I’ve been digging Crash Course’s series on statistics. They managed to pull off two good episodes about Bayesian statistics, plus one about the downsides of p-values, but overall Adriene Hill has stuck close to the frequentist interpretation of statistics. It was inevitable that one of their episodes would get my goat, enough to want to break it down.
And indeed, this episode on t-tests is worth a break.
Things have gotten quiet over here, due to SIGGRAPH. Picture a giant box of computer graphics nerds, crossed with a shit-tonne of cash, and you get the basic idea. And the papers! A lot of it is complicated and math-heavy or detailing speculative hardware, sprinkled with the slightly strange. Some of it, though, is fairly accessible.
This panel on colour, in particular, was a treat. I’ve been fascinated by colour and visual perception for years, and was even lucky enough to do two lectures on the subject. It’s a ridiculously complicated subject! For instance, purple isn’t a real colour.
Ok ok, it’s definitely “real” in the sense that you can have the sensation of it, but there is no single wavelength of light associated with it. To make the colour, you have to combine both red-ish and blue-ish light. That might seem strange; isn’t there a purple-ish section at the back of the rainbow labeled “violet?” Since all the colours of the rainbow are “real” in the single-wavelength sense, a red-blue single wavelength must be real too.
It turns out that’s all a trick of the eye. We detect colour through one of three cone-shaped photoreceptors, dubbed “long,” “medium,” and “short.” These vary in what sort of light they’re sensitive to, and overlap a surprising amount.
Your brain determines the colour by weighing the relative response of the cone cells. Light with a wavelength of 650 nanometres tickles the long cone far more than the medium one, and more still than the short cone, and we’ve labeled that colour “red.” With 440nm light, it’s now the short cone that blasts a signal while the medium and long cones are more reserved, so we slap “blue” on that.
Notice that when we get to 400nm light, our long cones start becoming more active, even as the short ones are less so and the medium ones aren’t doing much? Proportionately, the share of “red” is gaining on the “blue,” and our brain interprets that as a mixture of the two colours. Hence, “violet” has that red-blue sensation even though there’s no light arriving from the red end of the spectrum.
To make things even more confusing, your eye doesn’t fire those cone signals directly back to the brain. Instead, ganglions merge the “long” and “medium” signals together, firing faster if there’s more “long” than “medium” and vice-versa. That combined signal is itself combined with the “short” signal, firing faster if there’s more “long”/”medium” than “short.” Finally, all the cone and rod cells are merged, firing more if they’re brighter than nominal. Hence where there’s no such thing as a reddish-green nor a yellow-ish blue, because both would be interpreted as an absence of colour.
I could (and have!) go on for an hour or two, and yet barely scratch the surface of how we try to standardize what goes on in our heads. Thus why it was cool to see some experts in the field give their own introduction to colour representation at SIGGRAPH. I recommend tuning in.
Researchers have noted that, for decades, prison sentences have been just ever-so-slightly more harsh for black people than white people.
As a whole, these findings undermine the so-called ‘‘no discrimination thesis’’ which contends that once adequate controls for other factors, especially legal factors (i.e., criminal history and severity of current offense), are controlled unwarranted racial disparity disappears. In contrast to the no discrimination thesis, the current research found that independent of other measured factors, on average African-Americans were sentenced more harshly than whites. The observed differences between whites and African Americans generally were small, suggesting that discrimination in the sentencing stage is not the primary cause of the overrepresentation of African-Americans in U.S. correctional facilities.
Mitchell, Ojmarrh. “A meta-analysis of race and sentencing research: Explaining the inconsistencies.” Journal of Quantitative Criminology 21.4 (2005): 439-466.
Not as widely noted: incarceration sorta behaves like a contagious disease. [Read more…]
Before reading further, glance back up: what does the second half of that title bring to mind?
No really, spend a few moments pondering what you think the term “feminist glaciology” means.
Almost done?
Enough shenanigans, it’s time to meet the real thing. [Read more…]
You might have wondered why I didn’t pair my frequentist analysis in this post with a Bayesian one. Two reasons: length, and quite honestly I needed some time to chew over hypotheses. The default frequentist ones are entirely inadequate, for starters:
In chart form, their relative likelihoods look like this. [Read more…]
I like Dr. R (aka. Dr. Ulrich Schimmack), I’ve relied on his work in the past, but there is one area where we part ways: he’s not a fan of Bayesian statistics.
Like, REALLY not a fan. [Read more…]
A friend asked for an explainer on Bayesian statistics, and I instinctively reached for Yudkowsky’s only to find this at the top:
This page has now been obsoleted by a vastly improved guide to Bayes’s Theorem, the Arbital Guide to Bayes’s Rule. Please read that instead. Seriously. I mean it.
