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.”
After two days of posts on the state of our civil society, a palette-cleanser: Jordana Cepelewicz with a possibly-consoling reminder…
When he died in 1930 at just 26 years old, Frank Ramsey [see here] had already made transformative contributions to philosophy, economics and mathematics. John Maynard Keynes sought his insights; Ludwig Wittgenstein admired him and considered him a close friend. In his lifetime, Ramsey published only eight pages on pure math: the beginning of a paper about a problem in logic. But in that work, he proved a theorem that ultimately led to a whole new branch of mathematics — what would later be called Ramsey theory.
His theorem stated that if a system is large enough, then no matter how disordered it might be, it’s always bound to exhibit some sort of regular structure. Order inevitably emerges from chaos; patterns are unavoidable. Ramsey theory is the study of when this happens — in sets of numbers, in collections of vertices and edges called graphs, and in other systems. The mathematicians Ronald Graham and Joel Spencer likened it to how you can always pick out patterns among the stars in the night sky…
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… In fact, Ramsey theory isn’t just about inevitable patterns found in graphs. Hidden structure emerges in lists of numbers, strings of beads and even card games. In 2019, for example, mathematicians studied collections of sets that can always be arranged to resemble the petals of a sunflower. That same year, Quantareported on research into sets of numbers that are guaranteed to contain numerical patterns called polynomial progressions. And last year, mathematicians proved a similar result, about sets of integers that must always include three evenly spaced numbers, called arithmetic progressions.
In its hunt for patterns, Ramsey theory gets to the core of what mathematics is all about: finding beauty and order in the most unexpected places…
As we ponder patterns, we might send paradigm-shaping birthday greetings to a woman who found order and pattern of a different– and world-changing– sort: Rosalind Franklin; she was born on this date in 1920. A biophysicist and X-ray crystallographer, Franklin captured the X-ray diffraction images of DNA that were, in the words of Francis Crick, “the data we actually used” when he and James Watson developed their “double helix” hypothesis for the structure of DNA. Indeed, it was Franklin who argued to Crick and Watson that the backbones of the molecule had to be on the outside (something that neither they nor their competitor in the race to understand DNA, Linus Pauling, had understood). Franklin never received the recognition she deserved for her independent work– her paper was published in Nature after Crick and Watson’s, which barely mentioned her– and she died of cancer four years before Crick, Watson, and their lab director Maurice Wilkins won the Nobel Prize for the discovery.
Further, in a fashion, to yesterday’s post: the estimable Damion Searls argues for a literary approach to translating rigorous philosophical texts…
Ludwig Wittgenstein’s [here] Tractatus Logico-Philosophicus is a book with an aura. His name, let’s admit it, is already a vibe; the title sets an extremely highbrow tone; the paragraphs are all numbered, promising a very impressive logical rigor, even if questions linger. (Is 6.2322 really exactly one level more primary than 5.47321? What does “3.001” mean since there’s no 3.0 or 3.00?) And then the text itself has a kind of cryptic grandeur, awe-inspiring opacity, Olympian disregard for normal human understanding that gives us what we expect, what we want, from such an iconic philosopher. It’s an exciting challenge. A lot of the reason why the book has been so widely read in the century since its English publication in 1922, by philosophers and philosophy students and nonphilosophers alike, is how it makes its readers feel.
Several similarly forbidding-yet-thereby-thrilling books were published in English that same year—T. S. Eliot’s The Waste Land; James Joyce’s Ulysses—but unlike those, the Tractatus was a translation, and the question arises how much of its style was a byproduct of bringing it into English. The book’s title did not come from Wittgenstein: it was an esoteric pun on Spinoza’s Tractatus Theologico-Politicus from 1670, suggested by G. E. Moore, the Cambridge philosopher who was the fourth most important figure in getting the book into English, after the credited translator C. K. Ogden, the actual translator Frank Ramsey [here], and Bertrand Russell [here]. Wittgenstein’s own German title was the far more humble and straightforward Logisch-Philosophische Abhandlung, something like Essay on Logic and Philosophy. Russell’s introduction, included in the first edition and every subsequent one until this one, firmly placed the book in the context of technical academic philosophy. And the book’s language in English was simply not at all like Wittgenstein’s forceful, earnest, fluid, subtle German.
Yet the book in English is what it is; should it just stay that way? This same debate came up around the retranslation of yet another iconic book from 1922: C. K. Scott Moncrieff’s translation of Marcel Proust’s Swann’s Way. He too completely changed the title (from Proust’s In Search of Lost Time to the Shakespeare quote Remembrance of Things Past); he too created an English-language voice, lush and purple, that wasn’t the original’s. And yet his writing was what generations of English-language Proust readers knew and loved; his translation was modified slightly over the years but largely preserved; when Lydia Davis came along with a new translation faithful to other aspects of the original, such as Proust’s analytical rigor, many readers didn’t care whether or not her version was more like the real Proust—Scott Moncrieff’s Proust was the real thing as far as they were concerned.
