Macro Roundup

"...where is everybody?" Tim Urban, “The Fermi Paradox,” Wait But Why, May 21, 2014, https://waitbutwhy.com/2014/05/fermi-paradox.html The Fermi Paradox

There’s also a debate over what percentage of those sun-like stars might be orbited by an Earth-like planet (one with similar temperature conditions that could have liquid water and potentially support life similar to that on Earth). Some say it’s as high as 50%, but let’s go with the more conservative 22% that came out ofa recent PNAS study. That suggests that there’s a potentially-habitable Earth-like planet orbiting at least 1% of the total stars in the universe—a total of100 billion billion Earth-like planets.

So there are100 Earth-like planetsfor every grain of sand in the world. Think about that next time you’re on the beach.

Moving forward, we have no choice but to get completely speculative. Let’s imagine that after billions of years in existence, 1% of Earth-like planets develop life (if that’s true, every grain of sand would represent one planet with life on it). And imagine that on 1% ofthoseplanets, the life advances to an intelligent level like it did here on Earth. That would mean there were 10 quadrillion, or10 million billion intelligent civilizations in the observable universe.

Moving back to just our galaxy, and doing the same math on the lowest estimate for stars in the Milky Way (100 billion), we’d estimate that there are1 billion Earth-like planets and 100,000 intelligent civilizations in our galaxy.The Drake Equationprovides a formal method for this narrowing-down process we’re doing.

SETI (Search for Extraterrestrial Intelligence) is an organization dedicated to listening for signals from other intelligent life. If we’re right that there are 100,000 or more intelligent civilizations in our galaxy, and even a fraction of them are sending out radio waves or laser beams or other modes of attempting to contact others, shouldn’t SETI’ssatellite arraypick up all kinds of signals?

But it hasn’t. Not one. Ever.

Where is everybody?

It gets stranger. Our sun is relatively young in the lifespan of the universe. There are far older stars with far older Earth-like planets, which should in theory mean civilizations far more advanced than our own. As an example, let’s compare our 4.54 billion-year-old Earth to a hypothetical 8 billion-year-old Planet X.

If Planet X has a similar story to Earth, let’s look at where their civilization would be today (using the orange timespan as a reference to show how huge the green timespan is):

The technology and knowledge of a civilization only 1,000 years ahead of us could be as shocking to us as our world would be to a medieval person. A civilization 1 million years ahead of us might be as incomprehensible to us as human culture is to chimpanzees. And Planet X is 3.4billionyears ahead of us…

There’s something calledThe Kardashev Scale, which helps us group intelligent civilizations into three broad categories by the amount of energy they use:

AType I Civilizationhas the ability to use all of the energy on theirplanet. We’re not quite a Type I Civilization, but we’re close (Carl Sagan created a formula for this scale which puts us at a Type 0.7 Civilization).

AType II Civilizationcan harness all of the energy of theirhost star. Our feeble Type I brains can hardly imagine how someone would do this, but we’ve tried our best, imagining things like aDyson Sphere.

AType III Civilizationblows the other two away, accessing power comparable to that ofthe entire Milky Way galaxy.

If this level of advancement sounds hard to believe, remember Planet X above and their 3.4billionyears of further development. If a civilization on Planet X were similar to ours and were able to survive all the way to Type III level, the natural thought is that they’d probably have mastered inter-stellar travel by now, possibly even colonizing the entire galaxy.

One hypothesis as to how galactic colonization could happen is by creatingmachinerythat can travel to other planets, spend 500 years or so self-replicating using the raw materials on their new planet, and then send two replicas off to do the same thing. Even without traveling anywhere near the speed of light, this process would colonize the whole galaxy in 3.75 million years, a relative blink of an eye when talking in the scale of billions of years:

Source:Scientific American: “Where Are They”

Continuing to speculate, if 1% of intelligent life survives long enough to become a potentially galaxy-colonizing Type III Civilization, our calculations above suggest that there should be at least 1,000 Type III Civilizations in our galaxy alone—and given the power of such a civilization, their presence would likely be pretty noticeable. And yet, we see nothing, hear nothing, and we’re visited by no one.

