In order to bridge the yawning gulf between the humanities and the sciences, Gordon Gillespie suggests, we must turn to an unexpected field: mathematics…
In 1959, the English writer and physicist C P Snow delivered the esteemed Rede Lecture at the University of Cambridge [a talk now known as “The Two Cultures,” see here]. Regaled with champagne and Marmite sandwiches, the audience had no idea that they were about to be read the riot act. Snow diagnosed a rift of mutual ignorance in the intellectual world of the West. On the one hand were the ‘literary intellectuals’ (of the humanities) and on the other the (natural) ‘scientists’: the much-discussed ‘two cultures’. Snow substantiated his diagnosis with anecdotes of respected literary intellectuals who complained about the illiteracy of the scientists but who themselves had never heard of such a fundamental statement as the second law of thermodynamics. And he told of brilliant scientific minds who might know a lot about the second law but were barely up to the task of reading Charles Dickens, let alone an ‘esoteric, tangled and dubiously rewarding writer … like Rainer Maria Rilke.’
Sixty-plus years after Snow’s diatribe, the rift has hardly narrowed. Off the record, most natural scientists still consider the humanities to be a pseudo-science that lacks elementary epistemic standards. In a 2016 talk, the renowned theoretical physicist Carlo Rovelli lamented ‘the current anti-philosophical ideology’. And he quoted eminent colleagues such as the Nobel laureate Steven Weinberg, Stephen Hawking and Neil deGrasse Tyson, who agreed that ‘philosophy is dead’ and that only the natural sciences could explain how the world works, not ‘what you can deduce from your armchair’. Meanwhile, many humanities scholars see scientists as pedantic surveyors of nature, who may produce practical and useful results, but are blind to the truly deep insights about the workings of the (cultural) world. In his best-selling book The Fate of Rome (2017), Kyle Harper convincingly showed that a changing climate and diseases were major factors contributing to the final fall of the Roman Empire. The majority of Harper’s fellow historians had simply neglected such factors up to then; they had instead focused solely on the cultural, political and socioeconomic ones…
The divide between the two cultures is not just an academic affair. It is, more importantly, about two opposing views on the fundamental connection between mind and nature. According to one view, nature is governed by an all-encompassing system of laws. This image underlies the explanatory paradigm of causal determination by elementary forces. As physics became the leading science in the 19th century, the causal paradigm was more and more seen as the universal form of explanation. Nothing real fell outside its purview. According to this view, every phenomenon can be explained by a more or less complex causal chain (or web), the links of which can, in turn, be traced back, in principle, to basic natural forces. Anything – including any aspect of the human mind – that eludes this explanatory paradigm is simply not part of the real world, just like the ‘omens’ of superstition or the ‘astral projections’ of astrology.
On the opposing view, the human mind – be it that of individuals or collectives – can very well be regarded separately from its physical foundations. Of course, it is conceded that the mind cannot work without the brain, so it is not entirely independent of natural forces and their dynamics. But events of cultural significance can be explained as effects of very different kinds of causes, namely psychological and social, that operate in a sphere quite separate from that of the natural forces.
These divergent understandings underpin the worldviews of each culture. Naive realists – primarily natural scientists – like to point out that nature existed long before humankind. Nature is ordered according to laws that operate regardless of whether or not humans are around to observe. So the natural order of the world must be predetermined independently of the human mind. Conversely, naive idealists – including social constructivists, mostly encountered in the humanities – insist that all order is conceptual order, which is based solely on individual or collective thought. As such, order is not only not independent of the human mind, it’s also ambiguous, just as the human mind is ambiguous in its diverse cultural manifestations.
The clash of cultures between the humanities and the natural sciences is reignited over and over because of two images that portray the interrelationship of mind and nature very differently. To achieve peace between the two cultures, we need to overcome both views. We must recognise that the natural and the mental order of things go hand in hand. Neither can be fully understood without the other. And neither can be traced back to the other…
… The best mediator of a conciliatory view that avoids the mistake of the naive realist and the naive idealist is mathematics. Mathematics gives us shining proof that understanding some aspect of the world does not always come down to uncovering some intricate causal web, not even in principle. Determination is not explanation. And mathematics, rightly understood, demonstrates this in a manner that lets us clearly see the mutual dependency of mind and nature.
