The short New Yorker piece, by Patrick House, “What is elegance in science?“, bothers me, and for reasons I don’t quite understand. I’d appreciate it if readers could have a look (you can read it in 5 minutes) and weigh in below. What bothers me consciously about the piece is that is basically says nothing, but, in true New Yorker style, uses a lot of pretty words to do so. The last paragraph in particular suffers from that problem, especially the part I’ve bolded.
Last year, neuroscientists in the United Kingdom put expert mathematicians in an fMRI and tested whether their brains responded to equations the way that other people’s brains respond to, say, a beautiful painting or piece of music. They found that some equations—often simple, powerful ones like Euler’s identity, eiπ + 1 = 0, which joins together five mathematical constants—caused “activity in the same part of the emotional brain, namely field A1 of the medial orbito-frontal cortex (mOFC), as the experience of beauty derived from other sources.” Things are not always clear in the brain, though; it is impossible to say for certain whether activity in the mOFC is a response or a precursor to an emotion, or whether it’s the emotion itself. Likely, any full description will be messy, turbulent. But within that turbulence will be, finally, an explanation for what it means to know something when one sees it, or for what the “great liquid whip” of Roger Federer’s forehand and the “whip-like thrashing” of the roundworm tell us about string theory, or for how it came to be that three pounds of inelegance thought up such a concept as elegance in the first place.
Umm. . . .I don’t think so.
I suppose what bothers me unconsciously is the New Yorker’s seeming lack of understanding of, and respect for, science as it’s actually done. Yes, their medical articles are often good, but there’s far too much science-bashing. This often takes the form of using anecdotes to make generalities (often “counterintuitive generalities”), as does Malcolm Gladwell, or Jonah Lehrer’s specious “decline effect,” in which, he implied, scientific findings are inevitably doomed to being proven wrong. (Ironically, Lehrer resigned from the New Yorker after he was caught fabricating quotes and plagiarizing.) The idea that science undergoes a complete turnover is not true, of course: the formula for water, the fact of evolution, and the observation that DNA is a double helix are “truths” that, while provisional in a technical sense, are likely to remain true for the forseeable future!
My worry is that the magazine, which wields enormous influence among intellectuals, is wedded to a covert form of postmodernism—one that sees scientific truths as always dubious and liable to revision, and sees the humanities as just as much a source of objective truth as is science, if no more so. After all, Lehrer became famous for a book called Proust Was a Neuroscientist. (No he wasn’t!) I’m still open to debating whether the humanities and arts give us “other ways of knowing,” but that is surely questionable, and I haven’t yet seen an objective truth about the cosmos conveyed initially and solely by the humanities. What’s not debatable is that the humanities have given us as much objective truth as does science. They haven’t, though they’ve immensely enriched human existence in other ways. (Again, see my discussion in FvF.) Yes, rarely The New Yorker does have some good, hard science, but it’s hard to find amidst the anecdotes.
A knowledge of science is of immense value in modern life, and one would think that The New Yorker, which caters to the intellectuals, would give it some pride of place in their pages.
At any rate, the plaque below, affixed to a building at 28 W. 44th Street in New York, suggests that these attitudes have persisted for some time:
Re “What bothers me consciously about the piece is that is basically says nothing, but, in true New Yorker style, uses a lot of pretty words to do so.”
That would be true IMO of many of Pauline Kael’s film reviews which the New Yorker proudly carried for many decades.
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If the arts are another way of knowing, they are IMO a less reliable and less verifiable way of knowing than science, though in some cases they still produce truths of a kind.
I know mathematics likes the idea of elegance, but is it really anything more than saying “we have a simple theory & it just so happens that Nature has used exactly that as a ‘solution'”? Rivers traking the shortest course where there is a slope… but meandering when there is a plain.
Anyway, why sould baroque be the opposite of elegance? Many people like baroque. Nature is full of the baroque – it always makes kluges.
I agree – it expends all that space & yet says nowt of any consequence.
PS typo in foreseeable… that was unforeseeable!
In mathematics proper, elegance seems to be a synonym for the equally vague “short and sweet”, and maybe “explanatory”, but explanations in mathematics are hard to understand. (Work continues!)
As for the factual sciences, there does seem to be general aesthetic experiences noted by many researchers – Feynman’s “pleasure of finding things out”, but it is unclear what exactly we are latching on to. (This is true of beauty and the like in general, of course!)
