Carol of Birds, Beasts and Men

Christus natus est! the cockChrist is born
Carols on the morning dark.

Quando? croaks the raven stiffWhen?
Freezing on the broken cliff.

Hoc nocte, replies the crowThis night
Beating high above the snow.

Ubi? Ubi? booms the oxWhere?
From its cavern in the rocks.

Bethlehem, then bleats the sheep
Huddled on the winter steep.

Quomodo? the brown hare clicksHow?
Chattering among the sticks.

Humiliter, the careful wrenHumbly
Thrills upon the cold hedge-stone.

Cur? Cur? sounds the cootWhy?
By the iron river-root.

Propter homine, the thrushFor the sake of man
Sings on the sharp holly-bush.

Cui? Cui? rings the choughTo whom?
On the strong, sea-haunted bluff.

Mary! Mary! calls the lamb
From the quiet of the womb.

Praeterea ex quo? criesWho else?
The woodpecker in pallid skies.

Joseph, breathes the heavy shire
Warming in its own blood-fire.

Ultime ex quo? the owlWho above all?
Solemnly begins to call.

De Deo, the little stareOf God
Whistles on the hardening air.

Pridem? Pridem? the jack snipeLong ago?
From the stiff grass starts to pipe.

Sic et non, answers the foxYes and no
Tiptoeing the bitter lough.

Quomodo hoc scire potest?How do I know this?
Boldly flutes the robin-redbreast.

Illo in eandem, squeaksBy going there
The mouse within the barley-sack.

Quae sarcinae? asks the dawWhat luggage?
Swaggering from head to claw.

Nulla res, replies the assNone
Bearing on its back the cross.

Quantum pecuniae? shrillsHow much money?
The wandering gull about the hills.

Ne nummum quidem, the rookNot a penny
Caws across the rigid brook.

Nulla resne? barks the dogNothing at all?
By the crumbling fire-log.

House-of-love

Nil nisi cor amans, the doveOnly a loving heart
Murmurs from its house of love.

Gloria in Excelsis! Then
Man is God and God is Man.

Charles Causley (1917–2003)

A sociopath writes about “love”

Reading the London Times yesterday, I was struck by the following extract from the forthcoming Confessions of a Sociopath: A Life Spent Hiding in Plain Sight by ME Thomas. (ME Thomas is an assumed name.)

Love, I have come to realise, is a vital entry point into the inner worlds of other people, the universal Achilles’ heel. People are so hungry for love. They die a little every day for want of it, for want of touch and acceptance. And I find it immensely satisfying to become someone’s narcotic. It isn’t just that you have more power over someone through love than any other means, but you have access to more parts of them. There are more levers to pull and buttons to push. I can bring relief to pain of which I am the direct and sole cause. I think nothing of deceiving or manipulating them.

Sociopaths are typically confident, charming, intelligent people, who are further characterized as having “no conscience” because they “cannot feel guilt”.

I think that way of characterizing the condition is misleading, because it is misinformed by hedonism. By hedonism I mean the assumption that motivation boils down to the internal mental economics of pleasure and pain. We do things in order to get pleasure or avoid pain, the story goes, so when we act morally we do so in order to avoid the pain of feeling guilty. Sociopaths “don’t feel guilt”, the story continues, so they don’t have the normal human “spur” to act morally.

If we consider sociopaths from the perspective of hedonism, we might conclude that they are better off than the rest of us because they feel less pain. But that’s probably wrong. The passage above is reminiscent of a tone deaf person saying how good it is not to hear music. Or a person with diminished sex drive expressing relief at not having to cope with sexual frustration. Or a person who has no concept of loyalty extolling the carefree joys of disloyalty. These are all unfortunate conditions – disorders, if you like – in which something valuable is missing.

The word ‘sociopath’ is nowadays more common than the older word ‘psychopath’. The reference to pathology or illness remains, as it should. But the newer prefix ‘socio’ suggests that people who have this illness do not fit into society properly. If anything, the very opposite is true: sociopaths seem unusually eager to win a sort of “political” success. Furthermore, winning that success would normally involve behaving in morally mainstream ways, thereby winning society’s approval and the social power that comes with it. The most vocal opponents of racism, sexism and homophobia are more likely to be sociopaths than ordinary people who just quietly get on with avoiding these evils.

