Wednesday, September 18, 2013

The Optimist

Joel Mokyr is an Israeli-American academic and one of the most influential living historians of technological progress. In an article called Is technological progress a thing of the past? (Original article, Economist's View, Brad DeLong), he takes a techno-optimistic stance*.

He breaks the arguments of the pessimists down into three categories:
One school says, if not quite that “everything that can be invented has been invented,” but at least that the low-hanging fruits have been picked and the rest of the new inventions won’t have nearly as radical a welfare effect.

Another school says that, au contraire, there are lots of things we still can invent, but we won’t. This is because we are getting too risk-averse, too complacent, too regulated, and our institutions are turning anti-innovative and sclerotic. So, much like ancient Rome and Qing China, we are a once-dynamic world in decline.

And finally there are those who think that the new brave technology actually will come, but that it will eliminate our jobs and turn us into a Player Piano kind of dystopia in which all labor is replaced by machines and robots and humans will become marginalized.
For some reason, he leaves out the whole peak oil/resources criticism advanced at places like the Oil Drum or by commentators like Chris Martenson, Richard Heinberg and others.

Two points he makes that are important to his thesis:

1. As scientific instruments get better, our ability to answer questions and explore the world gets better: “The relation between scientific progress and technology is a complex two-way street. For example, 19th-century energy-physics learned more from the steam engine than the other way around.” He uses the example of the telescope, the microscope, the barometer, the vacuum pump, and the pile battery. Then he looks at things like adaptive optics, automatic gene sequencing, and something called the synchrotron. “Science depends on technology no less than technology on science: we were not hard-wired to see microbes, to watch the moons of Jupiter, to store terabytes of information in our brains and do 54 petaflops of calculations: tools and machines we build do this for us.”

2. Our ability to store, access, and locate information is greater than ever before. He points to past innovations like encyclopedias, indices and journals, and looks at the growth in searchable databases and the World Wide Web.
One might have feared that the explosion of scientific knowledge in the 20th century could outrun our ability to find what we are looking for. Yet the reverse has happened. The development of searchable databanks of massive sizes has even outrun our ability to generate scientific knowledge. Copying, storing, transmitting, and searching vast amounts of information today is fast, easy, and practically free. We no longer deal with megabytes or gigabytes. Instead terms like petabytes (a million gigabytes) and zettabytes (a million petabytes) are being bandied about. Scientists can now find the tiniest needles in data haystacks as large as Montana in a fraction of a second.
And if science sometimes still proceeds by ‘trying every bottle on the shelf’ – as in some areas it still does – it can search with blinding speed over many more bottles, perhaps even peta-bottles.
Haven’t we harvested the low-hanging fruit of discovery and technology? Mokyr says the analogy is flawed. In his words, “Perhaps the low-hanging fruits have been picked: running water, chlorination, electricity, etc? But science and technology’s main function in history is to make taller and taller ladders to get to the higher-hanging fruits. They are just as juicy. Moreover, these trees keep sprouting new fruits, if only we give them proper care.”

That's a big if. It's awfully vague too - don't we solve immediate problems first? Finding the Higgs Boson is nice, but it won't spur economic growth will it? He has some cautionary notes on technology however, that almost seem to contradict his claims:
Whenever a technological solution is found for some human need, it creates a new problem. As Edward Tenner put it, technology ‘bites back’. The new technique then needs a further ‘technological fix’, but that one in turn creates another problem, and so on. The notion that invention definitely ‘solves’ a human need, allowing us to move to pick the next piece of fruit on the tree is simply misleading.

•Each solution perturbs some other component in the system and sows the seed of more needs; the ‘demand’ for new technology is thus self-sustaining.

The most obvious example for such a dynamic is in our never-ending struggles with insects and harmful bacteria. In those wars, evolutionary mechanisms decree that after most battles we win, the enemy regroups by becoming resistant to whatever poison we throw at them. Drug-resistant bacteria are increasingly common and require novel approaches to new antibiotics. The search for novel antibiotics will resume with tools that Chain and Florey would never have dreamed of – but even such new antibiotics will eventually lead to adaptation.

