There is a large number of examples in which, of two possibilities that appear equally probable, only one is expressed in reality. In ways that will become apparent, this idea of symmetry-breaking is connected with several other ideas: positive feedback, chirality in the universe, and games of coordination. This essay will consist largely of an annotated list of some examples, either from a very stimulating article on economics, or others that have occurred to me while reading the article or later.

The article in question is “Positive Feedback in the Economy” by Brian Arthur. His main point is that, while negative feedback mechanisms predominate in conventional equilibrium economic theory, in some modern highly technological industries the line of development is determined by positive feedback, and therefore, like the weather, almost by chance (capable of being overturned by the flutter of a butterfly’s wings). As would be expected, such positive feedback mechanisms are non-linear (like turbulent flow), show instability, and are related to modern mathematical theories of Chaos. Conventional economic theory is quite the opposite: here the results of a competition between two technologies in an industry (e.g. between generating electric power by hydro dams or by burning coal) are deterministic and predictable, led by “unseen hand” market mechanisms, and use linear mathematics, which is much easier to handle. While conventional economics tends toward a single equilibrium, positive-feedback economics has at least two and maybe several equilibria which act as possible “attractors”, but only one can be “expressed” in reality. Also important is the fact that the alternative expressed in reality is not necessarily the best one – the choice is arbitrary and accidental.

Here then are his examples:

1. In the field of VCRs (Video Cassette Recorders), the VHS and Beta systems started on an equal basis and either could have prevailed. But VHS somehow got an initial advantage almost by chance, and then everybody flocked to it by a bandwagon effect, because it is so important to be “compatible” with everyone else’s equipment.
2. Among several firms entering a new field, and having about equal capability, the advantage goes to the first-comer, for reasons similar to the above.
3. He presents a diagram for a “random-walk” decision between two equally probable possibilities, which is very reminiscent of the symmetry-breaking decisions on chirality (left or right- handedness) presented in “The Mirror World” in Section II. More about that later.
4. Several centuries ago there used to be clocks whose hands turned “anti-clockwise”. (He shows a photograph of one.) Of course, it is only by convention that clocks now run clockwise; the other choice would have been just as good, but it is a great advantage if all the clocks run in the same direction. Such conventions abound (I name some in my own list of examples), and they illustrate “coordination games”. These are not games of conflict, but of cooperation, where it is to everyone’s advantage to make the same choice, though which of the two possibilities is chosen is a matter of indifference to all.
5. Location of industrial plants: in some cases, it is an advantage for them to be clustered, and which location of the several initially possible will house this concentration is largely determined by the early comers. An example is Silicon Valley in California. Late-comers tend to locate near already existing plants.
6. His theoretical model is one of adding colored balls to an already existing collection of such balls. Depending on the rules for selecting colors in relation to those already in the collection, we can simulate either a single-equilibrium or a positive-feedback system.
7. In a ferro-magnetic material, the molecular dipoles, initially in random orientations, will line up either all down or all up, depending on what the first few do by random chance. This is because the later ones are strongly influenced to line up in conformity with the early ones.
8. Rail gauges in the train systems of North America could have been either narrow-gauge or broad-gauge, but there is a strong advantage of compatibility in having them all the same. Again, everybody coordinates with the early comers.
9. Location of major cities is partly determined by geographical factors, such as nearness to rivers and/or resources and markets, but the choice among several nearly equal possibilities seems essentially random and arbitrary.
10. Why is Japan leading in high-technology industries over the US? Because Japanese firms coordinate their policies more, while US firms compete more with each other. “Japan Inc.” has an “industrial policy”, while the US is ideologically opposed to planning.
11. Early in the nuclear age, reactors for nuclear power plants had several possibilities: light- water cooled, gas-cooled, graphite-moderated, heavy-water moderated, sodium-cooled…Yet all US reactors are now of the light-water-cooled enriched-uranium type. (He fails to mention that, in contrast, Canada went for the CANDU reactor – deuterium-moderated natural-uranium.)
12. The dominance of the English language over French as the world’s “lingua franca” is really an accident of history, not pre-determined by its greater suitability. But it had to be only one language, regardless of which was chosen.
13. The number of lines per unit length in television scanning at first differed for different systems, but soon settled into a standard uniform format – and not really on the basis of any technical superiority.
14. Screw threads were similarly standardized after a brief time of indecision and confusion.
15. The arrangement of letters and symbols on a typewriter keyboard is the result of a standardization that could easily have produced a different keyboard if a different beginning had been made. (In fact, a better alternative exists: the Dvorak Keyboard.) (See Diamond.)
16. The predominant use of Fortran as a computer language is another example of accidental selection.
17. IBM computers and their “clones” (compatible machines) need not have come out on top – but did. Once they did, everybody flocked to them.
18. “Spin glasses” are materials in which magnetic spins are not aligned throughout, but local concentrations of “all of the same kind” are common.
19. He cites solid-state lasers as another example, without enlarging on it. I am not sure what he means.
20. In “punctuated evolution”, at the time of rapid change it is not necessarily the fittest who survive or the least fit that become extinct. There is a large element of chance, a small initial move that escalates by positive feedback.
21. A similar mechanism operates in human history. In fluid moments, events might easily move one way or the other, and a small impetus may initiate a big jump to one of several possibilities. This is partly what we mean in speaking of “the historic moment”, or “seizing the opportunity”. At other times, individual actions may have hardly any effect at all.

The author has amassed a large number of examples in his short article. Yet as I read it, I thought of other examples, which I now want to list. There is no thought of claiming that the list is exhaustive. My feeling is that this mechanism is very fundamental indeed, and that almost anyone could think of a host of other examples. It is a very common pattern.

