Lord Kelvin's Monkey
or, The Heat Death of the University

Vacationers returned from the Lands of Science can be expected to display the following reflections:

• Over-application of long-term or statistically relevant notions to a local, recent, or personally relevant context. (This winter is unusually long and harsh because the sun is contracting; this spring's line of Parisian hats was triggered by last year's degeneration of the species.)
• Mistaking analogy for definition. (The cultural force of Poincaré's arguments must be measurable in joules; entropy unexpectedly decreases when oil and vinegar separate; "the vital energy of a race" expresses anything more than a string of nonsense syllables.)
• Excessive allegiance to perceived orthodoxies, often based on obsolete, overblown, or fraudulent sources which happen to be more readily available than their corrections or dismissals.
• Alternatively, those of us eager to escape fellow tourists and immerse ourselves in the authentic native experience will become impatient with its authentic disputes, upheavals, and incomprehensible jibber-jabber, and conclude in premature despair or an ungrounded search for common ground.

Henry Adams displayed the usual range, and, like other humanist intellectuals then and since, came to suffer from science envy. His discipline must innovate to regain relevance, and relevant innovation means Science — or at least the sciences considered most newsworthy.

During Adams's decades as a professional historian, those sciences were geology and Darwinist evolution. Afterwards, at century's end and in his mid-fifties, he struggled to comprehend the hot topics of contemporary physics: thermodynamics and electromagnetism, and later, radioactivity.

His new studies were in some ways more intriguing and more satisfying than his old: the applications easier to see, the theories more convincingly law-like, the outlooks grimmer. Adams was particularly taken by Lord Kelvin's terse style and ultimate admission of FAILURE, announcing in one letter, "I am a dilution of a mixture of Lord Kelvin and St Thomas Aquinas" — a fair one-line summary of Adams's two best-known books.

But the physicists' mathematics were opaque; even their imagery could be daunting: "How then does the molecule bounce?" "Maxwell gives no definition of a dead molecule, yet a dead molecule must be something very different from a living molecule."

And Adams lacked a tutor or informant. In geology, he'd relied on his friend Clarence King, and even provided King with field reports from Polynesia. Brother Brooks served as prod and soundboard in the science of economics. (Economics has numbers, and numbers make a Science, and a Science must have Laws. As the big business monkeys at Cal used to state, if it's not quantifiable it doesn't exist. Quantify Excellence. Excel Excellence.™) In physics, however, Adams relied on the kindness of strangers, and the strangers often took their time about replying.

Hungry for explanations, corrections, angry denunciations, enthusiastic assent, or simple companionship, Adams slowly began to expose his worries and speculations more widely. By age 72, he felt ready to send a privately printed volume to a select audience of professional historians. To compensate for his deficiencies as a physics scholar, he equipped the Letter with a formidable barricade of quotes from eminent authorities and tried not to stray far from its protection.

And by this cautious route he stumbled into the final trap awaiting would-be straddlers of the Two-or-More1 Cultures: bad timing.

Lord Kelvin's Monkey, 2

While Adams struggled to make history a respectable science in a STEM-led university, his exemplary sciences struggled between themselves.

It was an age of theorizing inventors and toolmaking theorists, and Adams's earlier attempt at a global Law of Acceleration mostly described the codependent accumulation of scientific discoveries and engineering techniques. In physics and chemistry, theory, application, experimentation, and consensus fed each other in a tight, fast loop. In mathematics, each innovation could be redeployed almost immediately as a tool for more discoveries.

Even after discarding two millennia of Galenic humours and bloodletting,1 biology and medicine were handicapped by the relative slowness and uncertainty of their labwork. And despite their own conceptual revolutions, "historical sciences" such as geology, paleontology, and cosmology were built from uncontrolled, incomplete, and unrepeatable evidence, and therefore unfit to survive a game ruled by timely, immaculately isolated, and precisely replicable experiments.

Then as now "hard" scientists were aware of their advantage. Lord Kelvin, especially, was celebrated for his brusque interventions. First, he proved that the sun must be less than 300 million years old, most probably 100 million, and shrinking and cooling at a rate which would become uncomfortably perceptible over a million years or less. Since the earth couldn't be older than the sun, that did for the earth's age as well.

Adams had a ringside seat for the next development: based on Clarence King's lab results, Kelvin then lowered the earth's age to a scanty 20 million years.

