The value of idealized models

(First published on physicsfocus)

Every physicist has to know the joke about the dairy farmer. Seriously, if you don't know it, you can't call yourself a physicist. It really should be added to the IoP's requirements for the accreditation of physics degrees. If you have such a degree, and none of your lecturers ever told you the joke, please write a letter of complaint to your alma-mater immediately. In case you find yourself in that unhappy situation, here it is:

A dairy farmer, struggling to make a profit, asked the academic staff of his local university to help improve the milk-yield of his herd. Realising it was an interdisciplinary problem, he approached a theoretical physicist, an engineer and a biologist. After due consideration, the engineer contacted him. "Good news!" she said. "My new design of milking machine will reduce wastage, increasing your yield by 5%." The farmer thanked her, but explained that nothing short of a 100% increase could save the farm from financial ruin. The biologist came up with a better plan: genetically-modified cows would produce 50% more milk. But it was still not enough.

At last the theoretical physicist called, sounding very excited. "I can help!" he said. "I've worked out how to increase your milk yield by six hundred percent."

"Fantastic!" said the farmer. "What do I have to do?"

"It's quite straightforward," explained the physicist. "You just have to consider a spherical cow in a vacuum..."

I shouldn't break the cardinal rule never to explain a joke, but... the gag works because you recognize the theoretical physicist's habit of simplifying and idealizing real-world problems. At least, I hope you recognise it, although I wonder if it's a dying art. With the availability of vast computer-processing power and fantastically detailed experimental data in many fields, there is an increasing trend to construct hugely complex and comprehensive theoretical models, and number-crunch them into submission. Peta-scale computers can accurately simulate the trajectories of vast numbers of atoms interacting in complex biological fluids, and can even model the non-equilibrium thermodynamics of the atmosphere realistically enough to fluke an accurate weather forecast occasionally.

Superficially, it might seem like a good thing if our theoretical models can match real-world data. But is it? If I succeed in making a computer spit out accurate numbers from a model that is too complex for my meagre mortal mind to disentangle, can I claim to have learnt anything about the world?

In terms of improving our understanding and ability to develop new ideas and innovations, making a computer produce the same data as an experiment has little value. Imagine I construct a computer model of an amoeba, that includes the dynamics of every molecule and every electron in it. I can be confident that the output of this model will perfectly match the behaviour of the amoeba. So there is no point in wasting computer-time simulating that model; I already know what the results will be, and it will teach me precisely nothing about the amoeba.

If I want to learn how an amoeba (or anything) works, by theoretical modelling, I need to leave things out of the model. Only then will I discover whether those features were important and, if so, for what.

When I was a physics undergraduate, I remember once explaining Galileo's famous experiment to a classicist friend; the (possibly apocryphal) one where he dropped large and small stones from the leaning tower of Pisa, to demonstrate that gravity applies the same acceleration to all bodies. "But a stone falls faster than a feather," she protested. I said that was just because of the air resistance, so the demonstration would work perfectly if you could take the air away. "But you can't," she pointed out. "The theory's pointless if it doesn't apply to the real world. So Galileo was wrong." I have a strong suspicion that she was just trying to wind me up - and succeeding. The point, which she probably appreciated really, is that the idealized scenario teaches us about gravity, and we can't hope to understand the effects of gravity-plus-air before we understand gravity alone.

Similarly, if Newton had acknowledged that no object has ever found itself perfectly free of any unbalanced force, he would never have formulated his first law of motion. If Schroedinger had fretted that an electron and proton cannot be fully isolated from all external influences, he would have failed to solve the structure of the hydrogen atom and establish the fundamentals of quantum mechanics. The simplicity of the laws of nature can only be investigated by idealized models (like the one-dimensional "fluid" below), before adding the bells and whistles of more realistic scenarios.

With increasing research emphasis on throwing massive experimental and computational power at chemically complex biophysical and nanotechnological systems, and in the face of financial pressure to follow applications-led research, it would be easy to forget the importance of developing idealized models, elegant enough to deduce general principles that transcend any one specific application. So let's adiabatically raise a semi-infinite glass of (let's assume) milk, and drink to the health of the spherical cow.

