Year: 2016

What would an interplanetary economy look like?

PNRJ futurism, public policy, Uncategorized , , , , , , , , , , , , , ,

JDN 2457397

Today’s post is the second Reader’s Choice topic, chosen by a vote of my Patreons.

Remember, you too can vote on future topics if you pledge at least $10 per month.

Actually, there was a tie between two topics; since I was in an SF mood today, I decided to do this one as the official Reader’s Choice post. The second, “The challenges and possibilities of a global basic income”, I’ll do as a later post. (If I don’t get around to that before the next vote, you can of course always vote for it again.)

Will we ever colonize outer space? Many people thought we’d be there by now.

In Blade Runner, released in 1982, Roy was built and deployed to the outer colonies in 2015, which you may remember as the year that just ended.

Predictions of the future are often wrong, but predictions from the 20th century of the 21st century seem to be consistently overoptimistic about technology. In a past Idiot Free Zone post, I hypothesize that this is due to the confusion between exponential and logistic growth.

Paul Krugman is also a big fan of SF (it is actually about as likely that I’d run into Krugman at Worldcon as at an economics conference), and he wrote a paper on the possibility of interstellar trade way back in 1978. I think he’s kind of satirizing economic theorists actually; he uses sophisticated mathematics to address a problem that doesn’t exist in the real world—just like they do.

I think we will eventually at least reach the point of interplanetary colonization, if not actually interstellar. To begin, let me emphasize that vital distinction. Mars is currently about 60 million kilometers away at its closest approach. The core of the Alpha Centauri system is 4.24 light-years away, which is about 40 trillion kilometers. The distance from Ann Arbor to Toledo is about 84 kilometers. Thus, the difficulty of going to Alpha Centauri is about as much higher than that of going to Mars as the difficulty of going to Mars is compared to going from Ann Arbor to Toledo—each a factor of 700,000 times the distance.

With current technology, we can send robots to Mars (how cool is that? We did get some of the future we were promised). A typical trip takes about half a year. It costs us about $2.5 billion to do that, though India somehow managed to at least make Mars orbit for $75 million. Even if we use the $2.5 billion figure, that still means our current economic output the US and Europe alone could support hundreds of missions per year if we were willing to pay for it. (Devote the entire US military budget to NASA and we could land a new robot on Mars every day.) Interplanetary travel is most definitely feasible.

Interstellar travel on the other hand, is still far out of reach. In principle we are limited by the speed of light; in fact, it’s a good deal worse than that. The fastest we have ever gotten a spacecraft leaving the Solar System is about 60,000 km/h; at that speed it would take almost one billion hours to get to Alpha Centauri, which is over 100,000 years. We will need substantial breakthroughs in spacecraft propulsion before we can even consider sending anything to even the nearest stars. (I wouldn’t give up hope completely, however; in 1901 someone could just as well have criticized H.G. Wells’ The First Men in the Moon on the grounds that no one will ever invent a propulsion system powerful enough to reach the moon.)

By the time we manage interstellar travel, our technology will be so much more advanced it’s hard to even imagine what things will be like. But interplanetary travel we could probably do right now.

So let’s suppose we do in fact establish colonies on other planets—most likely Mars and Mercury, as well as several moons of Jupiter and Saturn. What would our economy look like once we did?

For a decidedly Game of Thrones take on this situation, see The Expanse. Their scientific accuracy is quite good (although they still have sound in space!); so far, their economic accuracy seems pretty good as well, but so far I haven’t seen enough yet to be sure.
One thing I think The Expanse does get right is that asteroid mining is a vital part of the interplanetary trade network. The thing that’s currently keeping us from colonizing other planets is a lack of economic incentives to bear the enormous cost of space travel. Asteroid mining is one thing that might actually provide those incentives, if we can leap just a few more technological hurdles in terms of mining robots and spacecraft propulsion.

