Failed Singularity Model

Noted Yale economist William Nordhaus has a new paper “Are We Approaching an Economic Singularity? Information Technology and the Future of Economic Growth”:

Assume that labor is constant, that all technological change is capital-augmenting at 10% per year, and that the elasticity of substitution between labor and information capital is 1.25. Figure 3 shows a typical simulation of the share of capital and the growth rates of output and wages.

NordhausSingularityIn this model, capital slowly gets a larger share of total income and the economic growth accelerates, even though the rate of innovation never changes. Nordhaus lists six empirical predictions for the sign of observed parameters, and finds that four of the six are rejected by our best estimates having the opposite sign. And this doesn’t include the fact that our best estimates find the elasticity of substitution between labor and capital to be less than one. The two sign predictions that match the data suggest it would take a century or more before growth rates exceed 20% per year. Nordhaus says, “The conclusion is therefore that the growth Singularity is not near.”

Of course this is far from the only possible economic model of a singularity. But it sets a good standard for future efforts. Can anyone find a concrete simple economic model of singularity that better fits the data?

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Help Me Pick Book Title

(No I’m not going to say more about the book now.)

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Monster Pumps

Yesterday’s Science has a long paper on an exciting new scaling law. For a century we’ve known that larger organisms have lower metabolisms, and thus lower growth rates. Metabolism goes as size to the power of 3/4 over at least twenty orders of magnitude:


So our largest organisms have a per-mass metabolism one hundred thousand times lower than our smallest organisms.

The new finding is that local metabolism also goes as local biomass density to the power of roughly 3/4, over at least three orders of magnitude. This implies that life in dense areas like jungles is just slower and lazier on average than is life in sparse areas like deserts. And this implies that the ratio of predator to prey biomass is smaller in jungles compared to deserts.

When I researched how to cool large em cities I found that our best cooling techs scale quite nicely, and so very big cities need only pay a small premium for cooling compared to small cities. However, I’d been puzzled about why biological organisms seem to pay much higher premiums to be large. This new paper inspired me to dig into the issue.

What I found is that human engineers have figured ways to scale large fluid distribution systems that biology has just never figured out. For example, the hearts that pump blood through animals are periodic pumps, and such pumps have the problem that the pulses they send through the blood stream can reflect back from joints where blood vessels split into smaller vessels. There are ways to design joints to eliminate this, but those solutions create a total volume of blood vessels that doesn’t scale well. Another problem is that blood vessels taking blood to and from the heart are often near enough to each other to leak heat, which can also create a bad scaling problem.

The net result is that big organisms on Earth are just noticeably sluggish compared to small ones. But big organisms don’t have to be sluggish, that is just an accident of the engineering failures of Earth biology. If there is a planet out there where biology has figured out how to efficiently scale its blood vessels, such as by using continuous pumps, the organisms on that planet will have fewer barriers to growing large and active. Efficiently designed large animals on Earth could easily have metabolisms that are thousands of times faster than in existing animals. So, if you don’t already have enough reasons to be scared of alien monsters, consider that they might have far faster metabolisms, and also very large.

This seems yet another reason to think that biology will soon be over. Human culture is inventing so many powerful advances that biology never found, innovations that are far easier to integrate into the human economy than into biological designs. Descendants that integrate well into the human economy will just outcompete biology.

I also spend a little time thinking about how one might explain the dependence of metabolism on biomass density. I found I could explain it by assuming that the more biomass there is in some area, the less energy each biomass gets from the sun. Specifically, I assume that the energy collected from the sun by the biomass in some area has a power law dependence on the biomass in that area. If biomass were very efficiently arranged into thin solar collectors then that power would be one. But since we expect some biomass to block the view of other biomass, a problem that gets worse with more biomass, the power is plausibly less than one. Let’s call a this power that relates biomass density B to energy collected per area E. As in E = cBa.

