Archive for the 'Science' Category

Gribbin: Six Impossible Things

October 25, 2020

Six Impossible Things
The Mystery of the Quantum World
John Gribbin
(MIT, 2019)
101 p.

The shelves of neighbourhood bookstores groan under the weight of popular science books about quantum theory. Six Impossible Things stands out from this crowd because it focuses not on the mechanics or the findings of quantum theory, but on how to interpret the theory. What is it saying the world is like?

Gribbin opens the book by describing two quantum phenomena in which the strangeness of quantum theory is most evident. The first is the famous double-slit experiment, and the second is entanglement. These form the main course in many popular books on quantum mechanics, but are here only the appetizers.

In the remainder of the book, Gribbin describes six different schools of interpretation of quantum theory, and discusses, in particular, what each of them says is happening in these two famous case studies. These six schools are really schools of interpretation; they all rely on exactly the same mathematics and make exactly the same predictions for experiments. They differ only in how they describe the entities and dynamics underlying the observations. They agree on what happens in the end; they differ on how and why it happens.

*

So, for example, the most common school of interpretation among working physicists is the so-called Copenhagen interpretation. On this view, there is an entity called the wave function, the time-evolution of which is described by the Schrodinger equation. Quantum states evolve into superpositions of states, and when a measurement is made the wave function collapses into one state with predictable probability. Quantum mechanical systems don’t have definite properties until measured, on this view. The biggest problem for this school is the “measurement problem”: the measurement intervenes in the physics and itself has no physical description. What is a measurement anyway? Does it require a conscious agent to carry it out? Many physicists have thought so, but this has led to thought experiments like the one with Schrodinger’s cat, which strain credulity as a sound description of the world.

A second interpretation is the “pilot wave” theory, pioneered in the early days by de Broglie and developed at length by David Bohm. On this view, particles (like electrons or photons) are always and only particles with definite properties — there is no wave/particle duality or superposition of states — but the particles interact with a “pilot wave” which evolves dynamically, like the wave function, and which guides particles on different paths through space depending on small variations in initial conditions. The theory is deterministic, but specific outcomes are impossible to predict without more information. This view has its attractions: much of the quantum weirdness found in the Copenhagen interpretation is gone, and there is no measurement problem. But the theory has features not obviously attractive too: the pilot wave affects particles but is itself un-measurable, and the theory requires non-locality — the properties of a particle depend on the properties of all other particles with which it has ever interacted, and on their properties now, not just their past properties.

Third comes my own least favourite: the “many worlds” interpretation. On this view there is no collapse of the wave function so that the outcome of a measurement is one of the range of possible states. Instead all of the possible outcomes are realized each time a measurement is made, each outcome in a different universe. The universe we live in is constantly branching into myriad new universes each time a quantum mechanical system is reduced from a superposition of states to a specific state. Every possible universe is realized somewhere, provided it obeys the laws of physics. The contempt I feel for this interpretation would be difficult to overestimate. Practically the sole consolation it provides is the reassurance that somewhere a living, breathing Elizabeth Bennett is living her life just as was so memorably recounted by Miss Austen in her story.

Another possible interpretation is the ‘decoherence’ view, which takes entanglement, sometimes an odd and slightly annoying phenomenon in the mental universe of physicists, and makes it the key to everything. On this view, quantum systems become entangled with their environments, and these macroscopic entangled states behave, on average, like classical (ie. non-quantum) systems. The larger the distance scale, the faster this entanglement causes the quantum system to ‘decohere’. This view has the advantage of explaining why quantum mechanical systems are generally very small and relatively simple: if they become large or complex, they decohere through interactions with their environments. In fact, to the degree that I understand it, this interpretation of the theory is my own favourite: it is metaphysically modest and makes a lot of sense. However, I may not understand its implications adequately; Gribbin devotes a chunk of his chapter to arguing that the decoherence interpretation is equivalent to something called the Many Histories interpretation, which he encapsulates in this way: “Everything that could possibly happen already has happened, and we only noticed part of it.” That sounds bad, but I confess I don’t understand this alleged equivalence.

Next is the ‘ensemble interpretation’, favoured by Einstein, which attempts to do away with quantum weirdness by claiming that the probabilistic predictions of the theory pertain not to any one quantum system, but to an ensemble (or collection) of such systems, if they existed. On this view, each individual quantum system behaves deterministically, but duplicates of the system could behave differently, according to the probabilities predicted by the theory. It makes a kind of sense, but has trouble explaining why this particular quantum system behaves as it does. The idea has been rejuvenated by Lee Smolin in recent years, who has proposed a highly non-local interpretation whereby the degree of “quantumness” exhibited by a system depends on how many instances of that system exist in the universe, with all such instances together forming an ‘ensemble’  in the relevant sense. Hydrogen atoms behave quantum mechanically because there are many of them, but you and I behave classically because we are unique (or, if you prefer, we know we are unique because we behave classically). This is an interesting view, if you can abide the radical non-locality.