What are exams for? On measuring ability and disability

(First published on physicsfocus)

Equal rights

I'm going to go out on a limb here and assert that equality of opportunity is a good thing. There, I've said it. Gone are the bad old days when jobs and privileges were determined at birth. No longer do you have to be an aristocrat or wealthy land-owner to study science; Michael Faraday broke that mould. Neither is being born with a Y-chromosome still a prerequisite for academic success. While that playing field may not be as level as it should be, at least officially-sanctioned sexism has been abolished since Rosalind Franklin's day. Encouragingly, I currently teach a cohort of undergraduate mathematicians, at Leeds University, with a near-equal female:male gender ratio of 52:48.

Belatedly, we have seen improvements in equality of opportunity for people with disabilities. An inspiring leap forward was made by the London 2012 Paralympics in dispelling some of our social prejudices. Meanwhile, with the introduction of the Equality Act 2010, educational establishments have set up new procedures to ensure that disability does not result in inequality.

For a simple and obvious example, consider a physics undergraduate student who uses a wheelchair. Their inability to walk has no bearing on their potential quality as a physicist. So their university has a responsibility to make sure that they are not disadvantaged during their learning and assessment. It would be unfair to arrange their exams to take place at the top of a steep flight of stairs. Their institution needs to be aware of their condition and make sure that they can access the exam.

Similarly, universities must make exams accessible to blind or partially-sighted students by printing their exam papers in Braille or large print. It is obvious that poor eyesight should not prevent a person being a good physicist. So we lecturers and examiners must make sure that our formal assessments of a physicist's abilities reflect only those abilities relevant to being a physicist, while taking appropriate account of a candidate's medical conditions.

A student with a disability can visit a university's Equality and Diversity Unit to have their needs assessed by a qualified professional, who will write a formal Assessment of Needs: a document that is circulated to their teachers, explaining what special provisions are required to prevent the student being disadvantaged by their condition. So a student with hearing difficulty might have an Assessment of Needs containing a statement such as, "Lectures should be arranged in a room with a hearing loop." It makes sense, and can be very helpful.

Learning equality

Things become a lot more complicated where a specific learning difficulty (SpLD) is involved because, whereas hearing or walking are not crucial abilities for STEM subjects (Science, Technology, Engineering, Mathematics), learning is a university's core business. The Equality Service at the University of Leeds has useful information about SpLDs. It says,

"Each SpLD is characterised by an unusual skills profile. This often leads to difficulties with academic tasks, despite having average or above average intelligence or general ability."

This makes a thought-provoking distinction between ability with academic tasks and intelligence. It presupposes particular definitions of "intelligence" and "academic". I don't know how to define either of those things, but it seems safe to say that the particular type of intelligence that is relevant to university work could be called "academic intelligence".

When learning is itself the subject of an Assessment of Needs, as it is for people with Asperger syndrome or dyscalculia, for two examples, then the assessor's own academic background becomes relevant. Assessors and staff of Equality and Diversity Units often have medical or humanities training. (I confess this is an anecdotal observation, not based on good data.) So their views of STEM-subject exams are not based on experience. Yet they and other medical professionals are required to write Assessments of Needs that carry the weight of law, and dictate some parameters of the teaching and assessment delivered by the subject-specialists.

For instance, while good writing style is deemed relevant to an English degree, physics examiners are often instructed not to mark a particular student's work on the basis of their grammar. The assumption is that ability to write good English is not part of the discipline of physics, and can be separated from it as easily as the ability to walk or to hear. The instruction assumes that the exam should only test the student's ability to calculate or recall facts, rather than a holistic ability to understand an English description, translate it into a calculation, solve the problem, interpret the solution and communicate it well. Of course, no examiner would mark a physicist's work exclusively on their writing style, so we are only talking about a handful of marks at stake.

Of necessity, when the 2010 Equality Act became law, new systems were hastily put in place, without much time for consultation. As a consequence, examiners were never asked, for instance, whether we should expect a physicist to demonstrate good communication ability. As we iron out the system's early teething troubles, we need to address these kinds of question. What exactly is an exam supposed to test? To what extent can we separate our assessment of a physics student's linguistic ability from their other skills? This is not a rhetorical question. I don't know the answer, but I do know that it is complicated and not obvious, and should be debated before the rules are set in stone.

Here is a cartoon that brings the issue into sharp focus.

Cartoon courtesy of QuickMeme www.quickmeme.com/p/3vpax2

It all hinges on what the selection is for. If this is the exam for a swimming qualification, it is entirely unsuitable. If it is a job interview for a steeplejack, then it's a fair test that discriminates appropriately between the best and the worst. It is easy to define the appropriate skills for a steeplejack. How should we define a scientist?