You can see why once you’ve clicked the link; it asks for your prior experience, then tailors the explanation appropriately. There’s also some good diagrams, and it tries to explain the same concept multiple ways to hammer the point home. Their bit on p-values is on-point, too.
Speaking of stats, I’ve also been drawn back into a course on probability I started years ago. MIT OpenCourseware has a lot of cool offerings, but this entry on probability has been worth my attention. While E.T. Jaynes’ Probability Theory still has my favourite treatment of the subject, the video lectures are easier to parse and proceed at a faster clip.
As I mentioned before, C.P. Snow’s “Two Culture” lecture is light on facts, which makes it easy to mould to your whims. Go back and re-read that old post, absorb C.P. Snow’s version of the Two Cultures, then compare it to Pinker’s summary:
A final alternative to Enlightenment humanism condemns its embrace of science. Following C.P. Snow, we can call it the Second Culture, the worldview of many literary intellectuals and cultural critics, as distinguished from the First Culture of science.[12] Snow decried the iron curtain between the two cultures and called for greater integration of science into intellectual life. It was not just that science was, “in its intellectual depth, complexity, and articulation, the most beautiful and wonderful collective work of the mind of man.” Knowledge of science, he argued, was a moral imperative, because it could alleviate suffering on a global scale …
[Pinker, Steven. Enlightenment Now: The Case for Reason, Science, Humanism, and Progress. Penguin, 2018. Pg. 33-34]
C.P. Snow went out his way to criticise scientists for failing to incorporate literature into their lives, and never ranked one culture as superior to another. Nor did he label them “First Culture” or “Second Culture.” And it wasn’t increased knowledge of science in general that would remove suffering, it was the two cultures intermixing. Pinker is presenting a very different argument than C.P. Snow, at least on the face of it.
But hang on, there’s a footnote right in the middle of that passage….
[12] Snow never assigned an order to his Two Cultures, but subsequent usage has numbered them in that way; see, for example, Brockman 2003.
[Pg. 456]
How is it “following C.P Snow” to call it “Second Culture,” when you acknowledge C.P. Snow never called it “Second Culture?!” What’s worse, look at the page numbers: that acknowledgement comes a full four hundred pages after the misleading phrasing. How many people would bother to flip that far ahead, let alone make the connection to four hundred pages ago? But all right, fine, maaaybe Steven Pinker is just going with the flow, and re-using a common distortion of C.P Snow’s original argument. The proof should lie in that citation to Brockman [2003], which fortunately is available via Google Books. In fact, I can do you one better: John Brockman’s anthology was a mix of work published in Edge magazine and original essays, and the relevant parts just happen to be online.
Bravo, John! You are playing a vital role in moving the sciences beyond a defensive posture in response to turf attacks from the “postmodernists” and other leeches on the academies. You celebrate science and technology as our most pragmatic expressions of optimism.
I wonder, though, if it’s enough to merely point out how hopelessly lost those encrusted arts and humanities intellectuals have become in their petty arms race of cynicism. If we scientists and technologists are to be the new humanists, we must recognize that there are questions that must be addressed by any thinking person which do not lie within our established methods and dialogs. …
While “postmodern” academics and “Second Culture” celebrity figures are perhaps the most insufferable enemies of science, they are certainly not the most dangerous. Even as we are beginning to peer at biology’s deepest foundations for the first time, we find ourselves in a situation in which vast portions of the educated population have turned against the project of science in favor of pop alternatives usually billed as being more “spiritual.”
It appears exactly once in that reference, which falls well short of demonstrating common usage. Even more damning is that Pinker’s citation references the 2003 edition of the book. There’s a 2008 version, and it doesn’t have a single reference to a “Second Culture.” I’ve done my own homework, and I can find a thesis from 2011 which has that usage of “Second Culture,” but falsely attributes it to Snow and never brings it up past the intro. There is an obscure 1993 book which Pinker missed, but thanks to book reviews I can tell it labels science as the “Second Culture,” contrary to how Pinker uses the term. Everything else I’ve found is a false positive, which means Pinker is promoting one mention in one essay by one author as sufficient to show a pattern.
And can I take a moment to call out the contrary labelling here: how, in any way, is science “First” relative to literature? Well before Philosophical Transactions began publishing, we’d already had the Ramayana, the Chu Ci anthology, the Epic of Gilgamesh, The Illiad, Beowulf, and on and on. Instead, Pinker and friends are invoking “Second” as in “Secondary,” lesser, inferior. Unlike de Beauvoir, though, they’re not doing it as a critique, they honestly believe in the superiority of science over literature.
Pinker didn’t invent this ranking, nor was he the first to lump all the humanities in with the literary elites. I think that honour belongs to John Brockman. Consider this essay of his; read very carefully, and you’ll see he’s a little confused on who’s in the non-scientific culture.