Many asteroids contain metals such as silver, gold and platinum at concentrations 20 times as great as anything found on the surface of the Earth. The amount of iron and nickel they contain is even larger; we could supply the entire iron production of the Earth (3.2 billion tonnes) with a single asteroid, 16 Psyche, for the next million years. That one asteroid over 2e19 kg of nearly pure iron-nickel, which is 200 quadrillion tonnes. Many asteroids also contain large concentrations of other useful and rare metals, such as lithium and neodymium.

It is unlikely we would actually try to colonize asteroids (they do in The Expanse, but I’m not sure I buy it). None are large enough to support an atmosphere (kind of by definition), so we’d have to build space stations large enough for permanent habitation. With such ludicrous amounts of iron all around us, that might be possible; but would it be cost-effective? I think it’s more likely that we would have temporary habitats, able to support people for several months or maybe a few years, and people would basically do “tours of duty” working in the asteroids, and then return home. This is similar to how we use space stations right now; you can live there for a long time—the standing record is over a year—but nobody lives their whole life there. It might be a sort of “seasonal” work, where the seasons are decided by large-scale orbital mechanics rather than local planetary axial tilt. (We might have to start doing “seasonal adjustments” to statistics based on this!) Provided that the workers are paid a substantial portion of the spoils—by no means a certainty, as we all know from sweatshops around the world—this work could easily be lucrative enough that you become a millionaire after a tour or two and then retire.

But they might well return home to Mars, since the orbital transfer from the asteroid belt to Mars is considerably easier (it has what we call a lower “delta-v”) than the same transfer all the way back to Earth, and the launch and landing are even easier still. Mars does support an atmosphere—currently very thin and not breathable, but that could change with terraforming. It is also large enough to spread out with room for many homes, greenhouses, power plants, etc., and has enough gravity to at least keep human bodies as a basic level of functioning without too much additional support. (Mars’ gravity is about 40% that of Earth’s.)

Of course, most of the products we make are going to be used on Earth—most of everything is going to be used on Earth, probably for centuries to come. It’s possible that we’ll end up like the British Empire did where the colonies are more populous than the source, but it will take a long time for that to happen. (Moreover, the primary reason—cheap, fertile agricultural land—will not apply unless we happen upon a habitable planet or get very good at terraforming.) This means we will need to ship something from Mars to Earth. But since the delta-v is exceptionally high, we’ll want to ship as little as possible. I think this means that we will do most of the refinement and even manufacturing on Mars, and then ship prefabricated components to Earth. Any process that removes mass will be done on Mars, to minimize the amount of mass that needs to make the trip to Earth.

And what will Earth provide in return? As we import this huge quantity of metal (or metal components), what will we export in return?
Well, one possibility is that we won’t—at first, we (by which I mean “our corporations”) will simply retain ownership of the entire supply chain and do all the accounting as though production were being done entirely on Earth. We won’t think of it as “trade”, just as corporations engaging in a series of prospecting and mining ventures. At least at first.

Yet this will become increasingly unwieldy, just as it became unwieldy for the British Empire to retain control of all its colonies and collect their taxes for the Crown. Communication between Mars, Earth, and the asteroid belt will be relatively fast—a few hours delay at worst—but travel will be very slow and very expensive. Local institutions will form and assert themselves, and may eventually topple the corporate managers, expropriate their assets, and create new governments. The corporations could see the rebellion coming a year in advance from the transmissions, and still be powerless to stop it because the ships will take too long to arrive.

Once new local governments form, we will start thinking of it as “trade”. So what will we be trading? To some extent people on Mars might simply accept Earth currency (perhaps US Dollars, or Euros, or as I like to imagine some unified currency, perhaps the Atlantic Union Dollar); but only if they can then use that Earth currency to buy things they actually need. What will they actually need?

