The Double Shame

When I first discovered poetry at about the age of 17, it was mainly through the works of (in chronological order of discovery) Siegfried Sassoon, Brian Patten, W.H.Auden and Stephen Spender. The Double Shame was one of my favourites then, but in recent years it has slipped down the pecking order because I eventually realised I didn’t actually know what it was about. In those days I cared less for meaning and more for the immediate impact of the words; wonderful poetic song lyrics were the order of the day, such as the many songs written for Cream by Pete Brown – e.g. “Yellow tigers crouched in jungles in your dark eyes” … marvellous!

But what was this one about? I have recently wondered whether it was addressed to the poet’s brother, whose wife Margaret died of cancer. It may be no accident that The Double Shame  immediately precedes Elegy for Margaret in the Collected Poems. But then I found a website whose author considered it to be a poem about a dead relationship. Hmm, that’s possible. What do you think?

You must live though the time when everything hurts
When the space of the ripe, loaded afternoon
Expands to a landscape of white heat frozen
And trees are weighed down with hearts of stone
And green stares back where you stare alone,
And the walking eyes throw flinty comments,
And the words which carry most knives are the blind
Phrases searching to be kind.

Solid and usual objects are ghosts
The furniture carries cargoes of memory,
The staircase has corners which remember
As fire blows reddest in gusty embers,
And each empty dress cuts out an image
In fur and evening and summer and spring
of her who was different in each.

Pull down the blind and lie on the bed
And clasp the hour in the glass of one room
Against your mouth like a crystal doom.
Take up the book and stare at the letters
Hieroglyphs on sand and as meaningless –
Here birds crossed once and a foot once trod
In a mist where sight and sound are blurred.

The story of others who made their mistakes
And of one whose happiness pierced like a star
Eludes and evades between sentences
And the letters break into eyes which read
The story life writes now in your head
As though the characters sought for some clue
To their being transcendently living and dead
In your history, worse than theirs, but true.

Set in the mind of their poet, they compare
Their tragic sublime with your tawdry despair
And they have fingers which accuse
You of the double way of shame.
At first you did not love enough
And afterwards you loved too much
And you lacked the confidence to choose
And you have only yourself to blame.

Stephen Spender

In Railway Halls

A poem from the 1930s I think – but it is sadly just as relevant today.

In railway halls, on pavements near the traffic
They beg, their eyes made big by empty staring
And only measuring Time, like the blank clock.

No, I shall weave no tracery of pen ornament
To make them birds upon my singing tree:
Time merely drives these lives which do not live
As tides push rotten stuff along the shore.

There is no consolation, no, none,
In the curving beauty of that line
Traced on our graphs through History, where the oppressor
Starves and deprives the poor.

Paint here no draped despairs, no saddening clouds
Where the soul rests, proclaims eternity.
But let the wrong cry out as raw as wounds
This time forgets and never heals, far less transcends.

Stephen Spender.

Life and Literature in Anita Brookner’s “Lewis Percy”

This piece was originally read to Roundhill Book Group on 16 August 2018

Lewis Percy is a rare thing among Anita Brookner’s 24 novels in that its main character is male. I know of only three others. In her other novels there are male characters but they are subsidiary, and mostly crude caricatures.

At the beginning of the book we see the 22-year-old Lewis doing his PhD research on French literature in Paris. It is 1959. His topic is “The Hero as Archetype”. He attends frequent soirees with his landlady and two other female tenants of the boarding-house, one of whom he secretly admires. When he returns to London Lewis lives with his ageing mother (his father died when he was young) and writes up his thesis at the British Museum.

After his mother’s death, Lewis courts and marries Tissy, who works in the public library. Tissy is a very quiet, undemonstrative girl who has agoraphobia and lives with, and under the shadow of, her larger-than-life mother, Thea. Again there is no father, but Thea has a lover, a doctor. Lewis takes a job in the university library.

Tissy comes out of herself a little as she moves into the role of the competent housewife. But it all starts to go wrong when Lewis invites his friend Penry and Penry’s sister Emmy for dinner. Tissy takes against the flamboyant, flirtatious Emmy while Lewis takes to her in equal measure. When Lewis is called to Penry’s house late one night to intervene in a quarrel between Penry and his gay lover, Emmy tries to seduce Lewis; at first he is responsive, but then changes his mind. However, as far as Tissy is concerned, Lewis’s merely going to the house is tantamount to adultery. She leaves Lewis and moves back to her mother’s. A few months later she gives birth to a baby girl, Jessica.

Back on his own, with no wife and little access to his daughter, and with little interest in his job, which is under threat from new technology, Lewis’s prospects look grim. Then one day an American academic turns up at the library and invites him to a visiting lectureship at his college in Massachusetts. At first reluctant to accept, he changes his mind, thinking of his daughter:

“But the little girl, who was growing to resemble her mother, would not be ready for him for many a long year. Suddenly he did not see why he should spend the intervening time alone, or waste it on people who did not, would never, love him. If he could make a home for them in America, might not his daughter want to live with him there? And would it not be an ideal solution, to welcome her to another country, a country which he imagined as a sort of paradise?”

However he still has reservations about this decision. Then, somewhat out of the blue, he sends a message to Emmy via Penry that he wants to marry her. But there is no reply, and Lewis prepares to depart on his own.

Unexpected endings are very rare in Brookner’s novels; normally they wind down to a conclusion that the reader has perhaps suspected from the very start. Lewis Percy is different. If you are not planning to read the book, here is its final sentence:

“Turning round for his last look at England, he saw Emmy, plunging through the crowd, necklaces flying, laughing, swearing, apologising, and waving her boarding pass in her upheld hand.”

Lewis’s first impression of Tissy: (p51)

“Lewis saw that despite her pallor, or because of it, she had an air of delicacy, or narrowness, that pleased him. Her clothes were asexual: a pale blue sweater and a grey flannel skirt, schoolgirl’s clothes, which made her seem younger than her age. He reckoned she was about twenty-five. What he noticed mostly were her long unmarked slightly upcurling fingers, white as if they had never been engaged in a common or unseemly task. The face, momentarily enlivened by her emotion and the forwardness she obviously thought she was exhibiting, was equally long and pale, and could, he thought, look mournful. The face was framed by thick hair, in a colour midway between blonde and beige, and held back by a black velvet band …. She had large, rather beautiful dark blue eyes, shadowed by long colourless lashes.”