Finally, Gribbin describes the “transactional interpretation”, a view inspired by the fact that the equations of quantum theory allow for solutions travelling both forward and backward in time. The backward-travelling solutions are usually regarded as spurious, but in this interpretation they are taken seriously. The proposal is that physics depends not just on where things have been, but also on where they are going. Not just on where and how a quantum system originated, but also on where and how, in the future, it will be measured. When worked out in detail, this view, rather surprisingly, produces exactly the formalism of quantum mechanics. One hardly knows what to do with this fact.

*

Gribbin summarizes the six interpretations he has described in this way:

  1. The world does not exist unless you look at it.
  2. Particles are pushed around by an invisible wave, but the particles have no influence on the wave.
  3. Everything that could possibly happen does, in an array of parallel realities.
  4. Everything that could possibly happen already has happened, and we only noticed part of it.
  5. Everything influences everything else instantly, as though space did not exist.
  6. The future influences the past.

Choose your poison.

A few closing remarks. First, there is no getting around the fact that quantum theory has upset our conventional views of what the world is like, but, as this books makes clear, just how it upsets them is not clear. Second, it strikes me as quite amazing that a single theory, the mathematical structure of which is uncontroversial, could produce such a wide variety of possible physical descriptions. Third, this is a very fine book, written without undue technicalities, and I recommend it to anyone with an interest in the subject.

Mansoulié: All of Physics

June 25, 2020

All of Physics (Almost) in 15 Equations
Bruno Mansoulié
(World Scientific, 2017)
138 p.

The usual rule in popular science writing is “No Equations!” Sometimes additional exclamation marks are added. But Bruno Mansoulié has taken the opposite tack and structured his little book around a curated set of basic equations that summarize many of the principal ideas of physics. He presents each equation and then, in the space of 5 or 8 pages, describes what it means, explains how it came about or what deep ideas it is connected to, or tells us a story about how the equation has affected his own life.

A good exercise, before opening the book, is to try to guess which 15 equations he chose, or to write down which 15 you would choose were you the author. Some of his are natural choices: Newton’s second law, the law of universal gravitation, the mass-energy equivalence, the Schrodinger equation, the Heisenberg Uncertainty Principle, and Maxwell’s equations. They are either pillars of the discipline or famous in their own right for the insights they encapsulate.

But the non-obvious choices are also interesting. We get one equation for thermodynamics (the ideal gas law) and one for fluid mechanics (Navier-Stokes equation [ugh!]). He opens the book with the laws of reflection and refraction, the former allowing him to reflect on the relationship between heuristics (like the law of reflection) and thorough understanding of the underlying physics (which in this case requires an advanced course in electromagnetism), and the latter providing a springboard to introduce the principle of least action, one of the deepest ideas in all of physics. He also spends time on the Einstein field equations of General Relativity (blessed be they), Feynman diagrams (which are pictorial representations of equations), and, at the end, the “Theory of Everything equation” that is, as yet, undiscovered, and may not exist.

Although the book is pitched at a general readership, and is gentle in a soft-vowel, French-professor way, there are nooks and crannies the full charm of which can, I am convinced, be appreciated only by a fellow physicist. A chapter on Maxwell’s equations contains a sweetly affectionate tribute to Jackson’s famous textbook on the subject, which many graduate students (yours truly included) have wrestled with, and the chapter on the Dirac equation (“the most beautiful, the purest of all”) won my heart as it swooned over the equation’s very typography:

the harmonious roundness of the \gamma, the gentleness of the \partial, the sharpness of the first i, the delicateness of the \mu indices set like appoggiaturas, and the deep mystery of the \psi.

It’s that kind of book: appreciative, open to wonder, musing, personal, occasionally philosophical, and sometimes digressive, and it’s a pleasant read too.

The tidal flood beneath the lunar sway…

April 20, 2020

… but in Latin.

Reading Seneca’s essay On Providence I came across a surprising passage in which, in an aside, he says:

If anyone observes how shores are laid bare as the sea withdraws into itself, and yet are covered again in the shortest of time, he will believe it is some unseen fluctuation that causes the waves now to diminish and flow inwards, now to burst forth and with a great surge reclaim their former home; but in fact the waves increase by degrees, approaching to the hour and day proportionately larger or smaller in volume as they are attracted by the star we call the moon, whose power controls the ocean’s surge.

Now, it is true that the translator (John Davie) does not use the word “tide” here, but that must be what he is talking about. This is fascinating to me, because I had thought that the connection between the moon and the tides was a post-Newtonian discovery.