For mathematical explanations are structural, not causal. Mathematics lets us understand aspects of the world that are just as real as the Northern Lights or people’s behaviour, but are not effects of any causes. The distinction between causal and structural forms of explanation will become clearer in due course. For a start, take this example. Think of a dying father who wants to pass on his one possession, a herd of 17 goats, evenly to his three sons. He can’t do so. This is not the case because some hidden physical or psychological forces hinder any such action. The reason is simply that 17 is a prime number, so not divisible by three…
… In his ‘two cultures’ speech, Snow located mathematics clearly in the camp of the sciences. But… mathematics doesn’t adhere to the explanatory paradigm of causal determination. This distinguishes it from the natural sciences. Nevertheless, mathematics tells us a lot about nature. According to Kant, it does so because it tells us a lot about the human mind. Mind and nature are inseparable facets of the world we inhabit and conceive. So, why should the humanities not also count as a science? They can tell us just as much about that one world on a fundamental level as the natural sciences. Mathematics demonstrates this clearly…
… Mathematics undermines the causal explanatory paradigm not only in its natural scientific manifestations, but also in its uses in the humanities. We give explanations for a wide variety of phenomena by hidden causes way too often and way too fast, where the simple admission to having no explanation would not only be more honest, but also wiser. Wittgenstein spoke of the disease of wanting to explain. This disease shows itself not just in our private everyday exchanges and in the usual public debates, but also in scholarly discourse of the humanities. When confronted with individual or collective human thinking and behaviour, it is tempting to assume just a few underlying factors responsible for the thinking and behaviour. But, more often than not, there really is no such neat, analysable set of factors. Instead, there is a vast number of natural, psychological and societal factors that are all equally relevant for the emergence of the phenomenon one wants to explain. Perhaps a high-end computer could incorporate all these factors in a grand simulation. But a simulation is not an explanation. A simulation allows us to predict, but it doesn’t let us understand.
The aim of the humanities should not be to identify causes for every phenomenon they investigate. The rise and fall of empires, the economic and social ramifications of significant technological innovations, the cultural impact of great works of art are often products of irreducibly complex, chaotic processes. In such cases, trying to mimic the natural sciences by stipulating some major determining factors is a futile and misleading endeavour.
But mathematics shows that beyond the causal chaos there can be order of a different kind. The central limit theorem lets us see and explain a common regularity in a wide range of causally very different, but equally complex, natural processes. With this and many other examples of structural mathematical explanations of phenomena in the realm of the natural sciences in mind, it seems plausible that mathematical, or mathematically inspired, abstraction can also have fruitful applications in the humanities.
This is by no means meant to promote an uncritical imitation of mathematics in the humanities and social sciences. (The overabundance of simplistic econometric models, for instance, is a huge warning sign.) Rather, it is meant to motivate scholars in these fields to reflect more upon where and when causal explanations make sense. Complexity can’t always be reduced to a graspable causal explanation, or narrative. To the contrary, often the most enlightening enquiries are not those that propose new factors as the true explainers, but those that show by meticulous analysis that far more factors are crucially in play than previously thought. This, in turn, should motivate scholars to seek aspects of their subject of interest beyond causality that are both relevant and amenable to structural forms of explanation. Besides probability theory, chaos theoretical methods and game theory come to mind as mathematical sub-disciplines with potentially fruitful applications in this regard.