So where is everybody?

_____________________

Welcome to the Fermi Paradox.

We have no answer to the Fermi Paradox—the best we can do is “possible explanations.” And if you ask ten different scientists what their hunch is about the correct one, you’ll get ten different answers. You know when you hear about humans of the past debating whether the Earth was round or if the sun revolved around the Earth or thinking that lightning happened because of Zeus, and they seem so primitive and in the dark? That’s about where we are with this topic.

In taking a look at some of the most-discussed possible explanations for the Fermi Paradox, let’s divide them into two broad categories—those explanations which assume that there’s no sign of Type II and Type III Civilizations because therearenone of them out there, and those which assume they’re out there and we’re not seeing or hearing anything for other reasons:

Explanation Group 1: There are no signs of higher (Type II and III) civilizations because thereareno higher civilizations in existence.

Those who subscribe to Group 1 explanations point to something called the non-exclusivity problem, which rebuffs any theory that says, “There are higher civilizations, but none of them have made any kind of contact with us because they all _____.” Group 1 people look at the math, which says there should besomany thousands (or millions) of higher civilizations, that at leastoneof them would be an exception to the rule. Even if a theory held for 99.99% of higher civilizations, the other.01% would behave differently and we’d become aware of their existence.

Therefore, say Group 1 explanations, it must be that there are no super-advanced civilizations. And since the math suggests that there arethousandsof them just in our own galaxy, something else must be going on.

This something else is calledThe Great Filter.

The Great Filter theory says that at some point from pre-life to Type III intelligence, there’s a wall that all or nearly all attempts at life hit. There’s some stage in that long evolutionary process that is extremely unlikely or impossible for life to get beyond. That stage is The Great Filter.

If this theory is true, the big question is, Where in the timeline does the Great Filter occur?

It turns out that when it comes to the fate of humankind, this question is very important. Depending on where The Great Filter occurs, we’re left with three possible realities:We’re rare, we’re first, or we’re fucked.

1. We’re Rare (The Great Filter isBehindUs)

One hope we have is that The Great Filter is behind us—we managed tosurpassit, which would mean it’sextremely rarefor life to make it to our level of intelligence. The diagram below shows only two species making it past, and we’re one of them.

This scenario would explain why there are no Type III Civilizations…but it would also mean thatwecould be one of the few exceptions now that we’ve made it this far. It would mean we have hope. On the surface, this sounds a bit like people 500 years ago suggesting that the Earth is the center of the universe—it implies that we’respecial. However, something scientists call “observation selection effect” suggests that anyone who is pondering their own rarity is inherently part of an intelligent life “success story”—and whether they’re actually rare or quite common, the thoughts they ponder and conclusions they draw will be identical. This forces us to admit that being special is at least a possibility.

And if we are special, when exactly did we become special—i.e. which step did we surpass that almost everyone else gets stuck on?

One possibility: The Great Filter could be at the very beginning—it might be incredibly unusual for life to begin at all.This is a candidate because it took about a billion years of Earth’s existence to finally happen, and because we have tried extensively to replicate that event in labs and have never been able to do it. If this is indeed The Great Filter, it would mean that not only is there no intelligent life out there, there may beno other life at all.

Another possibility: The Great Filter could be the jump from the simple prokaryote cell to the complex eukaryote cell.After prokaryotes came into being, they remained that way for almosttwo billionyears before making the evolutionary jump to being complex and having a nucleus. If this is The Great Filter, it would mean the universe is teeming with simple prokaryote cells and almost nothing beyond that.

There are a number of other possibilities—some even think the most recent leap we’ve made to our current intelligence is a Great Filter candidate. While the leap from semi-intelligent life (chimps) to intelligent life (humans) doesn’t at first seem like a miraculous step, Steven Pinkerrejects the ideaof an inevitable “climb upward” of evolution: “Since evolution does not strive for a goal but just happens, it uses the adaptation most useful for a given ecological niche, and the fact that, on Earth, this led to technological intelligence only once so far may suggest that this outcome of natural selection is rare and hence by no means a certain development of the evolution of a tree of life.”