There are two plausible scenarios for converting energy into new biomass. When the main resource need to make new biomass via metabolism is just energy to create molecules that embody more energy in their arrangement, then M = cBa-1, where M is the rate of production of new biomass relative to old biomass. When new biomass doesn’t need much energy, but it does need thermodynamically reversible machinery to rearrange molecules, then M = cB(a-1)/2. These two scenarios reproduce the observed 3/4 power scaling law when a = 3/4 and 1/2 respectively. When making new biomass requires both simple energy and reversible machinery, the required power a is somewhere between 1/2 and 3/4.

Added 14Sep: On reflection and further study, it seems that biologists just do not have a good theory for the observed 3/4 power. In addition, the power deviates substantially from 3/4 within smaller datasets.

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If Post Filter, We Are Alone

Me four years ago:

Imagine that over the entire past and future history of our galaxy, human-level life would be expected to arise spontaneously on about one hundred planets. At least it would if those planets were not disturbed by outsiders. Imagine also that, once life on a planet reaches a human level, it is likely to quickly (e.g., within a million years) expand to permanently colonize the galaxy. And imagine life rarely crosses between galaxies. In this case we should expect Earth to be one of the first few habitable planets created, since otherwise Earth would likely have already been colonized by outsiders. In fact, we should expect Earth to sit near the one percentile rank in the galactic time distribution of habitable planets – only ~1% of such planets would form earlier. …

If we can calculate the actual time distribution of habitable planets in our galaxy, we can then use Earth’s percentile rank in that time distribution to estimate the number of would-produce-human-level-life planets in our galaxy! Or at least the number of such planets times the chance that such a planet quickly expands to colonize the galaxy. (more)

New results:

The Solar System formed after 80% of existing Earth-like planets (in both the Universe and the Milky Way), after 50% of existing giant planets in the Milky Way, and after 70% of existing giant planets in the Universe. Assuming that gas cooling and star formation continues, the Earth formed before 92% of similar planets that the Universe will form. This implies a < 8% chance that we are the only civilisation the Universe will ever have. (more; HT Brian Wang)

Bottom line: these new results offer little support for the scenario where we have a good chance of growing out into the universe and meeting other aliens before a billion of years have passed. Either we are very likely to die and not grow, or we are the only ones who could grow. While it is possible that adding more filters like gamma ray bursts could greatly change this analysis, that seems to require a remarkable coincidence of contrary effects to bring Earth back to being near the middle of the filtered distribution of planets. The simplest story seems right: if we have a chance to fill the universe, we are the only ones for a billion light years with that chance.

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Why Have Opinions?

I just surprised some people here at a conference by saying that I don’t have opinions on abortion or gun control. I have little use for such opinions, and so haven’t bothered to form them. Since that attitude seems to be unusual among my intellectual peers, let me explain myself.

I see four main kinds of reasons to have opinions on subjects:

  • Decisions – Sometimes I need to make concrete decisions where the best choice depends on particular key facts or values. In such cases I am forced to have opinions on those subjects, in order to make good decisions. I may well just adopt, without much reflection, the opinions of some standard expert source. I have to make a lot of decisions and don’t have much time to reflect. But even so, I must have an opinion. And my incentives here tend to be toward having true opinions.
  • Socializing – A wide range of topics come up when talking informally with others, and people tend to like you to express opinions on at least some substantial subset of those topics. They typically aren’t very happy if you explain that you just adopted the opinion of some standard expert source without reflection, and so we are encouraged to “think for ourselves” to generate such opinions. Here my incentives are to have opinions that others find interesting or loyal, which is less strongly (but not zero) correlated with truth.
  • Research – As a professional intellectual, I specialize in particular topics. On those topics I generate opinions together with detailed supporting justifications for those opinions. I am evaluated on the originality, persuasiveness, and impressiveness of these opinions and justifications. These incentives are somewhat more strongly, but still only somewhat, correlated with truth.
  • Exploration – I’m not sure what future topics to research, and so continually explore a space of related topics which seem like they might have the potential to become promising research areas for me. Part of that process of exploration involves generating tentative opinions and justifications. Here it is even less important that these opinions be true than they help reveal interesting, neglected, areas especially well-suited to my particular skills and styles.