In agriculture, the advance in fertiliser use has helped avert the Malthusian disasters that various doom-and-gloom authors predicted. But the vast increase in nitrate use following Fritz Haber’s epochal invention of the nitrogen-fixing process before World War I has now led to serious environmental problems in aquifer pollution and algae blooms. Again, technology will provide us with a fix, possibly through genetic engineering in which more plants can fix their own nitrates rather than needing fertiliser or bacteria that convert nitrates into nitrogen at more efficient rates.

Another example is energy: For better or for worse, modern technology has relied heavily on fossil fuels: first coal, then oil, and now increasingly on natural gas. The bite-back here has been planetary in scope: climate change is no longer a prospect, it is a reality. Can new technology stop it? There is no doubt that it can, even if nobody can predict right now what shape that will take, and if collective action difficulties will actually make it realistic.
But he doesn’t pursue this line any further. He simply tosses off breezy confidence that whatever problem arises, we'll solve it, full stop. What about the fact that we’re substituting inferior resources as others are depleted? We will solve antibiotic resistance how, exactly? And there is “no doubt" that technology can stop climate change? Really? Talk about an argument without proof. As for technological unemployment, his argument is a familiar one:
There will be disruption and pain, but the new technology will also create new demand for workers, to perform tasks that a new technology creates.

• In 1914 who could have imagined occupations such as video game programmer or identity-theft security guard?

• Physical therapists, social media consultants, and TV sports commentators are all occupations created by new technology.

It seems plausible that the future, too, will create occupations we cannot imagine, let alone envisage. Furthermore, the task that 20th-century technology seems to have carried out the easiest is to create activities that fill the ever-growing leisure time that early retirement and shorter work-weeks have created. Technological creativity has responded to the growth of free time: a bewildering choice of programmes on TV, the rise of mass tourism, access at will to virtually every film made and opera written, and a vast pet industry are just some examples.
He acknowledges there will be winners and losers:
Here is Mokyr’s theorem: Technological progress is never Pareto superior. There are always losers. And we rarely compensate them. I am not the first to argue this: Schumpeter spoke of “creative destruction.” So there will be losers. What we gain as consumers, viewers, patients, and citizens, we may lose as workers.
But despite this, he seems to think, following Keynes, that we will have plenty of leisure time, and that filling it will be a new growth industry:
…robotics will be everywhere. These Robots will not be anything like the iron humanoids that follow the Asimov rules of robotics. Most of them will be nothing more than little chips connected by A.I. to sensors. But they will drive our trucks, perform open-heart surgeries, pick our tomatoes, walk our dogs, and cook our meals. But: only if we want them to. That, by definition, is a welfare improvement.

...the post-digital age may be the Age of Leisure. Remember that practically the entire leisure industry, from videogames to spectator sports, to radio, tv, movies was a product of the twentieth century. That’s because the workweek (in Europe) fell from 3,000 hrs a year to 1,500 hrs.

the “factory”, which arose in the Industrial Revolution is slowly being phased out. We will work, wherever, whenever it suits us. Workplace and commuting will slowly disappear. Three-dimensional printers will make whatever assembly line shopfloor workers were making.
Mokyr makes some good points that are worth consideration about the future: technology the results often are unexpected and take forms that are not easily measured by the criteria and measures of the technological ancient regime. Imagine an Englishman at a party celebrating the 50th anniversary of the first steam engine.
That would be in 1762. He would ask: “What has that machine done for us? Made a lot of noise, emitted a lot of smoke and stench, and pumped some water out of  a few coal mines. Big Deal.”

We don’t know what the adoption lags are today, probably less than then, but the really BIG results usually arrive toward the end when the technology is fully mature. Most of the disruptive and life-changing effects of digitalization have not been fully felt.The Digital Age will be to the Analog Age what the iron age was to the stone age. And we can’t even imagine what the Post-digital Age will look like. No more than Archimedes could imagine CERN.
That last point may be the best one. Perhaps I'm wrong in my pessimism, but I think there are a lot of things that he doesn't take into account.

Note that The entire computer revolution has taken place against a backdrop of falling wages and lower living standards for the vast majority of Americans. The peak of real wages came back in 1978, when no one even had a personal computer. Americans are now debt serfs with no decent retirement options, part-time and temporary low-wage work, and soaring health care bills, yet they have the internet at their fingertips and can stream movies at home, and somehow this is supposed to make up for it?