Ten years later, that fossil culture is in decline, replaced by the emergent “third culture” of the essay’s title, a reference to C. P. Snow’s celebrated division of the thinking world into two cultures—that of the literary intellectual and that of the scientist. …
In the twentieth century, a period of great scientific advancement, instead of having science and technology at the center of the intellectual world—of having a unity in which scholarship includes science and technology just as it includes literature and art—the official culture kicked them out. The traditional humanities scholar looked at science and technology as some sort of technical special product—the fine print. The elite universities nudged science out of the liberal arts undergraduate curriculum, and out of the minds of many young people, who abandoned true humanistic inquiry in their early twenties and turned themselves into the authoritarian voice of the establishment. …
And one is amazed that for others still mired in the old establishment culture, intellectual debate continues to center on such matters as who was or was not a Stalinist in 1937, or what the sleeping arrangements were for guests at a Bloomsbury weekend in the early part of the twentieth century. This is not to suggest that studying history is a waste of time. History illuminates our origins and keeps us from reinventing the wheel. But the question arises: history of what? Do we want the center of culture to be based on a closed system, a process of text in/text out, and no empirical contact with the world in between?
A fundamental distinction exists between the literature of science and those disciplines in which the writing is most often concerned with exegesis of some earlier writer. In too many university courses, most of the examination questions are about what one or another earlier authority thought. The subjects are self-referential. …
The essay itself is a type specimen of science cheer-leading, which sweeps all the problems of science under the carpet; try squaring “Science is nothing more nor less than the most reliable way of gaining knowledge about anything” with “Most Published Research Findings Are False,” then try finding a published literary critic doing literary criticism wrong. More importantly, Brockman’s December 2001 essay reads a lot like Pinker’s February 2018 book, right down to the “elite” and “authoritarian” “liberal arts” universities turning their back on science. Brockman was definitely ahead of his time, and while only three of his works show up in Pinker’s citation list he’s definitely had a big influence.
This also means Pinker suffers from the same confusion as Brockman. Here’s some of the people he considers part of the Second Culture:
It’s an oddball list. Karl Popper is a member, probably by accident. Adorno was actually an opponent of Heidegger and Popper’s views of science. Essayists (Wieseltier and Gopnik) rub shoulders with glaciologists (Carey, Jackson), sociologists (Bauman), and philosophers (Foucault, Derrida). It’s dominated by the bogey-people of the alt-right, none of whom can be classified as elite authors.
Stranger still, Thomas Kuhn isn’t on there. Kuhn should have been: he argued that science doesn’t necessarily follow the strength of the evidence. During Kuhn’s heyday, many physicists thought that Arthur Eddington’s famous solar eclipse data fell short of proper science. The error bars were very large, the dataset was small, and some contrary data from another telescope was ignored; nonetheless, scientists during Eddington’s heyday took the same dataset as confirmatory. Why? They wanted General Relativity to be true, because it offered an explanation for why light seemed to have a fixed speed and Mercury precessed the way it did. Kuhn called these “puzzles,” things which should be easily solvable via existing, familiar knowledge. Newtonian Mechanics violated that “easy” part of the contract, GR did not, so physicists abandoned ship even in the face of dodgy data. Utility was more important than truth-hood.
Conversely, remember the neutrinos that seemed to run faster than light? If science advanced by falsification, physicists should have abandoned General Relativity in droves; instead, they dismissed the finding and asked the scientists who ran the experiment to try again. In this case, they didn’t want GR to be false, so contrary evidence was rejected. That might seem like a cheap example, since the experimental equipment was shown to be the real problem, but consider that we already knew GR was false because it’s incompatible with Quantum Mechanics. Neither theory can be true at the same time, which means there’s a third theory out there which has a vague resemblance to both but has radically different axioms. Nonetheless no physicist has stopped using GR or QM, because both are effective at solving puzzles. Utility again trumps truth-hood.
Kuhn argued that scientists proposed frameworks for understanding the world, “paradigms,” which don’t progress as we think they do. For instance, Newtonian Mechanics says the International Space Station is perpetually falling towards Earth, because the mass of both is generating attractive forces which cause a constant acceleration; General Relativity says the ISS is travelling in a straight line, but appears to orbit around the Earth because it is moving through a spacetime curved by the energy and mass of both objects. These two explanations are different on a fundamental level, you can’t transform one into the other without destroying some axioms. You’ve gotta chose one or the other, and why would you switch ever switch back? Kuhn even rejected the idea that the next paradigm is more “truthful” than another; again, utility trumps truth-hood.