However, the main point of our discussion is not that mathematical applications in the humanities might bridge the gap between the natural sciences and the humanities. The point is that mathematics, not really belonging to either camp, shows them to be on an equal footing from the start. The natural scientific paradigm of explanation is not the role model any respectable form of enquiry has to follow. Mathematics shows that natural causes can’t explain every phenomenon, not even every natural phenomenon and not even in principle. So, there is no need for the humanities, the ‘sciences of the mind’, to always strive for explanations by causes that can be ‘reduced’ to more elementary, natural forces. Moreover, mathematics shows that causality, of any kind, is not the only possible basis on which any form of explanation ultimately has to stand. Take for example the semantic relationships between many of our utterances. It is not at all clear that these can be explained in terms of psychological causes, or any other causes. It is not unreasonable to believe that the world is irreducibly structured, in part, by semantic relations, just as it is structured by probabilistic relations…
… The divide between the natural sciences and the humanities does not stem from the supposed fact that only those mental phenomena are real that are explainable in natural-scientific terms. Nor is the divide due to some extra-natural mental order, determined by causal relationships of a very different kind than those studied in the natural sciences. The mental world and the physical world are one and the same world, and the respective sciences deal with different aspects of this one world. Properly understood, insofar as they deal with the same phenomena, they do not provide competing but complementary descriptions of these phenomena.
Mathematics provides the most impressive proof that a true understanding of the world goes beyond the discovery of causal relationships – whether they are constituted by natural or cultural forces. It is worth taking a closer look at this proof. For it outlines the bond that connects mind and nature in particularly bright colours. Kant understood this bond as a ‘transcendental’ one. The late Wittgenstein, on the other hand, demonstrated its anchoring in language – not in the sense of a purely verbal and written practice, but in the sense of a comprehensive practice of actions the mental and bodily elements of which cannot be neatly separated. In the words of Wittgenstein, ‘commanding, questioning, recounting, chatting are as much a part of our natural history as walking, eating, drinking, and playing.’
Mathematics too is part of this practice. As such, like every science, it is inseparably rooted in both nature and the human mind. Unlike the other sciences, this dual rootedness is obvious in the case of mathematics. One only has to see where it resides: beyond causality.
* C. P. Snow, The Two Culturesand the Scientific Revolution
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As we come together, we might send carefully calculated birthday greetings to a man with a foot in each culture: Frank Plumpton Ramsey; he was born on this date in 1903. A philosopher, mathematician, and economist, he made major contributions to all three fields before his death (at the age of 26) on this date in 1930.
While he is probably best remembered as a mathematician and logician and as Wittgenstein’s friend and translator, he wrote three paper in economics: on subjective probability and utility (a response to Keynes, 1926), on optimal taxation (1927, described by Joseph E. Stiglitz as “a landmark in the economics of public finance”), and optimal economic growth (1928; hailed by Keynes as “”one of the most remarkable contributions to mathematical economics ever made”). The economist Paul Samuelson described them in 1970 as “three great legacies – legacies that were for the most part mere by-products of his major interest in the foundations of mathematics and knowledge.”
From Liber Divinorum Operum (The Book of Divine Works) by Hildegard von Bingen, composed between 1163 and 1174
The quote above (in full, below) is the reigning substantive understanding of scientific naturalism that is commonplace today. Indeed, the modern era is often seen as the triumph of science over supernaturalism. But, as Peter Harrison explains, what really happened is far more interesting…
By any measure, the scientific revolution of the 17th century was a significant milestone in the emergence of our modern secular age. This remarkable historical moment is often understood as science finally liberating itself from the strictures of medieval religion, striking out on a new path that eschewed theological explanations and focused its attentions solely on a disenchanted, natural world. But this version of events is, at best, half true.
Medieval science, broadly speaking, had followed Aristotle in seeking explanations in terms of the inherent causal properties of natural things. God was certainly involved, at least to the extent that he had originally invested things with their natural properties and was said to ‘concur’ with their usual operations. Yet the natural world had its own agency. Beginning in the 17th century, the French philosopher and scientist René Descartes and his fellow intellectual revolutionaries dispensed with the idea of internal powers and virtues. They divested natural objects of inherent causal powers and attributed all motion and change in the universe directly to natural laws.