A matter of time

To avoid any misunderstanding, I want to make a clear distinction between teaching and examination. Any good teacher needs to have empathy for their students, and pitch their teaching at a suitable level and tempo for each individual. Being armed with the maximum possible information about the student's particular needs and abilities is always helpful, and the good teacher will make appropriate provisions whenever possible. The extent to which special provisions should be made during exams is an entirely separate question.

The most common provision in an Assessment of Needs is the stipulation that a particular student should be given extra time (typically 25% extra) to complete their exam. This raises a fundamental question. If a person can solve a particular puzzle more quickly that another person, although both might get there in the end, should their university award them a higher grade? A person's intellectual ability cannot be quantified on a single, one-dimensional scale. It is many-faceted, and speed of problem-solving is one aspect of it.

One might suggest that exams do not exist to test a person's intellectual ability, but only to test how much they have learnt during a particular course of study. That sounds like a reasonable idea but, in fact, we do not measure a student's scientific ability at the beginning and end of a science degree course, and award the qualification for self-improvement, irrespective of whether they are any good at the subject. On the contrary, the letters "BSc" are purported to be a standardized benchmark, indicating a particular absolute level of ability. That ability might have been innate when the student arrived at university, or might be the result of more-than-average hard work.

The most common method for determining ability in any academic subject is by timed exams. An exam tests what a student can achieve within a finite time interval. At the end of that interval, anyone who has not finished misses out on the marks that they were too slow to accrue. An exception is made if a medical professional has predicted, rightly or wrongly, that the student would need extra time for their exams, and has written their prediction in an Assessment of Needs. This inconsistency presents a problem. A more accurate and individually-tailored assessment of each student's needs could be made in the exam hall. We could unambiguously identify the students who need extra time, as a result of their own unique abilities and disabilities. They are the ones who run out of time!

So there would be advantages (as well as massive logistical difficulties) in having un-timed exams. They would allow each student to demonstrate their abilities, whilst removing the element of speed from the assessment of their expertise. With the best intentions, we have stumbled into the new age of equality with a flawed mixture of two systems. Candidates, whose needs have not been assessed, have their abilities measured by a fixed-duration exam, while others have the duration of their exam determined by their abilities.

The question that must urgently be addressed is this. Do we want exams to test what a candidate is able to achieve within a fixed time, or do we only want to know what they can achieve when given as much time as they require? Creating fair and meaningful methods of assessment requires an open debate on what we want from an exam, what we want from a degree classification, and what we want from a physicist.

When I sawed through my telescope

(You read it right; not "saw" but "sawed".)

Four years ago, after decades of prevarication, I finally bought the telescope that I had promised myself since childhood. Despite its modest price tag, the Chinese-built "Skywatcher" reflecting telescope is an impressively precise piece of equipment. Its mirror's surface is formed into a parabolic curve to an accuracy better than a quarter of a wavelength of light across its entire 4½ inch diameter. This optical perfection means that all of the light collected from a star is brought to an impeccable focus with no loss of brightness due to cancellation of light waves arriving out of kilter.

This incredible achievement of human civilization has shown me the wonders of the universe, channelling ancient light from distant galaxies into my pupil. For four years I have mollycoddled its pristine optical surfaces which would fail if scratched by any abrasives such as metal dust.

So, it was with some trepidation that I took a hacksaw to my pride and joy.

I had been toying with this drastic measure for a couple of years, ever since realising that the 'scope could not be coaxed into focussing starlight directly onto the sensor of my camera. The idea was always swiftly dismissed, knowing that one slip of the saw would write the thing off, and that even a successful cut would still leave me with a pile of telescope pieces and no experience of assembling and perfectly aligning them.

When, at last, I had a week's holiday to take at home, while the children were still at school, I decided to take the plunge and indulge two solitary obsessions: metalwork and astronomy. This blog entry takes the form of a photo diary and how-to manual for the foolhardy amateur astronomer.

How it works

You see, a telescope's job is to concentrate each star's light into a bright pinpoint. It actually creates a miniature reconstruction of the astronomical original, blazing away just inside the eyepiece holder. The astronomer then views this bijou stellar facsimilie using the eyepiece which is nothing more than a high-quality magnifying glass, making it appear at a comfortable viewing distance. The overall effect is both to magnify (spreading out the angular separations of the stars) and to brighten the stars. It gives a brighter view than the naked eye alone by collecting all of the light that falls through the big hole at the front of the telescope, and squeezing it through the much smaller area of the human pupil that limits the naked eye's light-collecting power.