It’s opposed to a lot of what Pinker is arguing for, and yet:
The most commonly assigned book on science in modern universities (aside from a popular biology textbook) is Thomas Kuhn’s The Structure of Scientific Revolutions. That 1962 classic is commonly interpreted as showing that science does not converge on the truth but merely busies itself with solving puzzles before flipping to some new paradigm which renders its previous theories obsolete, indeed, unintelligible. Though Kuhn himself later disavowed this nihilist interpretation, it has become the conventional wisdom within the Second Culture. [22]
[Enlightenment Now, pg. 400]
Weird, I can find no evidence Kuhn disavowed that interpretation in my source:
Bird, Alexander, “Thomas Kuhn“, The Stanford Encyclopedia of Philosophy (Fall 2013 Edition), Edward N. Zalta (ed.) URL = <https://plato.stanford.edu/archives/fall2013/entries/thomas-kuhn/>
Still, Pinker is kind enough to source his claim, so let’s track it down…. Right, footnote [22] references Bird [2011], which I can find on page 500…
Bird, A. 2011. Thomas Kuhn. In E. N. Zalta, ed., Stanford Encyclopedia of Philosophy . https://plato.stanford.edu/entries/thomas-kuhn/.
He’s using the same source?! I mean, score another point for Kuhn, as he thought that people with different paradigms perceive the same data differently, but we’ve still got a puzzle here. I can’t be sure, but I have a theory for why Pinker swept Kuhn under the rug. From our source:
Feminists and social theorists (…) have argued that the fact that the evidence, or, in Kuhn’s case, the shared values of science, do not fix a single choice of theory, allows external factors to determine the final outcome (…). Furthermore, the fact that Kuhn identified values as what guide judgment opens up the possibility that scientists ought to employ different values, as has been argued by feminist and post-colonial writers (…).
Kuhn himself, however, showed only limited sympathy for such developments. In his “The Trouble with the Historical Philosophy of Science” (1992) Kuhn derides those who take the view that in the ‘negotiations’ that determine the accepted outcome of an experiment or its theoretical significance, all that counts are the interests and power relations among the participants. Kuhn targeted the proponents of the Strong Programme in the Sociology of Scientific Knowledge with such comments; and even if this is not entirely fair to the Strong Programme, it reflects Kuhn’s own view that the primary determinants of the outcome of a scientific episode are to be found within science.
Oh ho, Kuhn thought it was unlikely that sexism or racism could warp science! That makes him the enemy of Pinker’s enemies, and therefore his friend. Hence why Pinker finds it useful to bring up Kuhn, despite their contrary views of science, and for that matter why Pinker can look at Snow’s arguments and see his own: utility trumps truth-hood.
I love it when Professor Moriarty wanders back to YouTube, and his latest was pretty good. He got into a spot of trouble at the end, which led me to muse on writing a blog post to help him out. I’ve already covered some of that territory, alas, but in the process I also stumbled on something more interesting to blog about. It also effects Sean Carroll’s paper, which Moriarty relied on.
The fulcrum of my topic is the distinction between inference and abduction. The former goes “I have a hypothesis, what does the data say about it?,” while the latter goes “I have data, can I find a hypothesis which explains it?” Moriarty uses this as a refutation of falsification: if we start from the data instead of the hypothesis, we’re not trying to falsify anything! To add salt to the wound, Moriarty argues (and I agree) that a majority of scientific activity consists of abduction and not inference; it’s quite common for scientists to jump from one topic to another, essentially engaging in a tonne of abductive activity until someone forces them to write up a hypothesis. Sean Carroll doesn’t dwell on this as much, but his paper does treat abduction and inference as separate things.
They aren’t separate, at least when it comes to the Bayesian interpretation of statistics. Let’s use a toy example to explain how; here’s a black box with a clear cover:
import ("math/rand")
func blackbox() float64 {
x := rand.Float64()
return (4111 + x*(4619 + x*(3627 + x*(7392*x - 9206)))/1213
}
Each time we turn the crank on this function, we get back a number of some sort. The abductive way to analyse this is pretty straightforward: we grab a tonne of numbers and look for a hypothesis. I’ll go for the mean, median, and standard deviation here, the minimum I’ll need to check for a Gaussian distribution.
Samples = 1000001 Mean = 5.61148 Std.Dev = 1.40887 Median = 5.47287
Looks like there’s a slight skew downwards, but it’s not that bad. So I’ll propose that the output of this black box follows a Gaussian distribution, with mean 5.612 and standard deviation 1.409, until I can think of a better hypothesis which handles the skew.
After we reset for the inferential analysis, we immediately run into a problem: this is a black box. We know it has no input, and outputs a floating-point number, and that’s it. How can we form any hypothesis, let alone a null and alternative? We’ve no choice but to make something up. I’ll set my null to be “the black box outputs a random floating-point number,” and the alternative to “the output follows a Gaussian distribution with a mean of 0 and a standard deviation of 1.” Turn the crank, aaaand…
Samples = 1000001 log(Bayes Factor) = 26705438.01142 (That means the most likely hypothesis is H1 (Gaussian distribution, mean = 0, std.dev = 1))
Unsurprisingly, our alternative does a lot better than our null. But our alternative is wrong! We’d get that impression pretty quickly if we watched the numbers streaming in. There’s an incredible temptation to take that data to refine or propose a new hypothesis, but that’s an abductive move. Inference is really letting us down.