Lewis’s first impression of Thea: (p55)

“The mother, thought Lewis, was a beauty, a bold, strenuous-looking woman, with a curiously out-of-date sexual appeal. She was heavily made up, her mouth a dark red, her eyebrows arched in permanent astonishment, an artificial streak of white inserted into her upswept dark hair. She had exactly the same look of disdain that he remembered from the screen goddesses of his childhood …. She was still in the prime of life, not much more than fifty, he supposed. She looked tricky, hard to please, and also capricious, exigent, the last person to be the guardian of a pristine semi-invalid daughter. A fur coat was flung back from a plumpish compact little body; her skirt was short enough to show fine legs in fine stockings.”

A common theme in Anita Brookner is the tension between “life” and “literature”. It is there right at the start: in the first sentence of her first novel, A Start in Life: “Dr Weiss, at forty, knew that her life had been ruined by literature.” After a valiant attempt to win her man with a home-cooked meal that goes horrendously wrong due to the man’s self-centred thoughtlessness, the young Ruth Weiss gives up her flat and returns to the family home:

“She did not really mind being at home. It was anonymous, familiar; she had no further need for independence. Her recent encounter with reality had shocked her and made her feel childish. Only her books and her notes allowed her some measure of dignity …”

(However, I don’t believe that it was literature that ruined Ruth’s life. What ruined her life was her selfish, thoughtless parents, who had not wanted her in the first place and treated her as though she were a servant, to step in and look after them when their housekeeper left. But literature was always there, waiting to claim her after each failure in life).

In Providence, Brookner’s second novel, the heroine, Kitty Maule, is passed over by the man she hopes to marry for one of her students; but a glittering academic career beckons as consolation. Kitty’s self-image incorporates these aspirations as though they belonged to two separate selves:

“To her not very great surprise, she had passed the test of her lecture with flying colours. Coming home alone, afterwards, she had felt a sense of well-being and almost of worth; she was assured of a permanent post for next year and could thus conclude that her apprenticeship was at an end. For two days she had rested secure in this knowledge and also in anticipation of a pleasant future … This would be, as it were, her daytime self. For stronger emotions and delights, for a more positive future, she would place her faith in the events that would be brought to birth by Maurice’s (and her) dinner party.”

Lewis Percy displays the same tension. In Paris, he appears to view his female neighbours as though they were characters in a book:

“As to his attitude towards [women], it was, given his extreme youth, still unformed, but he looked to his little group, the first representatives of the species he had been given to study at close quarters, with a mixture of love, respect, and innocent enquiry. He seemed to think that all knowledge would come to him in this context.”

Later, Lewis too contemplates two different versions of himself:

“Writing, which came easily, also underlined his indeterminate status … The life of action, which he could not quite visualise, remained out of reach. He had the disagreeable sensation of signing away his future. Having found that he could do this work he seemed to have sealed his fate. This idea unsettled him profoundly.”




The “Most Famous Equation”

In 2014 I posted a rather light-hearted blog piece about energy and mass in special relativity. Recently, in response to a talk I gave at the IHPS conference in June, and a discussion that arose during that conference, I have written a more serious piece about the same topic.

E = mc2 may well be “the most famous equation”, but what does it actually mean? In particular, what does special relativity say about the relationship between energy and mass? Scientists and philosophers do not all agree, among themselves or with each other, about this. In this short piece I will critically appraise one recent study, and suggest that, while it is welcome, there is still more work to do on this topic.

In his paper Interpretations of Einstein’s Equation E = mc2, Francisco Flores identifies six distinct positions on this question, which he believes constitute “all of the leading and influential interpretations of Einstein’s equation in the literature”. He then applies to each of the six three tests, which, he argues, a successful interpretation ought to satisfy. These tests then rule out five of the six, and Flores concludes that the remaining interpretation is the only viable one.

The Interpretations

Flores divides the six interpretations into two sub-groups. The first four he describes as property interpretations; the last two are ontological interpretations.

The property interpretations are possible answers to the question “do energy and mass describe the same, or distinct, properties of a body?” If the latter, a subsidiary question comes into play: “can one of these properties be converted into the other?” Flores identifies positions he describes as “same-property”; “different-properties, no-conversion”, and “different-properties, conversion”. He also highlights one view which he describes as “one-property, no-conversion”, in which only mass is regarded as a property (and hence there can be no conversion).

The last two interpretations, which Flores does not distinguish from one another very clearly, are described as “ontological” because he says they concern “the fundamental stuff of modern physics”. Both depend on the assumption that “there is no distinction between mass and energy as properties”, and hence they belong, in a sense, to the “same-property” camp.

My first worry about this contest is that he does not include an option analogous to “None of the Above” or “RON” (Re-Open Nominations) as sometimes used in elections and surveys. If one were to ask a random sample of physicists “how would you interpret the equation E = mc2”, one would be likely to find the response “I wouldn’t” among the most popular. Since the equation is usually presented to physics students as itself an option – and, furthermore, one that modern physics generally avoids – it would be difficult to know how else to answer the question. Luckily, the interpretations that Flores discusses will equally well do duty as interpretations of the rôles of, and relationship between, mass and energy in special relativity – a topic on which all physicists and philosophers of physics are likely to have a view.

The Tests

The first test Flores applies is described as “the familiar goal of philosophical interpretations of physical theories”, namely, that the theory is required to answer the question “what would the world be like if this theory were true?” In other words, the theory must make predictions about the world (and, though Flores does not say as much, we would surely hope that they were testable predictions). Secondly, he requires that “an interpretation I of a given physical theory T does not appeal to hypotheses outside T or theories other than T”. The third criterion tests the theory for what Flores calls “philosophical uniformity”: it asks whether the theory treats “elements in the mathematical formalism of T that are similar in type” similarly, or explains why these elements should be treated differently.