This is all summarized by the picture below, that shows some of the wavefronts of starlight being concentrated and funnelled into an observers eye. This picture demonstrates a refracting, rather than a reflecting telescope, because it allows the wavefronts to be shown more clearly. The objective mirror of a refracting telescope does exactly the same job as the big objective lens at the front of the refractor, except that it also sends the light back the way it came, to be viewed through an eyepiece near the top of the telescope tube. This would make the diagram more cluttered, with incoming and outgoing light overlayed in the tube's interior.

Astrophotography

So much for using a telescope with your eye. After doing so for a while, I could no longer contain my flabbergastedness (is that a word?) and wanted to share it. So, how do you photograph what the telescope sees? There are basically two options:

(1) Point a camera at the eyepiece, in place of your eye. This technique goes by the grandiose name of afocal astrophotography, (nicely explained here) and it supports an industry of various brackets and adapters to hold the camera steady and align it with the eyepiece. I used this method for a while, with some success. It allows you to choose the magnification of the final picture by selecting an appropriate eyepiece. But it has some drawbacks. A small fraction of the meagre starlight is lost due to imperfect transmission at all of the glass surfaces in the eypiece and in the camera's lens. Significantly more can be lost due to various apertures and lens-stops in the light-path.

A more crucial drawback is that anchoring a heavy camera to the end of a long eyepiece and then swiveling it around to follow the sky can put excessive bending forces on the poor old telescope, which was not bred for heavy lifting. This was a particular problem for my light-weight entry-level Skywatcher Skyhawk which, despite its top-quality optics, holds the eyepiece in a nasty plastic focusser.

The focusser had to go. I bought a well-engineered replacement for the plastic tat. Unfortunately, it was designed to fit a bigger scope, so had to be shortened to avoid it crashing into the secondary mirror when wound fully in. This meant re-making some of its parts.

Also, the new focusser barrel was wider, requiring a bigger hole in the side of the scope. So, after disassembling the optics and protecting most of the paintwork from scratches using masking tape and duct tape, I filed away at the thin aluminium.

The focusser's base-plate was designed to fit the cyllindrical surface of a larger-diameter 'scope. Re-shaping and fitting it involved making some bespoke aluminium brackets...

...and resin to fill the gaps, molded to the right shape by pressing it against the telescope itself. Greaseproof paper prevented it sticking to the paintwork.

A better way

(2) Rather than settling for the afocal technique, most astrophotographers prefer to remove the unwieldy eyepiece altogether, with a technique known as principal focus astrophotography.

It's very simple. You remove the camera's own lens and use the telescope as its lens. This means placing the camera's light-sensitive surface (the film in an old-fashioned camera, or the CMOS or CCD sensor nowadays) at the focal plane of the telescope, where all the starlight is concentrated. The focal plane is normally located inside the eyepiece-holder. It needs to be shifted if its going to fall on the camera's sensor, which can be done by moving the telescope's objective mirror (or lens).

Unfortunately, in the Skywatcher Skyhawk, the mirror's adjusting bolts won't move it far enough. So there was only one thing for it: to shorten the telescope by just the right amount. Too little, and the effort would be wasted as the focussed light would still not reach the sensor. Too much, and the focusser would never extend far enough to focus an eyepiece for normal operation.

Working out how much to cut off is easier said than done, since it's tricky to measure the current position of the focal plane, or the distance to the camera's sensor. These things can be calculated by focusing on a nearby object and measuring its distance from the mirror. The measurement needs to be accurate and the calculations error-free. How confident would you feel about sawing off the right amount, based on these scribblings?

A little saucepan came to the rescue.

By lucky chance, this saucepan was a perfect press-fit inside the telescope tube. So, by turning it into a temporary mount for the mirror...

...I could slide the mirror into a new position, to try it out before doing irrevocable violence to my treasured toy. The resulting affront to nature, henceforth known as the Saucescope, confirmed my calculation, that a little over an inch needed to be removed.

So, with everything carefully marked out...

...and heart in mouth, I took saw in hand and gingerly cut into the blue-anodized aluminium. There was no margin for error, because the cut end would not be hidden, but would simply butt up against the mirror housing, with any scratches or wobbles in full view.

With the nerve-wracking part of the job done, all that remained was to clean off every speck of glass-damaging metal dust, rebuild and collimate the scope.

The camera now fits snugly in the new focal plane.