Worse, this black box isn’t too far off from the typical science experiment. It’s rare any researcher is querying a black box, true, but it’s overwhelmingly true that they’re generating new data without incorporating other people’s datasets. It’s also rare you’re replicating someone else’s work; most likely, you’re taking existing ideas and rearranging them into something new, so prior findings may not carry forward. Inferential analysis is more tractable than I painted it, I’ll confess, but the limited information and focus on novelty still favors the abductive approach.
But think a bit about what I did on the inferential side: I picked two hypotheses and pitted them against one another. Do I have to limit myself to two? Certainly not! Let’s rerun the analysis with twenty-two hypotheses: the flat distribution we used as a null before, plus twenty-one alternative hypotheses covering every integral mean from -10 to 10 (though keeping the standard deviation at 1).
Samples = 100001 log(likelihood*prior), H0 = -4436161.89971 log(likelihood*prior), H1, mean = -10 = -12378220.82173 log(likelihood*prior), H1, mean = -9 = -10866965.39358 log(likelihood*prior), H1, mean = -8 = -9455710.96544 log(likelihood*prior), H1, mean = -7 = -8144457.53730 log(likelihood*prior), H1, mean = -6 = -6933205.10915 log(likelihood*prior), H1, mean = -5 = -5821953.68101 log(likelihood*prior), H1, mean = -4 = -4810703.25287 log(likelihood*prior), H1, mean = -3 = -3899453.82472 log(likelihood*prior), H1, mean = -2 = -3088205.39658 log(likelihood*prior), H1, mean = -1 = -2376957.96844 log(likelihood*prior), H1, mean = 0 = -1765711.54029 log(likelihood*prior), H1, mean = 1 = -1254466.11215 log(likelihood*prior), H1, mean = 2 = -843221.68401 log(likelihood*prior), H1, mean = 3 = -531978.25586 log(likelihood*prior), H1, mean = 4 = -320735.82772 log(likelihood*prior), H1, mean = 5 = -209494.39958 log(likelihood*prior), H1, mean = 6 = -198253.97143 log(likelihood*prior), H1, mean = 7 = -287014.54329 log(likelihood*prior), H1, mean = 8 = -475776.11515 log(likelihood*prior), H1, mean = 9 = -764538.68700 log(likelihood*prior), H1, mean = 10 = -1153302.25886 (That means the most likely hypothesis is H1 (Gaussian distribution, mean = 6, std.dev = 1))
Aha, the inferential approach has finally gotten us somewhere! It’s still wrong, but you can see the obvious solution: come up with as many hypotheses as you can to explain the data, before we look at it, and run them all as the data rolls in. If you’re worried about being swamped by hypotheses, I’ve got a word for you: marginalization. Bayesian statistics handles hypotheses with parameters by integrating over all of them; you can think of these as composites, a mash of point hypotheses which collectively do a helluva lot better at prediction than any one hypothesis in isolation. In practice, then, Bayesians have always dealt with large numbers of hypotheses simultaneously.
The classic example of this is conjugate priors, where we carefully combine hyperparameters to evaluate a potentially infinite family of probability distributions. In fact, let’s try it right now: the proper conjugate here is the Normal-Inverse-Gamma, as we’re tracking both the mean and standard deviation of Gaussian distributions.
Samples = 1000001 μ = 5.61148 λ = 1000001.00000 α = 500000.50000 β = 992457.82655 median = 5.47287
That’s a good start, μ lines up with the mean we calculated earlier, and λ is obviously the sample count. The shape of the posteriors is still pretty opaque, though; we’ll need to chart this out by evaluating the Normal-Inverse-Gamma PDF a few times.
Excellent, the inferential method has caught up to abduction! In fact, as of now they’re both working identically. Think: what’s the difference between a hypothesis you proposed before collecting the data, and one you proposed after? In frequentism, the stopping problem implies that we could exit early and falsely reject our null, when data coming down the pipe would have pushed it back to “fail to reject.” There, the choice of hypothesis could have an influence on the outcome, so there is a difference between the two cases. This is made worse by frequentism’s obsession over one hypothesis above all others, the null.
Bayesian statistics is free of that problem, because every hypothesis is judged on their relative likelihood in reference to a dataset shared by all hypotheses. There is no stopping problem baked into the methodology. Whether I evaluate any given hypothesis before or after I collect the data is irrelevant, because either way it has to cope with all the data. This also frees me up to invent hypotheses whenever I wish.
But this also defeats the main attack against falsification. The whole point of invoking abduction was to save us from asserting any hypotheses in the beginning; if there’s no difference in when we invoke our hypotheses, however, then falsification might still apply.