Against hedonism, I’d argue that humans (and all other animals) normally do things in order to bring about objective states of affairs. Any pleasure or pain involved are normally by-products of perceived success or failure in realizing those states of affairs. When we act morally, we try to bring about a state of affairs we regard as morally valuable. Guilt is the sense of failure we experience when we do not succeed. It is the by-product of a specific type of failure.

Now the author above has a very well-developed sense of success and failure. She takes evident pride in her many successes (in bringing about social rather than morally valuable states of affairs). In that pride, perhaps we can see the sociopath’s Achilles’ heel. People who take great pride in success tend to take great shame in failure. Most have a great aversion to admitting failure, even to themselves. Those who don’t admit their own mistakes can’t learn from them or correct themselves. I wonder how long it will take the author above to lose social credibility as she makes the same mistake over and over again, blind to the fact that it is a mistake?

Scientific realism versus “scientism”

I’m a scientific realist. That is, I think electrons, viruses, force fields and many other entities posited by scientific theories are fully real. I think “dinosaurs roamed the earth”, or at least used to walk around on it.

But I am vehemently opposed to “scientism”. Scientism is the view that “science” can answer all questions, and that “the scientific method” is the only legitimate way of solving problems. I put the words ‘science’ and ‘scientific method’ in scare-quotes there, because scientism typically misconceives the nature of both. For example, its over-optimistic expectations of what science can do are inspired by the mistaken assumption that science yields certainty or something approaching certainty. That assumption in turn is usually inspired by the idea that science eschews guessing. That is profoundly wrong. Scientism tends to respect technical rigor rather than explanation, and tends to prefer arcane formulae to skeptical plain speech. Pseudo-science and scientism are two sides of the same coin.

(Alas, there is no recognized term for proponent of scientism, as of course the word ‘scientist’ won’t do.)

I’ll expand a bit on scientific realism. What does it mean to say that scientific entities are real? – At an absolute minimum, it means that many scientific theories are literally true, at least in outline. Anyone who believes a theory – in other words, anyone who thinks it is true – is thereby committed to the existence of whatever has to exist in order for the theory to be true.

But there’s more to it than that, because some things can exist in a less robust way than we need in the present context. For example, suppose we believe the mathematical truth that there is a prime number greater than five but less than ten. Then we are committed to the existence of the number seven. But the number seven is an abstract, causally inert entity (it is probably best to think of it as a set of sets). There are many similar entities whose existence we are committed to in a merely “formal” way as soon as we accept the formalism that describes them. For example, we accept truths about centers of gravity and lines of latitude and longitude, but our descriptions don’t posit them as fully real entities in the most robust sense of having causal powers.

Only entities that have causal powers are capable of shaping our theories and causing our beliefs about them. Causal links between our theories and their subject matters are important epistemologically. This epistemological ingredient in scientific realism is essential, because it’s crucial to answer the question whether we are obliged to “take science seriously”. If we have sufficient reasons to believe a scientific theory (such as Darwin’s) and it comes into conflict with something else we already believe (such as that God created life), then we are rationally obliged to give serious consideration to our respective confidence in each, and to adopt or abandon one or the other accordingly. In this way, science is capable of “throwing its weight around”.

To put it in a nutshell, scientific realists think science yields knowledge of the real world. But a realist’s understanding of knowledge has nothing to do with certainty, or with knowing that we have knowledge of the world when as a matter of fact we do happen to have it. Ideally, scientific beliefs are sustained by reliable processes between our theories and the entities they purport to describe. Most of those entities can’t be observed directly, nor can we observe in their entirety the processes that connect those entities to our beliefs about them. So typically, scientific beliefs are epistemically risky, and our attachment to them should be tentative. Various alternative explanations are always possible for any given range of phenomena. Some scientific theories are well-corroborated, while others are more speculative. Some scientific theories have great predictive power but little explanatory power, and vice versa. Science isn’t a monolith: there is good science and mediocre science, and some science is so bad it should be labeled ‘pseudo-science’.