Evolution as explained by Darwin wasn't credible at that speed, and paleontologists scrambled to meet the threat. On a happier note for geologists, a dying sun would neatly explain the otherwise inexplicable Ice Age; on a sadder one, it would place humanity at the literal End of Days.

As you know, Bob, none of this was true. The source of Kelvin's mistake was the same as the source of his thermodynamics: the steam engine. Working in complete (but rarely acknowledged) absence of evidence, theorists assumed the interiors of the sun and earth must resemble their own familiar technology: heat comes from burning; burning consumes fuel; unless the store of fuel is replenished it shrinks into ashes and universal darkness buries all. Although the sun might sometimes be tossed the kindling of a meteor, that was unlikely to balance its extravagant expenditures. And since the earth's hot core couldn't be replenished at all, it must quickly be resolving into cold and solid rock.

Print and web are full of latter-day defenses of Kelvin by physicists and mathematicians. His methods were right and his calculations were correct but the data were incomplete. The poor fellow couldn't possibly have anticipated solar nuclear fusion or terrestrial radioactivity. Geologists and evolutionary biologists had made unrealistic assumptions — an infinitely old earth, unchanged over eternity except by erosion — and needed to wake up and smell the Real Science coffee. Besides, everything worked out in the end.

So sure, we can't fault Kelvin just for being wrong. Everyone was wrong about something; everyone probably still is. What we can fault him for is the vehemence of his wrongness, his refusal to acknowledge the incompleteness of his data, and his tendency to exclude inconvenient outside-the-laboratory realities from that data — and in one case inconvenient inside-the-laboratory reality as well, since the chief flaw in his calculation of the earth's age was raised by his ex-assistant, the impeccably credentialed John Perry.

As for those sleepy subpar mathematicians, the geologists, they were capable of brewing their own coffee. The evidence of sediment, erosion, and fossils required more than twenty million years but infinitely fewer than infinity, and the "doctrine of uniformity" had already been amended by better knowledge of volcanic activity, earthquakes, and climate change. As of 1877, Clarence King, again, was suggesting something not unfathomably far from punctuated equilibrium.

In my own amateurish readings, the most impressive figure of this debacle was Sir Archibald Geikie. His first response was good humored enough:

The geologist found himself in the plight of Lear when his bodyguard of one hundred knights was cut down. ‘What need you five-and-twenty, ten, or five?’ demands the inexorable physicist, as he remorselessly strikes slice after slice from his allowance of geological time. Lord Kelvin is willing, I believe, to grant us some twenty millions of years, but Professor Tait would have us content with less than ten millions.

In scientific as in other mundane questions there may often be two sides, and the truth may ultimately be found not to lie wholly with either. I frankly confess that the demands of the early geologists for an unlimited series of ages were extravagant, and even, for their own purposes, unnecessary, and that the physicist did good service in reducing them. It may also be freely admitted that the latest conclusions, from physical considerations of the extent of geological time, require that the interpretation given to the record of the rocks should be rigorously revised, with the view of ascertaining how far that interpretation may be capable of modification or amendment. But we must also remember that the geological record constitutes a voluminous body of evidence regarding the earth’s history which cannot be ignored, and must be explained in accordance with ascertained natural laws. If the conclusions derived from the most careful study of this record cannot be reconciled with those drawn from physical considerations, it is surely not too much to ask that the latter should be also revised. It was well said by Huxley that the mathematical mill is an admirable piece of machinery, but that the value of what it yields depends upon the quality of what is put into it. That there must be some flaw in the physical argument I can, for my own part, hardly doubt, though I do not pretend to be able to say where it is to be found. Some assumption, it seems to me, has been made, or some consideration has been left out of sight, which will eventually be seen to vitiate the conclusions, and which when duly taken into account will allow time enough for any reasonable interpretation of the geological record.

When Kelvin doubled down, Geike escalated to match him, pointing out John Perry's physics-based dissent and returning to the geologic evidence:

It is difficult satisfactorily to carry on a discussion in which your opponent entirely ignores your arguments, while you have given the fullest attention to his. In the present instance, geologists have most carefully listened to all that has been brought forward from the physical side. Impressed by the force of the physical reasoning, they no longer believe that they can make any demands they may please on past time. [...] Yet there is undoubtedly a prevalent misgiving, whether in thus seeking to reconcile their requirements with the demands of the physicist they are not tying themselves down within limits of time which on any theory of evolution would have been insufficient for the development of the animal and vegetable kingdoms. [...]