On the subsequent clear nights, I was relieved to find that the work had all been worthwhile and I had not ruined my beautiful telescope. What could have been a time-consuming disaster, given a moment's lapse in concentration, turned out to be the most satisfying project I've undertaken recently. Here are some of the results, photographed with the new set-up:

The Dumbbell Nebula

The Pleiades

The Orion Nebula

Good Old-Fashioned Technology

Remember the good old days when micro-electronics were traditional and wholesome? OK, perhaps my sense of nostalgia is a mite over-developed, but I have noticed an unfortunate trend in recent technological developments. While it is nice to have affordable tech with almost magical power, the slickness of the designers' art has a tendency to conceal the real world from us. I care about that because, as a physicist and an educator, my raison d'être is to reveal the real world.

I don't want to over-state the case because, actually, I love new gizmos that allow me to browse my music collection through my TV and to photograph the Orion Nebula in mere moments using the unbelievably sensitive ISO25600 setting on my camera. I wouldn't want to halt the inevitable march of progress even if I could. But I would like to take this opportunity to mark the passing of some dearly loved and enlightening technology that has gone the way of all flesh.

Magnetic entertainment

Take, for instance, the cathode ray tube (CRT). Until about ten years ago, all televisions lit up our livingrooms by smashing high-energy electrons into phosphorescent pixels inside a glass vacuum tube. The elementary particles were launched from an electron gun at the back of the TV, in which they leapt from a hot, negatively charged electrode and raced towards a positive electrode, narrowly missed it, and hit the screen instead. A negative electrode is called a cathode, hence the electrons were dubbed "cathode rays" before J. J. Thompson discovered their true identity. The name stuck.

The CRT was a real-life particle accelerator residing in every home and, in retrospect, it was an absolute gift to all physics teachers. It's harder to teach about electrons if students have to take their existence on trust, or observe them only inside some arcane laboratory glassware.

Credit: Marcin Białek

Anyone with a magnet and a sense of mischief could discover how their traditional telly steered its beam of charged particles magnetically. Before consigning my own idiot-lantern to the tip last month, I took these pictures that show a magnet exerting a Lorentz force on the electrons, making them swerve and hit the wrong pixel. (It's slightly risky to do this if you want to keep your TV, as it could become permanently magnetized!)

 

Analogue ghosts

The switch-over from analogue to digital TV signals has robbed us of another neat physics demo. "Ghosting" was an annoying artefact that appeared on the screen if you used the wrong type of aerial cable. The people in TV-land each seemed to be stalked by a spectral doppelganger standing a few inches to their right.

Credit: Cablefax.com

Back in the analogue age, it was a familiar sight in any students' TV lounge, and I used to discuss it in my "Vibrations and Waves" lectures as a nice example of impedance-mismatching. You see, the electromagnetic oscillations, picked up by the TV aerial, travel as waves down a co-ax cable to the television. Like any wave-carrying medium, this cable is characterised by a wave-impedance that indicates how much power is needed to push a given size of wave along it. If the wave meets a joint between two cables with different impedances, only part of its power continues through the second cable to the telly. Some fraction of the signal is reflected back along the first cable, where it bounces off the aerial and sets out again towards the TV, slightly delayed. So the same signal arrives twice at the TV, resulting in a double image.

These days, the electromagnetic waves still perform the same physics as ever, echoing off mismatched cables. But the digital encoding of audio-visual information lets clever circuitry reconstruct a pristine picture from a degraded signal. So we can enjoy our high-brow entertainment without the distraction of aberrant natural phenomena.

Of course, physics lecturers could preface their discussion of wave-impedance by explaining what TV looked like in the olden days, but the relevance of the example is lost. Still, I'm in no position to complain about this development since, like any consumer of electronics, given the choice, I'll opt for the TV with the clearest picture. 

 

Discotheque versus MP3otheque

My record player is another old friend that accompanied the CRT to the dump during this month's domestic clear-out (so I told my wife; it's really hidden in my workshop. Shhh!). Having at last finished converting all my old vinyl into the vastly more convenient MP3 format, before "throwing it out", I used the turntable to teach my young children about sound. It was great fun and, with the music safely backed-up, I could relax about the youngsters scratching the discs.

The wonderful thing about a record is that it's very obviously a frozen sound wave. Look closely at its surface, and the wiggling shape of the sound is there right before your eyes. Peer at the stylus as it follows the groove, and you can see how it shakes in time with the air.