But, for all their transformative influence, key agents in the scientific revolution such as Descartes, Johannes Kepler, Robert Boyle and Isaac Newton are not our modern and secular forebears. They did not share our contemporary understandings of the natural or our idea of ‘laws of nature’ that we imagine underpins that naturalism…
[Harrison traces the history of the often contentious, but ultimately momentous rise of naturalism, then considers the historical acounts of that ascension– and what they gloss over or miss altogether. He then turns to whay that matters…]
… the contrived histories of naturalism that purport to show its victory over supernaturalism were fabricated in the 19th century and are simply not consistent with the historical evidence. They are also tainted by a cultural condescension that, in the past at least, descended into outright racism. Few, if any, would today endorse the chauvinism that attends these older, triumphalist accounts of the history of naturalism. Yet, it is worth reflecting upon the extent to which elements of cultural condescension necessarily colour scholarly endeavours that are premised on the imagined ‘neutral’ grounds of naturalism. Careful consideration of the contingent historical circumstances that gave rise to present analytic categories that enjoy significant standing and authority would suggest that there is nothing especially neutral or objective about them. Any clear-eyed crosscultural comparison – one that refrains from assessing worldviews in terms of how they measure up to the standard of the modern West – will reinforce this. We might go so far as to adopt a form of ‘reverse anthropology’, where we think how our own conceptions of the world might look if we adopted the frameworks of others. This might entail dispensing with the idea of the supernatural, and attempting to think outside the box of our recently inherited natural/supernatural distinction.
History [that is, the “actual” history that Harrison recounts] suggests that our regnant modern naturalism is deeply indebted to monotheism, and that its adherents may need to abandon the comforting idea that their naturalistic commitments are licensed by the success of science. As for the idea of the supernatural, ironically this turns out to be far more important for the identity of those who wish to deny its reality than it had ever been for traditional religious believers…
* “There is only one world, the natural world, exhibiting patterns we call the ‘laws of nature’, and which is discoverable by the methods of science and empirical investigation. There is no separate realm of the supernatural, spiritual, or divine; nor is there any cosmic teleology or transcendent purpose inherent in the nature of the universe or in human life.” – Sean Carroll, The Big Picture
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As we rethink reality, we might recall that it was on this date in 1588 that Tycho Brahe first outlined his “Tychonic system” concept of the structure of the solar system. The Tychonic system was a hybrid, sharing both the basic idea of the geocentric system of Ptolemy, and the heliocentric idea of Nicholas Copernicus. Published in his De mundi aethorei recentioribus phaenomenis, Tycho’s proposal, retaining Aristotelian physics, kept the the Sun and Moon revolving about Earth in the center of the universe and, at a great distance, the shell of the fixed stars was centered on the Earth. But like Copernicus, he agreed that Mercury, Venus, Mars, Jupiter, and Saturn revolved about the Sun. Thus he could explain the motions of the heavens without “crystal spheres” carrying the planets through complex Ptolemaic epicycles.
A 17th century illustration of the Hypothesis Tychonica (source)
On this same date, in 1633, Galileo Galilei arrived in Rome to face trial before the Inquisition. His crime was professing the belief that the earth revolves around the sun– based on observations that he’d made further to Copernicus and Tycho.
How do creatives – composers, painters, writers, scientists, philosophers – find the time to produce their opus?
Each routine day is represented as a continuous 24 hour cycle. Midnight is placed at 12 o’clock position and noon at 6 o’clock. Colors mark major categories of activity including work, sleep, and exercise…
As we contemplate cultivating customs, we might send learned birthday greetings to Desiderius Erasmus Roterodamus, better known simply as Erasmus; he was born on this date in 1466. A Catholic priest, social critic, teacher, translator, and theologian, probably best remembered for his book In Praise of Folly, he was the greatest scholar of the northern Renaissance, the first editor of the New Testament (“Do unto others…”), and an important figure in patristics and classical literature.
Erasmus had contrasting experiences of routine: on being orphaned, Erasmus was sent to a series of monastic or semi-monastic schools, which he despised both for their discipline and for their disdain of inquiry. Graduating with few prospects, he joined an Augustinian monastery where he considered his superiors “barbarians” discouraging his classical studies. On ordination, he escaped– and began a career that began in struggle (as he balanced the demands of study with those of serving as a Clerk, and Priest, a tutor… all while trying to distinguish himself as a poet.