Most topics that are appropriate for research have little in the way of personal decision impact. So intellectuals focus more on research reasons for such topics. Most intellectuals also socialize a lot, so they also generate opinions for social reasons. Alas most intellectuals generate these different types of opinions in very different ways. You can almost hear their mind gears shift when they switch from being careful on research topics to being sloppy on social topics. Most academics have a pretty narrow speciality area, which they know isn’t going to change much, so they do relatively little exploration that isn’t close to their specialty area.

Research opinions are my best contribution to the world, and so are where I should focus my altruistic efforts. (They also give my best chance for fame and glory.) So I try to put less weight on socializing reasons for my opinions, and more weight on the exploration reasons. As long as I see little prospect of my research going anywhere near the abortion or gun control topics, I won’t explore there much. Topics diagnostic of left vs. right ideological positions seem especially unlikely to be places where I could add something useful to what everyone else is saying. But I do explore a wide range of topics that seem plausibly related to areas in which I have specialized, or might specialize. I have specialized in far more different areas than have most academics. And I try to keep myself honest by looking for plausible decisions I might make related to all these topics, though that tends to be hard. If we had more prediction markets this could get much easier, but alas we do not.

Of course if you care less about research, and more about socializing, your priorities could easily differ from mine.

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Excess Turbulence?

To help me imagine how different future cultures might be, I’ve been trying to learn about typical lives of our distant ancestors. One excellent source is Montaillou: The Promised Land of Error by Emmanuel Le Roy Ladurie in 1978. Around 1300 Jacquest Fournier, who eventually became pope but was then a bishop, led an Inquisition against heretics in the small town of Montaillou in southern France, population 200. He transcribed several years worth of interviews of them, revealing great detail about ordinary life there. One tidbit:

Instability was the hallmark of a shepard’s life, as of the lives of all rural workers in Occitania: ‘Every year’, says Oliveier de Serres in his book on agriculture, ‘change your farm hands, make a clean sweep. Those that come after will put all the more heart into their work.’ The people we are concerned with did not feel this instability as some kind of oppression or alienation. On the contrary, the migrant shepard changed his master more often than his shirt! (p.114)

I’m told that even in the modern world one tends to hire new ranch hands every year.

In the farming world, people like shepards, loggers, etc. who lived furthest from concentrations of people tended to have the lowest status and be the poorest. Such jobs were almost entirely done by men, and so such men rarely married until they switched careers. All of which makes some sense. But I’m puzzled that such people typically changed jobs every year, moving many miles away to work with very different people. It is hard to understand such behaviors as productivity maximizing ways forced on people living at the edge of subsistence. This seems instead to be one of the few luxuries such men purchased, so that they could feel less bored and enjoy variety.

A related phenomena is the puzzling fact that people tend to get weary of exerting effort, and so need to take breaks and rest periodically. Not only do people need to rest and sleep at the end of a work day, but on the job mental fatigue reduces mental performance by about 0.1% per minute. Since by resting we can recover at a rate of 1% per minute, we need roughly one tenth of our workday to be break time, with the duration between breaks being not much more than an hour or two (Trougakos and Hideg 2009; Alvanchi et al. 2012). This doesn’t seem to be due to any obvious physical wear or depletion; it seems to be all in our mind.

Both of these examples, a preference for variety in work locations and associates, and a preference for periodic work breaks during the day, seem plausible functional behaviors for our forager ancestors, and also for their more distant animal ancestors. But they make less sense today. Maybe our minds have embedded the assumption that these are functional behaviors at such a deep level that we are still better off following them today. Or maybe not.

Added 25Aug: In many animal species, a single male controls a harem of females, and the other males wander between the harems, looking for a chance to tempt females for illicit trysts, or to challenge a weak harem ruler. Maybe young low status human males are expressing very ancient animal behavioral patterns.

