I don’t think the US would actually benefit from nuking Russia, even if we could do so without retaliation. Likewise, I don’t think Russia would actually benefit from nuking the US. One of the things we’ve discovered—the hardest way possible—through human history is that working together is often better for everyone than fighting. Russia could nuke NATO, and thereby destroy all of their largest trading partners, or they could continue trading with us. Even if they are despicable psychopaths who think nothing of committing mass murder (Putin might be, but surely there are people under his command who aren’t?), it’s simply not in Russia’s best interest to nuke the US and Europe. Likewise, it is not in our best interest to nuke them.

Nuclear war is a strange game: The only winning move is not to play.

So I say, let’s stop playing. Yes, let’s unilaterally disarm, the thing that so many policy analysts are terrified of because they’re so convinced we’re in a Prisoner’s Dilemma or a Stag Hunt. “What’s to stop them from destroying us, if we make it impossible for us to destroy them!?” I dunno, maybe basic human decency, or failing that, rationality?

Several other countries have already done this—South Africa unilaterally disarmed, and nobody nuked them. Japan refused to build nuclear weapons in the first place—and I think it says something that they’re the only people to ever have them used against them.

Our conventional military is plenty large enough to defend us against all realistic threats, and could even be repurposed to defend against nuclear threats as well, by a method I call credible targeted conventional response. Instead of building ever-larger nuclear arsenals to threaten devastation in the world’s most terrifying penis-measuring contest, you deploy covert operatives (perhaps Navy SEALS in submarines, or double agents, or these days even stealth drones) around the world, with the standing order that if they have reason to believe a country initiated a nuclear attack, they will stop at nothing to hunt down and kill the specific people responsible for that attack. Not the country they came from; not the city they live in; those specific people. If a leader is enough of a psychopath to be willing to kill 300 million people in another country, he’s probably enough of a psychopath to be willing to lose 150 million people in his own country. He likely has a secret underground bunker that would allow him to survive, at least if humanity as a whole does. So you should be threatening the one thing he does care about—himself. You make sure he knows that if he pushes that button, you’ll find that bunker, drop in from helicopters, and shoot him in the face.

The “targeted conventional response” should be clear by now—you use non-nuclear means to respond, and you target the particular leaders responsible—but let me say a bit more about the “credible” part. The threat of mutually-assured destruction is actually not a credible one. It’s not what we call in game theory a subgame perfect Nash equilibrium. If you know that Russia has launched 1500 ICBMs to destroy every city in America, you actually have no reason at all to retaliate with your own 1500 ICBMs, and the most important reason imaginable not to. Your people are dead either way; you can’t save them. You lose. The only question now is whether you risk taking the rest of humanity down with you. If you have even the most basic human decency, you will not push that button. You will not “retaliate” in useless vengeance that could wipe out human civilization. Thus, your threat is a bluff—it is not credible.

But if your response is targeted and conventional, it suddenly becomes credible. It’s exactly reversed; you now have every reason to retaliate, and no reason not to. Your covert operation teams aren’t being asked to destroy humanity; they’re being tasked with finding and executing the greatest mass murderer in history. They don’t have some horrific moral dilemma to resolve; they have the opportunity to become the world’s greatest heroes. Indeed, they’d very likely have the whole world (or what’s left of it) on their side; even the population of the attacking country would rise up in revolt and the double agents could use the revolt as cover. Now you have no reason to even hesitate; your threat is completely credible. The only question is whether you can actually pull it off, and if we committed the full resources of the United States military to preparing for this possibility, I see no reason to doubt that we could. If a US President can be assassinated by a lone maniac (and yes, that is actually what happened), then the world’s finest covert operations teams can assassinate whatever leader pushed that button.

This is a policy that works both unilaterally and multilaterally. We could even assemble an international coalition—perhaps make the UN “peacekeepers” put their money where their mouth is and train the finest special operatives in the history of the world tasked with actually keeping the peace.

Let’s not wait for someone else to save humanity from destruction. Let’s be the first.

The power of exponential growth

pnrj cognitive science, core principles, statistics , , , , , , , , , ,

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.