No matter how you hang your ears, there’s a background hum to the world right now that’s hard to ignore. There’s nary an outlet avoiding the drop of the C-bomb of late (I also felt obliged to in my previous piece [hyperlnk]), and it got me thinking about bodies — everybody’s bodies — and how many of them there were, and how unavoidably near, despite the requirements for social distancing. Tall, short, round, thin, hairy, plucked bodies…hot bodies…heat flux. This raised two questions: 1) If an Inuit invites too many friends over to an igloo, will their body heat melt it? and 2) If a planet is packed full of people, will their body heat bake it? Let’s dwell on that second, sweaty question.
As all avid readers of New Scientist in the 1960s will know, the physicist John H. Fremlin wrote an interesting article called ‘How many people can the world support?’ (New Scientist, No. 415, October 1964). It reads like a work of speculative fiction (or SciFi to those of us too base to move beyond genre fiction): given that the planet’s human population doubles every 37 years or so, what will Earth look like 100, 300, 1000 years from now? Can we keep on keeping on for so long? Being a nuclear physicist, Fremlin’s limiting factors for growth weren’t human health and harvests, but heat. Diseases, for him, were “nearly, and will soon be entirely, eliminated as effective controllers of population growth” (Fremlin, 1964, p.285) and by the time the limit of our agricultural output is reached, new methods of food production will have been devised. But thermodynamics — no-one messes with thermodynamics. It’s the law. (Also, would everyone mind just getting along with one another, please? “This is quite evidently essential if the maximum world population is to be reached” (ibid.).)
Fremlin divided our socially unified future into five stages, each with its own challenges and solutions. Stage One begins around 2224. Earth’s population is around 400,000 million, and we’ve become acutely aware that our rural landscape is rather diminished. We decide to roof our cities and roads, and grow crops upon them. But wait — what’s this? Some cheeky quadrupeds are eating our crops! A decision is made to eliminate all land wildlife, which necessitates switching to a plant based diet (with the occasional side of sea food, if you can catch it). Happily housed under their harvests, the humans bed down to Stage Two.
It’s 2334, and the food chain needs more tweaking. We’ve reached 3 million million people and we’re intensively harvesting the sea; indeed, we’ve observed single-celled marine organisms that might photosynthesise more efficiently than the best land plants, providing a greater yield for us. Alas, there are a significant number of multi-cellular, complex organisms in the ocean eating them. Someone pores over the archives from 2224 and finds a solution: “We could…double our numbers a further three more times if all the wildlife in the sea, too, was removed and replaced by the most useful organisms growing under controlled conditions, with the optimum concentration of carbonates, nitrates and minerals” (ibid.). There’s some uncertainty, as the range of diverse complex life on Earth seems rapidly to be approaching a count-on-one-hand figure, but an arbiter of The Law is called in who declares that “for maximum efficiency we must harvest and consume directly the primary photosynthesis organisms, rather than allow the loss of efficiency involved in the food chains leading to such secondary organisms as zooplankton or fish” (ibid.). The people are comforted and, in this relaxed state, they reproduce some more.
We reach 2414 and it’s come to people’s attention that the plants are slacking off: too much respiration and not enough photosynthesis. 1960s physicists had calculated that the Earth’s surface receives around 1 kilowatt per square metre of solar power at the equator at midday, with the average value over the globe being a paltry quarter of this. What’s more, they’d noticed that over half of the light spectrum wasn’t even being used! What to do? Nuclear fission (uranium and thorium) and fusion (deuterium) are suggested as energy sources which could be used to produce light, but it’s unlikely converting this fuel will be any more efficient than harvesting the abundant, if sloppily utilised, sunlight. Gazing in the mirror one morning, someone has a great idea: large satellite reflectors in space. So many, in fact, that the Earth would be permanently lit from pole to pole. “Make it so!” And so they are made and fired into space, “100 million square kilometres of mirror which, in aluminium a tenth of a micron thick, [weighs] about 30 million tons” (ibid. p.286). But how is this all possible? How is scientific theory turned to practice? A peek behind the curtain reveals a scientific maxim: Time and toil foil failure. “With plenty of people to design and make the equipment it should not be difficult by the time it would be required” (ibid.). That’s cool, except that it’s not: all that additional energy reflected to Earth makes the globe one giant equatorial region. And wasn’t 60 percent of that light useless anyway? What if we construct satellites out of selectively reflecting material (reflecting only the useful 40 percent to Earth) and deploy a further cordon of satellites below these to reflect the useless 60 percent of the direct solar radiation out into space? That should keep the temperature down. It’s a lot more work, but should “not [be] difficult for the larger population with an extra 50 years of technical development” (ibid.). The humans lie down on a bed of laurels and arrive at a population of 15 million million.