Rest Mass and Relativistic Mass

Flores is careful to establish at the outset that he “will focus exclusively” on rest mass as opposed to relativistic mass in the paper. This is a sensible decision, not least because no other type of mass is recognised by most physicists nowadays. However, it does restrict the applicability of the equation E = mc2 to measurements made in the rest frame, and strictly speaking, as Lev Okun has pointed out, the equation should then be written in the form in which Einstein introduced it:

E0 = mc2

where E0 is the energy measured in the rest frame, and m is the rest mass [Okun p31].Yet at least one of the interpretations that Flores investigates – that of Bondi and Spurgin – makes it equally clear that the authors are considering relativistic mass, not rest mass: they claim that the equation holds in “all frames of reference” [Bondi & Spurgin p62] and use the symbols m, m0 to denote relativistic and rest masses respectively, so that, for them, E = mc2 is an equation relating energy to relativistic mass [1]. Flores does not mention this.

Another interpretation – that of Wolfgang Rindler – also clearly treats the equation as relating energy to relativistic mass. Rindler opts for a definition of relativistic momentum to coincide with the non-relativistic case, in other words, p = mv. This choice of definition then commits him to relativistic mass. For instance, he states that “if a momentum of the form mu is to be conserved, then the mass m must be of the form m = γm0” [Rindler p80]. This is somewhat more serious, since Rindler’s “different-properties, conversion” interpretation of the equation is the one singled out by Flores as the only viable one.

Units and Dimensions

One of the interpretations discussed by Flores – the “same-property” interpretation – rests heavily on an argument involving units and dimensions. This interpretation is associated with Arthur Eddington and R. Torretti. It is one of many claims made by certain physicists (among whom Eddington features prominently) on the basis of the assumption that, if a fundamental physical constant (such as c) is represented by a numerical value (and usually that value is 1) it becomes dimensionless. Clearly, if we make such a substitution in the equation E = mc2, we appear to have equality between energy and mass, which Eddington and Torretti then interpret as evidence that energy and mass are the same property.

Since the philosophy of measurement is a field largely neglected by most physicists (and many philosophers), misunderstandings about units and dimensions abound in the literature, as I have shown elsewhere [see e.g. Grozier (2017)]. Eddington’s mistake is to assume that, when “working in” a particular system of units in which c has the value 1, we can write Einstein’s equation as simply E = m and hence deduce that they are the same property. Apart from a worry about what happens when we move from that particular system of units to a system in which c does not have the value 1 (does it make sense to say that two properties are the same, but only when we are working in a certain system or systems of units?) we might reasonably object that, if we want to use a particular system of units, we must give those units names. It is legitimate to say that, in a certain system of units, the speed of light is “1 einstein” (where the “einstein” is my name for the unit of velocity in Eddington’s system) but it is not legitimate to just say that c is a pure number with the value 1. Flores treats Eddington and Torretti’s argument somewhat uncritically; he rejects it, but for different reasons. He does not seem to be aware of the particular problem I have just outlined.

Constructive and Principle Theories

Flores rightly points out, following Einstein, that special relativity is a principle theory (a “top-down” theory based on certain principles concerning the behaviour of macroscopic bodies) as opposed to a constructive theory (a “bottom-up” theory based on a what we know about matter at the fundamental level) and that such theories “do not afford bottom-up explanations” [Flores p259]. However, he fails to appreciate the full implications of this distinction.

Special relativity derives certain conclusions from its two assumptions (the principle of special relativity and the principle of the constancy of the velocity of light) by means of thought-experiments featuring “rigid bodies” which, as Harvey Brown has pointed out, and even Einstein himself acknowledged, are structureless [see Brown p.S89; also Einstein, pp 59,61]. Since these bodies have no internal structure, the theory cannot make any predictions concerning such things as the nature of heat; yet assertions that, because of E = mc2, a body gains mass when it is heated, are common in the literature [2]. Special relativity, as Einstein argued, ought to be deducible from first principles at the level of atoms, if not that of fundamental particles; but to do that would involve, at the very least, considerations of quantum mechanics: a simple model in which a photon is sent from one observer to the other and then reflected back to its source will not do when the “observers” are individual atoms or particles. Again, Flores does not seem to be aware of this problem, which, while it may not impact directly on the interpretation of E = mc2, is surely relevant [3]. For instance, in one of the interpretations considered by Flores – that of Marc Lange, who argues that energy is not a real property because it is frame-dependent (hence “one-property [mass], no-conversion”) – Lange requires the fundamental mass-energy relation of special relativity

E2 = p2c2 + m2c4

to hold simultaneously at the macroscopic and microscopic levels, and concludes that mass is not additive – a result which he uses to back up his argument that there is no conversion of mass to energy because the “mass defect” is a fiction based on the assumption of the additivity of mass. But how do we know that the equation holds for fundamental particles? Flores rejects Lange’s interpretation, but for a different reason.

Mass, Energy and Pluralism

Does it actually matter, though, which is the “correct” interpretation of the relationship between energy and mass in SR? Presumably not; it was, after all, perfectly possible that more than one of the six interpretations might pass Flores’ test, or that none would pass it: he was not necessarily looking for a single answer. As someone who has taken a physics degree within the last 20 years, I am inevitably inclined to avoid the concept of relativistic mass and to favour the “interconvertibility” view, since that is now the orthodoxy, at least among physicists. However, I can see the benefit of sometimes appealing to relativistic mass – for instance, in order to explain the unattainability of the velocity of light, since if mass increases with velocity it becomes harder to accelerate a body the faster it goes, and ultimately, as one approaches c, it becomes infinitely hard. Maintaining a pluralistic approach, and selecting a model that is appropriate to the problem in hand, seems a sensible, pragmatic way for philosophers and physicists to behave. And instead of worrying about which model is “true”, a better use of one’s time and energy would perhaps be to challenge the many inconsistencies and contradictions about mass and energy that one finds, not only in such likely places as press articles and popular science books, but also in physics textbooks, and even in some of the philosophical literature (and, indeed, on these “relativity mugs” on sale at the Science Museum shop! The small print says both “this formula suggests that tiny amounts of mass can be converted into huge amounts of energy” (conversion) and “matter and energy are really different forms of the same thing” (same-property).)