It seems kind of criminal for me that the article cites so many great scientists for no real purpose. You can bet that, if I got Robert Sapolsky or Edward Witten on the phone, I would have better things to ask them about than the definition of “elegance” in science.
I think that the problem with the article is that it is simply sloppy: lots of appealing soundbites slung together without much idea of a coherent theme. This is probably down to a lack of appreciation of science. For example, there is a very poor statement of the second law of thermodynamics, and the description of Edward Witten as “instrumental in advancing string theory” is just ridiculous; he is arguably the leading theoretician in the field.
Similarly, House’s description of the vertebrate eye makes it sound like it would work better with the lens behind the retina.
What bothers me about the article is that it is trying to find THE elegance of science.
As the fMRI showed in the article, elegance is an emotional response not something objective.
There is no equivalence between the elegance of someone dressed up for the evening or an appetizer plate before dinner or a certain kind of painting on the wall or sculpture in the garden.
“As the fMRI showed in the article, elegance is an emotional response not something objective.”
So sorry, but that the mathematicians were having a very specific emotional response to certain concepts, using the same brain region devoted to appreciation of “beauty” is most certainly an objective observation, and as in need of understanding as anything in physics or paleontolgy.
Why do our meat computers react emotionally to anything at all, and about different things in different ways? To slough off such things as mere subjectivity may well expalin why some people don’t go into studying human neuroscience, but it hardly a recipe for curiosity or explanation.
So, you’re saying that beauty is not subjective?
What we regard as beautiful is subjective. (There may be certain commonalities between people e.g. a liking for landscapes, but that’s not the issue here). The fact that ‘beauty’ (subjectively experienced) stimulates a certain specific area of the brain is an objective observation.
cr
Deadline, word count, schlock, and woo.
That explains it!
Had no time to read but this my friend found may be of interest
http://www.artshub.com.au/festival/news-article/features/festivals/richard-watts/what-science-and-the-arts-can-teach-each-other-248987
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Mathematicians are not scientists – neither are string theorists (they’re mathematicians). That’s something that bothers me about the article. It offers mathematics up for its devotion to elegance, but the example from science all contradict the idea of elegance as a virtue (Crick’s hypothesis, Newsome talking about evolution).
“My worry is that the magazine…is wedded to a covert form of postmodernism.” This, I think, is exactly it. The article basically tries (poorly) to say, “See? Science is all about the beauty too.”
Thank you for saying this.
So many people don’t understand that while science uses maths, maths is not science, and science is very different from maths it’s EMPIRICAL.
Another opportunity to procrastinate. I’ll get back to the research grant in a moment…
There is, in a generous interpretation, confusion in this article about what it means to perceive a motivationally relevant object or concept. All these experiences (smelling chocolate, tasting fruit juice when you’re thirsty, viewing drug cues if you’re an addict, viewing porn, listening to music) activate a network of brain areas, the salience attribution network, that includes the area referenced in the article in the medial orbitofrontal cortex.
So it is not surprising that mathematicians activate this network when they view cool mathematical statements. (XKCD has a take on Euler’s formula here: https://xkcd.com/179/ ) There is no doubt that the subjective experience of beauty has a neural basis. It is also no surprise that the experience of beauty is pretty much the same as the experience of other pleasures.
There is an interesting distinction between ‘natural’ reinforcers (e.g., food, drink, sex) and ‘learned’ reinforcers that turns out to be less of a distinction when one actually looks at brain function. Once one has learned that something is pleasurable, it looks to the brain just like a pastrami on rye (at some level of abstraction).
So, the problem with this article is that it mystifies a normal, rather pedestrian ability of the brain to identify things that give it pleasure. Now, the process that leads to Euler’s identity giving pleasure is perhaps a more interesting question. I am a person who thinks that exp(i*pi) + 1 = 0 is a very cool statement (especially if written in a more elegant notation). But the path to that feeling of coolness was preceded by many hours of fiddling with complex numbers, trigonometry, infinite series, calculus and what not. It was with the slow process of understanding how all those seemingly disparate concepts were inter-related (and, even more bizarre, how they related to my study of the brain) that led to my appreciation that Euler’s identity really was amazing (and not just because a dozen math instructors had said it was).
And by the way, I know a mathematician who thinks that Ramanujan’s 1/pi formula is ‘totally rad; it’s like a heavy metal, tattooed punk rock formula’. I’m sure Ramanujan would have been appalled by that description.
@squidmaster
I really appreciate your comment. Thanks.
Atanu
“So, the problem with this article is that it mystifies a normal, rather pedestrian ability of the brain to identify things that give it pleasure.”