Here’s where I return to giving Professor Moriarity a hand. He began that video by saying scientists usually don’t engage in falsification, hence it cannot be The Scientific Method, but ended it by approvingly quoting Feynman: “We are trying to prove ourselves wrong as quickly as possible, because only in that way can we find progress.” Isn’t that falsification, right there?
This is yet another area where frequentist and Bayesian statistics diverge. As I pointed out earlier, frequentism is obsessed with falsifying the null hypothesis and trying to prove it wrong. Compare and contrast with what past-me wrote about Bayes Factors:
If data comes up that doesn’t square well with a hypothesis, its certainty takes a hit. But if we’re comparing it to another hypothesis that also doesn’t predict the data, the Bayes Factor will remain close to 1 and our certainties won’t shift much at all. Likewise, if both hypotheses strongly predict the data, the Factor again stays close to 1. If we’re looking to really shift our certainty around, we need a big Bayes Factor, which means we need to find scenarios where one hypothesis strongly predicts the data while the other strongly predicts this data shouldn’t happen.
Or, in other words, we should look for situations where one theory is… false. That sounds an awful lot like falsification!
But it’s not the same thing. Scroll back up to that Normal-Inverse-Gamma PDF, and pick a random point on the graph. The likelihood at that point is less than the likelihood at the maximum point. If you were watching those two points as we updated with new data, your choice would have gradually gone from about equally likely to substantially less likely. Your choice is more likely to be false, all things being equal, but it’s also not false with a capital F. Maybe the first million data points were a fluke, and if we continued sampling to a billion your choice would roar back to the top? This is the flip-side of having no stopping problem: the door is always left open a crack for any crackpot hypotheses to make a comeback.
Now look closely at the scale of the vertical axis. That maximal likelihood is well above 100%! In fact it’s somewhere around 4,023,000% by my calculations. While the vast majority are dropping downwards, there’s an ever-shrinking huddle of points that are becoming more likely as data is added! Falsification should only make things less likely, however.
Under Bayesian statistics, falsification is treated as a heuristic rather than a core part of the process. We’re best served by trying to find areas where hypotheses differ, yet we never declare one hypothesis to be false. This saves Moriarty: he’s both correct in disclaiming falsification, and endorsing the process of trying to prove yourself wrong. The confusion between the two stems from having to deal with two separate paradigms that appear to have substantial overlap, even though a closer look reveals fundamental differences.
I’d never heard of C.P. Snow until Steven Pinker brought him up, but apparently he’s quite the deal. Much of it stems from a lecture Snow gave nearly sixty years ago. It’s been discussed and debated (funny meeting you here, Lawrence Krauss) to the point that I, several generations and one ocean away, can grab a reprint of the original with an intro about as long as the lecture itself.
Snow’s core idea is this: two types of intellectuals, scientists and elite authors, don’t talk with one another and are largely ignorant of each other’s work. His quote about elite authors being ignorant of physics is plastered everywhere, so I’d like to instead repeat what he said about scientists being ignorant of literature:
As one would expect, some of the very best scientists had and have plenty of energy and interest to spare, and we came across several who had read everything that literary people talk about. But that’s very rare. Most of the rest, when one tried to probe for what books they had read, would modestly confess “Well, I’ve tried a bit of Dickens”, rather as though Dickens were an extraordinarily esoteric, tangled and dubiously rewarding writer, something like Ranier Maria Rilke. In fact that is exactly how they do regard him: we thought that discovery, that Dickens had been transformed into the type-specimen of literary incomprehensibility, was one of the oddest results of the whole exercise. […]
Remember, these are very intelligent men. Their culture is in many ways an exacting and admirable one. It doesn’t contain much art, with the exception, and important exception, of music. Verbal exchange, insistent argument. Long-playing records. Colour photography. The ear, to some extent the eye. Books, very little, though perhaps not many would go so far as one hero, who perhaps I should admit was further down the scientific ladder than the people I’ve been talking about – who, when asked what books he read, replied firmly and confidently: “Books? I prefer to use my books as tools.” It was very hard not to let the mind wander – what sort of tool would a book make? Perhaps a hammer? A primitive digging instrument?
[Snow, Charles P. “The two cultures.” (1959): pg. 6-7]
To be honest, I have a hard time comprehending why the argument exists. If I were to transpose it to my place and time, it would be like complaining that Margaret Atwood, Alice Munro, and Michael Ondaatje are shockingly ignorant of basic physics, while if you were to quiz famous Canadian scientists about Canadian literature you’d eventually drag out a few mentions of Farley Mowat. I… don’t see the problem? Yes, it would be great if more people knew more things, but if you want to push the frontiers of knowledge you’ve got to focus on the specifics. Given that your time is (likely) finite, that means sacrificing some general knowledge. It would be quite ridiculous to ask someone in one speciality to explain something specific to another.