His luck changed in 1499, when he connected with a reformist English circle (notably John Colet and Thomas More), then with radical French Franciscan Jean Vitrier, and later with the Aldine New Academy in Venice… which led, in the Reformation, to his emergence as a prime influencer of European thought. Among fellow scholars and philosophers of that era he was– and is still– known as the “Prince of the Humanists.”
Erasmus’ views were contentious on his time and elicited a good bit of criticism. While we don’t know too much about his daily routine, we do know that for the last half of his life it included enough time on a regular basis to read these attacks and to prepare and publish apologetic works in his own defense, in many cases leading to a long series of back-and-forth polemical books… kind of like Twitter feud, but at the speed of Gutenberg.
Portrait of Erasmus of Rotterdam (1523) by Hans Holbein the Younger
But perhaps some of these concerns are simply Western preoccupations, rather than universal human concerns?
In the recent book Fluke (which is fantastic! [your correspondent heartily agrees]), Brian Klaas noted the following provocative point about differences between Western and Eastern thinking—and their views on human distinctness—and how it might have been due to the ecological milieu that each one arose from:
In this vision of a world humans are distinct from the rest of the natural world. That felt true for the inhabitants of the Middle East and Europe around the time of the birth of Christianity. Camels, cows, goats, mice, and dogs composed much of the encountered animal kingdom, a living menagerie of the beings that are quite unlike us.
In many Eastern cultures, by contrast, ancient religions tended to emphasize our unity with the natural world. One theory suggests that was partly because people lived among monkeys and apes. We recognized ourselves in them. As the biologist Roland Ennos points out, the word orangutan even means “man of the forest.” Hinduism has Hanumen, a monkey god. In China, the Chu kingdom revered gibbons. In these familiar primates, the theory suggests, it became impossible to ignore that we were part of nature—and nature was part of us.
This is almost a Guns, Germs, and Steel-kind of approach, but for ideas. At the risk of creating too much determinism here, it’s intriguing to explore the path dependence of ideas and concepts that organize how we think about the world and ourselves.
This reminds me of other research that examined how small historical distinctions can still affect our modern world, even if they are no longer relevant. For example, there is research that looks at how certain locations betray their histories as portage sites—places where boats or cargo were transported over land, allowing travel between more traversable waterways—despite this being obsolete. And yet it still has a certain long-term effect, as per this paper “Portage and Path Dependence”:
In the end, simply being more aware of the ideas and history that suffuse our thinking—rather than taking them for granted—is something important, whether or not we are trying to understand humanity’s place in the world, how technology should impact humanity, or why cities are located where they are…
As we ruminate on the roots of our (received) realities, we might recall that it was on this date in 3 BCE that a planetary conjunction of Jupiter and Venus was visible… and may have been the Star of Bethlehem mentioned in the New Testament.
In this pre-dawn, “morning star” conjunction, the two planets appeared very close to each other in the sky (a mere 0.07° apart as viewed from Earth). It occurred when the planets were in the last degrees of the zodiacal sign of Cancer which was the concluding sign for interpreting that astrological year. The same two planets met again just ten months later (June 17, 2 BCE), even more closely, almost touching (0.01°), in an “evening star” conjunction in the first degrees of Leo, the beginning sign of the new astrological year. These two unions of Jupiter and Venus might well have been interpreted as the close of one age in history and the beginning of another age in 2 BCE.
For more on these conjunctions and other potential candidates for “historical Star of Bethlehem” (and an explanation of how/why the astronomers/astrologers who sighted the star became Magi/Wise Men in Church teaching) see here.
A photo of the most recent conjunction, 2023 (source)
The estimable Ted Gioia is exploring the possibility that we are at the cusp of a major change in the zeitgeist– the beginning of a new age of Romanticism…
I made a flippant remark a few months ago. It was almost a joke.
But then I started taking it seriously.
I said that technocracy had grown so oppressive and manipulative it would spur a backlash. And that our rebellion might resemble the Romanticist movement of the early 1800s.
We need a new Romanticism, I quipped. And we will probably get one.