To demonstrate even more directly that sound is nothing more than shaking air, we did away with the intervention of the amplifier by creating a primitive gramophone. It was easily done by rolling a sheet of paper into a cone, and sticking a sharp pin through it near the apex. Gently resting the pin's point on the record as it turns on the turntable makes the paper cone sing with a scratchy human voice. If you still own a turntable, I recommend trying out this magic, but only on discs that you don't mind scratching. With a bit of practise, the demo can be simplified even more, using only a flat sheet of paper and resting one corner of it in the record's groove.

True beauty is flawed

Many new devices distance us from physical phenomena, for the valid reason that they are just much more complicated, and often much smaller, than their forebears. I have little chance of showing my children how MP3 files create sound because, unlike a gramophone stylus, all of the processing is complex and rather abstract.

Other devices shield us from reality only because it is fashionable to do so. For example, when you switch on a fairly old radio - even one with automatic tuning - you hear a few seconds of white or coloured noise as the tuner seeks the right frequency. It's a nice sound, evocative of the electromagnetic physics of the carrier wave. Newer models refuse to engage the speaker until their furtive tuning is completed, and the sterile perfection of the user's experience can be guaranteed. This trend is not confined to radios; it's the reason why a lot of new gadgets are slow to switch on. They are designed not to betray the imperfect physical nature of their workings. That is a shame, because imperfections are important in helping us to understand the world.

Biologists learn how complicated organisms work by observing them going wrong in various ways. One standard technique that geneticists use, to discover the purpose of a gene, is to deliberately break it. They breed organisms in which a particular gene is switched off or made to malfunction. This sheds light on the workings of the genome. In humans, where ethics prevents tampering for the purposes of research, doctors glean the most knowledge by observing imperfections and accidents that arise randomly. Oliver Sachs's book, "The man who mistook his wife for a hat" gives many fascinating examples of brain function that could not have been understood without observing the results of some unfortunate mishaps.

By hiding imperfections from us, the designers of new gadgets are doing us a disservice. Back in the days when cars were basic and unreliable, every motorist knew how an engine worked. Now that they are flawlessly controlled by microprocessors, we have lost those skills and knowledge. As the technologists get better at polishing their performance, our opportunities for insight diminish.

I am glad that some new devices buck the trend and flaunt their mechanisms for all to see. Among the products not afraid to bare all are the TAG Heuer belt-driven wrist-watch, Dyson's celebrated vacuum cleaners, and most motorbikes. Let's encourage manufacturers to do more of this sort of thing.

Meanwhile, I am making the most of the old gadgets while they are still with us. It's a race against time to show the children how to build a crystal set before the analogue radio signal is switched off. And I have lost count of the number of steam engines and beam engines that we have visited together. Perhaps you can share some other examples of illuminating venerable technology that I should introduce them to before it's too late.

Although I feel misty-eyed at the demise of old machines with all their educational potential, I feel no kinship for the luddites or for King Canute. As simple contraptions disappear, we educators will just have to raise our game. Sic transit gloria mundi.

Universality

(Published on physicsfocus as "Universality: which types of physics qualify as 'fundamental'?")

What qualifies as “fundamental” physics? The answer might seem straightforward. It is science that investigates the universal properties of nature, like the interactions between quantum fields studied at CERN or the shape of the cosmos observed by astronomers. In the other camp, science that is not fundamental includes things like strength testing of new materials, or sports science to optimize the trajectory of a javelin. Both types of research use scientific methods to design good experiments that remove any potential observer-bias.

Straightforward as it seems, I posed the question because I want to tell you about research on Non-equilibrium Statistical Physics. Because it contains the word “Statistical”, you might put this subject into the non-fundamental category. To see why that would be wrong, you need to know some little-understood facts about how nature works – about which aspects of nature are in fact universal.

Some of the fundamental properties of nature can be found by studying matter in ever finer detail. By doing so, our predecessors have discovered that matter is made of atoms that are made of electrons and nuclei that are made of quantum fields constituting quarks, gluons, leptons etc. These are clearly fundamental properties of nature. The universe has, for some as-yet unknown reason, decided to allow these particular fields to exist, so we must study them to find out, fundamentally, how the universe works.

But nature has other fundamental properties that evade detection by this microscopic exploration. They are properties that emerge only when a large number of particles interact. Of course, once you know the behaviours of elementary particles, you can use a computer to simulate a large number of them and predict what they will do en masse. The particles’ motions become more complicated the more of them you have. For instance, here (right) is a picture of the paths of two classical particles attracted by gravity, or they could be charged particles interacting via electrostatic attraction. They follow simple elliptical paths. Introduce a third particle (below right) and their paths become chaotic.