Relativity Mugs


Bondi, H. & Spurgin, C. 1987. Energy Has Mass. Physics Bulletin 38, 62-63.

Brown, H. 2005. Einstein’s Misgivings about his 1905 Formulation of Special Relativity. Eur. Jnl. Phys. 26, S85-S90.

Eddington, A. 1929. Space, Time & Gravitation. (Cambridge UP)

Einstein, A. 1969. Autobiographical Notes. in Schilpp, Albert Einstein: Philosopher-Scientist, vol.1, pp 1-94. (Open Court).

Flores, F. 2005. Interpretations of Einstein’s Equation E = mc2. Int. studies in the Phil. of Science 19, 245-260

Grozier, J. 2017. Should physical laws be unit-invariant? Studies in the History and Philosophy of Science (under review)

Lange, M. 2002. An Introduction to the Philosophy of Physics. (Oxford UP)

Okun, L. 1989. The Concept of Mass. Physics Today 42 (6) 31-16.

Rindler, W. 1977. Essential Relativity (Springer-Verlag)

[1] Hence Bondi and Spurgin do not even appear to be restricting this statement to inertial frames, which is usual when considering special, as opposed to general, relativity.

[2] These predictions remain mere conjectures, since they cannot be tested using current technology.

[3] This is not to suggest that the behaviour of fundamental particles is not consistent with SR; on the contrary, one of the first and most convincing verifications of SR was the observation that the lifetimes of muons from cosmic rays (and hence travelling at near light-speed relative to the observer) are significantly greater than those of muons moving slowly in the laboratory. However, a theory describing the behaviour of macroscopic objects cannot explain this fact.

Do the Laws of Physics Lie? (part 2)

[Continuing my earlier blog on Nancy Cartwright’s book How the Laws of Physics Lie.]

One thing about the philosophy of science is that it tries to cover a very wide spectrum of disciplines – not just physics, chemistry and biology but other subjects such as psychology and medicine. I have grave doubts about this approach; while applying a given method or concept across the entire spectrum may be beneficial in some sense, I think the individual sciences are too different for the same philosophical approach to work on all of them.

Nancy Cartwright certainly espouses the wide-spectrum approach. She regularly quotes examples from botany and medicine, despite the fact that her book is about the laws of physics. This may, however, be done partly to contrast physics with the other sciences. For instance, she maintains that a physical law such as the law of gravitation is not a causal law because it “provides no account of what makes things happen”. In contrast, she argues, laws such as “smoking causes cancer” and “aspirin relieves headache” are causal. But these sorts of statement are so woolly that they can surely hardly be classed as laws at all. I find myself screaming “How much smoking? What kind of cigarette? What sort of cancer? In what sort of body?” etc. Surely we all know at least one  person who has smoked all their life but not contracted cancer – so how can this be causal?

Her problem with laws such as that of gravitation may be simply because of the way in which it is often presented – in algebraic form. An algebriac equation can be changed around so as to make any quantity the subject, so there is no sesne of a “flow” of causation in the bald algebraic statement. But when I was at school, we learnt our physical laws in verbal form first. The law of gravitation would have been rendered something like this: “The gravitational force exerted by one body on another is proportional to the product of the masses divided by the square of the distance between them”. The term “exerted by” surely indicates causality here. No-one would say that the force is causing the masses to exist. And in the case of electromagnetic induction, we would say that “the induced emf is proportional to the rate of change of flux, and acts in a direction so as to oppose the change of flux”. Clear causality there, surely? And these are laws that always apply – every single time – and not just in certain circumstances, as in the case of smoking and cancer.

I think another part of the problem might be that Cartwright, like many “mainstream” philosophers, is stuck in a qualitative groove, and is used to dealing with statements about discrete entities that can be regarded as having, or not having, various properties – a very discrete world, where everything either is or isn’t something, with nothing in between. The grey world of continuously-varying quantities seems to take such people by surprise. In the book, she complains over and over again that the laws of physics do not “state the facts”.  She is very keen on “the facts”, but does not explain what they are, or how, and whether, we might know them. But she wants laws to be “true” – she wants them to make predictions that are at one with “the facts”. Earlier, I showed that this cannot be done in the case of the sort of “facts” that modern physics addresses – where the laws make predictions about quantities that are continuous variables, capable of taking any rational value, and possibly irrational ones too.

She actually addresses the question of approximations quite early in the book, on page 14. She says that “realistically-oriented philosophers are inclined to think that approximations raise no problems in principle. The “true” solution is the rigorous solution, and departures from it are required only because the mathematics is too difficult or too cumbersome …”

The second sentence here is disappointing. As I showed earlier, approximations are all we get – and not because the maths is too difficult, but because measurement, which can supposedly verify or falsify a law, returns not a number, but a confidence interval; and confidence intervals cannot be equal or unequal. So she says a sensible thing, but for the wrong reasons; and in any case, she then goes on to disagree with the view she has just set out.

Cartwright does not actually mention the Principle of Superposition by name, but she makes vague references to it. On page 59 she says that there is a presumption that “the explanatory laws ‘act’ in combination just as they would ‘act’ separately. I think this is probably somehting more than “a presumption”; I think it has probably been tested quite thoroughly. For instance, in the Thomson e/m experiemtn for the electron, it would be quite surprising (and very noticeable) if the deflection of the electron beam when either the magnetic or the electric field is turned off, were not explainable by exactly the same equations (including numerical values) as when the two fields act together. I could be wrong here, of course, adnd have to admit that i have not verified it myself (yet). But I bet you someone, somewhere, has.

When discussing how the cooking time of potatoes is affected by the salinity of the water and the altitude, she produces complicated-looking expressions in formal logic for each individual case but claims that “neither of these tells us what happens when we both add salt to the water and move to higher altitudes”.

Really? Surely this is a classic example of a function of two variables. We can express the cooking time T as a function of the salinity S and the altitude A in differential form as follows:

dT =  – k dS + m dA

where k and m are constants; then integrate to find

T = T0 kS + mA

 where T0 is a constant, i.e. does not depend on salinity or altitude. When both the salinity and the altitude are varied, this equation will tell us what happens, as long as we know the values of the constants, which can be found empirically.