Rather pedestrian ability? Perhaps Patrick House (who is a researcher in the neuroscience field) is more intrigued by the underlying reasons for seemingly mundane and familiar.
This mathy loved your math examples:-)
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Before I read the article I wrote down my notion for what is elegant in science: ‘Great explanatory power, but involving few components. Simple enough so that outsiders of a field can appreciate it’.
The article itself, in a moment of clarity provides the quote: “When a theory or a model explains a phenomenon clearly, directly and economically, we say it is elegant: one idea, easy to understand, can account for a large amount of data and answer many questions.”
So I guess I got lucky and wound up being close to quoted definition of elegance in science.
What was clearly lacking in the article, though, was a clear conclusion to the very question that it asked. Perhaps it meant to conclude that what is elegant in science is inconclusive and relative to the beholder. But if that is what it was going for I failed to see it be clearly stated.
Simple? “Simplicity isn’t simple.” (Bunge, _The Myth of Simplicity) What counts as simple?
Appreciate is tricky. I appreciate general relativity, but I cannot say I understand more than the very tiniest amount. I am not sure that’s appropriate for an aesthetic evaluation.
But simplicity is paramount to prediction . I cannot predict with any value the outcome of a particular order parameter of a system by solving Schrodinger’s equation in three dimensions for in particles . But I can make significant headway by making major approximations to assist me in getting valuable predictive capabilities.
Reproducing and system completely get you that system . That is a tautology. Simplifying is the only way to make pragmatic predictions and science .
On the other hand, you are guided by principles you can barely state to not *over* simplify when solving the equations. For example, I remember when my mechanics instructor simplfied an expression at one point by noting that pi was a factor in the denominator of a fraction and root(10) was one in the numerator. Otherwise there was to be another term in the final result. Is this justified? Sure, sometimes. When? Well, there are no general rules here. That’s one reason why simplicity isn’t simple.
There is a related idea that simplicity by itself is not necessarily or always desirable, but that specific fields of research periodically seek out simple or minimalist experiments, models, and systems in order to clear the clutter and noise in the current state of the science and to find its essential features. Then people working in that field build on those generalizations, and add complexity and detail, until the field again reaches a state where a return to minimalism and simplicity is once more needed. Lawrence Slobodkin wrote an under-appreciated essay about this (DOI: 10.1086/284484).
Mark, I think you’ve hit the nail on the head. In physics at least, a simple but surprising formula that is also true (as far as we can tell) should indeed strike us with awe. We can describe any physical behavior of the world if we give ourselves enough free variables and equations. The fewer variables we use, the “deeper” our laws are. If just a couple of variables, tightly related by just a few clean math functions, explain everything, then we’ve reached very deep into the heart of reality. Simplicity + empirical truth is also strong evidence that the theory is actually right in some kind of absolute sense. It becomes more and more difficult to be accidentally accurate as the number of variables and functions decreases. This goes beyond explanatory power alone. Or, to distill my rambling comment:
Explanatory power + simplicity = truth.
As for what I think rubs me the wrong way: the failure to address the *content* and the *actual literature*, such as it is, on explanations in science, for example, which the literature does link to aesthetics in an odd sort of way.
I think that’s part of it. Science as wallpaper. Name-dropping. Like a 10 minute whirlwind tour of Florence. There seems to be a condescension in it too somehow: “look at the creatures in the zoo, distracted so easily by the bright, shiny elegance.”
I dispute the claim that the New Yorker caters to “the intellectuals”. I have known few hard-knowledge friends who read it, but many mush-minds and poseurs who seek to see themselves as part of an intellectual elite. I do hear from NY readers about the evils of “scientism”, the virtues of the “natural”, and “other ways of knowing.” I think that the attitude JAC (rightly) worries about is part and parcel of the magazine’s identity and cachet.
I did not find that House espoused the general idea that science was destined to wrong. Jerry accused the New Yorker magazine in general of this erroneous concept. House was merely asking the question, What is elegance in science? This is a perfectly legitimate question to ask because it crops up all the time. The point that mathematicians are different from scientists is irrelevant. Both are responsible for models which is what science is all about. When models are attractive they are considered elegant. But elegance has nothing to do whether they work or not. Therefore, he did not come up with an answer to the question but merely tossed things around, because as he suggests it is still a nebulous concept.
Well, there’s always Solomonoff Induction, which isn’t very nebulous, and has a lot to do with simplicity.