For instance, in his defence of a heliocentric model, Galileo argued that the tides are caused by the rotation of the earth. This was wrong; I’d thought it was put forward in the absence of a better explanation. But apparently not. Fascinating.

Lucretius: On the Nature of Things

September 21, 2018

On the Nature of Things
T. Lucretius Carus
Translated from the Latin by Ronald Melville
(Oxford, 1997) [c.55 BC]
xxxviii + 275 p. Second reading.

\; \; \; \;  \; \;  \; My purpose is
With the sweet voice of Pierian song
To expound my doctrine and as it were to touch it
With the delicious honey of the Muses;
So in this way perchance my poetry
Can hold your mind, while you attempt to grasp
The nature of the world, and understand
The great design and pattern of its making.”
(I, 943-50)

Lucretius’ De Rerum Natura is one of the great epic poems of the ancient world, and, as is claimed in this volume’s introduction, “perhaps the greatest didactic poem ever written in any language”. It is a work plump with fascinating scientific theories, and one with interesting and influential philosophical ideas also; it is, arguably, the latter that account for much of its continuing appeal.

We know little about the author, and the securest dating of the poem derives from a reference to it in a letter of Cicero; it was probably first published in around 55 BC.

The poem consists of about 7400 lines of Latin hexameter, and is divided into six books. The overall argument of the poem is to present and defend the natural philosophy of the Epicurean philosophical school.

Lucretius’ basic metaphysical principles and atomistic physics are described in the first two books; the middle books are devoted to the human person, soul and body; and the final two treat the development of human societies before culminating in an ambitious (if, alas, mostly wrong) naturalistic account of dramatic natural phenomena like lightning, earthquakes, volcanoes, and disease.

Lucretius is famous for his spirited and resourceful defence of atomism. The idea is not original with him — that honour is usually bestowed upon the Greek Democritus, of course — but he presents it seasoned “with the delicious honey of the Muses”, a sweetener intended to help the medicine go down. For him, atoms are small, indivisible, infinite in number, eternal, and indestructible. From these characteristics he derives two overarching metaphysical principles which govern all that follows. The first is that atoms do not come into being:

“We start then from her [nature’s] first great principle
That nothing ever by divine power comes from nothing.”
(I, 148-9)

and the second is that they do not pass out of being:

\; \; \; \;  \; \;  \; nature
Resolves all things back into their elements
And never reduces anything to nothing.”
(I, 215-7)

Thus the picture he presents us with is that of a world composed of an infinite number (though a finite variety) of indestructible material bits in motion. These bits, he argues (against Aristotle), are surrounded by a void. The existence of this void he rather deftly deduces from the fact of translational motion, for if there were no void it would be impossible for atoms to move from one place to another, their being impeded by the presence of other atoms. And these two categories, atoms and the void, exhaust his ontology:

“…apart from void and matter no third substance
Can remain to be numbered in the sum of things,
Neither one that falls within the range of senses
Nor one that mind can grasp by reasoning.”
(I, 445-7)

Thus for Lucretius, as for his intellectual descendants, such things as mathematical objects, moral principles, and immaterial souls have no reality.

Atoms move about, bumping into one another and combining in new ways to make new things. He uses a nice metaphor to describe this process, one particularly apt for use by a poet writing poetry:

“Moreover in my verse it matters much
How letters are arranged and linked with others.
The same denote sky, sea, land, rivers, sun,
The same denote crops, trees, and animals,
And, if not all, by far the greater part
Are alike; but the position decides the meaning.
So with real things, when the combination of their atoms,
Their motions, order, forms, shapes, and positions
Are changed, the thing itself must change.”
(II, 1013-21)

Because he believes that the number of atoms is infinite, and that this process has been taking place for infinite time, he does not shrink from the conclusion that our world itself came to be out of just such chance encounters:

“The seeds of things
In random and spontaneous collision
In countless ways clashed, heedless, purposeless, in vain
Until at last such particles combined
As suddenly united could become
The origins always of mighty things,
Of earth, sky, sea, and breeds of living creatures.”
(II, 1058-62)

Thus, step by haphazard step, the world around us has taken shape. Perhaps the most famous section of the poem, in Book V, is that in which he traces for us the slow development of the world from its origins to the establishment of early civilizations: the production of animals, the origins of speech, the discovery of fire, the origin of religion (which he, oddly, considering his other principles, attributes to apparently genuine visions of the gods), the beginnings of metallurgy and agriculture, the advent of music, and the building of cities. The atomic theory he puts to use in a variety of creative ways: to explain sense perception, and the laws of optics, for instance. It is interesting that this broadly evolutionary view of history does not include any conception of the evolution of life; for Lucretius, animal species are distinct and unchanging (V, c.920).