About halfway through the book, we finally encounter some pretty heavy equations, and some circuit diagrams. Unfortunately that is the point at which I stop for now. I am fed up with reading it, I have more important things to do, and besides it is due back in the library. I will come back to it later. Maybe.

Do the Laws of Physics Lie?

Nancy Cartwright’s 1983 book How the Laws of Physics Lie is a classic of contemporary philosophy of science. I have dipped into it once or twice in the past, but never managed to read it all. Now, however, as I anticipate studying for an MSc in Philosophy of Science at LSE, for which it is on the suggested pre-reading list, I thought I ought to work my way through it a bit more methodically. As I read it, I plan a series of blog pieces on what I find.

Cartwright’s main thesis is that laws such as the law of gravitation do not apply to the real world because in the real world there are always other forces acting, such as electromagnetic ones. Newton’s law of gravitation, and Coulomb’s law for the electrostatic force, are true only in isolation – they are idealisations. She points out that when these laws are stated, they should be subject to a ceteris paribus condition (“all other things being equal”) – but this is rarely done.

Let’s assume from the outset that the use of the rather provocative word “lie” in the title can be attributed to a publisher bending over backwards to boost sales in a competitive market. I don’t think even Cartwright is suggesting that laws can “lie”, since that implies saying something while knowing it’s not true, and thus suggests that it is the work of a conscious mind and not an inanimate intellectual concept. People can lie; laws can’t. Let’s assume, therefore, that the title merely sums up what Cartwright states frequently in the book: that the laws of physics (or, at any rate, most of them) are false.

One problem I have with her argument is that she does not properly explain her objection to these laws. There are two possibilities: one is that they are just wrong because they assume ideal conditions, without any consideration of their numerical accuracy; the other is that, because of the additional forces which can’t be entirely eliminated, their numerical predictions do not match up with the values obtained by actual measurement.

I think that most scientists and philosophers, if asked, would say that the main function of a physical law is to predict the value of some quantity which can be measured (to test the theory), or to produce a predicted value which can be used in some process (such as the design of a bridge). So I think it is the second of the above possibilities that we are really concerned with here.

Cartwright says that “for bodies which are both massive and charged, the law of universal gravitation and Coulomb’s law … interact to determine the final force. But neither law by itself truly describes how the bodies behave”.

Here I assume she is talking about the numerical predictions made by these laws, and implicitly comparing them with the actual value of the force between the bodies. Now, it is possible that all she is saying is that we cannot ignore either of the component forces, and as long as we remember to allow for both, everything will be all right. But then, two lines further on she says “These two laws are not true; worse, they are not even approximately true”.[1] She is implying here that they are both separately false, and not just that using one of them on its own and ignoring the other one is no good.

I will deal with “approximate truth” later on. For now, let us try to reconstruct what Cartwright means when she says that either of these laws (say the Coulomb law) is “not true”.

She quotes Coulomb’s law as follows: “the bodies … produce a force of size qqʹ/r2.” (She doesn’t actually define q and qʹ, but we assume that they have their usual meaning, namely the charges on the two bodies). This is effectively a rather old-fashioned statement of Coulomb’s Law which only applies in a particular system of obsolete units. To give it its modern, unit-independent format, we say that the force F between two charged bodies, a distance r apart, is given by the formula

Coulomb Equationwhere the term 4πε0 is a constant. To say that this formula is “false” in a numerical sense is to suggest that, when one has inserted the measured values of q, qʹ and r together with the value of the constant, the resulting value of F will not be the same as the measured value of the force.

But there are several things wrong with this statement; category errors have been committed. We do not have “measured values” for the charges, the distance or the force. We have an exact value for the constant if we use the SI system of units. But testing the law by comparing the values of the two sides of the equation is not a case of comparing two numbers with each other. The entities we compare with each other are intervals, consisting of a measured value and an uncertainty; for instance, we may judge that the distance between the bodies is (1.000 ± 0.001) metres, meaning we have measured the distance to the nearest millimetre. (The interpretation of the “±” is by no means straightforward, but to fully go into that would take us too far from our current topic. Suffice it to say, for now, that the uncertainty defines some sort of interval).

Given that, all we can say, when we compare the intervals together, is that they agree to within a certain margin, or that they agree at a significance level of X, where the value of X is something we choose – it is not an objectively defined quantity.

It is, I believe, a common misconception among philosophers of science that numerical laws can be tested by simply comparing numbers to see whether they are the same: whether they “agree”. Recognising, at some level or other, that this is not possible, philosophers have introduced the term “approximate truth” to cover the fact that the agreement is not precise, but may be “good enough”, but approximate truth has not in itself been defined, let alone a particular definition accepted by the entire community.

It might seem a major stumbling-block if we have to conclude that we cannot test whether certain hypotheses are “true”, since the concept of truth is so central to philosophy, and also, hopefully, to science. But all is not lost. We can simply work to a level of precision that is suitable for the task in hand.

Let’s look at an actual example from the history of physics. In 1919 Arthur Eddington photographed certain stars during a solar eclipse, in order to test the theory of general relativity. The theory predicted a deflection of starlight by the gravitational field of the sun, by an amount 1.75 seconds of arc if the light ray just grazed the surface of the sun. He compared his measured angles of deflection with this predicted value, and with two alternative predictions based on two versions of Newtonian gravitation. The results, when put into a modern format, are quoted by Earman and Glymour, in a paper about the experiment, as (1.61 ± 0.44) and (1.98 ± 0.18) seconds of arc for two separate series of observations [2]. Given that the various theoretical values being tested were 1.75, 0.87 and 0 seconds, it is clear that these experimental results were not conclusive, despite the fact that the experiment has been hailed as a great triumph for general relativity. Karl Popper, who saw the Eddington experiment as a good template for how science should be done – which, for Eddington, meant by trying to “falsify” theoretical predictions – commented on the result that “Even if our measuring instruments at the time did not allow us to pronounce on the results of the tests with complete assurance, there was clearly a possibility of refuting the theory”.[3] But this “complete assurance” is a myth.