Most leaps donotqualify as Great Filter candidates. Any possible Great Filter must be one-in-a-billion type thing where one or more total freak occurrences need to happen to provide a crazy exception—for that reason, something like the jump from single-cell to multi-cellular life is ruled out, because it has occurred as many as46 times, in isolated incidents, just on this planet alone. For the same reason, if we were to find a fossilized eukaryote cell on Mars, it would rule the above “simple-to-complex cell” leap out as a possible Great Filter (as well as anything before that point on the evolutionary chain)—because if it happened onbothEarth and Mars, it’s almost definitely not a one-in-a-billion freak occurrence.

If we are indeed rare, it could be because of a fluky biological event, but it also could be attributed to what is called theRare Earth Hypothesis, which suggests that though there may be many Earth-likeplanets, theparticularconditions on Earth—whether related to the specifics of this solar system, its relationship with the moon (a moon that large is unusual for such a small planet and contributes to our particular weather and ocean conditions), or something about the planet itself—are exceptionally friendly to life.

2. We’re the First

For Group 1 Thinkers, if the Great Filter isnotbehind us, theonehope we have is that conditions in the universe are just recently, for the first time since the Big Bang, reaching a place that would allow intelligent life to develop. In that case, we and many other species may beon our wayto super-intelligence, and it simply hasn’t happened yet. We happen to be here at the right time to become one of the first super-intelligent civilizations.

One example of a phenomenon that could make this realistic is the prevalence of gamma-ray bursts, insanely huge explosions that we’ve observed in distant galaxies. In the same way that it took the early Earth a few hundred million years before the asteroids and volcanoes died down and life became possible, it could be that the first chunk of the universe’s existence was full of cataclysmic events like gamma-ray bursts that would incinerate everything nearby from time to time and prevent any life from developing past a certain stage. Now, perhaps, we’re in the midst of anastrobiological phase transitionand this is the first time any life has been able to evolve for this long, uninterrupted.

3. We’re Fucked (The Great Filter isAheadof Us)

If we’re neither rare nor early, Group 1 thinkers conclude that The Great Filtermustbe in our future. This would suggest that life regularly evolves to where we are, but thatsomethingprevents life from going much further and reaching high intelligence in almost all cases—and we’re unlikely to be an exception.

One possible future Great Filter is a regularly-occurring cataclysmic natural event, like the above-mentioned gamma-ray bursts, except they’re unfortunately not done yet and it’s just a matter of time before all life on Earth is suddenly wiped out by one. Another candidate is the possible inevitability that nearly all intelligent civilizations end up destroying themselves once a certain level of technology is reached.

This is why Oxford University philosopher Nick Bostromsays that“no news is good news.” The discovery of even simple life on Mars would be devastating, because it would cut out a number of potential Great Filtersbehindus. And if we were to find fossilizedcomplexlife on Mars, Bostrom says “it would be by far the worst news ever printed on a newspaper cover,” because it would mean The Great Filter is almost definitelyaheadof us—ultimately dooming the species. Bostrom believes that when it comes to The Fermi Paradox, “the silence of the night sky is golden.”

Explanation Group 2: Type II and III intelligent civilizationsareout there—and there are logical reasons why we might not have heard from them.

Group 2 explanations get rid of any notion that we’re rare or special or the first at anything—on the contrary, they believe in theMediocrity Principle, whose starting point is that there is nothing unusual or rare about our galaxy, solar system, planet, or level of intelligence, until evidence proves otherwise. They’re also much less quick to assume that thelackof evidence of higher intelligence beings is evidence of their nonexistence—emphasizing the fact that our search for signals stretches only about 100 light years away from us (0.1% across the galaxy) and suggesting a number of possible explanations. Here are 10:

Possibility 1) Super-intelligent life could very well have already visited Earth, but before we were here.In the scheme of things, sentient humans have only been around for about 50,000, a little blip of time—if contact happened before then, it might have made some ducks flip out and run into the water and that’s it. Further, recorded history only goes back 5,500 years—a group of ancient hunter-gatherer tribes may have experienced somecrazyalien shit, but they had no good way to tell anyone in the future about it.