As for the common "jobs we can't imagine" argument, I don't think there is much of a demand for TV sports commentators, internet security guards (!!) or social media consultants. People already complain that they have no idea what they actually do for a living anymore.Our jobs are already increasingly bullshit jobs. Were it not for government spending on defense and predatory industries like education and healthcare, much of flyover country would already be unemployed.

All those people who talk about how well we managed deindustrialization ought to take a drive through the rust belt to see all the "new" jobs that were created once the factories went away. It turned out that the jobs of the future were actually security guard, gang leader, mercenary, DJ, meth cook, cannabis farmer, drug dealer, hairdresser, astrologer, preacher and sex worker. I don't expect robots to fix this.

1.) A large consumer market drove a lot of innovation in the twentieth century. This is disappearing rapidly in the developed world thanks to extreme inequality. Without a mass consumer market to sell to, companies will not invest profits in R&D, as no one will be able to afford the result aside from a small number of super-wealthy. Already Americans are living from paycheck to paycheck and turning to food stamps to feed themselves (according to conservatives, due a spontaneous mass outbreak of laziness).

As in past societies, the people at the top will continue to see the benefits of the new technology. The rest of us, not so much. Just this week the news is out that incomes have declined to 2007 levels, household income to 1989 levels, the poverty rate has increased, and inequality is back to 1927 levels. At the same time, the wealth of the Forbes 400 continues to increase dramatically. We're not going forwards, we're going backwards.

I may have made fun of Matt Yglesias' blast-chiller "fridge of the future." But his point is a good one - if workers don't have the income to buy these things, companies won't produce them and improvements will grind to a halt.

2.) Fighting a desperate rearguard action is not the same thing as innovations that enhance people’s lives. If we’re spending all our research dollars trying to mitigate global warming or find energy substitutes, that not moving forward, it’s innovating desperately to stay in place. While new energy sources and efficiency measures will undoubtedly be discovered, there is no energy source more energy dense and easily accessible than coal and petroleum. And those are finite and subject to the laws of thermodynamics. One of the great findings of science is that there are limits.

3.) He ignores the reality of social and political collapse.  Syria doesn't look too innovative lately, does it? After years of drought, that society has been blown apart by a civil war destroying landmarks that have stood for thousands of years. Greece doesn't look to innovative either.

Or look at the Soviet Union. This was a country that led the world in space exploration in the 1950s - it was the first to put a satellite into orbit and a man into space. After its collapse, life expectancy dramatically shrank and birthrates fell. Wealth concentration is similar to the United States, reporters are regularly harassed, authoritarian legislation is being passed, and it has been called a "Mafia State." Is it much more innovative now than in the past?

I’ve used this example many times before, but roads in many parts of the country are being turned back to gravel and streetlights are being shut off. In Detroit, 40 percent of the streetlights don’t work. Harrisburg, Pennsylvania went broke trying to build an incinerator. The poorest residents of Jefferson County Alabama were cut off from water service. Recently, a brain eating amoeba has been found in Louisiana water supplies because they could not afford chlorine. In Greece, hospitals are short of medicines and people are burning wood for fuel.

Yes, these are isolated examples, but I fully expect them to become more common and widespread as breakdown continues apace. This looks more like the decline of the Roman Empire than the Industrial Revolution. Yet the optimists continue to look at technological development as if it occurs in a social vacuum. It doesn’t.

4.) We will sooner collapse than make the necessary social changes described. Critical to Mokyr’s arguments is the idea that we will make the necessary social changes that the new technology requires. I agree with him that this is necessary. But where is the evidence? Instead what to we actually see? We see consistently refusing or resisting the necessary changes due to social inertia, stasis, corruption, political failure, etc. One of the things I’ve done on the blog over the years is describe the necessary social changes that need to take place for our recent technological innovation to be successful. But I see no evidence of these taking place. In fact, I see the opposite occurring. That’s a major reason for my pessimism. Some examples:
  • Decreased work hours – instead we see more work hours on the part of technocratic elites, with reduced hours for the rest not because of voluntary leisure, but to prevent companies from paying benefits. This is reduced hours not because of productivity gains, but merely to punish workers resulting in  income loss which is self-defeating.
  • Universal basic income – instead we see the safety net under assault by plutocrats who deride the unemployed as “lazy moochers.”
  • Education reform – instead, education budgets are being slashed, with expensive four+-year college more as a social differentiator than anything else. Online education is doing some good things, but without the necessary jobs, it’s merely self-enrichment.
  • Broadly distributed ownership – instead it’s more concentrated than ever before in history. Privatize profits and subsidize losses is the order of the day. Most business sectors are dominated by monopolies/oligopolies.
  • Debt repudiation – instead we see self-reinforcing austerity even as societies fall apart. Austerity actually benefits elites by "disciplining" workers, and since the rich are still getting richer and they control the agenda, austerity isn't going anywhere soon.
  • Flexible workplaces – instead we still mostly trudge to work in an office for 8 hours a day causing ill-health, traffic jams, etc. Yahoo! ordered all its workers back to the office so the could be exploited monitored more efficiently.
I could go on, but you get the point. Does Mr. Mokyr pay no attention to politics? Does he really think we'll see the society of leisure he's describing? Things didn't automatically get better for the workers of the Industrial Revolution. They had to fight, and sometimes die, to secure those benefits. Yet today, thanks to control of the media, we see a sort of French Revolution in reverse (up with the aristocracy!)