If we forget the scientific culture, then the rest of western intellectuals have never tried, wanted, or been able to understand the industrial revolution, much less accept it. Intellectuals, in particular literary intellectuals, are natural Luddites. [pg. 11-12]
The academics had nothing to do with the industrial revolution; as Corrie, the old Master of Jesus, said about trains running into Cambridge on Sunday, `It is equally displeasing to God and to myself’. So far as there was any thinking in nineteenth-century industry, it was left to cranks and clever workmen. American social historians have told me that much the same was true of the
U.S. The industrial revolution, which began developing in New England fifty years or so later than ours, apparently received very little educated talent, either then or later in the nineteenth century. [pg. 12]… do we understand how they have happened? Have we begun to comprehend even the old industrial revolution? Much less the new scientific revolution in which we stand? There never was any thing more necessary to comprehend. [pg. 14]
Yep, that’s Snow trashing authors of high fiction for not having an understanding of the Industrial Revolution. It’s not an isolated case, either; Snow also criticises Cambridge art graduates for not being aware of “the human organisation” behind buttons [pg. 15]. He might as well have spent several paragraphs yelling at physicists for being unable to explain why Houlden Caulfield wanted to be a gas station attendant, he’s that far from reality.
Which gets us to the real consequences of Snow’s divide, and how he proposes heading them off at the pass.
To say we have to educate ourselves or perish, is a little more melodramatic than the facts warrant. To say, we have to educate ourselves or watch a steep decline in our own lifetime, is about right. We can’t do it, I am now convinced, without breaking the existing pattern. I know how difficult this is. It goes against the emotional grain of nearly all of us. In many ways, it goes against my own, standing uneasily with one foot in a dead or dying world and the other in a world that at all costs we must see born. I wish I could be certain that we shall have the courage of what our minds tell us. [pg. 20]
This disparity between the rich and the poor has been noticed. It has been noticed, most acutely and not unnaturally, by the poor. Just because they have noticed it, it won’t last for long. Whatever else in the world we know survives to the year 2000, that won’t. Once the trick of getting rich is known, as it now is, the world can’t survive half rich and half poor. It’s just not on.
The West has got to help in this transformation. The trouble is, the West with its divided culture finds it hard to grasp just how big, and above all just how fast, the transformation must be. [pg. 21-22]
So we need to educate scientists about the works of elite authors, and those authors about the work of scientists… because otherwise Britain will become impoverished, and/or we’d end poverty faster?! That doesn’t square up with the data. Let’s look at what the government of Namibia, a well-off African country, thinks will help end poverty.
- Improving access to Community Skills Development Centres (Cosdecs) in remote areas and aligning the curriculum with that of the Vocational Training Centres.
- To improve career options and full integration into the modern economy, there is need to introduce vocational subjects at upper primary and junior secondary levels. This will facilitate access to vocational education and labour market readiness by the youth.
- Improving productivity of the subsistence agriculture by encouraging the use of both traditional and modern fertiliser and by providing information on modern farming methods.
- The dismantling of the “Red Line” seems to hold some promise for livestock farmers in the North who were previously prevented access to markets outside of the northern regions.
- Consider establishing a third economic hub for Namibia to relief Khomas and Erongo from migration pressure. With abundant water resources, a fertile land and being along the Trans Zambezi Corridor, Kavango East is a good candidate for an agricultural capital and a logistic growth point.
- Given persistent drop-out rates especially in remote rural areas, there is need for increased access to secondary education by addressing both the distance and the quality of education.
- Educate youth on the danger of adolescence pregnancy both in terms of exclusion from the modern economy and health implications.
- Given the established relationship between access to services, poverty and economic inclusion, there is need for government to strive towards a regional balanced provision of access to safe drinking water, sanitation, electricity and housing. [pg. 58-59]
I don’t see any references to science in there, nor any to Neshani Andreas or Joseph Diescho. Britain’s the same story. But who knows, maybe an author/chemist who thought world poverty would end by the year 2000 has a better understanding of poverty than government agencies and century-old NGOs tasked with improving social conditions.
There’s a greater problem here, too. Let’s detour to something Donald Trump said:
How would we prove that Democrats don’t care about the military, the US border, or crime? The easiest approach would be to look at their national platform and see it those things are listed there (they’re not, I checked). A much harder one would be to parse their actions instead. If we can find a single Democrat who does care about crime, then we’ve refuted the claim in the deductive sense.
But there’s still an inductive way to keep it alive: if “enough” Democrats don’t care about those things, then Trump can argue he meant the statements informally and thus it’s still true-ish. That’s a helluva lot of work, and since the burden is on the person making the claim it’s not my job to run around gathering data for Trump’s argument. If I’m sympathetic to Trump’s views or pride myself in being intellectually “fair,” however, there’s a good chance I’d do some of his homework anyway.