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Life’s Laminar Endgame

I turn 56 in a week, and I’ve been thinking about how life changes with age. I’ve come up with a view expressed in terms of two key distinctions:

Foregame vs. Endgame Actions in games often have both direct local immediate consequences, and also more indirect global delayed consequences, such as those that result from how other players react to your actions, then more others react to those actions, and so on. The longer a game that stretches ahead, and the more other players who interact, the more that these indirect consequences can matter. In contrast, at the end of a game there are fewer moves others make after you, and fewer other players that your moves might influence. So endgame play focuses more on direct local immediate consequences. Cooperation often breaks down in endgames, as it often depends on threats of future and wider reprisals against uncooperative behaviors.

Turbulent vs. Laminar When fluids like water flow slowly, their flow patterns tend to be simple, stable, predictable, and efficient. As one increases the pressure pushing a fluid while holding constant its environment, the flow velocity also increases, and at some point the fluid switches to flowing in complex, unstable, and unpredictable ways. Turbulent flows are less efficient; if you must pay to push fluids then you want to keep your flow laminar. But turbulent flows also mix fluids much better. Each part of a turbulent flow could end up in far more possible future locations, and next to far more other parts, than can similar parts of a laminar flow.

My view is: Young life is a turbulent foregame, while old life is a laminar endgame. That is, when young we are in the foregame of life, where our life paths are more turbulent, and when older we transition into the endgame of life, where our life paths are more laminar.

In youth, the main consequences of our actions tend to be indirect, global, and delayed. Especially important are social consequences such as what others think of us, and who allies with us. We can end up with very different reputations, mates, communities, occupations, industries, and so on. The life paths of young people also tend to be complex, unstable, unpredictable, and inefficient. For any one young person, it is hard to guess their future mates, jobs, communities, and status, and they may inefficiently change directions and paths many times.

In old age, in contrast, we tend to make fewer and smaller changes to our mates, jobs, communities, and status. We don’t adapt as much to changing opportunities as when young, but this is mostly reasonable given our many investments. We are mostly stuck with existing associates and allies, and wider communities involve themselves with us less. So while we need to worry about how our immediate associates will react soon to things we do, we don’t need to concern ourselves as much with wider more delayed circles. And even our immediate associates can do less to help or hurt us. So we focus more on direct, local, immediate consequences of our actions.

When young, we collect and explore many options, including in associates. We meet many people, and while we don’t want to commit to strong relationships with most of them, we like the option of exploring those possibilities more later, especially if these people should become powerful and high status. The mean value of a future association may be much larger than its median value. That is, we can sometimes mostly care about the chance that they will later become especially powerful or high status.

The young should be especially wary of creating enemies with powerful allies. So when young we tend more to endorse and adopt the standard social norms of our world, including those that say everyone that meets certain criteria should be treated with minimal respect, as if they might become high status someday. As a result, younger people acquire thicker longer distance networks of associations, which can create powerful incentives to seem and act cooperative on larger social scales. The future weighs heavily, and a wide social circle matters more. Also, since when young we understand the social world less, and a wider social world is more complex, we are then more worried about unexpected consequences.

When older, in contrast, we are less worried about wider social punishment of our behaviors. Fewer people matter to us, their and our life paths are more predictable, and we understand our smaller social world much better. So we can more directly calculate the consequences of what we do to people. Thus we are more willing to betray distant allies of allies, as we less fear their future reprisal. So when older we are more in a laminar endgame, where our actions are less guided by generic social norms on how to uniformly treat a wide circle, and more guided by calculating the personal consequences of doing particular things to particular people. For example, we need less to pretend that everyone might become high status, as it becomes safer to treat associates differently by their now stable status.

In many job promotion ladders, and also many other kinds of status ladders, previous status sets a rough lower bound on current status. Thus people tend to rise in status over time until a point in time when they stop rising and then mostly stay near the same status. In such cases, those who are still rising have a more turbulent life path, while those who have stopped have a more laminar path. This creates a correlation between status and turbulence. Thus high status people tend to have more turbulent lives, more like the lives of the young, helping to make the turbulent lives of the young seem higher status. And high status people can less see the age pattern I’m describing.