2644 and the sound of rumbling stomachs spreads across the globe the way that thunderclouds don’t. There are now around 1000 million million mouths to feed and Earth is overgrazed. Cultural historians (of which there are many — there are many of every career at this point) posit a solution: 20th century humans imagined 24th century humans to be in possession of a ‘Replicator’, a device which converts energy into matter, and reconstitutes that matter into known molecular structures, e.g. food. There’s much laughter, but then some serious thought is given to the idea. Food synthesis, yes. Most of our macro- and micronutrients could be synthesized, and at minimum heat and energy cost. It’s pointed out that humans only use “about 100 watts per person” (ibid.) converting food into waste products, i.e. extracting most of what they need from it and excreting the rest. If solar power could be efficiently used, “waste products could in principle be changed back into food compounds with the absorption of little more energy” (ibid.). Eat shit! becomes the rallying cry of the 27th century. Citizens everywhere (and they are everywhere) settle down to several meals of tasty “porridge” a day. But it’s a little more sinister than that. Behind closed doors, the scientists have reasoned beyond the bounty of their toilet bowls. There’s something more nutritious than human faeces: humans themselves. When space is at a premium and hunger is on the rise, why bury the dead? Why not eat them? “Cadavers could be homogenized and would not, at least for physical reasons, need to be chemically treated at all” (ibid.).
Maths in brief: the sum of your 27th century existence is 100 watts in the feeding, 100 watts in the digestion, and a generous 50 watts for your phone and light bulb. 250 watts per person. Therefore, with a solar heat income of 500 watts per square metre, the Earth can support two people per square. Yes, it’s intimate, but it’s doable. Any more than that will leave us with refrigeration problems, and Fremlin’s Stage Four-A.
We simmer to the year 2764. There are close to 12,000 million million people, and we’ve reached a thermal dead end. “I’m giving her all she’s got, Captain! She cannae take any more.” The planet is becoming so hot that we start using the oceans as heat sinks. We need them to absorb anthropogenic warming of 500 watts per square metre, causing their mean temperature to rise about 1 degree Celsius per year. (For historical reference, “averaged over Earth’s surface, the 1993–2018 heat-gain rates were 0.36 to 0.4 (±0.06) watts per square meter for depths from 0–700 meters, and 0.14 (±0.0) to 0.32 (±0.03) for depths of 700–2,000 meters. For depths between 2000–6000 m, the estimated increase was 0.07 (±0.04) watts per square meter for the period between September 1992 to May 2011.”) This buys us a bit more time to bump and grind. We reach four people per square metre. We want more; our libido is insatiable. “Half another [population] doubling…could be gained if efficient heat pumps…could be used to bring the ocean to the boil” (ibid.). In a collective scream of ecstasy (or expiration) we let the pumps run wild, converting the oceans into steam and buying us time for two more sweet doublings but “creat[ing] an atmospheric pressure comparable with the mean ocean bottom pressure [in 1964]” (ibid.). We smile, sigh, and die: “Since the resulting steam blanket would also be effectively opaque to all radiation, no further heat sink could be organized and this procedure would therefore seem to lead to a dead end” (ibid.).
Dreamers of a dynasty, fear not! Future nerds have engineered an alternate timeline. The year is 2854; Buck Rogers has come and gone twice, and we’re just short of 800 millennia behind H.G. Wells’ Time Traveller. Instead of evaporating the oceans, civilization roofs them. Indeed — retcon — this has already been done, as we needed the surface area to build upon. Further to this, we erect an additional outer surface about the Earth which hermetically seals it: all atmosphere above this skin is extracted and pumped into compression tanks on the ocean floor if not needed for ventilation. Heat pumps transfer heat to this solid outer skin which, “in the absence of air, […] would be radiated directly into space” (ibid.). Fremlin posits an outer skin temperature of 1000°C. Assuming heat is the only limitation on growth, this will allow around 120 people per square metre. That’s around 60,000 million million people across the globe. Beyond this, we would enter into diminishing returns. “The difficulties in raising [the outer skin temperature] much further while keeping all thermodynamic efficiencies high would…be formidable. A rise to 2,000°C would give us less than three further [population ]doublings.” (ibid. p.287)
There are other limitations though, aren’t there? Living space, for example. As ancient scholastic philosophers may once have thought: how many humans can dance on the head of a pin? Lots, as it turns out, as long as that pin is 2000 storeys high and the dancers are of the pole variety. For physicists, accommodation is not an absolute barrier like the laws of thermodynamics. Therefore, the Scientist’s Maxim is deployed once more: “We can safely assume…that in 900 years’ time the construction of [such] buildings over land and sea alike should be quite easy” (ibid.). It’s not quite as luxurious as it might seem though; the top half of each building is given over to cooling equipment and the generation and distribution of the nutritious shit-cadaver shakes. Still, that leaves 1000 storeys of 7.5 square metre prime real estate per person. This is a future for agoraphobic introverts. As Dr. Emmett Brown might say: “Clothes? Where we’re going, we don’t need clothes.”