Food, for one. Some amount of food production will be done on Mars by necessity—you can’t survive if you depend entirely on imported food to survive. But it will be expensive, and most likely nutrient-dense but tasteless and monotonous genetically-engineered vegetable products. People will get tired of eating bricks of processed Aresoy(TM) for the 17,000th time and will crave real food; Earth will respond by selling them frozen steaks at $12,000 per kilogram. Probably only luxury foods will be imported, actually; why spend $11,900 for a hamburger when you can spend $12,000 for filet mignon? Nominal income on Mars will be huge—millionaires will be ubiquitous. At purchasing power parity, it may not be so impressive, once you account for the ridiculous cost of food and housing. It’ll be like living in Silicon Valley—on steroids.

Water, perhaps. This one is not as obvious as it may seem. While Earth does have the largest concentration of liquid water (except for a couple of moons of the gas giants), there is plenty of ice in them thar asteroids. It will most likely be cheaper (albeit not cheap) to obtain water by capturing and melting down asteroid ice than to ship it all the way from Earth.

But I think the most important Earth export will beculture. The main products that Martians will want to buy from us will be books, movies, songs, video games, hologram simulations. They will be blueprints, patents, 3D printer schematics. Those who travel to Mars will be bold, adventurous, many of them loners and misfits—but deep down they will still sometimes long for the comforts of the books they read as children, the songs they listened to as teenagers. The beautiful thing about selling culture is that it can be transported almost for free—just add it to the radio transmissions you were already sending. Mars will also produce its own culture, of course, but the much smaller population and constant struggle for survival will mean that most of the cultural flow will be outward from Earth to the colonies rather than the reverse. The Internet won’t work normally between Earth and Mars due to the time delay, but there will be something like it, a local MarsNet that caches material from the Internet on a delay of a few hours and then shares it with the colony. You won’t download webpages in real time, you’ll request them a day in advance. You won’t send instant messages, but sending email will be hardly any different. (Instead of Nigerian princes we’ll start getting scam spam about Martian mining entrepreneurs.) Whoever owns this communication monopoly will become fantastically rich, perhaps even more so than the mining companies themselves—because the mining companies have overhead.

Overall, the increased availability of previously-scarce metals like gold, lithium, and neodymium will make new technologies possible and also widely available, including battery technologies that might finally allow Earth to wean itself off of carbon emissions. (Unfortunately, our current means of spacecraft launch are all very carbon-intensive. We will need to invent nuclear engines that don’t leave fallout so that we can launch with them from the ground.) Like all trade, the mutual imports and exports between Earth and Mars will benefit both societies.

But unless we change course dramatically as a society, interplanetary trade will make one problem even worse, and that is inequality. I am having trouble foreseeing an interplanetary trade system that doesn’t involve making the middlemen who own the shipping and networking companies rich even beyond the wildest dreams of today’s plutocrats. We will witness the birth of humanity’s first trillionaires, individual men (and let’s face it, probably men, unless we figure out gender equality too) who own as much as not just entire countries, but as entire large First World countries. The GDP of France today is $2.8 trillion per year; the CEO of Aresoy or MarsNet could well make more than that on dividends. Of course, that provides him a great incentive to start the project now—but what will it mean for our societies when one person can buy a spaceship as casually as we would buy a cup of coffee?

Saudi Arabia is becoming a problem.

PNRJ current events, public policy , , , , , , , , , , , , , , , , , , , , ,

JDN 2457394

There has been a lot of talk lately about what’s going on in the Middle East, particularly in Syria, Iran, and Iraq, where Daesh (I like to call them that precisely because they don’t like it), also known as ISIS or ISIL, has been killing people and destroying things–including priceless ancient artifacts.

We in the United States actually have little to fear from Daesh. Pace Ben Carson and Lindsey Graham, Daesh is absolutely not an existential threat to the United States. We have them completely outnumbered and outgunned—indeed, we have the world outgunned, as we ourselves account for 40% of the world’s military spending and a comparable portion of the world’s nuclear missiles, naval tonnage, and air fleet.
The people who need to worry are those living in (or fleeing from) the Middle East.