The formula actually being tested in the Eddington experiment gave the deflection δϕ in radians in terms of the speed of light c, the gravitational constant G, the solar mass M and angular separation of the star from the solar surface r:

Eddington Equation

For each star being observed, the deflection could be reduced to the solar surface by multiplication by a factor with r/R where R is the solar radius. Thus the predicted value of the deflection depends on the values of four quantities, two of which are fundamental constants and two of which are solar properties which have to be measured separately. All of these quantities therefore have uncertainties (although, if we are using SI units, the value of c is nowadays taken as exact, though not then) and so, therefore, does the predicted value of δϕ. Eddington appears to have thought that by improving the measuring instruments, one could arrive at a situation where both the measured value and the predicted value could be calculated exactly; but as we have seen, neither can. All the instrumental improvements in the world (including improvements to measurements of G and the mass and radius of the sun) cannot deliver Popper’s “complete assurance”, since there is always a finite uncertainty, and hence always a requirement for scientists to decide for themselves whether the uncertainty is “small enough”. After the advent of radio astronomy (in which measurements could be repeated many times, as it was not necessary to wait for an eclipse) the prediction was verified to a high level of precision; but even now, we cannot say that the deflection exactly matches the theoretical value. It simply can’t be done, and never will be.

So what I am saying with this example is that we can never say that numerical laws are simply “true” or “false”. We can only say that they have been found to agree with measurements to within some level of uncertainty, and we can then comment on that uncertainty, and compare it with the predictions of rival theories. Going back to what Cartwright said – if, when measuring the gravitational force between two bodies, the electrostatic force can be shown to be significantly smaller than the uncertainty in the measured force (where “significance” is once again a subjective matter) then the electrostatic force can be ignored, and the gravitational formula regarded as “true” at that level of significance.

Finally, I should add that it seems reasonable to me to believe that a particular physical quantity does have a “true value”, even though we can never know what it is. Modern metrology guidelines recognise this fact. For example – it is quite possible that the distance between the bodies in the Coulomb’s Law example (assuming it can be adequately defined) is a precise multiple of the length of the standard metre, and that each body has a precise deficit or excess of electrons, so that it has a precise charge. Furthermore, it seems reasonable to assume that the constant of proportionality also has a “true value” and that the law is in this sense “true”, giving a value of the force which is also precise. We can surely believe that, as long as we acknowledge that we can never know these precise values.

If you would like to read a more in-depth treatment of this topic, see my MSc dissertation: Falsificationism, Science and Uncertainty. This blog is continued here.

[1] Cartwright p 57.

[2] Earman, J., & Glymour, C., Relativity and Eclipses: The British Eclipse Expeditions of 1919 and their Predecessors. Historical Studies in the Physical Sciences 11 (1) 1980, 49-85

[3] Popper, K., Conjectures and Refutations (Routledge 1963)  pp 7-8

No Road

I’m conscious that of the five or six Larkin poems that I consider to be truly excellent, I have posted all except this one. And as it’s Hull City of Culture year and there are going to be all sorts of Larkin events, I thought I ought to rectify that omission.

It’s another miserable one, of course.

Since we agreed to let the road between us
Fall to disuse,
And bricked our gates up, planted trees to screen us,
And turned all time’s eroding agents loose,
Silence, and space, and strangers – our neglect
Has not had much effect.

Leaves drift unswept, perhaps; grass creeps unmown;
No other change.
So clear it stands, so little overgrown,
Walking that way tonight would not seem strange,
And still would be allowed. A little longer,
And time would be the stronger,

Drafting a world where no such road will run
From you to me;
To watch that world come up like a cold sun,
Rewarding others, is my liberty.
Not to prevent it is my will’s fulfillment.
Willing it, my ailment.

Philip Larkin (1950)

Blood and Belonging – Part 5

A year or so ago I wrote a series of blog pieces entitled “Blood & Belonging” which investigated the various factors that cause people to feel part of, or excluded by, various communities – whether defined by place of residence, religion, race, or other factors. (Click here for the previous post in the series).

I have been motivated to continue the series by two recent articles in the Guardian.

One of these was a comment piece by Giles Fraser, entitled Assimilation threatens the existence of other cultures (9 December). The other was a report about an attempt by parents in Switzerland to have their children exempted from mixed swimming classes ar school. The latter reported that the parents claimed that “their religion prevented their children from taking part” in the classes. Of course, “their” can be interpreted in two ways here – as referring to the parents or the children. If the latter, I must say that I cannot accept that children can be considered to have a religion if they are not yet at an age at which they are capable of making an adult assessment of religious beliefs, independent of any such “beliefs” that may have been thrust upon them. And if “their” relates to the parents, it is not clear why the parents’ religion should affect their children’s rights. After all, when parents send their children to school, they give up some of the responsibility for their upbringing. Why should the question of whether they can attend mixed swimming classes override this delegation of authority?

The Fraser article highlighted the case of “a lad of 20 who has lived in the borough of Hackney all his life. He was born here and grew up here. And he’s a bright boy – yet he speaks only a few very rudimentary words of English”. Fraser is a former Canon Chancellor at St Paul’s, who rose to prominence during the occupation of land adjacant to the cathedral in 2011, which he supported. His regular Guardian column is entitled Loose Canon, which is presumably meant to indicate that he writes as a Christian, but is happy to criticise the church’s “party line”.

Fraser says that he admires the insularity of the community in which the young man lives. He takes issue with Louise Casey, who, at the time of writing in early December, had just published her report on integration of immigrant communities in the UK. He queries her apparent assumption that integration is “a self-evidently good thing”.

Fraser appears to see only two options for such communities, namely isolation and assimilation. He admires “the resilience of a community that seeks to maintain its distinctiveness and recognises, quite rightly, that assimilation into the broader culture would mean the gradual dilution, and the eventual extinction, of its own way of life”. I wrote to the Guardian’s letters page, pointing out that this was a somewhat simplistic view, but sadly the letter was not published. This may have been out of concern that my letter would offend members of the community in question; yet regardless of considerations of community, surely bringing up a child without allowing him to learn the language of the country in which he lives is a simple case of cruelty. For however tighly-knit the community he belongs to, there must surely come a time when he will need to ask directions, or buy a train ticket, or conduct one of the myriad other transactions that we all take for granted every day.