By the same reasoning which leads us to view our world in this way, we conclude that other worlds, too, have and will come to be. Moreover, turning the coin over, they will eventually fall apart again, just as our world one day will:

“So death rightly comes, when by constant flow
All things are thinned, and all things, struck from without
By an increasing hail of blows, succumb;
Since at the end great age finds food to fail,
And without ceasing bodies from outside
Beating on things subdue them and destroy them.
So shall the ramparts of the mighty world
Themselves be stormed and into crumbling ruin
Collapse.”
(II, 1139-47)

The naturalness with which his minimalist ontology — atoms and the void alone — leads to this final, whimpering destruction of all that the we know and love accounts for his dousing it with “the delicious honey of the Muses”, even if, perhaps, we doubt that we could be wholly convinced to part with our inheritance even for so sweet-seeming a mess of pottage.

As with many of his modern descendants Lucretius’ forthrightness about the ultimate fate of everything is paired with a strange lacuna. He is quite explicit that his ultimate purpose in writing this poem — his moral purpose — is to provide peace of mind, to teach his reader the art of “being undisturbed”. He aims at this in part by providing naturalistic explanations for unusual and frightening natural phenomena, so as to free the minds of his readers from the anxiety induced when they are experienced as signs of divine displeasure,

“Proceeding to set free the minds of men
Bound by the tight knots of religion.”
(IV, 7-8)

And Lucretius, following “the first who dared / Raise mortal eyes against” religion — namely, Epicurus, the hero of his tale — understands that a central part of achieving this peace of mind must be coming to peace with death. He therefore argues at length, in Book III, that the Epicurean universe in which only atoms and the void exist is necessarily one in which:

“… we may be certain that in death
There is nothing to fear, that he who does not exist
Cannot feel pain”
(III, 866-8)

There is a dignity in this paradoxical conviction that the way to avoid losing all is to definitively lose all, that the creature’s fear can be overcome by its accepting its total self-destruction, fear and all. Perhaps we are impressed by the vision of a philosopher who attends quietly to truth even as the world around him is consumed in a great conflagration. We may feel the persuasive power of Lucretius’ belief that

“True piety is for a man to have the power
To contemplate the world with quiet mind.”
(V, 1199-1200)

If we do feel that persuasive power, we ought to honour it, on the likelihood that there is some good in it. And Lucretius puts our good will to the test when he yields no quarter to those who, though not fearing death, wish nonetheless to extend their lives for as long as possible, for what difference, he argues, could longevity possibly make?

“Live though you may through all ages that you wish,
No less that eternal death will still await,
And no less long a time will be no more
He who today from light his exit made
Than he who perished months and years ago.”
(III, 1090-4)

Perhaps we respond to this detachment by doubling-down on our admiration: here is a man who truly wears his metaphysical hairshirt with Roman fortitude. Or perhaps we doubt that a philosophy that can so readily relativize the value of life is worth our uncritical adherence. The shelter, after all, which the Epicurean seeks from the metaphysical black hole that devours his world is his own interior life: his untroubled mind, his calmness in the face of disorder, his contemplation of truth. Yet do these things survive the destruction that lays all else to waste? Not in the long run — Lucretius tells us that much — but in the short? Now? It is here, I think, that the armour is pierced most effectively. The Epicurean moral universe, like our less systematic but substantially similar reigning view today, is underpinned by the presumed reality of human freedom, which imparts to all the Epicurean virtues a nobility and even a reality they cannot otherwise possess. There is no virtue in patience if one is not free to be impatient — indeed, there is no virtue of patience if there are only atoms and the void. Likewise for courage, and for prudence, and for all the virtues, and for the very notion of virtue as a moral quality, and for moral qualities tout court. Take his mandorla of freedom from him and you take all; yet his own principles do just that.

Famously, Epicurus, and Lucretius after him, tries to save human freedom in his system by introducing “the swerve” — an apparently random motion which atoms make from time to time to prevent the universe’s being deterministic:

“While atoms move by their own weight straight down
Through the empty void, at quite uncertain times
And uncertain places they swerve slightly from their course.”
(II, 217-9)

But this was feeble, being both arbitrary and inadequate to the purpose.

We therefore find, I think, that the Epicurean materialist metaphysics, like the modern one, consumes the metaphysician, leaving no-one to live out his moral ideal. We are left only with random motion and ultimate dissolution. And this, I think, even by Epicurean standards would be a counsel of despair.