Another doctor said something else: we don’t need all that macro-engineering. We’ve returned to our 21st century with Viorel Badescu and Richard B. Cathcart who, despite living in a society more populous and more technologically advanced than Fremlin’s, propose a “more relaxed” situation: a future with an unmodified Earth-biosphere (Badescu and Cathcart, 2006, p.131). How?
They first postulate some simple vales for the Earth’s albedo (diffuse reflection of solar radiation) and emissivity, generously overestimating both the amount of radiation absorbed and the amount of flux emitted. They then postulate the flux of the average mensch: 120W. This is close to Fremlin’s baseline of 100W, but nudged a little north “to account for the heat generated indirectly by active persons” (ibid.). These data are fed into an equation for the steady state energy balance of the entire surface of the Earth (which also includes a variable for cloud cover), which yields some interesting figures. For example, when global population is calculated as a function of cloud cover and Earth surface temperature, a value of 1,300 million million people is obtained if an upper limit of 300K (26.85°C) for the surface temperature is accepted. According to Fremlin’s calculations, this figure was only possible through advanced technological manipulation. So what if we do engineer the Earth?
Badescu and Cathcart adopt Fremlin’s idea of roofing the ocean and sealing the planet’s outer land surface, creating a living space and dual-function skin comprised of solar collectors (for power) and thermal radiators (for cooling). These would be regulated according to the Earth’s diurnal rotation to ensure that there is no interruption to either vital service: the sunny side of the Earth would always be harvesting energy while the dark side would be actively pumping and radiating out living space heat. The efficiency of this operation would be affected by the number of hot bodies under The Skin™. With less heat to expel, the collector / radiator complex currently on the Earth’s sunny side could deactivate some collectors and switch to radiators: less energy would be needed to power the heat pumps allowing more of The Skin™ surface to be utilised for radiating. This increased radiator surface area would result in a cooler radiator temperature, meaning the temperature difference between the Earth’s outer skin and inner habitation area would be smaller, meaning the heat pump would work more efficiently. Fantastic! The population of Future Earth enjoys the balmy and seductive 300K climate and is aroused to amorous and reproductive heights. Soon there are more bodies radiating and the sunny-side outer skin panels are switched back from radiators to collectors. “Scotty, we need more power!” Now, alas, the heat pumps are operating less efficiently. Soon, the number of hot bodies on the planet exceeds the refrigerator’s capacity to expel the heat: Fremlin’s thermal ceiling has been reached.
How many bodies? Badescu and Cathcart calculate the maximum population range to be between 1,600 and 4,000 million million. This is an order of magnitude lower than Fremlin’s Stage Five figure. Comparing their own pre- and post-macro-engineering calculations, the authors found the latter “allows one or two [further] population doublings as compared to the ‘natural solution’…If a population doubling lasts about 37 years then the ‘macro-engineering’ solution allows humanity the gift of 74 more years of confined life during Earth’s Geological Time” (ibid. p.138).
From space our future planet may well be viewed as a monoculture experiment gone awry. From a future Fremlin-Badescu-Cathcart-Earth, we might look up to the night sky and see…nothing but The Skin™. Maybe we won’t care; Fremlin appealed to the huge population numbers to argue that “One could expect some ten million Shakespeares and rather more Beatles to be alive at any one time” (Fremlin, 1964, p.287). We’d have entertainment in abundance. And if not? Well, even caged hens lay eggs.
References.
Badescu, V. & Cathcart, R. B. (2006) ‘Environmental thermodynamic limitations on global human population’, International Journal of Global Energy Issues, vol. 25(1/2), p129-140.
Fremlin, J. H. (1964) ‘How many people can the world support?’, New Scientist, vol. 24(415), p285-7
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