I am not surprised if it is an expression of postmodernism, because as soon as “elegance” isn’t expressing quantifiable measure of a low degree of complexity, overfitting et cetera, it becomes mysticism or a loose appeal to esteticism instead of usefulness as far as I can see.
One of the major gripes that physicists have with the standard model of particles is its lack of elegance. Yes, it has symmetries that makes for generations of particles with similar characteristics. But it has also some 20 or so ad hoc parameters. Which inelegance in combination with the lack of new physics – so far – at energy levels where the theory should naturally stop working, seem to give physicists concern.
But it may just be the kludge (to borrow from Dominic) that nature is. Evolution is an obvious process of tinkering, where stuff like the triplet code may freeze in. Maybe cooling down from very hot states in the early universe is prone to freezing in accidents too. Then the strategy of searching for ultimate elegance – as opposed to moderate elegance – may bring its own ultimate failure.
As I posted this I noted that the spell checker suggested “aestheticism”. This is Why WordPress Is Wrong in not providing a comment editor.
In my view the New Yorker has a certain investment in being in the forefront of intellectual movements. And this article has to do with the current interest in mindfulness and meditation practices and their effects on the brain. And how we can come to understand in an experiential way rather than only from a prior set of conceptsand extending from that to how we recognize pattern or elegance or whatever and then put that sudden understanding into language. Kind of the inverse of how we often visualize intellect working. My way of interpreting the phrase’different ways of knowing’ should more understandably be couched as ‘different ways of getting to know’. As a now retired hard scientist I remember struggling with batches of data(sparse in those days)putting forward one hypothesis after another and testing and then suddenly recognizing how it all really went together. The educated intuition recognized the pattern. So perception comes before concept. Scientists often conceive of that happening only in the other direction.
ie. That is understanding How intellect and intuition work together.
So, all the talk of suddenly recognizing string theory in Roger Federer’s swing is an ill thought out metaphor for that route to conceptualised understanding.
There is a University in NY which is dealing with scads of genetic data and has the idea(and the money) to hire-part time an abstract artist to construct sculptures or paintings to convey the feelings/patterns that might be conveyed by the data displayed in different formats. (Presumably highlighting what the scientists consider significant parts of the data). In my view it is in very preliminary stages as of now and not too satisfactory.
Maybe it is all woo but I prefer to try to understand it as a very beginning effort to try to understand the relationships between intellect and intuition-how the brain recognizes pattern and forms that into concept or emotion or whatever.
Anyway, with my heart in my mouth I press ‘send’
And I agree it is a rather quickly and messily put together article.
And if anyone is interested in the university project I mentioned I will send the info.
The Euler identity is indeed nice, I’m not surprised that some people might like it.
The rest of Patrick House’s piece is a too vague or difficult for me.
I’m not a scientist or mathematician, but my impression of the article is that the term “elegance” is an unhelpful one in the pursuit of how things are and what works. To me “elegance” is synonymous with ” beauty” which as the old saw says “is in the eye of the beholder”.
Before basking in my retirement I was an architect (the technical kind as opposed to the designer kind – although that distinction is a whole conversation in itself) and dealt with “elegance”. In my experience if I had approached solutions with the intent that they be elegant I would never have gotten anything done. The point was to follow the evidence (in an architect’s case the program, building codes, site constraints, designer’s whims …) and “solve the problem”. The elegance took care of itself and in its detail wasn’t necessarily obvious to someone outside the process. The article seems to me to be an exercise in futility.
The turbulent results hold the answer (or maybe not), which we are not much closer to understanding than we were when we first beheld the convoluted brain and understood that it is the source of the mind.
It’s the kind of science reporting that is pervasive now. Everything is revolutionary.
I think the essence of the article’s problem is in this sentence:
Despite Crick’s injunction, scientists have continued to seek elegance in their work.
That’s an assertion which he neither clarifies, qualifies, nor provides evidence for. I don’t know what exactly he means to imply with it.
Then he hares off to ask a bunch of scientists the leading question, “What is elegance?” and uses their unsurprisingly vague answers as proof that scientists have been seeking elegance in their work but they don’t even know what they’re looking for!.
It looks a bit like high brow “gotcha journalism” to me. He should have asked whether they do in fact “seek elegance in their work” and if so in what ways. I doubt any of them would have said that the search for elegance is what guides their work — which is what he seems to be implying.
typo?