5.) Satisfying fundamental human needs is more essential than entertainment. Some things can only happen once, as Gordon says. Robert Gordon remarked, “have we invented anything better than the toilet?” That remark may be facetious, but as we saw last week, plumbing and sanitation measures have been the single greatest factor in the much lauded increase in life expectancy during the twentieth century (with antibiotics a close second). The article featured last week described it:
...the steepest increase in life expectancy occurred from the late 1800s to the mid-1900s. Even some dramatically successful medical treatments such as insulin for diabetics have kept individual people alive...but haven’t necessarily had a population-level impact on average lifespan....The credit largely goes to a wide range of public health advances, broadly defined, some of which were explicitly aimed at preventing disease, others of which did so only incidentally....Mathematically, the interventions that saved infants and children from dying of communicable disease had the greatest impact on lifespan....Clean water may be the biggest lifesaver in history. Some historians attribute one-half of the overall reduction in mortality, two-thirds of the reduction in child mortality, and three-fourths of the reduction in infant mortality to clean water.
Which proves Gordon’s point. How many lives has Facebook saved?** Twitter? Cell phones***? Yet, despite this, India has more cell phones than toilets.

6.) The breakdown and bankruptcy of governments. Despite the “innovation comes from the private sector” claptrap promoted by the courtesans of the wealthy, most significant innovation comes from public money. For example, solar panels, fuel cells and aerogel all came out of NASA labs.

The synchrotron, one of his examples, provides a useful point. Such large machines are incredibly costly, and it’s hard to see how we will make leaps forward in this type of gigantic scientific infrastructure in a time of shrinking budgets and high energy prices. According to Wikipedia:
Synchrotrons which are useful for cutting edge research are large machines, costing tens or hundreds of millions of dollars to construct, and each beamline (there may be 20 to 50 at a large synchrotron) costs another two or three million dollars on average. These installations are mostly built by the science funding agencies of governments of developed countries, or by collaborations between several countries in a region, and operated as infrastructure facilities available to scientists from universities and research organisations throughout the country, region, or world. 
How much science funding can we expect in the future? Already one of America’s two political parties, controlled exclusively by plutocrats, promises to shutdown the government rather than pay tax hikes. This is not what happens in a successful society. When budgets shrink, governments just try to maintain what they already have. If money’s going to soup kitchens and pensions, it’s not going into physics research. I think we can expect this situation to get much worse in the future. NASA’s budget is on the chopping block every year, even as the rich get richer and blast off into space on their own dime.

The money that would be devoted to research increasingly ends up in the hands of plutocrats who use it to build mansions, buy political influence, throw lavish parties, purchase rare art, and generally inflate prices for the rest of us. This is a self-reinforcing cycle. Look at the Internet - created through government funding during the cold war. Could that be done today in the era of "limited government?" (well, maybe the mass surveillance part could be)

6.) Education levels are falling for the majority. Access to education is increasingly out of reach as education becomes a class differentiator rather than a method of public education. Education has always been seen as a threat to the powers-that-be; the Texas school board has said that "critical thinking skills" should be avoided. They are also attempting to inject religious-based theories like "creation science" into textbooks. Polls routinely show large numbers of Americans subscribing to young earth creationism, the existence of demons, and even the geocentric model of the universe.