So cogent do these geological and palæontological arguments appear, to those at least who have taken the trouble to master them, that they are worthy of being employed, not in defence merely, but in attack. It seems to me that they may be used with effect in assailing the stronghold of speculation and assumption in which our physical friends have ensconced themselves and from which, with their feet, as they believe, planted well within the interior of the globe and their heads in the heart of the sun, they view with complete unconcern the efforts made by those who endeavour to gather the truth from the surface and crust of the earth. That portion of the records of terrestrial history which lies open to our investigation has been diligently studied in all parts of the world. A vast body of facts has been gathered together from this extended and combined research. The chronicle registered in the earth’s crust, though not complete, is legible and consistent. From the latest to the earliest of its chapters the story is capable of clear and harmonious interpretation by a comparison of its pages with the present condition of things. We know infinitely more of the history of this earth than we do of the history of the sun. Are we then to be told that this knowledge so patiently accumulated from innumerable observations and so laboriously co-ordinated and classified, is to be held of none account in comparison with the conclusions of physical science in regard to the history of the central luminary of our system? These conclusions are founded on assumptions which may or may not correspond with the truth. They have already undergone revision, and they may be still further modified as our slender knowledge of the sun, and of the details of its history, is increased by future investigation. In the meantime, we decline to accept them as a final pronouncement of science on the subject. We place over against them the evidence of geology and palæontology, and affirm that unless the deductions we draw from that evidence can be disproved, we are entitled to maintain them as entirely borne out by the testimony of the rocks.

Lord Kelvin's Monkey, 3

Kelvin's firm misguidance was no anomaly. As recounted by geologists Jeff Dodick and Nir Orion, mathematical physics has laid down the (dubious) law from James Hutton's perfectly Newtonian balance to Harold Jeffreys' proof that continents couldn't move. Underlying the law-laying was a hierarchy decided more by political than material realities: deduction from established premises encourages certainty; allowing a choice of narratives does not; in battles for dominance, certainty beats admitted fallibility.

Still, the historical sciences remain, for lack of a better word, "science": explicable, falsifiable, and governed by empiricism; agreeing on valid evidence, systematizing that evidence, and working toward (or against) consensus that the systematization matches the evidence in a worthwhile way.

"Soft" (that is, specifically human) sciences such as sociology and psychology should sit higher in the hierarchy of certainty insofar as they announce quantified generalizations which allow ample wiggle room for exceptions and can be tested at will by the generation of new evidence. Unfortunately, the result of regeneration's been a replication crisis. A labile pattern-making species will have no trouble finding patterns when it introspects. Isolating and stabilizing them is another story, and another.

Where does the intersection of "historical" and "soft" fit on this scientistic scale?

In 1852, Thomson contented himself by saying that a restoration of energy is “probably” never effected by organized matter. In 1910, there is nothing “probable” about it; the fact has become an axiom of biology. In 1852, any University professor would have answered this quotation by the dry remark that society was not an organism, and that history was not a science, since it could not be treated mathematically. Today, M. Bernhard Brunhes seems to feel no doubt that society is an organism [...] As an Organism society has always been peculiarly subject to degradation of Energy, and alike the historians and the physicists invariably stretch Kelvin's law over all organized matter whatever.

- A Letter to American Teachers of History by Henry Adams

In Adams's terms, I expect most of us have reverted to 1852. Inside the blip of human existence the crawl from Big Bang towards Big Lukewarm is barely detectable. Our sun is slowly expanding, not quickly shrinking, and by the time it blossoms no humans will be lolling on a beach to catch the rays. Narrative history incorporates more statistical analysis than it used to but hasn't become "mathematical" in a predictive or formulaic sense except when packaged as propaganda.

Instead of history hardening, sciences may have softened. The organism and the species have become more permeable and pluralistic concepts, and even the inorganic sciences have repeatedly struck limits on their ability to predict and control outcomes. Avoiding the over-trampled murk of post-Bohr physics, let's take the mundane field of meteorology as an example.