Lurking behind all of the logical stuff, however, is an emotional component. The US-Mexico border, the military, and crime all stir strong emotions in his audience; by positioning his opponents as being opposed to “positive” things, at the same time implying that he’s in favour of them, Trump’s angering his audience and motivating them to being less charitable towards his opponents.
That’s the language of hate: emotionally charged false statements about a minority, to be glib. It’s all the more reason to be careful when talking about groups.
The non-scientists have a rooted impression that the scientists are shallowly optimistic, unaware of man’s condition. On the other hand, the scientists believe that the literary intellectuals are totally lacking in foresight, peculiarly unconcerned with their brother men,
in a deep sense anti-intellectual, anxious to restrict both art and thought to the existential moment. And so on. Anyone with a mild talent for invective could produce plenty of this kind of subterranean back-chat. [pg. 3]
If you side with either scientists or elite authors, this is emotionally charged language. At the same time, I have no idea how you’d even begin to prove half of that. Snow’s defence consists of quoting Adam Rutherford and T.S. Elliot, all the rest comes from his experiences with “intimate friends among both scientists and writers” and “living among these groups and much more.” [pg. 1] Nonetheless, that small sample set is enough for Snow to assert “this is a problem of the entire West.” [pg. 2] Calling scientists or elite authors a minority is a stretch, but the net result is similar: increased polarisation between the two groups, and the promotion of harmful myths.
Yes, Snow would go on propose a “third culture” which would bridge the gap, but if the gap doesn’t exist in the first place this amounts to selling you a cure after convincing you you’re sick.
What’s worse is that if you’re operating in a fact-deficient environment, you’ve got tremendous flexibility to tweak things to your liking. Is J.K. Rowling a “literary intellectual?” She doesn’t fit into the highbrow culture Snow was talking about, but she is a well-known and influential author who isn’t afraid to let her opinions be known (for better or worse). Doesn’t that make her a decision maker, worthy of inclusion? And if we’ve opened the door for non-elite authors, why not add other people from the humanities? Or social scientists?
This also means that one of the harshest critics of C. P. Snow is C. P. Snow.
I have been argued with by non-scientists of strong down-to-earth interests. Their view is that it is an over-simplification, and that
if one is going to talk in these terms there ought to be at least three cultures. They argue that, though they are not scientists themselves, they would share a good deal of the scientific feeling. They would have as little use-perhaps, since they knew more about it, even less use-for the recent literary culture as the scientists themselves. …I respect those arguments. The number 2 is a very dangerous number: that is why the dialectic is a dangerous process. Attempts to divide anything into two ought to be regarded with much suspicion. I have thought a long time about going in for further refinements: but in the end I have decided against. I was searching for something a little more than a dashing metaphor, a good deal less than a cultural map: and for those purposes the two cultures is about right, and subtilising any more would bring more disadvantages than it’s worth. [pg. 5]
He’s aware that some people regard “the two cultures” as an oversimplification, he recognises the problem with dividing people in two, and his response amounts to “well, I’m still right.” He’s working with such a deficiency of facts that he can undercut his own arguments and still keep making them as if no counter-argument existed.
I think it is only fair to say that most pure scientists have themselves been devastatingly ignorant of productive industry, and many still are. It is permissible to lump pure and applied scientists into the same scientific culture, but the gaps are wide. Pure scientists and engineers often totally misunderstand each other. Their behaviour tends to be very different: engineers have to live their lives in an organised community, and however odd they are underneath they manage to present a disciplined face to the world. Not so pure scientists. [pg. 16]
Snow makes a strong case for a third culture here, something he earlier said “would bring more disadvantages than it’s worth!” He’s seeing gaps and division everywhere, and defining things so narrowly that he can rattle off five counter-examples then immediately dismiss them (emphasis mine).
Almost everywhere, though, intellectual persons didn’t comprehend what was happening. Certainly the writers didn’t. Plenty of them shuddered away, as though the right course for a man of feeling was to contract out; some, like Ruskin and William Morris and Thoreau and Emerson and Lawrence, tried various kinds of fancies which were not in effect more than screams of horror. It
is hard to think of a writer of high class who really stretched his imaginative sympathy, who could see at once the hideous back-streets, the smoking chimneys, the internal price—and also the prospects of life that were opening out for the poor, the intimations, up to now unknown except to the lucky, which were just coming within reach of the remaining 99.0 per cent of his brother men.
Snow himself mentions Charles Dickens earlier in the lecture, a perfect fit for the label of “a writer of high class who really stretched his imaginative sympathy.” And yet here, he has difficulty remembering that author’s existence.
It’s oddly reminiscent of modern conservative writing: long-winded, self-important, and with only a fleeting connection to the facts. No wonder his ideas keep getting resurrected by them, they can be warped and distorted to suit your current needs.