Some 17,000 civilians were killed by warfare in Iraq in 2014, the plurality killed by Daesh and only a small fraction killed by US or NATO forces. Contrary to the belief of people like Noam Chomsky who think the US military is comprised of bloodthirsty genocidal murderers, we actually go quite far out of our way to minimize civilian deaths, up to and including dropping pamphlets warning of bombing raids before we carry them out (I love the “admits” in that headline. You keep using that word…). Then there’s Syria, where there have been over 200,000 deaths, though actually more attributable to Bashir al-Assad than to Daesh.

Daesh, on the other hand, has no qualms about killing anyone they consider not a “true Muslim”, which basically means anyone who doesn’t support them—it certainly doesn’t exclude all Muslims. Daesh is so brutal and extreme that Al Qaeda has condemned their tactics. Yes, that Al Qaeda, the one that crashed airplanes into the World Trade Center in 2001. If you really want to know the sorts of things Daesh has been doing (and have the stomach for it), there are plenty of photos and video footage, many of them openly promoted by Daesh itself, including on their Twitter feed which also shows lots of (I am not kidding) kitten photos called “Mewjahideen”.

But today I’m not actually going to focus on Daesh itself. I’m going to focus on a country that is ostensibly our ally in the fight against them—yet the way they’ve been behaving is a lot more like being an ally of Daesh. As I gave away in the title, I mean of course Saudi Arabia.

Between the time that I drafted this post as a Blog From the Future on Patreon and the time that you are now reading this, Saudi Arabia did another terrible thing, namely executing an important Shi’ite cleric and triggering the possibility of war between Saudi Arabia and Iran. (I think it helps support the point I’m about to make shortly that the focus of this article is on the effect on oil prices.)

First, remember what Saudi Arabia is—namely, an absolute theocratic monarchy founded upon the same Wahhabi Islamist ideology that drives Daesh. They teach Wahhabi Islam as their state religion in schools. This by itself should make us wonder whether they are really our allies—they after all agree a lot more with our enemies than they do with us. And indeed, while they speak of joining the “war on terror”, they are actually the leading source of funds for global Islamist terrorism. In theory, with their large, powerful military and a majority-Muslim population (which would help avoid the sense that this is some kind of Christian/atheist versus Muslim neo-Crusade, which it absolutely must not be), Saudi Arabia could be a valuable ally in this war—but they don’t particularly want to be.

Saudi Arabia is now paying to support refugees, but they aren’t actually accepting any refugees themselves. It would make sense for the US to do this, because we are very far away and it would be very difficult to transport refugees here. It does not make sense for Saudi Arabia to do this, except in order to look like they’re doing something while actually doing as little as possible. (Also, I’ve read conflicting reports as to whether they’ve pledged $10 million to Jordan or $10 billion—which is kind of like saying, “The car was either $1,000 or $1,000,000, I’m not sure.” The most credible estimate I’ve seen is $300 million, $10 million to Jordan. In my favorite unit of wealth, they’ve donated a romney. It’s a whopping… 0.04% of their country’s income in a year.) They should be doing what Turkey is doing, and taking on hundreds of thousands of refugees themselves.

As is fairly common among tyrants (look no further than North Korea), Saudi Arabia’s leaders often present some rather… eccentric beliefs, such as the claim that Daesh is actually secretly a wing of the Israeli military. Maybe this is Freudian projection: Knowing that they are secretly supporting Daesh and its ideology, they decide to accuse whomever they most dislike—i.e., Israel—of doing that very thing. And they certainly do hate Israel; Saudi Arabia’s state-run media frequently compare Israel to Nazis because apparently irony is completely lost on them.

