I have a couple of small potted rosemary bushes on my balcony, with a third that I’m trying to coax to grow out some roots in a cup of water inside. All three of these grew from a cutting Beatrice’s husband Santiago gave me when he and Beatrice moved to Holland late last year; I have perhaps quintupled his investment in me in five months, if we measure in rosemary biomass. If I can continue this rate of exponential growth for the rest of the year, by way of judicious propagation, in 7 more months I will have multiplied my current rosemary holdings by a factor of 10, a factor of 50 for the whole year, a 4900% internal rate of return on this project, a doubling time of about 66 days.
Of course, we don’t usually account for agriculture this way. And I probably won’t actually have 20 rosemary bushes in August, nor four rosemary bushes each five times the size of the ones I have. The exponential growth of the plants will eventually outstrip my balcony space, pots, and watering time; if I don’t attend to them, they may die of dehydration, but also, they face other dangers which themselves grow exponentially: they may be choked out by faster-growing weeds, or they may suffer attacks by insects, fungus, or root nematodes. In any case, the last five months have been summer months, with temperatures around 25°, while the next few months will be winter months, with temperatures around 15°, so the Arrhenius law predicts that the plants will grow about half as fast. Ultimately, the limiting factor for my rosemary production will probably not be the capital equipment of rosemary plants, nor my labor or mineral resources, but the energy I have available: rosemary will not grow in the dark.
I also have an Aloe vera plant I found discarded in a gutter, which has rooted nicely after a few weeks of early failure, and another aloe that was a gift from my girlfriend Alejandra. In a third pot, I’m trying to root a leaf I accidentally knocked off the gutter plant. The aloe plants, too, are growing exponentially, though apparently at a slower rate.
Although these growth processes are exponential, they are also slow. Even on the rosemary plants, the difference from one day to the next is very hard to see; calculation suggests that it averages about 1%. Several days can go by without a noticeable change.
(Post scriptum: the above was written 2019-03-26. The cutting finally grew out roots (one root of 15mm and two roots of 5mm) on 2019-04-02, one week later. I’m not sure how long the whole rooting process took, since I’m not sure when I made the cutting, but it must have been a couple of weeks or so. As of 2019-04-05, the roots had increased to seven in number, including a tiny fork from one of the oldest ones, which itself had lengthened to some 40mm; this quantity of daily root growth is also on the order of 1% of the volume of the cutting per day, which is some 150 mm long. On 2019-04-07, the root tips had increased to, I think, 20 in number; on 2019-04-08 a root had sprouted from a node higher up the stem as well, though now I count only 15 tips.)
Rosemary and aloe are perennial plants adapted to somewhat harsh conditions: their ecological niche does not demand that they grow especially fast or reproduce abundantly, but rather that they successfully survive a variety of temporary adversities. Ruderal annual plants, on the other hand, survive by growing rapidly in soils that have been rendered temporarily plantless by plowing or some other catastrophe, ending their lives in a riotous explosion of sex called “going to seed”; the champion among cultivated ruderal annuals is corn (“maize”), which can grow several millimeters per day. Each corn plant — a corn kernel’s way of making more corn kernels — normally produces several ears of corn, each bearing 200 to 400 kernels, in a single growing season, which normally only occurs once per year. But this means that a single kernel of corn can multiply into several thousand kernels within a year, not just the factor of 50 or so I’m estimating for the rosemary.
This means that corn’s rate of capital growth is on the order of 100,000% per year.
I’m eating a small jar of yogurt I made the night before last. In the refrigerator right now I have another liter or so of it. The yogurt, like poop, consists mostly of dead bacteria, in this case mostly Streptococcus salivarius subspecies thermophilus and Lactobacillus delbrueckii subspecies bulgaricus, mixed with chemicals the bacteria couldn’t digest, mainly a casein gel in this case (though the bacteria do digest some of the protein), and bacterial waste chemicals such as lactic acid and acetaldehyde. The jar contained perhaps 100 mℓ of yogurt, which was made from about 200 mℓ of milk through about 24 hours of fermentation after being seeded with about 1 mℓ of living yogurt culture. The bacteria are, say, about three cubic microns each, and occupy over 50% of the yogurt volume, so I just ate tens of trillions of bacteria which I produced overnight from only hundreds of billions of bacteria.
Probably, under better-controlled conditions, I could have gotten the yogurt to finish in under 8 hours; most of the jars were already relatively thick after 12 hours, though some had not fermented at all — perhaps I had inoculated them with the starter culture when they were still too hot, so I added more starter culture to them at this point. The 24-hour timescale suggests an average rate of bacterial reproduction of, conservatively, about 20% per hour, which amounts to doubling every three or four hours.