Contrast that view with scientism, which assumes that scientific beliefs are the most trustworthy beliefs we can have. Under the spell of scientism, people think all problems should be approached by rigorously applying what they imagine to be “the scientific method” – which more often than not is just a version of bog standard traditional “empiricism”. That is, they tend to suppose we should start off making observations, so that we have a “basis” for theory. Scientism tends to understand science as a monolithic body of information determined by observations. All science has much the same status, it assumes, being the hallowed product of throwing off the yoke of superstition.

Scientism assumes that scientific theories are the product of rigor rather than creative use of the imagination. But that’s wrong: theory is under-determined by “data”. And there are many questions that science has no hope of answering. For example, take questions of value. Science might be able to discover psychological facts such as whether or not cats like ice cream, but it cannot tell us whether ice cream is nice. The latter is an expression of value rather than a description of fact, and it’s “subjective” in the sense that it differs from one individual to the next, and even from one moment to the next.

Wherever we find an “ought”, we are dealing with a matter of value rather than of fact. Obviously ethics is concerned with such matters, and although science is relevant to answering questions about value, it does not itself answer them. And “ought”s are found in nearly all human endeavors, from art to zoo-keeping. Epistemic “ought”s are critically important for the objectivity of science itself, as scientists have to judge how much a theory ought to be believed. They have to decide whether to adopt or abandon theories when they come into conflict. This judgment is “subjective” – it depends on each individual scientist’s other beliefs, and on that scientist’s particular weighting of theoretical “virtues” (simplicity, generality, etc.). The history of science reveals that the best scientists often made judgments that nowadays would be regarded as distinctly odd. Value judgments are an unavoidable aspect of all science, but they are the subject matter of no science.

If I had to identify scientism’s worst misconception about science, I would choose its assumption that the “probability” of a theory’s being true – in other words, how much it ought to be believed – is a matter of numerical measurement. There is deep confusion there between statistical relative frequency and credibility. But that’s another can of worms.

Using GREP in InDesign to find prime numbers

Prime numbers are those that are divisible only by themselves and by the number one. Now I dislike arithmetic, and my heart sinks whenever I hear the word ‘divisible’, because it suggests boring activities such as counting or doing “long division sums”.

But I enjoy working with text, and trying out clever things with “find” and “change to” in applications such as InDesign. So it was a real pleasure to learn recently that GREP can be used to find prime numbers. (GREP is InDesign’s implementation of “regular expressions” for matching text.) Grasping how it can do that also helps to throw light on the concept of a prime number. And it does so in an intuitive and simple way that does not involve doing arithmetic.

Imagine an old-fashioned pavement made out of a fixed number of rectangular paving slabs laid side by side. Imagine a child walking from one end of the pavement to the other. By “avoiding the cracks” between them, the child can always reach the last slab, whatever their number, by simply stepping from one slab to the next. But by jumping over alternate slabs (i.e. every second slab), the child might not be able to land on the last slab – it depends whether there is an even number of them. Likewise, by taking big leaps of three slabs at a time, our child will only be able to land on the last slab if their total number is a multiple of three. And so on.

I hope you can see how this might continue into larger and larger numbers. So imagine this going on, with our child taking larger and larger steps, possibly with the help of a pair of stilts. For example, if the pavement is 15 slabs in length, the fifteenth slab can be reached by taking five big leaps of three slabs each, or three even longer stilted strides of five slabs each.

Now here’s the really important thing about prime numbers: the last slab of a prime number of such slabs can only be reached by taking a single step over all of the slabs that precede it.

GREP can be used to find prime numbers, because a simple GREP expression can match non-prime numbers. It manages to do that by mimicking the behavior of a child stepping over multiple paving slabs as just described.

Let’s build up a GREP expression slowly to see how this works. By analogy with reaching all the way to the final slap of a pavement, we want our GREP expression to match an entire series of letters. Let’s choose any letter at random, such as capital M.