If you are young, you might wonder how much people do things because they are good people who really believe in the morality of the standard norms, as opposed to doing things out of fear of social reprisal. You might wonder in particular what your associates would do to you if they less feared such reprisal. Good news: when older you will have much clearer data on this. And typical older people around you also have data now, if you will ask them. Haven’t asked? Perhaps you don’t like the answer you think they will tell. Or maybe you don’t trust them to tell you the truth. (And if they’d lie, which theory does that support?)

In the above, I have told a functional story about how behavior should reasonably change with age. However, I should admit that human behavior has not adapted very much to big changes that appeared only in the last few centuries. One of those big changes is that young lives are far more turbulent than those of our forager or farmer ancestors. So turbulent in fact as to call into question the plausibility of social reprisal. For example, high school students often invest greatly in their social reputation, an investment that is mostly lost when they go off to separate colleges and jobs. A more adaptive response to the modern world would be to more ignore wider social reprisal when very young and turbulent, then pay it more attention at a middle age of moderate turbulence, and then less attention again when old.

Let me also note that for some kinds of behavior young people can be at an endgame. Warring drug dealers who don’t expect to live more than a decade longer may feel they are in a local endgame. Also, evolution might have primed young men trying to impregnate young women while they are still promiscuous and fertile to treat that part of their lives as an endgame, since the consequences can be so huge there compared to later opportunities.

This whole perspective suggests another explanation for the puzzle of why we express more interest in people who have the potential to achieve X, relative to people who have already achieved X. Perhaps we presume that someone with the potential to X is younger with a wider social network that we might join by affiliating with them. In contrast, we presume that a person who has already achieved X is older, more tied to their key social network, and less open to new alliances with us.

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Yay Soda Firms

It is usually bad for people to die, and so good for them to keep living. Overall in our society, people who weigh more for their age and gender tend to die more, and so many are concerned about an “obesity epidemic”, and seek ways to reduce people’s weight, such as by getting them to consume fewer calories. Such as from drinking sugary soda.

TIME magazine says that evil soda firms, like evil tobacco firms before them, are lying about science to distract us from their evil:

You may not have noticed it yet, but sodamakers are working hard to get you off your couch. On Aug. 9, a New York Times article revealed that Coca-Cola was quietly funding a group of scientists called Global Energy Balance Network that emphasizes the role of exercise, as opposed to diet, in fighting obesity. … This has some nutrition and obesity experts charging soda companies, whose sales of carbonated soft drinks have hit a 20-year low, with cherry-picking science to make its products more appealing. … Indeed, there isn’t strong evidence to show that exercise alone … can help people shed pounds and keep them off. … It’s not the first time science has been used to sway public perceptions about the health effects of certain behaviors; the tobacco industry famously promoted messaging passed on studies that claimed to prove that “light” or “low-tar” cigarettes were less harmful that regular ones. (more)

Yes, it is true that the literature usually suggests that for most people exercise won’t do much to change their weight. However, another consistent result in the literature (e.g., here, here) is that when we predict health using both weight and exercise, it is mostly exercise that matters. It seems that the main reason that heavy people are less healthy is that they exercise less. Obesity is mainly unhealthy as a sign of a lack of exercise.

So if we cared mainly about people’s health, we should cheer this effort by soda forms to push people to exercise. Even if that also causes people to cut down less on soda. A population that exercises more doesn’t weight much less, but it lives much longer. In fact, exercise seems to be one of the biggest ways we know of by which an individual can influence their health. (Much bigger than medicine, for example.)

I suspect, however, that what bothers most people most about fat people isn’t that they’ll die younger, its instead that they look ugly and low status, and so make them also look low status by association. So we don’t want people near us to look fat. All else equal we might also want them to live longer, but that altruistic motive can’t compete much with our status motive.

So boo soda firms if you want your associates to not seem low status. But yay soda firms if you want people to live and not die (sooner).

Added 11a: The New York Times reports this as the main message:

… Global Energy Balance Network, which promotes the argument that weight-conscious Americans are overly fixated on how much they eat and drink while not paying enough attention to exercise. Health experts say this message is misleading …

Actually that message seems exactly right to me, and not at all misleading.