Fraser points out that “the very nature of community is that there is a boundary between those who are in it and those who are not”. A boundary, yes – but not a barrier, not a Trump-style wall. Boundaries can be crossed; what the unfortunate lad lives in sounds more like a prison.

“Community” is an interesting concept. Many of us lament the death of local communities, citing the disappearance of local shops and workplaces, not knowing our neighbours, anonymous concrete jungles, etc etc. But there are, of course, other types of community than those based on locality – there are religious communities, expatriate communities, communities based on hobbies and interests, communities based on gender identity, workplace and even, of course, on-line communities. It is not, to use Fraser’s term, a “self-evidently good thing” for these communities to exist or survive, although in most cases, I think most of us would say that they were worth preserving, and certainly did not do any harm by existing. But if the continuation of the community comes at the price of an individual’s basic rights, then we should think very carefully about this.

The community Fraser is talking about is, I believe, a community based on religion. No doubt the parents of the boy in question had two things in mind when deciding not to allow him to learn English: firstly, their wish to do the right thing as parents, and secondly, the interests of the community. However, it is difficult to see how the first of these fits in with their decision. Wouldn’t any parent want their child to have the means to communicate?

Without knowing any more about why they made the decision, it is difficult to understand it. But it is difficult to see how it could have been interpreted as being in the interests of the child.

All of this reminds me of the words of Kahlil Gibran:

Your children are not your children.
They are the sons and daughters of Life’s longing for itself.
They come through you but not from you,
And though they are with you yet they belong not to you.

You may give them your love but not your thoughts,
For they have their own thoughts.
You may house their bodies but not their souls,
For their souls dwell in the house of tomorrow, which you cannot visit, not even in your dreams.
You may strive to be like them, but seek not to make them like you.
For life goes not backward nor tarries with yesterday.

(From The Prophet)

Mysterious Minutes, Arcane Agendas

Over the past 40-odd years, I have attended a vast number of meetings; I’ve no idea how many but a lot. I’ve been motivated to write this blog piece by a fascination with the bizarre ways that some people conduct meetings – particularly when it comes to small voluntary groups. If ever I could claim to have possessed a “transferable skill”, organising meetings and writing minutes would come top of the list; so I think I have a certain amount of authority in the matter.

I gained most of my meeting experience through my job as a project engineer for British Rail from 1974 to 1987. I attended meetings of all sizes, from big project team meetings with perhaps 20 attendees, down to small site meetings involving maybe only 2 people. I wrote minutes for some of these. From 1987 to 2000, my job changed (though with the same organisation) and meetings became less central – I was now more “hands-on” – but they were certainly still a prominent feature.

Overlapping that period, between 1990 and 2003 I attended some rather different meetings as a member of the Labour Party; I had two periods as a ward secretary, and wrote lots of minutes. Then from 2000 onwards I got involved in a plethora of voluntary organisations, some tiny, some bigger, including one international association, and one charitable company.

Now let me describe a typical meeting of a small voluntary group – one in which I play only a background role and thus have not had a chance (yet) to influence

It starts with the Chair “calling the meeting to order” and asking for Apologies for Absence, which the Secretary notes down in the minutes. Next is Minutes of Last Meeting. The Chair asks the meeting if they are an accurate record. This may take some time, as very often, the minutes have only just been circulated – so there may be a few minutes’ silence while everyone reads them.

Next the Chair will announce “Matters Arising”. He or she will usually have gone through the minutes in advance and identified which matters are “arising”, and may also ask the floor whether there are any more. This item may take quite a while, as there are usually updates on ongoing topics and reports from anyone who was tasked to perform some action.

Then we are onto the main agenda. Quite often, one finds that the topics listed on the agenda are more or less the same as at the last meeting, and hence many of these topics will have already been discussed under “Matters Arising”. People are often confused by this; I often wish I had £1 for every time I’ve heard someone ask “are we still on Matters Arising, or are we on the main agenda?”

Included on the agenda may be several “Reports”. These should include a Treasurer’s Report if the organisation in question has funds (and I can’t think of many that don’t) but often there are also “Chair’s Report” and “Secretary’s Report”. These can vary from nothing at all to a blow-by-blow account of what the officer in question has done since the last meeting.

Finally we have “Date of Next Meeting” and “Any Other Business” where anyone present can suggest an additional topic to be discussed.

This kind of procedure, though alarmingly common in small voluntary groups, bears little resemblance to the kind of process I grew up with in my work. Where do these ideas come from? I get the feeling that people believe that “you are supposed to do it this way”, but don’t really know what they are doing, or why. Yet meeting procedures are seldom detailed in organisations’ constitutions. For want of any other name, let’s call what I have outlined above “the standard procedure”

The craziest aspect of the standard procedure is the doubling-up of topics under “Matters Arising” and the main agenda. Of course, organisations vary tremendously in the size and diversity of their workload, and also in the frequency of meetings. I can understand that a group with a fairly light and simple workload, which has infrequent meetings, may be in a position to deal with each issue between one meeting and the next and then “sign it off”; there will then be little overlap between Matters Arising and the main agenda. But most, in my experience, deal with the kind of topics that keep recurring; and even a one-off item may not be completed before the next meeting. Doesn’t it make sense, then, to do what we did on the railways and combine these two sections of the agenda? This is done by treating all matters as “arising”, so that a discussion of the minutes will inevitably cover all “live” issues, and then if there are new ones, they can be discussed after that. Any items that do reach completion are marked as such in the minutes, and then removed at the next meeting; ongoing items are left in the minutes until complete, but updated each time. Some items may not be discussed at all at the current meeting, and if so, they are left as they are in the minutes. The agenda then consists of just 4 or 5 sections: Apologies for Absence, Minutes, [new topics, if any], Date of Next Meeting, AOB.

This kind of minute-taking is what I call “working” or “rolling” minutes. The minutes are an up-to-date summary of the whole project; they are the collective memory of the group. Used properly, this system guarantees that nothing ever gets forgotten.