(More aggressive bacterial cultures like Escherichia coli can reproduce much faster, doubling every half-hour or so under ideal conditions, around 37° with all the nutrients it needs.)
Doubling every four hours would give you 2191.4 doublings per year, which works out to a multiplication by about 4.8 × 10⁶⁵¹. But only about 1 × 10⁹⁸ of these yogurt bacteria would fit into the observable universe. So if these yogurt bacteria were to double 325 times, which would take less than two months at four hours per doubling, they would fill the observable universe, out to the farthest galaxies and quasars. After about the first month, the yogurt sphere would have to be expanding outward faster than the speed of light, which is probably impossible. Even if you could find a way to defeat relativity, where would you get the milk?
Some time ago I was the proud owner of a number of confused flour beetles. Confused flour beetles are marvelous little self-reproducing automata, about three millimeters long, which can acquire sufficient water by metabolizing the dry flour they eat to survive and reproduce, although if the flour is very dry, they reproduce more slowly. They can also survive a thousand grays of radioactivity (in about 10% of cases) and thus probably more than a thousand sieverts, more than cockroaches can. Five grays will usually kill a person; radiation therapy usually kills tumors with 20–80 grays. Confused flour beetles are commonly raised for use as laboratory animals, particularly in studies of genetics.
I didn’t measure the rate of growth of my capital holdings of confused flour beetles, but Wikipedia’s marvelous “Home Stored Product Entomology” article tells me that a female flour beetle can lay 300–400 eggs over a 5–8 month lifetime. So a mating pair of beetles can produce, conservatively, 150 mating pairs of beetles in 8 months, which amounts to a doubling time of 34 days, once exponential growth kicks in after an initial linear ramp-up period, and a multiplication factor of some 1800 per year, a return on investment of 180,000% per annum — nothing like the universe-consuming rate of growth of yogurt, but comparable to that of corn.
Rather than submitting my fortune to appraisal by counting my flour beetles, I took them, the grain they were eating, and the basket they were eating it in, and threw them all together into a dumpster, in hopes that they would cease their self-reproducing in my house. Thus I preserved my holdings of flour, beans, and other grains. This is because I could not program the beetles; they came preprogrammed from an optimization process which did not, for instance, offer me a quiescent mode in which a stock of flour beetles I already judged as more than sufficient would cease to increase, nor a practical way to employ the beetles to construct mosaics, murals, or sculptures directed by an STL file.
So far this measure has apparently been successful, though I live in fear of the beetles’ return. Every new bag of flour I get spends some time in my freezer to kill any insects inside.
Capitalism, of course, is based on the exponential growth of productively employed capital. Wikipedia clarifies the terminology thus:
In economics, “capital”, “capital goods”, or “real capital” refers to already-produced durable goods used in production of goods and services. The capital goods are not significantly consumed, though they may depreciate in the production process. “Capital” is distinct from “land” in that capital must itself be produced by human labor before it can be a factor of production. At any moment in time, total physical capital may be referred to as the “capital stock”, a usage different from the same term applied to a business entity. In a fundamental sense, capital consists of any produced thing that can enhance a person’s power to perform economically useful work — a stone or an arrow is capital for a caveman who can use it as a hunting instrument, and roads are capital for inhabitants of a city. Capital is an input in the production function. Homes and personal autos are not capital but are instead durable goods because they are not used in a production effort.
The name “capital” refers originally to the heads of herds of livestock, which feature this same exponential growth through biological processes, except when limited by available feed. But, compared to an internal rate of return of 4900% or 4.8% × 10⁶⁵³, the traditional rates of return on capital investments, about 3%–10% per annum, seem fairly pitiful. The outrageous rates of exponential capital growth we see in gardening or herding invariably slam quickly into other resource limits: the sunshine on my balcony, for example, or the milk I have on hand to grow yogurt in, or the difficulty in controlling exponential-growth processes to produce the desired outcomes.
One of the rosemary plants, for example, has a blade of ruderal grass coming up in its pot. Grass is a relative of corn (more properly, corn is a sort of ruderal grass) and it grows much faster than the rosemary does. If I don’t want a pot full of grass shading the rosemary, sooner or later I need to pluck out the weed. And this same rosemary plant had a close call with death when I was still rooting the cutting it in water: fungus started to grow on its bark, and if the process had continued, might have started to digest the living plant. I lowered the water level in its jar so that its bark could dry out, and the fungus disappeared and hasn’t returned. This latest batch of yogurt all turned out without problems, but the previous batch had a couple of jars that grew some fungus after the bacteria, causing an off flavor.