Possibility 2) The galaxy has been colonized, but we just live in some desolate rural area of the galaxy.The Americas may have been colonized by Europeans long before anyone in a small Inuit tribe in far northern Canada realized it had happened. There could be an urbanization component to the interstellar dwellings of higher species, in which all the neighboring solar systems in a certain area are colonized and in communication, and it would be impractical and purposeless for anyone to deal with coming all the way out to the random part of the spiral where we live.

Possibility 3) The entire concept of physical colonization is a hilariously backward concept to a more advanced species.Remember the picture of the Type II Civilization above with the sphere around their star? With all that energy, they might have created a perfect environment for themselves that satisfies their every need. They might have crazy-advanced ways of reducing their need for resources and zero interest in leaving their happy utopia to explore the cold, empty, undeveloped universe.

An even more advanced civilization might view theentire physical worldas a horribly primitive place, having long ago conquered their own biology and uploaded their brains to a virtual reality, eternal-life paradise. Living in the physical world of biology, mortality, wants, and needs might seem to them the way we view primitive ocean species living in the frigid, dark sea. FYI, thinking about another life form having bested mortality makes me incredibly jealous and upset.

Possibility 4) There are scary predator civilizations out there, and most intelligent life knows better than to broadcast any outgoing signals and advertise their location.This is an unpleasant concept and would help explain the lack of any signals being received by the SETI satellites. It also means that we might be the super naive newbies who are beingunbelievablystupid and risky by ever broadcasting outward signals. There’s a debate going on currently about whether we should engage in METI (Messaging to Extraterrestrial Intelligence—the reverse of SETI) or not, and most people say we should not. Stephen Hawking warns, “If aliens visit us, the outcome would be much as when Columbus landed in America, which didn’t turn out well for the Native Americans.” Even Carl Sagan (a general believer that any civilization advanced enough for interstellar travel would be altruistic, not hostile)calledthe practice of METI “deeply unwise and immature,” and recommended that “the newest children in a strange and uncertain cosmos should listen quietly for a long time, patiently learning about the universe and comparing notes, before shouting into an unknown jungle that we do not understand.” Scary.Thinking about this logically, we should disregard all the warnings get the outgoing signals rolling. If we catch the attention of super-advanced beings, yes, they might decide to wipe out our whole existence, but that’s not that different than our current fate. And maybe, instead, they’d invite us to upload our brains into their eternal virtual utopia, which would solve the death problem and also probably allow me to achieve my childhood dream of bouncing around on the clouds. Sounds like a good gamble to me.

Possibility 5) There’s only one instance of higher-intelligent life—a “superpredator” civilization (like humans are here on Earth)—who isfarmore advanced than everyone else and keeps it that way by exterminating any intelligent civilization once they get past a certain level.This would suck. The way it might work is that it’s an inefficient use of resources to exterminate all emerging intelligences, maybe because most die out on their own. But past a certain point, the super beings make their move—because to them, an emerging intelligent species becomes like a virus as it starts to grow and spread. This theory suggests that whoever was thefirstin the galaxy to reach intelligence won, and now no one else has a chance. This would explain the lack of activity out there because it would keep the number of super-intelligent civilizations to just one.

Possibility 6) There’s plenty of activity and noise out there, but our technology is too primitive and we’re listening for the wrong things.Like walking into a modern-day office building, turning on a walkie-talkie, and when you hear no activity (which of course you wouldn’t hear because everyone’s texting, not using walkie-talkies), determining that the building must be empty. Or maybe, as Carl Sagan has pointed out, it could be that our minds work exponentially faster or slower than another form of intelligence out there—e.g. it takes them 12 years to say “Hello,” and when we hear that communication, it just sounds like white noise to us.

Possibility7) Wearereceiving contact from other intelligent life, but the government is hiding it.This is an idiotic theory, but I had to mention it because it’s talked about so much.