**

I enjoyed re-reading this poem, which I first read at least 20 years ago. In the Roman reading project in which I am presently engaged it was my first sustained dose of Roman philosophy — just Greek philosophy at second hand, admittedly, but who among us can do better? — and I found a good deal to engage with. It is true that the very notion of a great poem about natural science seems slightly quixotic, rather like singing a Mass in honour of, say, Charles Darwin. But one soon forgets this genre-busting aspect, and falls into enjoyment of the poem on its own terms.

The translation of Ronald Melville I found good apart from the title (“On the Nature of the Universe”), which might well be a more fitting translation of De Rerum Natura on some grounds, but to which I nonetheless prefer the traditional English title (“On the Nature of Things”). I do harbour a regret that I didn’t splurge for Anthony Esolen’s translation, not least because I expect his commentary would have been superior to that found in this Oxford edition. But this, admittedly, is speculation, and I suppose that, in a Lucretian spirit, I could moderate my regret by meditating on the Epicurean counsel that, whatever translation I chose, “eternal death will still await”.

Electroweak anniversary

October 17, 2017

Today marks 50 years since Steven Weinberg submitted his famous paper, “A Model of Leptons”, to Physical Review Letters. In this short paper (of just 3 pages) he proposed a theoretical framework within which the electromagnetic force and the weak nuclear force could be understood as two different aspects of a single underlying force, dubbed “electroweak”.

The paper was actually published on 20 November 1967, and it has had an interesting history. At first it was ignored, garnering just 2 citations in the first 3 or 4 years. When this neglect changed, it changed dramatically, and for several decades “A Model of Leptons” was the most cited paper in the literature on high-energy, fundamental physics. It won Weinberg the Nobel Prize in Physics (shared with Salam and Glashow) in 1979.

The idea that the fundamental forces of nature (electromagnetism, weak, strong, and gravitational) might be different aspects of a single, simpler force that could be described more economically has been, it is fair to say, one of the leading ideas in physics in the last 100 years or so. Einstein tried to unify electromagnetism and gravity, and huge piles of ink were lavished on the effort to unify electromagnetism with the weak and the strong forces into a “grand unified theory”. String theory, for several decades now the sexiest branch of theoretical physics, is another example of this same ambition.

But it is noteworthy that Weinberg’s proposal is the only successful example of unification that we have managed to find.

Here is a good history of the paper’s composition and reception from CERN Courier.

Way over yonder

June 16, 2017

A few interesting items I’ve stumbled upon in the last few weeks:

  • When Mother Teresa was canonized last year, I missed this superb reflection on her life by Fr George Rutler, who knew her personally. “The canonization of Teresa of Calcutta gives the kind of satisfaction that comes from having your mother declared Mother of the Year.” It’s a quite beautiful tribute to her and her significance for the rest of us.
  • Bob Dylan’s Nobel lecture finally appeared, and it’s well worth a listen (or, if you must, a read). Fr Schall has interesting things to say about it, both for better and worse, although I think he underestimates the degree to which Dylan’s body of work has a transcendent dimension.
  • Speaking of Dylan, one of the best things I’ve read about him since he won the Nobel last year is this essay by Carl Eric Scott, published in Modern Age. Scott selects “To Ramona” as one of Dylan’s most underrated songs, a judgement with which I heartily agree.
  • At City Journal, John Tierney writes about something we don’t hear much about: the left-wing war on science.
  • Ben Blatt has written a book called Nabokov’s Favorite Word is Mauve: What the Numbers Reveal About the Classics, Bestsellers, and Our Own Writing, in which he subjects famous works of literature to statistical analyses. It prompted one of the most enjoyable scathing reviews that I’ve seen in a long while, from Matthew Walther: “Never, I think, has a purported piece of “literary criticism” been so disconnected from literature and non-suggestive of all the things that might, and very frequently do, induce people to read.” The review was so withering that I actually got the book, just to see how bad it was. It’s tremendously bad.
  • In the midst of a stew of troubles, Anthony Esolen wrote a graceful critique of illiberal habits of education. It was an elegant farewell note to Providence College.
  • And finally, from New Criterion, a very interesting biographical essay about Fr Reginald Foster, an American priest who was for many years the Vatican’s chief Latinist.

For an envoi, here is Bob Dylan singing “To Ramona”, live in Manchester in 1965:

Briggs: Uncertainty

November 4, 2016

Uncertainty
The Soul of Modeling, Probability & Statistics
William Briggs
(Springer, 2016)
278 p.

Being something of a beginner in the art of statistical analysis, I thought this book on the philosophical and conceptual underpinnings of statistical methods would be instructive, and I was right. I learned so much I’m not sure I want to learn any more.