High on the success of their nuclear bomb simulations, post-WWII mathematicians, physicists, and engineers tackled weather as both natural threat and potential weapon, only to be halted at a durational border. Daily and weekly regional weather forecasts can be drastically improved by tracking technologies and computer analysis. And we seem able to make some broad generalizations about global climate trends. But the territory between is unmappable:

If Laplace’s mathematical intelligence were replaced by a computing machine of unlimited speed and capacity, and if the atmosphere below 100km were spanned by a computational lattice whose mesh size were less than the scale of the smallest turbulent eddy, say one millimeter… [all predictions would prove inaccurate within a month] not because of quantum indeterminacy, or even because of macroscopic errors of observation, but because the errors introduced into the smallest turbulent eddies by random fluctuations on the scale of the mean free path (ca 10-5mm at sea level), although very small initally, would grow exponentially… The error progresses from 1mm to 10km in less than one day, and from 100km to the planetary scale in a week or two.

- Jule Charney and Walter Munk, Institute for Advanced Study, 1972

Although history hasn't become the sort of "real" science Henry Adams had in mind, could it attain the relatively respectable status of a latter-day historical science? After all, like geologists and paleontologists, human-historians attempt plausible guesses at the service and the mercy of whatever evidence happens to turn up, no matter how irreversible, indeterminate, incomplete, or inconvenient it might be. Models tend to be narrative rather than timeless formulae, deductive along the lines of Sherlock Holmes rather than Euclid, attentive to anomalies rather than discarding them as noise. Any universally applicable systematization threatens to become a map larger and more rigid than the territory itself. Instead, simpler models of causality accrete with no clear way to quantify their relative effects.

I suppose, as with most such categorizations, it's a matter of degrees. In a (human) chronicle or history, outliers are even more likely to play leading roles. And since it's almost unheard of for us to perform any halfway complex action for only one reason, Ockham's Razor is more likely to maim than reveal, and potential models proliferate. Over the long run historians can provide as verifiable a prediction and exhaustive a summary as any lab report: "Everyone died." In the meantime, irreducible ambiguities and the tides, currents, backwaters, eddies, and catastrophes of human culture block most hope of objectively settled generalizations.

Which makes "history as a science" look an awful lot like the sort of history Henry Adams actually practiced: attentive to a wide range of evidence, aware of competing models, straightforward about his choices, and uncomfortably aware that his impressively coherent narratives might at any time be shattered by new or revived or rejected evidence, or swept away by an attractively novel interpretive angle, or might unknowably be built on little better than noise.

That may sound discouraging, but it's just another way of saying "Everyone hasn't died yet." Carry on, historian!

Lord Kelvin's Monkey, conclusion

He [the historian] was therefore obliged either to deny that social energy was an energy at all; or to assert that it was an energy independent of physical laws. Yet how could he deny that social energy was a true form of energy when he had no reason for existence, as professor, except to describe and discuss its acts? He could neither doubt nor dispute its existence without putting an end to his own; and therefore he was of necessity a Vitalist, or adherent of the doctrine that Vital Energy was independent of mechanical law.

- A Letter to American Teachers of History by Henry Adams

Science circa 1900 taught that orgasms shortened lifespans and that thinking was unhealthy for women. Popular and academic presses were full of confident (if conflicting) and well-credentialed (if unfounded) pronouncements about Will and Vital Energy and Racial Degeneration. Evolution implied progress toward perfection, organisms were treated as if they were (ideally) closed systems, and social phenomena were theorized as chemical or mechanical phenomena.

In later decades straying humanists would be unattractively preserved by coats of Freud, Jung, Marxist millennialism, behaviorism, computer science, or the remnants of evolutionist-determinism. Science circa 1900 was the particular tarpit proffered to Adams, and he obediently submerged himself.

The posthumous result for him, like other interdisciplinary victims, was (a bit unfairly) unflattering. His bold 1 stuck-in-the-tar attempts to future-proof historiography now stiffen somewhere between tedious and offensive, whereas the dull stick-in-the-mud particulars of his political histories, art histories, and personal histories seem almost as vital as ever.

Out of his depth or not, Adams remained a brilliant writer and a clever thinker. Some of Adams's many prognostications of calamity happened to hit on genuinely calamitous years,2 and similarly some of the Letter's remarks still strike a spark:

For purposes of teaching, the figure is alone essential, and the figure of Rise and Fall has done infinite harm from the beginnings of thought. That of Expansion and Contraction is far more scientific, even in history. Evolution, again, is troublesome, and has already yielded to the less compromising figure of Transformation. Expansion and Transformation are words which commit teachers to no inconvenient dogma; indeed, they are so happily adapted for Galileos who are wise enough not to shock opinion, that they seem to impose themselves on the lecture-room.