Possibility8) Higher civilizations are aware of us and observing us (AKA the “Zoo Hypothesis”).As far as we know, super-intelligent civilizations exist in a tightly-regulated galaxy, and our Earth is treated like part of a vast and protected national park, with a strict “Look but don’t touch” rule for planets like ours. We wouldn’t notice them, because if a far smarter species wanted to observe us, it would know how to easily do so without us noticing. Maybe there’s a rule similar to theStar Trek’s“Prime Directive” which prohibits super-intelligent beings from making any open contact with lesser species like us or revealing themselves in any way, until the lesser species has reached a certain level of intelligence.

Possibility 9) Higher civilizations are here, all around us. But we’re too primitive to perceive them.Michio Kakusums it uplike this:

Lets say we have an ant hill in the middle of the forest. And right next to the ant hill, they’re building a ten-lane super-highway. And the question is “Would the ants be able to understand what a ten-lane super-highway is? Would the ants be able to understand the technology and the intentions of the beings building the highway next to them?

So it’s not that we can’t pick up the signals from Planet X using our technology, it’s that we can’t even comprehend what the beings from Planet Xareor what they’re trying to do. It’ssobeyond us that even if they really wanted to enlighten us, it would be like trying to teach ants about the internet.

Along those lines, this may also be an answer to “Well if there are so many fancy Type III Civilizations, why haven’t they contacted us yet?” To answer that, let’s ask ourselves—when Pizarro made his way into Peru, did he stop for a while at an anthill to try to communicate? Was he magnanimous, trying to help the ants in the anthill? Did he become hostile and slow his original mission down in order to smash the anthill apart? Or was the anthill of complete and utter and eternal irrelevance to Pizarro? That might be our situation here.

Possibility 10) We’re completely wrong about our reality.There are a lot of ways we could just betotallyoff with everything we think. The universe might appear one way and be something else entirely, like ahologram. Or maybewe’rethe aliens and we were planted here as an experiment or as a form of fertilizer. There’s even a chance that we’re all part of a computer simulation by some researcher from another world, and other forms of life simply weren’t programmed into the simulation.

________________

As we continue along with our possibly-futile search for extraterrestrial intelligence, I’m not really sure what I’m rooting for. Frankly, learning either that we’re officially alone in the universe or that we’re officially joined by others would be creepy, which is a theme with all of the surreal storylines listed above—whateverthe truth actually is, it’s mindblowing.

Beyond its shocking science fiction component, The Fermi Paradox also leaves me with a deep humbling. Not just the normal “Oh yeah, I’m microscopic and my existence lasts for three seconds” humbling that the universe always triggers. The Fermi Paradox brings out a sharper, more personal humbling, one that can only happen after spending hours of research hearing your species’ most renowned scientists presentinsanetheories, change their minds again and again, and wildly contradict each other—reminding us that future generations will look at us the same way we see the ancient people who weresurethat the stars were the underside of the dome of heaven, and they’ll think “Wow they really hadnoidea what was going on.”

Compounding all of this is the blow to our species’ self-esteem that comes with all of this talk about Type II and III Civilizations. Here on Earth, we’re the king of our little castle, proud ruler of the huge group of imbeciles who share the planet with us. And in this bubble with no competition and no one to judge us, it’s rare that we’re ever confronted with the concept of being a dramatically inferior species to anyone. But after spending a lot of time with Type II and III Civilizations over the past week, our power and pride are seeming a bit David Brent-esque.

That said, given that my normal outlook is that humanity is a lonely orphan on a tiny rock in the middle of a desolate universe, the humbling fact that we’re probably not as smart as we think we are, and the possibility that a lot of what we’re sure about might be wrong, sounds wonderful. It opens the door just a crack that maybe, just maybe, there might be more to the story than we realize.

The science world isn’t in total agreement about what percentage of those stars are “sun-like” (similar in size, temperature, and luminosity)—opinions typically range from 5% to 20%. Going with the most conservative side of that (5%), and the lower end for the number of total stars (1022), gives us 500 quintillion, or500 billion billion sun-like stars.

As many stars as there are in our galaxy (100 - 400 billion), there are roughly an equal number of galaxies in the observable universe—so for every star in the colossal Milky Way, there’s a wholegalaxyout there. All together, that comes out to the typically quoted range ofbetween 1022and 1024total stars, which means that forevery grain of sand on Earth, there are10,000 starsout there.