Historically, the main determinant of power in agricultural and pastoral societies — those whose most important means of production grows by these insane exponential biological growth rates, rather than being human-designed machinery — has been control over land, particularly arable land. Landowners had power, and nobles and gentry were distinguished by their land holdings, not their wisdom, learning, machinery, or industry, nor even martial virtues like their honor and bravery, and certainly not by the amount of grain stored in their granaries. This was the rule in Europe from the time of the late Roman Republic, when Senators derived their income from the latifundia they owned, and of course in every feudal society too.
Consider, also, for example, Imperial China’s 士 “shi”; until the Warring States Period they were noble-born charioteers. The 秦 “Qin” dynasty and its successor 汉 “Han”, 隋 “Sui”, 唐 “Tang”, and 宋 “Song” dynasties needed to reduce the power held by the feudal nobility, for which purpose they established an empire-wide civil-service bureaucracy, redefined the 士 “shi” class to include it, and staffed it increasingly with commoner scholar-bureaucrats they hired according to their performance on 科举 standardized tests. But these scholar-bureaucrats also became agrarian landlords, and were generally landed gentry even before sitting for the examination.
Thus, even though Ricardo and Smith’s classical economics was born at the moment and center of England’s transition from such a feudal society to the new capitalist society, they do not consider plants or plant seeds to be capital, precisely because they multiply too rapidly for their scarcity to be a major limiting reagent in the production function in an economy with functioning agriculture. Only in extreme cases, like when the Lykov family’s millet crop was killed by a late frost, leaving them hungry until seven forgotten seeds sprouted the following year, or in Israel’s destruction of generations-old olive trees in the Palestinian occupied territories, are we forced to confront the crucial nature of self-replicating automata to the economic production process. Under normal circumstances, they are either nonexistent or superabundant, and in either case their stock is not a relevant variable.
So, what will happen to human society when we develop programmable self-replicating robots that can work from inorganic feedstock? No longer will we measure the assets of a company by its stock of capital goods — indeed, apart from a few exceptions like railroads, it’s been quite passé for a company’s book value to be based on tangible assets like railroad cars since at least the 1980s, much less its market cap. Nobody would think to argue that Microsoft has a competitive advantage against software startup firms because Microsoft owns a lot of computers to produce software with, while the startups would have to buy them, though it seems reasonable to think that Ford, GM, and Chrysler had an edge over late-20th-century startup car firms because the Big Three already owned factories. (Tesla is the first successful automobile startup in the US in decades, although China’s success at bringing new brands to market since 2005 suggests that US industrial policy has as much to do with the late-20th-century oligopoly in the US automotive market as raw economic factors did.)
But what happens when we can grow factories like rosemary plants, or even yogurt? How do we think about the effects on human society and future economic prospects?
Perhaps as we learn to garden programmable machines we will find ourselves thinking more in biological terms than in mechanical terms. We’ll be constantly watching out for something or other going wrong, hoping to notice problems that could grow exponentially and stop them while they’re small. We’ll accept some degree of parasitism and predation on our production as the cost of having a system that works at all. We’ll try to manipulate conditions to disfavor the growth of the elements we don’t want, even at the cost of those we do — as I let the roots of my rosemary dry out a bit to get rid of the fungus on its bark. To a great extent, these sound like the skills of a turn-of-the-millennium business manager, drawing on the best of 20th-century management practice and Taoist practice.
Industrial-age machinery is prized in part by its stability, size, and durability; and it is repaired. But self-reproducing machinery need not work this way, and its logic will invert industrial-age logic in interesting ways.
A lathe which, left idle overnight, can no longer cut in the morning is hardly a lathe at all. Great efforts go into ensuring that form materials are dimensionally stable so that changes in humidity will not drive them out of tolerance. It is common for a machine left unused for decades to remain usable, perhaps with a few minor repairs.
But many bacteria will die if left without food for a few hours. Suppose some strain can reproduce itself by a factor of a thousand in ten hours. A left-behind cell that lacked resources to reproduce itself during that time can only, at best, result in a single cell at the end of it. Even if it happens to fall back into the nutrient broth, its descendants will be outnumbered a thousandfold by those who multiplied the whole time. So, many such bacteria spend no resources on surviving lean times.
Similarly, a self-reproducing machine that requires continuous homeostatic control to remain viable, and “dies” irreversibly if that control fails for a significant length of time, may be a perfectly reasonable replicator. So stability is not necessary to self-replication if homeostasis can replace it.