We should start off with the simplest of GREP expressions (for clarity, they have this dark red color): the single letter M will match any single instance of the letter M. If I have a long series of Ms (like this: MMMMMMMMM) the GREP expression M+ will match the whole series at once. That’s because the plus sign asks it to match one or more Ms, and by default GREP is “greedy” – it will match as much as it can, in this case the whole series. We can change that default behavior by adding a question mark. In isolation, M+? will match the same as M on its own.

What we want to build is a GREP expression that will mimic the behavior of a child skipping over whole paving slabs (plural) rather than one-by-one by simply stepping over the cracks between them. The expression MM+? works for that purpose, because it will match two or more instances of the letter M, at the same time as matching as little as possible thanks to the ? at its end. This gets really useful when combined with parentheses to make a “unit” (MM+?), and \1 to match whatever that unit matches (the number one is used here because it’s the “first unit” in the entire expression).

Bearing in mind what I have just said about the default “greediness” of GREP and the way it can be overridden with a question mark ?, consider the following expression:

(MM+?)\1+

This expression is nearly what we’re looking for, as it matches as much as can be matched by repeatedly re-using its smallest constituent parts, where the parts in question are anything bigger than single letters. To illustrate, consider this series of six Ms: MMMMMM.

The MM+? in parentheses matches the first two Ms in MMMMMM. It won’t match all of them because the ? tells it to match as little as possible, and it won’t match just one, because it must match at least two. So now \1 matches a pair of Ms. So \1+ matches as many pairs of Ms as it can, to try and match all six Ms. As it happens, just two further pairs are needed.

This is analogous to a child reaching the final slab of a pavement of six slabs by jumping over the first two slabs in one go, then repeating the same feat twice. Reaching the last of any even number of slabs involves the same procedure, repeating the initial jump as many times as may be necessary.

But now suppose we use the same expression to try to match nine Ms. Just repeating matching pairs won’t work this time, because nine isn’t a multiple of two. This is where GREP does something clever. It “backtracks” as soon as it has to give up on its initial attempt to match the whole series by repeating a matching pair. Next, it tries matching MM+? to three Ms instead of two. This is what it must do, if you think about it, since it is trying to match as little as possible with the part of the expression in parentheses, yet as much as possible with the entire expression. The default “greediness” of GREP remains the “prime directive”, and it might be able to match more by trying repeated triples rather than repeated pairs of matched letters. And in the case of nine letters, it turns out happily again, with \1+ matching two further triples.

This is analogous to a child reaching a ninth slab by leaping over three in one go at first, then repeating it two more times.

I hope it’s obvious how this continues. GREP will keep trying out larger and larger initial matches as long as it fails to match the entire series by repeating its initial match. With non-prime numbers of letters, it will eventually succeed. But with prime numbers, it will never arrive at an initial match whose repetition succeeds in matching the entire series. So prime numbers are those that GREP can’t match when searching in series of the same character (such as the letter M).

There are couple of loose ends to tie up. GREP needs to recognize the start and the end of such a series. We might tell it only to look within entire paragraphs, in which case we should put ^ at the start of the expression and $ at the end (this is a standard GREP convention). Or we might use spaces between series to mark them off from each other, and look for any character except spaces instead of the letter M. Using standard GREP code for “positive lookbehind” (?<= ), “positive lookahead” (?= ), and “anything but” [^ ] set to spaces, it ends up like this:

(?<= )([^ ][^ ]+?)\1+(?= )

The expression (?<= )([^ ][^ ]+?)\1+(?= ) matches any series of the same character whose length is non-prime, but it won’t match any whose length is prime. It’s a straightforward matter to apply this in InDesign or any equivalent application to find prime numbers. (Interested readers familiar with InDesign can download a simple Javascript that demonstrates the basic idea here.)

I have tested several scripts for generating and testing quite large prime numbers, and GREP works remarkably efficiently when put to this unintended purpose. In doing so, I have acquired a more intuitive grasp of what prime numbers are, and why they are part of nature. For example, 13-year cicadas and 17-year cicadas only have to compete against each other every 13 × 17 = 221 years, when they emerge in the same year. It is no accident that evolution stumbles upon prime numbers in this sort of situation.

I can see why we might we might call primes the “building blocks” of the counting numbers. Best of all, I haven’t had to do any arithmetic! Hate arithmetic!