7.) Small things make a big difference. Big things make a small difference. As we said above, clean water and hand washing has saved more lives than the millions spent on developing the latest "me too" pill for some invented disease. I've used the example of glass - adding a second and third pane has made the biggest efficiency gains. It made greater gains than even low-e coating which only emerged after many years and many dollars spent in research, and is comprised of expensive materials (like silver)****. Our future gains will be more expensive to find, and take more resources to implement. That is to say, there are diminishing returns to discovery.

Recently my washing machine broke down. Shopping for machines, I noticed they aren't all that different from the ones in my grandma's house which were bought in the 1950's, just more bells and whistles, and a little bit better efficiency.

8.) Science is increasingly alienated from the public. Most people could understand the technology of the second industrial revolution. The average “gearhead” today can build and engine in his garage and probably has only a high-school education. The same is not true for future technology, which can only be done in clean rooms, university laboratories and robotic facilities after decades of spcecialized education that very few people have the aptitude for.

There seems to be a mighty disconnect between the work done in research universities by a small scientifically-trained elite and the common man who lives in a world of bankrupt governments, corrupt politicians, declining wages, militarized police, closed schools, bare-bones public services, and failing infrastructure. Conspiracy theories are rampant. The system is only functioning now by incarcerating large numbers of people. My question to people like Mokyr is: why do you think this can continue? Scientists seem more and more like the distant priesthood depicted in A Canticle for Liebowitz than people who make any sort of difference in the lives of regular people. There are barbarians at the gates. If ordinary people don’t see their lives getting better, they’ll want to tear the whole system down, and the innovators along with it.

Not to mention that science and scientists are being discredited by a plutocrat class who is threatened by the findings of biologists, ecologists, etc. PR firms loyal to the oil industry put out ideas like scientists "fabricate data" in order to "get research funding." Witch hunts are conduced against scientists who go against the agenda of the powers that be. I expect this to get worse, not better.

9.) We don’t need to grow, we need to grow exponentially. The economy that has to grow is the economy of 2013, not 1950. That means we need to introduce more innovations every single year. Can we keep doing this forever?

10.) And, last but not least, is our declining energy reserves, something ignored by all techno-optimists. In a declining energy situation, we will not have as much money or resources to innovate. Note that all innovation to date has occurred under a regime of growing energy supplies thanks to fossil fuels. More and more, we will have to just preserve the status quo. Note that innovations seem to follow the same curve as EROEI.

Then there are the natural disasters. As societies are forced to respond to this, there is less money for innovation. Twenty percent of Kansas’ wheat yields may be cut by global warming. Colorado is currently experiencing flooding of biblical proportions. “Hundred year storms” are occurring every single year now. And other resources are getting in short supply, like helium and uranium.

I'm not saying he's totally wrong, or that my view of the future is the correct one. It is true that we've never had a professional regime of large-scale, professional scientific discovery operating before. I'm certainly not as bearish as commentators like Kunstler. But I do think the pessimists are generally correct. And I think that even they are ignorant of larger historical trends. History shows that when resources that underpin a society get in short supply, that society tends to contract. It also shows that as wealth is increasingly concentrated into the hands of a few, and economies unravel, and societies tend to fall apart. Rome, imperial China, the Mayans, and the Islamic world, some of the most technologically innovative societies in earth, eventually reached a peak and declined. Are we so sure we won't follow in their footsteps?

* I have also used a PowerPoint presentation available on the Web by the author which makes the same arguments.

** There is evidence it has actually cost lives, in decreased life satisfaction, greater incidents of depression and suicides from stalking/cyberbullying. See this. And this.

*** Probably a few thanks to being able to contact emergency responders in remote locations. But this number is probably so small as to be negligible.

****per Wikipedia: "There are two primary methods in use: Pyrolytic CVD and Magnetron Sputtering. The first involves deposition of fluorinated tin oxide (SnO2:F see Tin dioxide uses) at high temperatures. Pyrolytic coatings are usually applied at the Float glass plant when the glass is manufactured. The second involves depositing thin silver layer(s) with antireflection layers. Magnetron sputtering uses large vacuum chambers with multiple deposition chambers depositing 5 to 10 or more layers in succession."