One of the things Daesh does to display its brutality is behead nonbelievers; yet Saudi Arabia beheads far more people, including for thoughtcrimes such as apostasy and political dissent, as well as “crimes” such as sorcery and witchcraft. The human rights violation here is not so much the number of executions as the intentional spectacle of brutality, as well as the “crimes” cited. In the summer of 2014, they beheaded about one person per day—in a country of 27 million people, it wouldn’t be that odd to execute 30 people in a month, if they were in fact murderers. That’s about the size and execution rate of Texas. The world’s real execution leader is China, where over 2,000—and previously as many as 10,000—people per year are executed. China does have a huge population of almost 1.4 billion people—but even so, they execute more people than the rest of the world combined.

I mean, one can certainly argue that the death penalty in general is morally wrong (it is certainly economically inefficient); but I never could quite manage to be outraged by the use of lethal injection on serial killers (which is mainly what we’re talking about in Texas). But Saudi Arabia doesn’t use lethal injection, they use beheading. And they don’t just execute serial killers—they execute atheists and feminists.

Saudi Arabia’s human rights record is one of the worst in the world. (And that’s from the US Department of State, so don’t tell me our government doesn’t know this.) Freedom House gives them the lowest possible rating, and lists several reasons why their government should be considered a global pariah. Even the Heritage Foundation (which overweights economic freedom over civil liberties, in my opinion—would you rather pay high taxes, or be executed for thoughtcrime?) gave Saudi Arabia a moderate freedom rating at best.

So, the question really becomes: Why do we call these people our allies?

Why did President Obama cut short a visit to India—which is, you know, a democracy—to see the new king—as in absolute monarch—of Saudi Arabia? (Though good on Michelle Obama for refusing to wear the hijab. You can see the contempt in the faces of the Saudi dignitaries, but she just grins smugly. You can almost hear, “What are you gonna do about it?”) Why was “cementing ties with Saudi Arabia” even something we wanted to do?

 

The answer of course is painfully obvious, especially to economists: Oil.

Saudi Arabia is by far the world’s largest oil exporter, accounting for a sixth of all crude oil exports.

The United States is by far the world’s largest oil importer, accounting for an eighth of all crude oil imports.

As Vonnegut said, we are rolling drunk on petroleum. We are addicts, and they’re our dealer. And if there’s one thing addicts don’t do, it’s rat out their own dealers.

Fortunately, US oil imports are on the decline, and why? Thanks, Obama. Under policies that really were largely spearheaded by the Obama administration such as expanded fracking and subsidized solar power investment, a combination of increased domestic oil production and reduced domestic oil consumptionhas been reducing the need to continue importing oil from other countries.

Of course, the “expanded fracking” and “increased oil production” part gives me very mixed feelings, given its obvious connection to climate change. But I will say this: If we’re going to be burning all that oil anyway, far better that we extract it ourselves than that we buy it from butchers and tyrants. And indeed US carbon emissions have also been steady or declining under Obama.

The sudden crash in oil prices last year has been damaging to both Saudi Arabia and other major oil exporters such as Russia and Venezuela, which are nowhere near as bad but also hardly wholesome liberal democracies. (It also hurt Norway, who didn’t deserve it; but they’re wisely divesting from fossil fuels, starting with coal.) Now is the perfect time to implement a carbon tax; consumers will hardly feel it—it’ll just feel like prices are going back to normal—but oil exporters will have even more pressure to switch industries, and above all global carbon emissions will decrease.

Ideally we would also combine this with what I call a “human rights tariff”, a tariff applied to the goods a country exports based upon that country’s human rights record. We could keep it very simple: Another percentage point added to the tariff every time you execute someone for political, religious, or ideological reasons. A percentage point off every time you go at least a month without executing anyone for any reason except murder.

Obviously that wouldn’t deal with the fact that women can’t drive, or the fact that hijab is mandatory, or the fact that homosexuality is illegal—but hey, it would at least be something. Right now, every barrel of oil we buy from them is basically saying that we care more about cheap gasoline than we do about human rights.

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.