Machine size was the distinguishing feature of the mass-production era. A steam shovel that carried 100 tonnes per shovel-load would move rock 10 times as fast as a shovel that only carried 10 tonnes, and might require only 5 times as much material, and the same number of fabrication and assembly operations, though each handling pieces 5 times as big. Moreover, a 20-tonne rock could be moved by the 100-tonne shovel without being broken first. A bigger lathe could make bigger parts, and due to its greater rigidity and power, it could make the same parts faster and to tighter tolerances. So, bigger machines made more efficient use of material, tooling, and labor, and could do things smaller machines could not.
But replicators need not follow this logic. There is every reason to believe that a one-kilogram object can be built as easily by a thousand tiny replicators each processing a gram of material, followed by a final assembly, as by processing the kilogram in one operation with a large replicator. Indeed, it seems likely that the smaller replicators will work faster, working as they do in parallel. So the size pressure on replicators may indeed be opposite: toward the smallest practical dimension, to maximize flexibility.
Biological life certainly has followed this design. Despite the existence of large single-celled creatures like foraminifera and slime molds, and the occasional large cell like the squid’s neuron with its giant axon, the typical size of a eukaryotic replicator — a cell — is close to a nanogram in complex organisms. You could argue that, for example, a human neuron is not a replicator because most of them die without ever producing a new neuron, and they are rather specialized to their climate-controlled environment; on the other hand, nearly all human neurons are produced by the replication through mitosis of a neuron, and they can be coaxed to grow and even replicate in vitro.
This composition from such a large number of quasi-independent replicators certainly has major disadvantages, including cancer, but it seems to have sufficient compensatory advantages that the cells of multicelled creatures are hardly ever big enough to see without a microscope. So we should expect artificial replicators to find significant advantages in smallness, as well.
Conventional machinery is considered better when it is durable. A lathe whose chuck or gears or ways wear out after a few hours of use is a very poor lathe. Often we go to great effort to improve the durability of our machinery so that it can continue operating reliably for long periods of time, including measures such as jewel bearings in wristwatches, hardened steel gears, hardened steel calipers, all manner of bearings, and many others. One of the great benefits of vacuum tubes over relays in the history of computing was that they lasted for many more operations than relays did.
This industrial-age logic has come under assault by disposable products over the last few decades, with some degree of rationality: if money you invest has a 10% rate of return on investment, you can quite reasonably use a 9.1% discount rate to devalue the future use-value of your machinery. To be more concrete, suppose you spend US$1000 (of resources, energy, and labor) to build a machine that will last for 20 years. At the end of these 20 years, you will need to spend another US$1000 (inflation-adjusted, of course) to replace it. To be prepared for that eventuality, you can invest US$149 today into something productive, which will have grown to that US$1000 in 20 years. So if you had the option to extend the machine’s life to 40 years by building it in a more expensive way that cost US$1200, it would be a poor economic choice. Indeed, by investing US$175 today, you can obtain enough investment income to replace the machine every 20 years for eternity; even increasing its lifetime to millennia for the extra US$200 cannot compete.
But replicators, as described above, have a rate of return many orders of magnitude greater than that of industrial-age capital. Their dynamics have a phase transition when they last long enough, on average, to produce more than one offspring: at 0.99 offspring before death, their population would gradually exponentially decrease, while at 1.01 offspring before death, it would gradually increase.
But suppose you have an autotrophic clanking replicator that can self-replicate in a week, and which lasts only three weeks before irreversibly failing. For the first week, you have one replicator; in the second week, you have it and the one it produced during the first week, each producing a child replicator. In the third week, you have four replicators, each producing a twin, but at the end of this week, your original replicator dies, so you have seven replicators in the fourth week; they produce seven new replicators, but the two oldest die, so you have 12; and so the process continues, with 20, 33, 54, and so on, with an exponential growth rate of φ ≈ 1.618, the golden ratio, per week.
This means that, once you have reached an adequate population of replicators, you can use φ-1 ≈ 61.8% of the total to produce non-replicator products, while the remaining 38% are occupied with replacing the dying replicators. This 38% is the “overhead cost” of this limited durability; if some redesign would extend the replicator’s lifespan to dozens or hundreds of offspring, it would increase the end-product productivity of the replicator “biomass” only by eliminating up to that 38%, working out to a 61.8% improvement.
The same logic applies regardless of the generation time: if your replicator needs an hour to self-replicate and dies after three hours, you still have a growth rate of 61.8% per generation. Three hours is a very poor lifetime for conventional industrial machinery; industrial products that are consumed this quickly, such as arc-welding electrodes and TIG-welding cups, are categorized as “consumables” rather than machinery.
As a specific example, suppose one of the cycles in our clanking replicator’s fabrication process graph cuts steel.