When confronted with the topic of stars and galaxies, a question that tantalizes most humans is, “Is there other intelligent life out there?” Let’s put some numbers to it (if you don’t like numbers, just read the bold)—

A really starry sky seemsvast—but all we’re looking at is our very local neighborhood. On the very best nights, we can see up to about 2,500 stars (roughly one hundred-millionth of the stars in our galaxy), and almost all of them are less than 1,000 light years away from us (or 1% of the diameter of the Milky Way). So what we’re really looking at is this:

________________

Physicist Enrico Fermi felt something too—”Where is everybody?”

Some people stick with the traditional, feeling struck by the epic beauty or blown away by the insane scale of the universe. Personally, I go for the old “existential meltdown followed by acting weird for the next half hour.” But everyone feelssomething.

Everyone feels something when they’re in a really good starry place on a really good starry night and they look up and see this:

"In a recentstudy, Mr Fernald and Charles Jones of Stanford University break down the inexorable 2 per cent growth in US output per person from 1950 to 2007 in a different way. They find almost none of it comes from more capital per worker. About 0.4 percentage points comes from human capital (better education). But by far the largest contribution - 1.6 percentage points of the total - comes from the fact that more people are working on research and development....It is also impossible for the US to keep devoting ever more of its population to working in research and development. But this is not true of the world as a whole. Huge populations in China, India and elsewhere are joining the global economy, improving their education systems and putting more researchers to work at the scientific frontier. Any discoveries they make can be used in the US as easily as anywhere else.In that case, the improvements that come from scientific discovery may be sustainable. Productivity growth need only slow to about 1.6 per cent. Add in some modest increase in population and the economy as a whole could expand at 2 per cent per year or a little more. Mr Fernald’s long-run forecast is 2.1 per cent. This suggests that the Fed open market committee’s latest projection of 2.2 per cent is not far off."

June 29, 2014 5:23 pm

By Robin Harding

To glimpse the miracle of productivity growth there is nowhere better to look than the bountiful fields of the US Corn Belt. A hundred years ago, an army of farmers toiled to produce 30 bushels an acre; now only a few hands are needed to produce 160 bushels from the same land.

The rise of modern civilisation rested on this trend: for each person to produce ever more. For the past 120 years, as if bound by some inexorable law, output per head of population increased by about 2 per cent a year. That is, until now.

The USFederal Reserveis already edging down its forecasts for long-term interest rates. “The most likely reason for that is there has been some slight decline... of projections pertaining to longer-term growth,” said Janet Yellen, chairwoman, at her most recent press conference.There is a fear - voiced by credible economists such as Robert Gordon of Northwestern University - that 2 per cent is no law but a wave that has already run its course. According to Prof Gordon’s analysis, 2 per cent could easily become 1 per cent or even less, for the next 120 years. But it is not the only issue. Growth in gross domestic product, the familiar statistic by which all economies are measured, can come about in several ways: more workers, with better skills; more capital such as factories, roads and machines, or new technology. Leaving aside the latter category, the consensus among economists is that most of these will not contribute as much to economic growth as they have in the past.

The US Bureau of Labor Statistics uses a range of tools to measure computing power. One argument in favour of its data - which suggests the pace of progress in computer chips has slowed massively - is that consumers seem to be replacing their desktops less frequently.

In about 2006, Mr Oliner continues, “Intel itself had a major breakthrough and developed multi-core chips.” Instead of driving up “clock speed”, the most familiar way of measuring the processing speed of a chip using megahertz or gigahertz, it started including multiple copies of the basic processor within the same chip. If computing power were still measured using clock speed, however, the pace of improvement would appear to suddenly decline.

Mr Oliner, currently at the American Enterprise Institute, a Washington think-tank, has a few ideas about what may be happening. One is an increase in Intel’s market power. “Starting in about 2006, which is when the break occurred, Intel really solidified its market position relative to AMD,” its main competitor, he says. Less competition may mean slower price declines for its older products.