Another aspect of common meeting (mis)practice that intrigues me is that of not issuing the minutes until just before the next meeting, or even, not until the start of the meeting. This is utterly pointless, and minutes which are treated in that way are themselves pointless, except as a historical record. The purpose of minutes is to make a record of decisions reached at the meeting, and actions arising from those decisions; the Chair then asks for updates from those who are actioned. If the actions are not flagged up until the next meeting, it is quite likely that they will not have been done. OK, people can make their own notes of any actions they have been given, but in my experience a surprising number of people wait for the minutes to come out first – either because they didn’t take notes, or lost their notes, or were a bit confused about what they were supposed to do.  Minutes also need to be issued in a timely fashion, of course, to inform anyone unable to attend of what went on.

The delaying of minutes reaches its most extreme form when AGM minutes are not issued until just before the next AGM – in other words, a year later. It is then quite amusing to hear the Chair ask if they are an accurate record – who on earth would be able to remember whether they were or not?

Now, the reader might well object that rolling minutes are all very well for a large engineering project, but needlessly complicated for the church fête organising committee. Well, I can see that some very small, informal bodies might not need them; but for most voluntary bodies they are completely appropriate; it is, on the contrary, the “Matters Arising” format that leads to confusion. And what about those Reports? Does anyone really want to know what the Chair has been up to? Well, it depends on what role the Chair plays, but generally speaking I would maintain that the Chair is not actually a very important role. It is a “traditional” role, and along with the Secretary and Treasurer, is usually classed as a “statutory” post, because it is usually referred to in the constitution, though not always with any duties laid down.

The most important job of the Chair is actually to act as spokesperson between meetings, and the relevance of this will vary tremendously; clearly important for political groups, but much less so for your average voluntary body. Ditto the Secretary, although this post may involve a fair amount of correspondence, which may need reporting to the meeting. But chairing meetings and taking minutes are both jobs that can rotate around a committee. Far more important are the functional officers – such as event organiser, newsletter editor, membership secretary, webmaster etc. If you are going to have Reports that cover items not already in the minutes, all these officers should produce them – but better presented orally than in writing.

Before writing this blog, I thought I ought to do some sort of research into exactly what guidelines there are “out there” regarding how to organise meetings and write minutes, given that constitutions do not contain such detail. Over the years, there is only one book that I have heard of in this context, and until now I had never read it. It is Citrine’s ABC of Chairmanship, published in 1952. But this book deals almost exclusively with political meetings, which are, admittedly, rather different. For a start, there are fewer ongoing issues, and there are likely to be motions or resolutions. There are other differences, which I’ll come to later. And of course things have changed quite a bit since 1952. Citrine speaks of the minutes being written in a “minute book” and read out at the next meeting. At a time when not only was there no email, but even producing multiple copies of a document was pretty difficult, it does make sense for the minutes to not be “issued” at all but simply read out. The problem is that a lot of organisations haven’t kept up with the times – not only do some bodies (such as banks, in forms for opening accounts) still talk about the organisation having “passed the following resolution and entered it into the Minute Book”, but clearly the whole practice of minutes being withheld until the meeting itself – together with the bizarre practice of asking if they are an accurate record, as though minute-writing were a particularly difficult job, or minute-writers prone to inaccuracy – is a relic from those times. However, I can’t say I have ever attended a meeting at which the minutes were actually read out!

Regarding minutes, people often seem to have the mistaken idea that they should contain a complete record of the meeting, right down to “who said what”. This makes for very long, almost unreadable minutes. I am with Citrine on this: he says minutes are “a brief but accurate record of the business transacted”. In fact, I would go so far as to say that, political meetings apart, the names of the attendees should appear in only three places: the attendance list, Apologies for Absence, and the action column. (In political meetings it is usual to record the names of movers and seconders of motions, and sometimes one or more individuals may ask for a particular view to be minuted, even if it does not represent the majority view.)

At the end of the day, organisations should chooose their own format for conducting meetings and registering their results. It is fine to follow the archaic procedures if the group agrees that that is what it wants to do; the worst thing is to adopt a particular format simply because you think that’s what you’re “supposed to do”.

Lament on a Linguistic Monoculture

In the reception area at my local GP surgery, there is a small notice that says “Have you had Great Care today?”

I can’t honestly say I have ever seen the words “great” and “care” juxtaposed (except in the context of “taking great care” over something, which is not what is meant here, I fear), and seeing them together today made it feel as though I was witnessing a milestone in the deterioration of language.

Every era – every generation – has its own special words, of course, and in the age of communications – radio, TV, computers, mobile phones – it does not take long for a particular word to become fashionable. In the 1960s, thanks to a certain TV pop show, everything suddenly became “fabulous”, at least for the younger generation. I forget what followed, but in more recent times we have had “wicked”, “awesome”, and even, I understand – something I find difficult to grasp in terms of a superlative, which is probably the point of it – “sick”.

These words tend to be “in” for a short while before being replaced by something else. Sometimes they can even come back. In recent times we have seen the return of “cool”, a word that, for me, sums up the pre-1960s, US-obsessed generation; it amuses me that probably a lot of people who used it (and still use it) thought it was a modern term.

But nowadays it seems that either the process of finding new “in” words has slowed, or we have simply run out of them. For some time now, it has been disturbingly common to find “great” used as an all-purpose superlative, and one cringes at its use in one inappropriate context after the other. However, “great care” surely breaks all the records for crassness.

It is not, unfortunately, an isolated example. Views are almost universally described as “stunning”, rendering that word almost meaningless. This occurs, not just in the writings of estate agents (never known for their command of language) but also in brochures and websites on holiday cottages. Now surely, if there is any group of people who ought to have the full richness of language at their disposal, it is those whose job involves convincing us of the delights of a particular holiday location; surely they could chuck in the odd “arresting”, “breathtaking”, or even – heaven forbid – the occasional “beautiful”? Yet all we get are stunning views. But then, since people in the holiday industry also habitually refer to the cottages as “properties”, it is clear that they are in fact the same people as those writing the estate agents’ blurb. How else can one understand the use of a term which emphasises the role of a house as a commodity or investment, in a context in which we are supposed to see it very differently – as a cosy nook? In fact, I’ve noticed that even the Youth Hostel Association now describes its hostels as “properties”. They just don’t get it, do they?