...

Matter indeed, is energy itself, and its economies first made organic life possible by thus correcting nature's tendency to waste.

And he sketched one development as straightforwardly as anyone might.

Oftentimes processes which can't be precisely controlled to produce precisely predictable outcomes can be radically disrupted to produce grossly foreseeable catastrophes. Burning a library or museum, for example, is an experiment whose result is far more certain and far less costly than waiting out centuries of writing, painting, and sculpting would be.

Changes in human culture aren't micromanaged by the Second Law of Thermodynamics or by biological evolution, but human culture can easily make both of them more perceptible. To return to meteorology:

Probably intervention in atmospheric and climatic matters will come in a few decades, and will unfold on a scale difficult to imagine at present. [...] Such actions would be more directly and truly worldwide than recent or, presumably, future wars, or than the economy at any time. Extensive human intervention would deeply affect the atmosphere's general circulation, which depends on the earth's rotation and intensive solar heating of the tropics. Measures in the arctic may control the weather in temperate regions, or measures in one temperate region critically affect another, one quarter around the globe. All this will merge each nation's affairs with those of every other, more thoroughly than the threat of a nuclear or any other war may already have done.

- "Can We Survive Technology?" by John von Neumann, 1955

Neumann wrote those words about the prospect of intentional intervention, but they apply just as well to the unplanned intervention mentioned elsewhere in his essay:

The carbon dioxide released into the atmosphere by industry's burning of coal and oil — more than half of it during the last generation — may have changed the atmosphere's composition sufficiently to account for a general warming of the world by about one degree Fahrenheit.

Or, as Adams phrased it forty-five years earlier:

From the physicist’s point of view, Man, as a conscious and constant, single, natural force, seems to have no function except that of dissipating or degrading energy. Indeed, the evolutionist himself has complained, and is still complaining in accents which grow shriller every day, that man does more to dissipate and waste nature s economies than all the rest of animal or vegetable life has ever done to save them. “Already,”— one may hear the physicists aver —“man dissipates every year all the heat stored in a thousand million tons of coal which nature herself cannot now replace, and he does this only in order to convert some ten or fifteen per cent, of it into mechanical energy immediately wasted on his transient and commonly purpose less objects. He draws great reservoirs of coal-oil and gas out of the earth, which he consumes like the coal. He is digging out even the peat-bogs in order to consume them as heat. He has largely deforested the planet, and hastened its desiccation. He seizes all the zinc and whatever other minerals he can burn, or which he can convert into other forms of energy, and dissipate into space. His consumption of oxygen would be proportionate to his waste of heat. He startles and shocks even himself, in his rational moments, by his extravagance, as in his armies and armaments which are made avowedly for no other purpose than to dissipate or degrade energy, or annihilate it as in the destruction of life, on a scale that rivals operations of nature. What is still more curious, his chief pleasures, so far as they are his own invention, consist in gratifying the same unintelligent passion for dissipating or degrading energy, as in drinking alcohol, or burning fireworks, or firing cannon, or illuminating cities, or deafening them by senseless noises. Worse than all, such is his instinct of destruction that he systematically exterminates or degrades all the larger forms of animal life in which nature stored her last creative efforts, while he breeds artificially, at great expense of his own energies, and at cost of the phosphorus and lime accumulated by nature’s mostly extinct organisms, the feebler forms of animal and vegetable energies needed to make good the prodigious waste of his own. Physicists and physiologists equally complain of these tendencies in man, and a large part of their effort is now devoted to correcting them; but the physicist adds that, compared with this enormous mass of nature’s economies which man dissipates every year in rapid progression, the little he captures from the sun, directly or indirectly, as heat-rays, or water-power, or wind-power, is trifling, and the portion that he restores to higher intensities would be insignificant in any case, even if he did not instantly degrade and dissipate it again for some momentary use.” [...] The sun can keep up its expenditure indefinitely, subject to occasional fits of economy; while man is a bottomless sink of waste unparalleled in the cosmos, and can already see the end of the immense economies which his mother Nature stored for his support.