In a nutshell: Briggs is critical of most of the standard apparatus of statistical methods, both technical and interpretive. Hypothesis testing, regression, data smoothing, quantification of everything, and, above all, p-values he condemns to perdition. The problem is not that such methods have no value, but that they are widely misunderstood and misapplied, with the result that the conclusions drawn from statistical analyses are often either simply wrong or the uncertainty in those conclusions is underestimated (and by an unknown amount). He gives many examples of ways in which standard techniques lead to spurious “significant” results.

By criticizing standard statistical methods, one might get the impression that Briggs’ is a lone voice crying in the wilderness, but he has plenty of citations to offer for most of his arguments. He belongs to an alternate, minority, but not negligible tradition.

Some of the important points he makes:

Probability is logical. Logic concerns relationships between propositions, and so does probability, except that in the latter case the logic is extended to propositions the truth of which is uncertain. This point was made lucidly and rather beautifully by Jaynes, and reading Briggs has made me want to return to that book to read more of it.

Probability is not a cause. Probability can tell us about correlations, but nothing at all about causes. The habit of inferring causes from statistical correlations, absent a corresponding causal model, is a bad habit that leads many astray. In general, uncertainty reflects our ignorance of causes rather than our knowledge of them.

Probability is conditional. Probability statements are always conditional on a set of premises. This is no such thing as Pr(X), but only Pr(X|Y) — that is, the probability of X given some set of premises Y. If the premises change, the probability of X will, in general, change. Thus Briggs, while not quite a Bayesian, does think the Bayesians have it over the frequentists when it comes to the debate over whether probability is objective (ie. out there) or subjective (ie. in the mind). Probabilities reflect the uncertainty in propositions given what we know; they do not exist outside our minds, and they change when our knowledge changes. A corollary is that one should never say, “X has a probability of Z”. Nothing has a probability. Probability does not exist. One should only say, “Given premises Y, the probability of X is Z.”

Probability is often not quantifiable. If we know “Most people like ice cream and Sue is a person”, the probability that Sue likes ice cream cannot be naturally or unambiguously quantified unless the meaning of “most” is clarified. Moreover, it is often a mistake to force probabilistic arguments into a quantified form. Briggs argues that the habit of doing so (as with “instruments” for assessing subjective attitudes about politics or emotional responses to stimuli, for instance) often leads to misleading results and promotes the vice of scientism.

Statistical significance is not objective. No probability model can tell one whether a given probability is significant or not. This is an extra-statistical, and often an extra-scientific, question. Whether it is judged significant is a matter of prudential judgment based on the specific question at issue and the decisions to be made about it. Thus he would like to disrupt the “turn the crank” model of statistical analysis in which “significant” results pop out of the sausage-maker, returning such questions to spheres of deliberation and judgment.

Probability models should be predictive. Briggs’ principal constructive suggestion (apart from shoring up our understanding of what probability is) is that statistical models should be predictive. They should state their premises in as much detail as possible, and should predict observations on the basis of those premises (taking into account uncertainties, of course). If the models fail to predict the observables, they are not working and should be amended or scrapped. As I understand it, he is proposing that fields which lean heavily on statistics should, by following his proposals, become more like the hard sciences. True, progress will be slower, and (acknowledged) uncertainties larger, but progress will be surer and causes better understood.

***

Briggs has some fun pointing out common fallacies in statistical circles. There is, for instance, the We-Have-To-Do-Something Fallacy, in which a perceived imperative to do something about something (usually something political) leads to the employment of some defective or fallacious statistical method, the defectiveness or fallaciousness of which is then ignored. Or the Epidemiologist’s Fallacy, in which a statistician claims “X causes Y” even though X was never measured and though statistical models cannot in any case discern causes. (This fallacy is so-called because without it “most epidemiologists, especially those in government, would be out of a job”.)  Or the False Dichotomy Fallacy, which is the foundational principle of hypothesis testing. Or the Deadly Sin of Reification, whereby statisticians mistake parameters in their statistical models for real things. And so on.

***

Much of this might seem rather obvious to the uninitiated. I’m not an adept of the standard techniques, so I was at times a little puzzled as I tried to discern the particular bad habit Briggs was criticizing. But, as is increasingly appreciated (here and here, for instance), the use and abuse of the standard techniques have led wide swathes of the scientific community into error, most commonly the error of over-certainty, which is actually an uncertainty about what is true. An audience for this book clearly exists.

Were his recommendations to be followed, he argues that the effects would be

a return to a saner and less hyperbolic practice of science, one that is not quite so dictatorial and inflexible, one that is calmer and in less of a hurry, one that is far less sure of itself, one that has a proper appreciation of how much it doesn’t know.

But, on the other hand, it would reduce the rate at which papers could be published, would make decisions about significance matters of prudential judgment rather than scientific diktat, and would make scientific conclusions more uncertain. He is fighting an uphill battle.