Moore’s Law - the trend identified by Intel co-founder Gordon Moore that computer power doubles every two years - has continued apace. But at the same time, whereas the measured price of computing power was falling at a rate of 70 per cent a year between 1998 and 2000, the pace of decline more recently has slowed to 3 or 4 per cent. That translates into a slower pace of measured productivity growth.

Is the recent slowdown in productivity growth nothing but a statistical mirage? A recent study by economistsDavid Byrne, Stephen Oliner and Daniel Sichelnotes a fascinating discrepancy between price and performance data for microprocessors (see chart above). This is important because the rapid progress of processing power is what drives the technology revolution.

Intel, clock speed and the measurement of productivity growth Harding, Robin, "The Productivity Puzzle," Financial Times, June 29, 2014. Available at:http://www.ft.com/intl/cms/s/0/c1149cda-fd39-11e3-8ca9-00144feab7de.html

Climate Corporation shows how innovative the US still is - and how computers can yet boost productivity in unexpected ways. To sustain that magical run of 2 per cent growth in output per person, however, the US may need more Silicon Valleys to emerge in China and India, and add their heft to the eternal pursuit of another bushel of corn from the same acre of land.

In that case, the improvements that come from scientific discovery may be sustainable. Productivity growth need only slow to about 1.6 per cent. Add in some modest increase in population and the economy as a whole could expand at 2 per cent per year or a little more. Mr Fernald’s long-run forecast is 2.1 per cent. This suggests that the Fed open market committee’s latest projection of 2.2 per cent is not far off.

But this is not true of the world as a whole. Huge populations in China, India and elsewhere are joining the global economy, improving their education systems and putting more researchers to work at the scientific frontier. Any discoveries they make can be used in the US as easily as anywhere else.

This analysis allows for a more grounded forecast than speculation about what technologies remain to invent. “The pessimistic part of that equation for the future is human capital,” notes Mr Fernald, as the contribution from better education is petering out. It is also impossible for the US to keep devoting ever more of its population to working in research and development.

In part, that is because there are more people (and thus more bodies to do research). But mainly it is the result of devoting a steadily larger portion of the total population to work on research and development.

About 0.4 percentage points comes from human capital (better education). But by far the largest contribution - 1.6 percentage points of the total - comes from the fact that more people are working on research and development.

In a recentstudy, Mr Fernald and Charles Jones of Stanford University break down the inexorable 2 per cent growth in US output per person from 1950 to 2007 in a different way. They find almost none of it comes from more capital per worker.

Yet economics has quite a lot to say about the process of making discoveries, based on the less than revolutionary insight that breakthroughs depend on the effort put into researching them.

One curious aspect of both professors’ arguments is how uneconomic they are. Their focus is more about what is left to discover than the economy’s ability to make those discoveries. Prof Gordon’s approach would struggle to explain the 1996 acceleration in productivity growth, while Prof Brynjolfsson’s has little to say about the slowdown after 2004.

He is more impressed by the potential of robotics but less convinced the moment has arrived when they are sufficiently powerful to supplant humans. “Think of every employee you’ve had contact with in the last two or three days, and think, is that person going to be replaced by a robot in the next 20 years?”

Prof Gordon is also dismissive of the potential productivity gains from inventions such as driverless cars: being able to answer email instead of turning the steering-wheel, for example. “The real productivity gains would presumably come from driverless trucks,” he says, but then points out that a UPS delivery van would still need a driver to remove the parcels from the vehicle.

The heart of his argument is that the discoveries of the past - running water, the internal combustion engine, the electric lightbulb - were simply more important than those of today. From 1870 to 1972, he points out, American homes went from lightless, isolated places of drudgery to buildings of air-conditioned comfort, with a dishwasher in the kitchen and a car in the garage.

By contrast, Prof Gordon expects a lower pace of productivity growth, perhaps in line with that achieved in the past 10 years. To hit even that target, he points out, means keeping up a steady stream of new creations such as smartphones.

Rather than referring to historical data, he points toGoogle’s self-driving car, to the potential for computer systems that diagnose disease and answer legal queries, and the growing flexibility of robotics. Such automation will free up a host of labour for new tasks, just as other innovations did in the past. “Whether it’s robotics or software for knowledge work, if you take the labour input to zero you get a pretty astronomical productivity number,” he says.