The situation with the Tractatus is clearer and less debatable, for two reasons. First, the earlier translations are more deeply flawed than Scott Moncrieff’s Proust ever was. Second and perhaps more important, Wittgenstein’s book is explicitly about the relationships between language and thought, between language and the world, making it imperative to get these relationships right in translation. And so I have retranslated the book, paying special attention to where the assumptions of typical academic philosophy translation would lead us away from expressing Wittgenstein’s thought in English. Implicitly, I am making the case for a certain kind of approach that is generally called “literary”—attentive to emotional nuances, subtle connotations, and expressive power—even when translating rigorous philosophical texts…
* The equally estimable Emily Wilson, paraphrasing Searls
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As we emphasize essence, we might spare a thought for the creator of the inspiration of the title of Wittgenstein’s work, Baruch Spinoza; he died on this date in 1677. One of the foremost thinkers of the Age of Reason, he was a philosopher who contributed to nearly every area of philosophical discourse, including metaphysics, epistemology, political philosophy, ethics, philosophy of mind, and philosophy of science. His rationalism and determinism put him in opposition to Descartes and helped lay the foundation for The Enlightenment; his pantheistic views led to his excommunication from the Jewish community in Amsterdam.
As men’s habits of mind differ, so that some more readily embrace one form of faith, some another, for what moves one to pray may move another to scoff, I conclude … that everyone should be free to choose for himself the foundations of his creed, and that faith should be judged only by its fruits; each would then obey God freely with his whole heart, while nothing would be publicly honored save justice and charity.
There’s much discussion of what’s causing the sudden-feeling spike in prices that we’re experiencing: pandemicdisruptions, nativist and protectionist policies, the over-taxing of over-optimizedsupply chains, and others. But Robinson Meyer argues that there’s another issue, an underlying cause, that’s not getting the attention it deserves… one that will likely be even harder to address…
Over the past year, U.S. consumer prices have risen 7 percent, their fastest rate in nearly four decades, frustrating households and tanking President Joe Biden’s approval rating. And no wonder. High inflation corrodes the basic machinery of the economy, unsettling consumers, troubling companies, and preventing everyone from making sturdy plans for the future…
For years, scientists and economists have warned that climate change could cause massive shortages of major commodities, such as wine, chocolate, and cereals. Financial regulators have cautioned against a “disorderly transition,” in which the world commits only haphazardly to leaving fossil fuels, so it does not invest enough in their zero-carbon replacements. In an economy as prosperous and powerful as America’s, those problems are likely to show up—at least at first—not as empty grocery shelves or bankrupt gas stations but as price increases.
That phenomenon, long hypothesized, may be starting to actually arrive. Over the past year, unprecedented weather disasters have caused the price of key commodities to spike, and a volatile oil-and-gas market has allowed Russia and Saudi Arabia to exert geopolitical force.
“This climate-change risk to the supply chain—it’s actually real. It is happening now,” Mohamed Kande, the U.S. and global advisory leader at the accounting firm PwC, told me.
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How to respond to these problems? The U.S. government has one tool to slow down the great chase of inflation: Leash up its dollars. By raising the rate at which the federal government lends money to banks, the Federal Reserve makes it more expensive for businesses or consumers to take out loans themselves. This brings demand in the economy more in line with supply. It is like the king in our thought experiment deciding to buy back some of his gold coins.
But wait—is it always appropriate to focus on dollars? What if the problem was caused by too few goods? Worse, what if the economy lost the ability to produce goods over time, throwing off the dollars-to-goods ratio? Then what was once an adequate number of dollars will, through no fault of its own, become too many...
… if the climate scars on supply continue to grow, does the Federal Reserve have the right tools to manage? Stinson Dean, the lumber trader, is doubtful. “Raising interest rates will blunt demand for housing—no doubt. But if you blunt demand enough to bring lumber prices down, you’re destroying the economy,” Dean told me. “For us to have lower lumber prices, we can only build a million homes a year. Do you really want to do that?
“Raising rates,” he said, “doesn’t grow more trees.” Nor does it grow more coffee, end a drought, or bring certainty to the energy transition. And if our new era of climate-driven inflation takes hold, America will need more than higher interest rates to bring balance to supply and demand.
As we dig deeper, we might send carefully calculated birthday greetings to 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.”
100,000 incredible objects now have a photograph online, the online collection regularly receives 100,000 views each month and we’ve just recorded 3,000,000 visitors since launching the website in late 2016.
Each time you visit our online collection you can see more than ever before. Almost a quarter of the remarkable objects we care for (24.9% or 105,715 objects to be exact) have a photograph online, with hundreds of new photographs added each month as we digitise our vast collection.
However, it can be difficult to spot recently photographed objects in the collection. So today we have published a new tool to help you explore these new items.
Never Been Seen shows objects from the Science Museum Group Collection that have never been seen online before. Each time you refresh this webpage an object with zero views is shown, making you the very first person to see it…
The spatula at the top of this post is no longer in that category, as your correspondent has seen (and now shared) it. But there’s so much more! Explore as yet unnoticed items in the collection of the Science Museum (London): “Never Been Seen.”
* Plato
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As we uncover the unobserved, we might spare a thought for a man who saw much that had hitherto been unseen: Frank Plumpton Ramsey, a philosopher, mathematician, and economist who made major contributions to all three fields before his death (at the age of 26) on this date in 1930.
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