Say you wanted to know how much force will be applied to the piston of an engine by a large collection of particles that constitute some gas. The pressure felt by the piston fluctuates wildly in the presence of three or more molecules that sporadically collide with it. But it turns out that, for a large enough collection of particles, although their individual trajectories become effectively random, their collective motion becomes completely predictable. Here’s the crucial point. The pressure averages out as the number of molecules approaches infinity and, amazingly, the pressure ceases to depend on what the molecules are made of or how they interact. Its value is given by the ideal gas law that you probably learned at school. It only depends on how densely the molecules are packed into the container and on the temperature.

As Ludwig Boltzmann, the founding father of statistical physics discovered, even the temperature doesn’t depend on any detailed features of the gas molecules, only on the amount of energy that they have been given and on their symmetries – the number of ways you can rotate one of the molecules without changing its appearance.

This is a very important fact. It means that the detailed features of elementary particles do not determine how the universe works. Large-scale physics is not controlled by those details, but only by a few of their symmetries and by the statistical properties of large numbers.

Specifically, most of the macroscopic properties of matter depend only on how many different ways there are to rearrange its particles and energy. The preceding sentence sounds too bizarre to be true, and needs to be read several times. All that we experience around us; the wetness of water, the clarity of glass, the viscosity of treacle and the conductivity of silicon, are manifestations of combinatorics. They result from the mathematics of large numbers of interactions, not from the microscopic properties of those interactions.

If you still doubt that a theory based on statistics (on counting arrangements of particles) can constitute fundamental physics, you need look no further than the second law of thermodynamics, that most intriguing of laws, which states that the amount of entropy (disorder) in the universe can only increase with time. It is a consequence of statistical physics. Boltzmann realised that entropy is simply a way of counting large numbers of configurations, and yet it is responsible for our sense of the direction of time, a fundamental concept.

As a crude example of the unifying effect of large numbers, look at the flowing fluids depicted below. Their macroscopic properties, such as flow rate, diffusivity, compressibility, viscosity... are affected by a few basic features like the hardness of their particles, the packing density of those particles and the presence of gravity. At this scale, we don't notice what the constituent particles are made of, or their detailed features like the fact that the fluid on the right is made of red blood cells in a capillary, whereas that on the left is composed of athletes in the Engadin Ski Marathon.

A more precise (but rather complicated) correspondence exists between the behaviour of a fluid, such as water, at its critical point (where the pressure is just high enough to make the gas identical to the liquid, thus removing the boiling transition) and certain types of magnet, known as Ising magnets, at their Curie point (the temperature where they lose their permanent magnetism). These very different systems behave in identical ways as they approach the critical/Curie temperature. Fundamentally, the reason for this is that they both comprise large numbers of interacting particles that can each be found in one of two states: for Ising magnets, each atom's magnetic north pole can point either up or down while, within a sample of water, at any given location, a molecule can be either present or absent. No other microscopic features of these radically disparate sets of particles govern their collective behaviour. As a result, water and Ising magnets share identical large-scale physics and are said to belong to the same universality class.

Another material sharing the same universal features as these two is the "surfactant sponge phase". It is an arrangement of molecules that often forms spontaneously when you mix washing-up liquid with water. The detergent molecules group together, forming thin membranes that curve and connect into a sponge-like arrangement of pipes, depicted here.

This elaborate surface divides the water into two interpenetrating labyrinths. So, once again, within the sponge phase, each point in space can be characterised by a single binary digit, specifying which of the two labyrinths it belongs to. It also undergoes a transition at a critical temperature - not from gas to liquid, or from non-magnetic to magnetic, but from a "symmetric" state in which the labyrinths have equal volumes, to a state in which their symmetry is broken, with one region bigger than the other. [Roux D, Coulon C and Cates ME, "Sponge phases in surfactant solutions", J. Phys. Chem 96, 4174-4187 (1992)].

Since Kenneth Wilson's Nobel-prize-winning development of "Renormalization Group" theory in the 1970s - the mathematical tool for dealing with universality - many different “universality classes” have been discovered amongst a mid-boggling variety of interacting systems. Wilson and Boltzmann's theories apply to systems of particles at thermodynamic equilibrium, meaning that they are not flowing. More recently, there have been hints that the behaviour of flowing systems may be governed by a unifying statistical theory of “Large Deviations”, giving them universal features that are not obvious in the microscopic laws of nature. I honestly cannot image a more captivating subject to research.