“The reason I’m optimistic is that I don’t rely primarily on extrapolating past economic trends,” says Prof Brynjolfsson. After visiting labs, he says, “I just come away astonished at what’s in the pipeline. Most of it has not yet reached commercialisation.”

Computation is the root of Prof Brynjolfsson’s optimism: his book with Prof McAfee is calledThe Second Machine Ageand argues that the impact of information technology has only just begun to be realised. Exponential expansion in computing power, and the ability to diffuse innovations rapidly, could mean growth like that of the late 1990s.

The dispute is this: in the coming decades, should we expect growth like that which we experienced from 1996 to 2004, at 2.5 per cent, or like the period since 2004, of 1.3 per cent? While Prof Brynjolfsson has Star Trek visions of utopian technological progress, Prof Gordon is more of a cyberpunk, imagining a world in which the computers may become more powerful but living standards for average humans improve only slowly.

The internet boom pushed the rate up to 2.6 per cent - it was this period that led Alan Greenspan, former Fed chairman, to talk about a “productivity feast” - but by 2004, well before the financial crisis, the surge was over. Since 2004, barring a measurement problem, growth in output per hour has been 1.3 per cent.

Growth in GDP per hour worked depicts an interesting pattern over time. According to Prof Gordon, at a rate of 2.4 per cent, it was fast from the 19th century until 1972. It then slowed to 1.4 per cent a year until 1996.

That leaves technology. “I agree with much of what he says about the slowing demographics,” says Prof Brynjolfsson. “Where he and I differ is prospects for future innovation.”

The expansion of primary, then secondary and then college education has helped the economy grow for generations, but average years of education have now reached a plateau. “The US is slipping back in the league tables of college completion and high school completion,” says Prof Gordon, suggesting this will account for another 0.2 percentage points off per capita growth.

The truest measure of economic progress, though, is the growth of GDP per hour worked. For every hour of human toil, how much is created? Here too, some factors that drove growth in the past are weakening, such as skills and education.

“Everybody is pretty much in agreement in expecting slower growth in hours worked relative to what we’ve seen in the last 50 years,” says John Fernald, a senior research adviser at the Federal Reserve Bank of San Francisco.

Prof Gordon estimates that demographics could knock 0.3 percentage points off the long-run trend of 2 per cent growth.

On top of that, demographics will also slow growth in GDP per capita, which does affect living standards. Ageing will mean fewer active workers per head of population; most women have now joined the US labour force so that source of extra workers is running out.

To start with, US population growth is at its lowest since the 1930s, having fallen from about 1.2 per cent a year in the 1990s to 0.7 per cent in recent years. This does not affect growth in living standards - it means fewer consumers as well as fewer workers - but adding less extra labour will slow the headline GDP growth rate that the Fed worries about.

Whether computers can keep making broad contributions to productivity is one of the most important immediate issues.

The boost to yields could be as much as 5 per cent - and that is just the start. “We’ve identified about 40 different decisions a farmer makes where there’s potential to apply data science,” says Anthony Osborne, the company’s head of marketing.

For example, the company says that by combining fertiliser use, soil type, weather data and other information in a single database, it can tell farmers exactly how much nitrogen is in a field and thus how much fertiliser they need to apply.

Climate Corporation, which wasbought last year by Monsanto for $930m, works on “precision agriculture”, bringing the power of data science to bear on farming.

The answer depends on companies such as Climate Corporation, which fights the battle for agricultural productivity growth from its new front line, in the office buildings of Silicon Valley.

The productivity question is of the greatest possible consequence for the US economy, affecting everything from when interest rates should rise to where they should peak, from the sustainability of US debt to what is the wisest level of investment for every business in the country.

Then there are more phlegmatic economists, whose answers are less exciting but also less speculative - and come in a bit below 2 per cent for growth in output per head.

Yet there are also techno-optimists, such as Erik Brynjolfsson and Andrew McAfee of the Massachusetts Institute of Technology, whosefaith in new discoveriesis such that they expect growth to accelerate, not decline.