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just as much a source of objective truth as is science, if no more so
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I think you meant, “if not more so”
— Sean
I don’t think it’s just the New Yorker that fails with, “…seeming lack of understanding of, and respect for, science as it’s actually done.” And I will use the word “science” here to mean any of the established knowledge arts. It has been my experience that most western education systems largely ignore methodology until you reach the final one or two years of your undergraduate major (noting that the hard sciences at least give it a day-long hat tip at the beginning of individual courses). In fact, I completed a social science major, with a hard science minor, and was never required to complete a pure humanities methodological course.
I realize we must balance the teaching of the established consensus with how critical thinking methods established this consensus, but I think we overweight the first at the expense of the second.
I thought that Lehrer’s essay on the decline effect was as hard to read as House’s essay, and for some of the same reasons noted by other commenters. But the decline effect does seem to be a real thing, at least in some areas of research. Rich Palmer, who was quoted at length in the Lehrer essay, wrote a detailed and convincing review (DOI: 10.1086/303223) of the magnitude of publication bias in three specific areas of evolutionary ecology. Publication bias is one of the likely mechanisms leading to the decline effect: apparently large effect size of some independent variable on a dependent measure in the first (small) published study of that relationship, followed by smaller effect sizes in subsequent (larger) studies or experiments that follow up on the initial observation. The inference is that the effect size of the independent variable on the dependent variable is in reality small, but that statistical weak earlier studies of the same relationship produced smaller or nonsignificant effect sizes, and were therefore never published (the file drawer effect).
Well said. Also relevant: replication failures in psychology.
John Brockman who operates The Edge asks a question of the year. Elegance came up in 2012 when the question was “What is your favorite deep, elegant, or beautiful explanation.” There were about 200 responses from a wide range of scientists and mathematicians.
Frank Wilzek, an MIT physicist who was awarded (with two others) the Nobel Prize in physics (2004?)), gave a talk which is on the web titled “Quantum Beauty: Real and Ideal” in which he focused on the question “Does the world embody beautiful ideas?” (or elegance)
I think this talk preceded his most recent book “A Beautiful Question.” It might have been given while he was writing this book. It is not a book I’m likely to read but I have read a few reviews. It is described as difficult (physics concepts I think and perhaps the maths, too) and that his answer is not satisfying. I’m not sure it can be but it can be provocative.
Elegance strikes me as very elusive. Clearly given the ink spend on it, it is tantalizing. In my (very)simple way I’m inclined to consider evolution’s answers as elegant in the way that living organisms are tinkered and cobbled together which is not the physicist’s or mathematician’s idea of elegance!
If there’s anyone who’s a sucker for belles-lettres and flashy erudition, it’s me. (And I pray any belletrists out there to forgive me my use of the objective case pronoun in the terminal clause of the preceding sentence.) But even I, with my fan-boy affection for fine writing, can see through to the hollow core of this New Yorker piece. Writing about scientific elegance elegantly doesn’t mean you’ve got anything meaningful to say.
Crick was alluding specifically to biology as being a messy business due to the nature of natural selection yet the double helix is the epitome of biological elegance. Euler wasn’t aiming for beauty it just fell out of his mathematical machinations. When the identity appears it is something to behold. Make it as simple as necessary – and no more: Which equates to as complicated as necessary and no more. Just musing.
Sounds like a Stanford student gabfest. Lots of detail, but no coherence. No consistent theme, no rational progression and no valid conclusion.
Straining at a gnat, swallowing a camel; or vice versa.
Math and science are very important elements of art and music. The humanities includes art and music. Humanities,in general, are not as rigorous or elegant as math and science, but are useful ways of knowing and additions to knowledge.
I can think of very few, if any, high-brow publications in the humanities that don’t adhere to that dismissive, po-mo view of science and scientific truth. It’s enormously reassuring for writers with a background in the humanities to tell themselves that what they do is just as deep and epistemologically revealing as the hard sciences. So to do so they either build up their own field or(attempt to) tear down science.
I think elegance is the sensation we get when our own internal sense of how things should be turns out to be in alignment with reality. And the easier to build the mental construct of “should” the more elegant. Also, of course, observations or somebody else’s explanation or what-not can create within us a new sense of “should” which can form the basis of elegance.
A false sense of elegance would happen when you pretend that “is” and “should” are aligned even when they’re not.
With that in mind, consider physics. Most would describe Newton as “elegant,” because the basic concepts are simple and provide a good match with reality. But they’re not complete…and, if you want a model that can deal with Mercury, you’re going to have to go all the way to Relativity…which is notoriously difficult for amateurs to fully appreciate. Most people would describe Newton as more elegant and Einstein as more Baroque…simply because Newton is more easily digested.