Briggs is an adjunct professor at Columbia, and has done most of his scientific work in climate science (and is, as you would expect, skeptical of the predictions of statistical climate models, which provide a few of his case studies). He seems to be something of an atypical academic: this book, for instance, includes approving reference to Aristotle, Thomas Aquinas, and even John Henry Newman (whose Grammar of Assent he cites as an example of non-quantitative probabilistic argumentation). It’s quite a rollicking read too. Briggs has a personality, and doesn’t try to hide it. Personally I found the tone of the book a little too breezy, the text sometimes reading almost as if it were transcribed lecture notes (I make no hypothesis), but overall the book is smart and clear-eyed, and I’m glad to have read it. Now back to Jaynes.

***

I found a good video which illustrates the problem with relying on p-values to determine statistical significance. When I consider that many of the findings of the social sciences are based on this criterion I’m not sure whether to cringe or weep. No wonder there is a replication crisis. Witness the dance of the p-values:

Here is a short video illustrating why it is reasonable to doubt the putative findings of many (and perhaps most) published research papers employing statistical methods. This argument and others are set forth in detail by Ioannidis.

Rovelli: Seven Brief Lessons on Physics

September 6, 2016

Seven Brief Lessons on Physics
Carlo Rovelli
(Riverhead, 2016)
96 p.

These short “lessons” were originally serialized in the Italian press, and are here collected and rendered into elegant English. Rovelli is an eminent physicist who gives us a series of meditations on developments in physics since 1900.

They are arranged in order of increasing speculation: he begins with general relativity and quantum mechanics, presenting in non-technical language the main points — space and time are dynamic and responsive, and are filled with a restless boil of quantum fields. He proceeds to give brief — and I do mean brief — overviews of modern cosmology and the Standard Model of elementary particles. All of this is solid science; questions linger, of course, and he draws attention to those loose threads and nagging problems, but basically he is describing successful theories.

In the last three sections of the book he moves to topics of greater uncertainty. The outstanding problem of how to reconcile general relativity with quantum mechanics he broaches with a very interesting discussion of theories of loop quantum gravity, the basic postulate of which is that space-time is quantized. (Rovelli is himself one of the architects of this theory.) Amazingly, and rather gratifyingly, he doesn’t even mention the other principal effort to solve this problem: string theory. This is unquestionably the book’s finest witticism, one that I imagine has raised a few consternated eyebrows in faculty lounges.

The last section specifically about physics tackles the vexing puzzles that arise at the intersection of gravity, quantum mechanics, and thermodynamics. Laying great stress on the time-irreversibility of thermodynamic processes, he argues that thermodynamics has something crucial to tell us about the uni-directionality of time itself. This is a common trope in physics circles, but, correlation not being causation, it seems to me suggestive at best. But then he reminds us of Hawking radiation, in which quantum effects near black holes actually cause them to radiate heat, and one feels a chill of delight running up the spine.

Alas, the same cannot be said of the book’s final chapter, in which Rovelli takes a step back to ponder the implications of all this for human self-understanding. He emphasizes that modern physics has revealed the world to be radically different from the way we intuitively think of it, which is fair enough, and then argues that more such intuitions — those pertaining to human freedom, for instance, or consciousness — are due to be superseded by counter-intuitive scientific explanations. There appears to be nothing more to his argument than the power of analogy. He tries to declare a peace between his commitment to the power of physics to completely describe the world, on one hand, and his commitment to the legitimacy of humanistic values, on the other, but it is far from convincing. And he is rather dispiritingly emphatic in his devotion to immanence:

“Immersed in this nature that made us and that directs us, we are not homeless beings suspended between two worlds, parts of but only partly belonging to nature, with a longing for something else. No: we are home.”

Nothing new here, of course, and this view does have about it a certain poetry — he even cites Lucretius, the patron poet of materialism — but there are such a host of issues being passed over in silence that such poetry as it possesses sounds rather hollow.

The book is written in a lyrical tone, and would be accessible, I imagine, to anyone who has an interest in the subject matter. There is only one equation — Einstein’s field equation for general relativity, which he describes as “the most beautiful of theories,” and I’ll not argue with that.

Lecture night: psychology and politics

August 23, 2016

Jonathan Haidt is an unusually interesting academic. He is a psychologist who has in recent years turned his attention to matters of public import, and has especially emerged as an advocate of greater “viewpoint diversity” in the academy. To that end, he has founded Heterodox Academy, a forum for highlighting findings that run counter to received opinion in academic disciplines, particularly in the social sciences.

Earlier this month he gave the keynote address at the annual meeting of the American Psychological Assocation. His lecture is entitled “What’s Happening to Our Country? How Psychology Can Respond to Political Polarization, Incivility and Intolerance”, and in it he considers a number of long-term polarizing trends in American society and what to do about them.