Images:

1. Two particles attracted to each other following simple ellipitcal paths.
2. Three mutually attracting particles create more complicated, chaotic paths. Credit: Daniel Piker
3. Athletes in the Engadin ski marathon behaving like particles of a fluid
4. Red blood cells flowing through a capillary.
5. A sponge-like arrangement of molecules, such as that which forms when mixing detergent and water. Source: Physical Review Focus
   
   

Soldiers in Schools

(Published on physicsfocus as "Why Michael Gove's plan to fast-track soldiers into schools is worrying")

Could anything be more important to the future of our society than education? I truly believe not. That’s partly why I chose a career in lecturing, believing it a worthwhile use of my skills as a physicist. There are plenty of other topics causing concern at the moment, such as unemployment, crime and international tensions. We, as a society, need to tackle those issues but, in doing so, we are treating symptoms, not solving the problems. The root causes all involve shortcomings in people’s attitudes and in the quality of their decisions. Education is the means to improve things in the long term.

Tomorrow’s society is shaped by today’s parents and teachers. Bad education and upbringing is where our future problems begin. Good quality education creates the best chance of a socially and economically healthy world. I don’t imagine many people would disagree with those self-evident assertions.

Obviously then, being intelligent folk not intent on self-destruction, we only entrust this most crucial and difficult task — of educating and shaping the next generation — to the brightest and best. Surely, as a nation of sane people wanting a harmonious future, education is our top priority, into which we channel the majority of our resources, right? We don’t? Then I hope the government is going to put that right and turn teaching into the most prestigious and highly-trained of all professions.

What’s that you say about out-of-work soldiers? I thought we were discussing the future of education. Please tell me that the Secretary of State for Education, Michael Gove, is joking about the new ‘Troops to Teachers’ scheme, introduced this month, for fast-tracking ex-military personnel into the classroom! Under the scheme, those leaving the armed forces will be the only people able to start training as a teacher without a degree and be qualified within two years.

I don’t intend to make a party-political point, since I have not seen any recent government give education the priority that it’s due. ‘Troops to Teachers’ is just the latest down-grading of the kudos afforded to academic excellence. According to this policy, being successful in a particular academic subject at school apparently makes you less suitable to teach it than someone who trained for a career in the army.

According to BBC News:

A DfE spokesman stressed that top military specialists often have relevant experience, particularly in science and technology which could help redress the shortage of teachers in some subjects.

Well that’s a relief then. The DfE spokesman says science doesn’t need all the years of methodical rigour that university degrees squander on it. It can be picked up on the job by non-graduates trained to operate some electronic equipment. Now I feel foolish for wasting my time on all that pointless study.

I fear for our children’s prospects in the mathematical sciences if they are taught by people who share the spokesman’s confusion between technological proficiency and scientific education. And, while some schoolchildren would benefit from bootcamp drill, the DfE’s implicit endorsement of military discipline, as an adequate substitute for nurturing critical thinking, is a worrying message.

Don’t get me wrong, I don’t mean to disparage military personnel. In fact, I admire them for their extraordinary bravery and unquestioning loyalty. I don’t primarily admire them for their scholarship and child-rearing skills. Undoubtedly, some ex-forces people have those skills and could become excellent teachers. Rightly, they have always had the same opportunities as anyone else to embark on teacher training. But the idea that everyone else is less suitable, requiring more training than an ex-soldier before educating our children, is ridiculous.

This strikes me as a transparent ruse to use our education system to absorb the impact of the recent downsizing of the armed forces. What next? I hear there’s a mounting crisis in hospital overcrowding. Why not fast-track patients into the classroom. I’m sure that, like soldiers, many of them have a rich life-experience to draw upon, so there’s no need to consider their academic achievements.

Perhaps I shouldn’t be facetious about this most crucial and disappointing turn of events. But I begin to wonder whether the government is being facetious when it so often proclaims its commitment to promoting STEM subjects (Science, Technology, Engineering and Mathematics), and claims to appreciate their importance to our society and economy. STEM subjects require a great deal of dedication, inspirational teaching and uninterrupted hard study by academically gifted people. I would like to see more young people arriving at university well prepared for higher education in the STEM subjects. That would require a real commitment to academic excellence in schools. I can hardly believe I need to say this, Mr Gove: academic excellence is not the same as military training.