Here then are my additions to the list:

1. Chirality or “handedness” in nature. For example, d-sugars and I-amino acids are the only enantiomers (spatial isomers) operating in Earth life. It could have been the other choice in each case. Perhaps on some other planet it is. (See “The Mirror World” in Section II.)
2. But in the whole universe, the weak force (one of the four fundamental forces) shows a preference for one chiral form over the other, i.e. “parity is not conserved”.
3. Also in the whole universe, matter predominates over anti-matter – at least we think so. It could have been otherwise. Probably the “decision” occurred in the first few micro-seconds after the Big Bang. I think this is where the term “symmetry-breaking” was first used.
4. Coming to more mundane forms of arbitrary conventions and social games of coordination, we can cite the choice of driving on the right or on the left. In most countries, motor traffic moves on the right, and the few hold-outs (e.g. Britain) will probably eventually convert. Some years ago the switch occurred in Sweden, and it is my favorite example of VERY rapid social change – it had to be instantaneous (in fact separated by half an hour of clearing all roads entirely). (The joke was “cars will drive on the right and trncks on the left”).
5. Of a similar nature is the system of weights and measures, where the metric system is now winning, again with a few hold-outs like the US. Their early conversion to metric seems imminent.
6. Various sign conventions exist in different branches of science, conventions which are purely arbitrary, but had to be made one way or the other. For example, who says that an electron has a NEGATIVE charge? The University of Toronto chemistry department has long used a different sign convention in the equations of thermodynamics than the rest of the world, introducing great confusion in the minds of its graduates when they entered the real world.
7. If we accept the idea (which I don’t) that someone has to be boss in the family, then it might as well be the father rather than the mother, to conform te traditional principles of patriarchy. To reverse this would be confusing. (But here we have the third alternative of equality or partnership.)
8. Why are some countries (those in Northern mid-latitudes and a few in Southern mid- latitudes) rich and industrialized, while other countries (largely those in the tropics) are poor or still “developing”? Is it climate? (The correlation is quite good; but why should this be causal?) Is it race? (It is not fashionable to think so.) Is it the result of rapacious colonialism? (Many radical thinkers believe this.) But perhaps the facts can be explained on the basis of “first-comers’ advantage”, and whoever came first into the industrial revolution is more or less a historical accident. Then, once some get rich, they get richer by positive feedback and the poor get poorer.
9. The same mechanism operates to generate the rich-poor differences within a country. In fact, George Bernard Shaw in one of his essays about socialism described, in a piece of anthropological fiction, how first-comers parcelled out the land and became land-owners; second-comers had to resort to processing primary products in factories; and last-comers only had their labour to sell. Even within that general paradigm, the very earliest first-comers got the best land and later ones the less fertile land. It is like the first-born son inheriting the estate while the second son goes in the army and the third son into the church. The order of arrival is all-important; wealth and poverty simply escalate from there. Thus poverty is no one’s fault, it is the result of a natural process; which does not mean that we should acquiesce to inequality, for we can devise countervailing mechanisms to correct it. But it does mean that we should moderate revolutionary rhetoric which blames the “exploiters” as morally culpable.
10. Discussing the Law of the Sea (LOS) Convention, Jesper Grolin described certain mild regulations as merely a coordination game, in which nations agree to do things one way or the other as long as all do the same; which is easy to do if they really do not care much which alternative is taken. But the more difficult parts of this treaty (or any other treaty) are those that are more like a Prisoner’s Dilemma game, in which countries do have strong preferences, and might slide into a less-than-optimal DD outcome through their unwillingness to yield. In Grolin’s interpretation, the principle of the Common Heritage of Mankind, which implies redistribution of real resources (mineral nodules, fisheries, navigation rights) remained highly controversial throughout LOS negotiations, was drastically shrunk in scope to the high seas only, and eventually wrecked the treaty when the US under Reagan opted out. This is because this principle is in the Prisoner’s Dilemma class of difficult problems. On the other hand, the Antarctic Treaty of an earlier time (1959) merely arranged for the abandonment (temporarily) of overlapping claims where no real resources were involved. And Reagan’s proposed “Mini-Treaty” among industrialized states to replace LOS would simply coordinate regulations in a very minimal fashion. (This never did happen.)
11. Divergent weather systems were the first instance where the “butterfly effect” was observed. The book “Chaos” by James Gleick describes a weather-prediction simulation on a computer being done and running into a snag; whereupon the frustrated experimenter, now in a hurry to predict before the real weather arrives, decided to take a shortcut in repeating the run, by using one less decimal place in his figures. To everyone’s surprise, the simulation soon diverged to a totally different outcome. The slight numerical differences in the data were enough to change the whole course of future weather. Non-linear systems of all kinds are similarly super-sensitive to slight variations in starting conditions, and therefore unstable. This is the basis of the new theories of chaos. There is still determinism, but very difficult to pin down with imperfect knowledge.
12. Two alternatives also exist along the two branches of stability in a cusp catastrophe diagram. (See the essay “Swallowtail and Butterfly” in this Section.). Where the system jumps depends, in this case, on whether we are approaching the bifurcation region from the left or the right side. This phenomenon has been termed “hysteresis”, but it seems to be related to symmetry-breaking.
13. The “chaos equation”, y = ax(l-x), when iterated with certain values of a and x, shows values of y gradually approaching a single equilibrium or “attractor”; i.e. y thereafter no longer changes with repeated iterations. (See the essay “From Chaos to Extinction” in Section I.) However, at somewhat higher values of a (keeping x constant), the values of y oscillate between two values (“attractors”). If we continue increasing a, we get 4 attractors, then 8, with increasing speed, and soon the bifurcations heads into “chaos” (apparent randomness). Here we have a case where no choice was made between two equally good attractors or outcomes. The result was chaos. Perhaps making a choice by symmetry-breaking is essential for creating a Cosmos.