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Specific vs. General Foragers & Farmers

Scott Alexander in 2013:

Rightism is what happens when you’re optimizing for surviving an unsafe environment, leftism is what happens when you’re optimized for thriving in a safe environment. … “Take actions that would be beneficial to survival in case of a zombie apocalypse” seems to get us rightist positions on a lot of issues. We can generalize from zombie apocalypses to any desperate conditions in which you’re not sure that you’re going to make it and need to succeed at any cost.

What about the opposite? Let’s imagine a future utopia of infinite technology. Robotic factories produce far more wealth than anyone could possibly need. … Even death itself has disappeared. What policies are useful for this happy state? …

If the brain finds itself in a stable environment where everything is abundant, it sort of lowers the mental threat level and concludes that everything will always be okay and its job is to enjoy itself and win signaling games. If it finds itself in an environment of scarcity, it will raise the mental threat level and set its job to “survive at any cost”. … Leftism wins over time because technology advances over time which means societies become more secure and abundant over time. …

Both Greece and Rome were relatively leftist, with freedom of religion, democratic-republican governments, weak gender norms, minimal family values, and a high emphasis on education and abstract ideas. After the Fall of Rome, when Europe was set back technologically into a Dark Age, rightism returned with a vengeance. …

“So you mean rightism is optimized for tiny unstable bands facing a hostile wilderness, and leftism is optimized for secure, technologically advanced societies like the ones we are actually in?” And this conclusion, too, I will mostly endorse. (more)

Much of this is pretty compatible with the forager-farmer perspective I outlined in 2010. To review, as foragers our attitudes and inclinations were well adapted to our environment, but the farming environment was so different that to become effective farmers we had to drastically change such things in a short time. So we cranked up the pressure on social conformity, religion, etc. in order to enforce strong new social norms favoring new farming behaviors. But because these were built on fear, and went somewhat against our deeper natures, rich safe elites have often drifted back toward forager styles, and the whole world has drifted that way together since we’ve all gotten rich and safe with industry. This view makes sense of many long term trends over the last few decades, such as trends toward more leisure, travel, product variety, egalitarianism, democracy, peace, and slavery aversion.

However, in addition to the forager-farmer or survive-thrive distinction, there is another related distinction that I think I, and Scott above, haven’t been thinking clearly enough about. And that is the distinction between supporting specific ways of foragers and farmers, and generalizing their attitudes toward simpler more general principles. Let me explain. Continue reading "Specific vs. General Foragers & Farmers" »

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Why News?

Google Alerts has failed me. For years I’d been trusting it to tell me about new news that cites me, and for the last few years it has just not been doing that. So when I happened to go searching for news that mentions me, I found 135 new articles, listed on my press page. I’d probably find more, if I spent a few more hours searching.

Consider for the moment what would have happened if I had put up a blog post about each of those press articles, as they appeared. Even if I didn’t say much beyond a link and a short quote, some of you would have followed that link. And the sum total of those follows across all 135 articles would be far more than the number of you who today are going to go browsing my press page now that you know it has 135 new entries.

Similarly, I now have 2829 scholarly citations of my work, most of which appeared while I was doing this blog, and this blog has had 3640 posts, many of which were written by others when this was a group blog. So I might plausibly have doubled the number of my posts on this blog by putting up a post on each paper that cited one of my papers. Or more reasonably, I might have made one post a month listing such articles.

For both news and academic articles that cite me, I expect readers to pay vastly more attention to them if I announce them soon after they appear than if I give a single link to a set of them a few years later. Yet I don’t think, and I don’t think readers think, that the fundamental interest or importance of these articles declines remotely as fast as reader interest. This is also suggested by the fact that readers follow so many news sources, like blogs, instead of looking at only the ‘best of’ sections of far more sources.

Bottom line, readers show a strong interest in reading and discussing articles soon after they appear, an interest not explained by an increased fundamental importance of recent articles. Instead a plausible hypothesis is that readers care greatly about reading and talking about the same articles that others will read and talk about, at near the time when those others will do that reading and talking. In substantial part, we like news in order to support talking about the news, and not so much because news communicates important information or insights.

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