The standard industrial process for this nowadays cuts the steel ceramic inserts made of tungsten carbide cemented with cobalt, pressed to shape in molds.
The previous standard industrial process for this, still in use in places, used a special “high-speed” steel alloy, sufficiently harder at high temperatures than ordinary steel to cut it rapidly and last a long time, cut to shape by abrasive grinding with a grinding wheel. The grinding wheel was made of, for example, crystals aluminum oxide or silicon carbide cemented with, for example, magnesium oxychloride, cast into the shape of a grinding wheel, and then trimmed to an accurately circular shape using star wheels, made of hardened steel. (Older grinding wheels might have been cut from stone.)
The process before that used cutting tools made from high-carbon steel, annealed and cut to shape using either steel tools or a grinding wheel, and then heat-treated to harden them.
The ancient process used cutting tools made from wrought iron, hot-forged, then cut to final shape using either hardened steel tools or a grinding wheel, and then case-hardened to harden them.
But abrasive cutting with, for example, a grinding wheel or abrasive sawblade, works fine for cutting steel. It’s often used for cleaning up after welds, where it easily copes with oxide deposits, and it’s often used as the most expedient alternative at construction sites. It’s also used, in the form of “surface grinding”, to cut surfaces more accurate than those that can be cut with steel tools, due to lower temperatures and deflection forces. The litany of other steel-cutting tools described above is purely a result of optimizing the cutting process; a high-speed steel or especially ceramic tool can cut much deeper into the workpiece with each cut than the microscopic spark removed by a grain of abrasive, and it also lasts much longer. Even the use of super-hard abrasives like silicon carbide and aluminum oxide is an optimization to cut faster and wear slower.
A clanking replicator might quite reasonably use only abrasive cutting or only case-hardening, thus dramatically shortening the time per generation by reducing the number of processes in the cycle; and, in the abrasive case, it might quite reasonably use only low-grade abrasives barely hard enough to cut the steel, such as quartz, soda-lime glass, feldspar (orthoclase feldspar being the defining mineral of Mohs hardness 6) or even apatite (Mohs hardness 5). Glass is especially promising here because of its isotropy, low-temperature thermoplasticity, and lack of need of time for crystallization.
This example also illustrates why small size could be a big advantage: the diffusion process of case-hardening, the crystallization processes of the crystalline abrasives, and the heating and cooling processes of a mass of glass all take time proportional to the characteristic dimension of the thing. So a replicator of one centimeter in diameter could reproduce its steel-cutting tools, all other things being equal, in one hundredth the time of a replicator of one meter in diameter.
When my bicycle malfunctions, I debug it; I compare my mental model of the ideal bicycle to the actual observed bicycle to discover where the reality departs from the ideal, meanwhile updating my conception of the ideal in accordance with the things I learn from the observed bicycle, and modifying the observed bicycle with wrenches to sharpen my observations. Once I have found the root cause of the problem — a spalled bearing ball, for example — I repair the bicycle, reconstructing the deviant parts in accordance with the ideal, perhaps an ideal I have improvised in the moment rather than my original conception. For example, when the derailleur bent irreparably, I removed it and shortened the chain, converting it into a fixed-gear bicycle for the time being.
In this way, my behavior provides the bicycle with the homeostatic processes it needs to continue working, which it is too simple to provide for itself.
When my rosemary malfunctions, I usually do not repair it; usually the malfunctioning part dies on its own, but sometimes I prune it. Self-replication takes care of replacing the damaged rosemary more easily than figuring out that, for example, some xylem channels are blocked in this branch due to excessive bark growth on the inside of a tight bend compressing the inner bark, and carrying out microsurgery to widen the xylem channels. The same kind of process usually handles malfunctions in my own body, and it will apply to autotrophic mechanical replicators as well: it will commonly be more practical to recycle broken replicators than to repair them.
However, this is not the case for “malfunctions” that happen so frequently that they would reduce machine fertility below the replacement rate; those must be repaired by either internal or external homeostatic processes, such as a dude with a wrench. In the initial stages of replicator bootstrapping, we can expect to have to repair many faults manually at first, until we have improved the replicators to intervention-free replacement-level fertility.
Also, malfunctions that affect the overall system of replicators, rather than an individual replicator, require a different approach. If the rosemary comes under attack from caterpillars, pruning it may not be adequate — the caterpillars will just eat the healthy part I didn’t prune. Malfunctions that are themselves replicators, such as viruses, parasites, and cancer, may be able to outrun mere apoptosis-based approaches. Debugging such system problems promises to remain as challenging as in gardening, and presumably the future of humanity will be decided in this way, as different people or groups struggle for the power to program replicator populations.