A new Romanticism? Could that really happen? That seems so unlikely.
Even I didn’t take this seriously (at first). I was just joking. But during the subsequent weeks and months, I kept thinking about my half-serious claim.
I realized that, the more I looked at what happened circa 1800, the more it reminded me of our current malaise.
Rationalist and algorithmic models were dominating every sphere of life at that midpoint in the Industrial Revolution—and people started resisting the forces of progress.
Companies grew more powerful, promising productivity and prosperity. But Blake called them “dark Satanic mills” and Luddites started burning down factories—a drastic and futile step, almost the equivalent of throwing away your smartphone.
Even as science and technology produced amazing results, dysfunctional behaviors sprang up everywhere. The pathbreaking literary works from the late 1700s reveal the dark side of the pervasive techno-optimism—Goethe’s novel about Werther’s suicide, the Marquis de Sade’s nasty stories, and all those gloomy Gothic novels. What happened to the Enlightenment?
As the new century dawned, the creative class (as we would call it today) increasingly attacked rationalist currents that had somehow morphed into violent, intrusive forces in their lives—an 180 degree shift in the culture. For Blake and others, the name Newton became a term of abuse.
Artists, especially poets and musicians, took the lead in this revolt. They celebrated human feeling and emotional attachments—embracing them as more trustworthy, more flexible, more desirable than technology, profits, and cold calculation.
That’s the world, circa 1800.
The new paradigm shocked Europe when it started to spread. Cultural elites had just assumed that science and reason would control everything in the future. But that wasn’t how it played out.
Resemblances with the current moment are not hard to see.
These considerations led me, about nine months ago, to conduct a deep dive into the history of the Romanticist movement. I wanted to see what the historical evidence told me.
…
I’m now structuring my research in chronological order—that’s a method I often use in addressing big topics.
I make no great promises for what I share below. These are just notes on what happened in Western culture from 1800 to 1804—listed year-by-year.
Sharing these is part of my process. I expect this will generate useful feedback, and guide me on the next phase of this project…
Because music is always my entry point into cultural changes, it plays a key role here in how I analyze past (and present) events. I firmly believe that music is an early indicator of social change. The notes below are offered as evidence in support of that view…
[There follows a fascinating– and compelling– account of those five years, featuring Napoleon, Haydn, Beethoven, Woodsworth, Coleridge, Herder, Schelling, the Marquis de Sade, Novalis, Ann Radcliffe, and others]
… Beethoven turns against Napoleon—and this is emblematic of the aesthetic reversal sweeping through Europe. Not long ago, Beethoven and other artists looked to French rationalism as a harbinger of a new age of freedom and individual flourishing. But this entire progress-obsessed ideology is unraveling.
It’s somehow fitting that music takes the lead role in deconstructing a tyrannical rationalism, and proposing a more human alternative.
Could that happen again?
Imagine a growing sense that algorithmic and mechanistic thinking has become too oppressive.
Imagine if people started resisting technology as a malicious form of control, and not a pathway to liberation, empowerment, and human flourishing—soul-nurturing riches that must come from someplace deeper.
Imagine a revolt against STEM’s dominance and dictatorship over all other fields?
Imagine people deciding that the good life starts with NOT learning how to code.
If that happened now, wouldn’t music stand out as the pathway? What could possibly be more opposed to brutal rationalism running out of control than a song?
But what does that kind of music sound like? In 1800, it was Beethoven. And today?…
As we review vibes on the verge, we might send rational birthday greetings to an avatar of the Enlightenment against which the Romantics rebelled, Francois-Marie Arouet, better known as Voltaire; he was born on this date in 1694. The Father of the Age of Reason, he produced works in almost every literary form: plays, poems, novels, essays, and historical and scientific works– more than 2,000 books and pamphlets (and more than 20,000 letters). He popularized Isaac Newton’s work in France by arranging a translation of Principia Mathematica to which he added his own commentary.
A social reformer, Voltaire used satire to criticize the intolerance, religious dogma, and oligopolistic privilege of his day, perhaps nowhere more sardonically than in Candide.
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