He’s an engaging speaker. If you’re interested in understanding the Trump phenomenon, or fancy the thought of seeing a crowd of left-wing academics called out for bias by one of their own guild, this lecture might be for you. If you’re of conservative temperament, you might be pleasantly surprised to hear that an eminent academic considers you anything other than roadkill on the upward way of enlightenment. As he says in the lecture, every healthy society needs a party of order and stability as well as a party of change and progress. It sounds sensible to me (except the bit about change and progress). The lecture is about 50 minutes long, once the introductions are over.

If you enjoy this talk, you might also enjoy a TED talk he gave on the respective moral motivations of liberals and conservatives.

Books briefly noted

February 23, 2016

A few quick notes on books I’ve read recently. The theme for today is Books With Subtitles:

veryshort-medievalMedieval Literature
A Very Short Introduction
Elaine Treharne
(Oxford, 2015)
144 p.

I acquired this book in the hopes that it would help extend my list of “to read” medieval literature. I was interested in learning about medieval masterworks a little off the beaten trail (viz. not Dante, Chaucer, or Malory). As such, I was fairly disappointed with the book, which makes only brief mention of particular works. Instead, the book takes a wide view of medieval literature, discussing its social context, some principal themes, methods of book production, and so on. It has a rather academic tone (“Literary spaces, literary identities” is the title of one chapter, for instance). This is fine; no doubt it was what the author was going for. It just wasn’t what I was looking for.

veryshort-classicalClassical Literature
A Very Short Introduction
William Allan
(Oxford, 2014)
135 p.

This is more like it. In an effort to organize my Greco-Roman reading lists, I nabbed this brief volume to get a bird’s eye view. I could hardly have done better. Allan gives a brief introduction to the historical and social context for classical literature, and then proceeds by genre — epic, lyric poetry, drama, historiography, oratory, pastoral poetry, satire, and novel — summarizing the principal features of each literary type and highlighting a few of the principal works. I didn’t need him to tell me about Homer or Herodotus, but I’m happy to have a better understanding of where Horace and Juvenal fit into the picture, not to mention Plautus and Petronius. My reading list is now in pretty good shape, I’d say. I faint to think how long it will take to get to all these books, but it is nice that there is always more to look forward to.

kapilow-what-makesWhat Makes It Great?
Short Masterpieces, Great Composers
Rob Kapilow
(Wiley, 2011)
314 p.

Rob Kapilow takes about twenty short pieces of music, mostly excerpted from larger works, and examines each of them in detail, highlighting the compositional techniques and describing the musical structure. The pieces are presented chronologically, beginning with the early eighteenth century (“Spring”, from Vivaldi’s Four Seasons) and finishing with the early twentieth century (“…Des Pas sur le Neige”, from Debussy’s Preludes). They range in length from about one minute (the ‘Trepak’ movement from Tchaikovsky’s Nutcracker Suite) to ten minutes (Wagner’s prelude to Tristan und Isolde), with the median being around 3-4 minutes. The book is written at a level appropriate for a general reader with some musical education: each piece is illustrated with numerous excerpts from the score, so he assumes a competence with musical notation, and he uses some, but not too much, technical language to describe what the composer is doing. This is just the sort of mini-listening project that I relish, and it was enjoyable for me to see the musical logic of the various pieces unveiled. For instance, the piece by Debussy is one that I’ve heard numerous times, but I’d never stopped to appreciate the fact that it is based on such a simple musical idea, suitably varied and lavishly harmonized. Likewise, I’d not discerned the musical reasoning informing a little piece like Schumann’s Traumerei, or the way in which Bach’s Prelude in C grows from a tiny musical seed. The book is full of little insights into the craft of musical composition, and I found it very enjoyable.

physics-on-your-feetPhysics On Your Feet
Berkeley Graduate Exam Questions
Dmitry Budker & Alexander O. Sushkov
(Oxford, 2015)
216 p.

This was great fun. I did not have to take many oral exams during my graduate studies, but this book gives a flavour (minus the stress) of what I might have encountered. The authors have selected about sixty oral exam questions given to Berkeley grad students over the years, providing both the questions and, on the flip side, the solutions. The questions are drawn from across the spectrum: mechanics, fluids, electromagnetism, squalid state, nuclear & particle, astrophysics, optics, and molecular physics. Because of the oral exam context, none of the questions can call for lengthy calculations; more often they lean on physical intuition, approximations, and a basic (but wide) knowledge of principles. Which is not to say that they are easy! Admittedly, I have been out of the game for a decade now, and I am getting rusty, but these questions are meant to be challenging, and they succeed. Still, I enjoyed trying my hand at one question each day. I’d like to find another such book and continue the practice.