As such, elegance should always be sought after; the less work you have to do, the better. But, if you’ve over-simplified and your model doesn’t accurately predict reality within your requirements…well, tough shit. In that case, you can have elegance or you can have reality, but not both.
b&
The first sentence in the bolded portion looks like a paraphrase of something the neuroscientists may have told him. The rest looks more like a fail at coming up with a profound ending than flippantly anti-science. Maybe the neuroscientists gave him a snort of oxytocin as a practical joke and overdid it on the dosage.
The first half of the quoted paragraph seems intuitively credible to me. I recall (decades ago) when I finally realised just why logarithms worked (I knew all the facts but it suddenly ‘clicked’ with me). Same sensation decades later contemplating the way an astonishingly simple algorithm led to the staggering complexity of the Mandelbrot set.
But it was the same sensation (subjectively) as first hearing Dire Straits’ version of ‘Wild Theme’ from ‘On The Night’ CD. I’m not putting these up for aesthetic comment, just instancing three occasions when I recollect the feeling of – awe.
Most of the bolded quote, though, is complete crap. There is NO possible link** between Federer’s serve, roundworms, and string theory other than a coincidence of metaphors.
** I say that with about the same conviction as I say G*d does not exist.
By the way I find the mention of turbulence suggestive, it seems to be one of those favourite buzzwords of po-mo. (I’ll admit I haven’t studied po-mo; Sokal & Bricmont – and Dawkins – are as near as I want to go to it http://www.physics.nyu.edu/sokal/dawkins.html).
But I am a hydraulic engineer and the analogy is – very shaky. In fact it’s worng.
cr
I haven’t read Lehrer’s book, but its title suggests it is of a piece with the premise Pinker set out in his controversial New Republic cover story, wherein he contended that Descartes, Spinoza, Hobbes, Locke, Hume, Rousseau, Leibniz, Kant, and Smith were all “evolutionary psychologists,” of a sort.
I don’t know if they provide “other ways of knowing,” but the humanities — literature, in particular — have the capacity to put us in the skin of another human being in a way nothing else, not even science, can. They furnish us empathy, the kind that found its highest expression in Terence’s declamation “I am human, and nothing of that which is human is alien to me.”
Funny that Kant should be mentioned. He’s one of the folks that some people discuss when the “split” is discussed. Kant did not, for example, understand Newton’s laws (I’ve never seen M. Friedman or other Kant-and-exact-science-people explain otherwise) because he seems to fail to understand inertia. Nevertheless, he felt the need to talk (at length) about Newton. He also expounded how psychology could not become a science, and arguably such as well for the then just-starting social sciences. Not only this, but his philosophy was subjectivistic (in spite of his protests to the contrary) and so on. Hume had many of these flaws but did not dwell on them, nor did he have the influence. The other figures were to varying degrees more science-friendly – and Rousseau is a corner case for another reason, since he was not interested in natural science as far as I can tell.
To me, it read like someone came up with an interesting idea for an article… and then couldn’t be bother to actually write it. Started OK and then got progressively worse, though I did like the observation that (due to evolution) biology is often not elegant – something which the Intelligent Design crowd can never adequately explain.
The New Yorker piece is a bit of fluff, not to be taken seriously.
Jerry: “I’m still open to debating whether the humanities and arts give us “other ways of knowing,” but that is surely questionable…”
I would say it’s not even a sufficiently well-defined question to have a right answer. How different to two ways of thinking have to be to count as different ways of knowing, rather than variations on the same way of knowing?
It’s not as if science and the humanities have two different formulas for making inferences. There is no formula for doing science or the humanities. All inferences require individual, non-formulaic judgements, arising from a complex mess of non-conscious cognitive processes. This complex mess cannot be neatly partitioned into fundamentally distinct “ways of knowing”. Of course, science tends to be more methodical and precise, with some specific methods and subject areas of its own, which makes it worth drawing a very rough division between science and the humanities. But this rough division is being imposed on what is more like a continuum, from the hardest science to the softest humanities, with fields like psychology and archaeology being somewhere in the middle. Also, the division in terms of precision coincides very roughly with the division between those disciplines whose objects of study don’t or do involve human minds (the latter we broadly call the “humanities”). That’s because human brains taken as a whole (and consequently human minds and behaviour) are so complex, messy and relatively unpredictable that they can’t be modelled with anything like the precision of the hard sciences.
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