ADDENDUM: I couldn't ask for a better example of what I'm saying than this article: NASA’s Plutonium Problem Could End Deep-Space Exploration (Wired)
The country’s scientific stockpile has dwindled to around 36 pounds. To put that in perspective, the battery that powers NASA’s Curiosity rover, which is currently studying the surface of Mars, contains roughly 10 pounds of plutonium, and what’s left has already been spoken for and then some. The implications for space exploration are dire: No more plutonium-238 means not exploring perhaps 99 percent of the solar system. In effect, much of NASA’s $1.5 billion-a-year (and shrinking) planetary science program is running out of time. The nuclear crisis is so bad that affected researchers know it simply as “The Problem.”

But it doesn’t have to be that way. The required materials, reactors, and infrastructure are all in place to create plutonium-238 (which, unlike plutonium-239, is practically impossible to use for a nuclear bomb). In fact, the U.S. government recently approved spending about $10 million a year to reconstitute production capabilities the nation shuttered almost two decades ago. In March, the DOE even produced a tiny amount of fresh plutonium inside a nuclear reactor in Tennessee.

It’s a good start, but the crisis is far from solved. Political ignorance and shortsighted squabbling, along with false promises from Russia, and penny-wise management of NASA’s ever-thinning budget still stand in the way of a robust plutonium-238 production system. The result: Meaningful exploration of the solar system has been pushed to a cliff’s edge. One ambitious space mission could deplete remaining plutonium stockpiles, and any hiccup in a future supply chain could undermine future missions.

Many of the eight deep-space robotic missions that NASA had envisioned over the next 15 years have already been delayed or canceled. Even more missions — some not yet even formally proposed — are silent casualties of NASA’s plutonium poverty. Since 1994, scientists have pleaded with lawmakers for the money to restart production. The DOE believes a relatively modest $10 to 20 million in funding each year through 2020 could yield an operation capable of making between 3.3 and 11 pounds of plutonium-238 annually — plenty to keep a steady stream of spacecraft in business.


  1. The author you talk about has a religious faith in Science and Technology. Touching. The fact remains, however, that energy in large quantities and cheap prices is a prerequisite for any kind of industrial future similar to what we have been enjoying.

    I just don't see how reifying science into some godlike status that automatically delivers miracles for its adherents will really work out in the real world.

    Then there is the fact that no matter what, the earth has a finite carrying capacity. Technology allows humans to harvest a greater and greater proportion of the free energy falling on the earth, and available in the earth, but the effects on the rest of the biosphere have been catastrophic.

    Just look at Boulder, Colorado - a small taste of what is to come.

    Nope. All species overpopulate and over-exploit their environments. Period.

    The best we can hope for is to become ascetics and preadapt to not needing what will not be available.

    You make a good point on the plutocrats, and the fact that the system is evolving in the opposite manner to what is needed: reducing the social safety net, worse education, etc.
    Yet perhaps that process, too, is simply humanity doing what humanity does.
    For individuals and families, forming a "new monasticism" or commune-like communities of like-minded people is the way to have a better life in the midst of the growing chaos.

  2. I don't buy his argument. Here is one more counterargument which I have never seen addressed by those who maintain we'll invent our way out of it. They argue that while Earth is limited, human ingenuity isn't. Which I agree with.

    But they forget to mention that human ingenuity is a subset of the Earth, and is cradled within, and sustained, by the limited Earth. It's as though they assume human brains are already disconnected from flesh and blood and living on fairy dust. Hello?

    I am so sick of bullshit. It's everywhere. On bad days, I think Pol Pot was right. You gotta wipe out all the sick pointy heads that are filling every nook and cranny of our world with endless bullshit while living on cushy salaries. C'mon plague! :-(

    1. That's a good way to put it, just as the economy is a subset of the environment. I'm fumbling towards that idea in my conclusion to this series of posts. I'm not even sure human ingenuity is unlimited. That argues that there are no problems we're not clever enough to solve. I don't think that's true, certainly not at a group level. There are problems festering every single day that there are relatively simple solutions to, and that we know the solutions for, but we cannot implement them for one reason or another (climate change and national debts are but two of many).

      As Einstein supposedly said, the only two things that are infinite are the universe and human stupidity, and he was unsure about the former.

    2. Just because human ingenuity is not limited per se does not mean that every problem is solvable. Two different issues. I was thinking (and I think they do too) in terms of human ingenuity as an unlimited resource (or at least, the limit is not known, and cannot be conceptualized).


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