CHAPTER 14: Ideality


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Matter could be moved, but was incapable of moving itself.

The Royal Society was a male preserve, demonstrating a gendered view of matter inherited from Judeo-Christian and Greek traditions. Margaret Cavendish, an early feminist natural philosopher, criticized the views of her male contemporaries, who were “so much afraid of self-motion, as they will rather maintain absurdities and errors, than allow any other self-motion in Nature, but what is in themselves: for they would feign be above Nature, and petty Gods, if they could but make themselves Infinite.” [Margaret Cavendish Observations 114, quoted in Deborah Taylor Bazeley “An Early Challenge to the Precepts and Practices of Modern Science: the Fusion of Fact, Fiction, and Feminism in the Works of Margaret Cavendish, Duchess of Newcastle (1623-1673)” Dissertation, U. of Calif. San Diego, 1990, chp 4.4,


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This may hardly be an issue for many scientists, yet in the opinion of others there remains a grander enterprise of undertanding the world.

Of course, many scientists might define understanding, or intelligence, in terms of useful problem solving, particularly when the problem is understood in general terms that allow the solution to be applied to many variations. The effectiveness of such intelligence suggests a match between it and the world it evolved to model but does not imply that the world itself is simple. Nor does the fact that human intelligence (or its computer surrogates) can employ cognitive strategies that allow it to thrive imply that these are true or complete descriptions of reality. For, they may succeed biologically even when reality is not correspondingly simple. Most instinctive behavior is of this kind. Circumstances can change, and unsuspected influences can come into play, which render present strategies obsolete. “Understanding” can thus involve more than a gratuitous mental satisfaction, but rather a deeper level of adequacy upon which survival could depend.


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Occam’s Razor… a metaphysical assumption with little empirical basis.

Cf. Einstein, c1938, quoted in Holton TO, p259: “The logically simple does not, of course, have to be physically true; but the physically true is logically simple, that is, it has unity at the foundation.” However, “unity” does not imply simplicity; and the requirement for either may reflect human need as much as the reality of nature. Perhaps nothing natural is truly simple, and the proposition that “the physically true is logically simple” is mere wishful thinking.


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Yet the more…widely shared…the more likely they are to escape critical notice.

It may be argued that this is the necessary ground upon which science is built. Nevertheless, that ground has been shaken a number of times, the house rebuilt on new foundations. This is no disaster but a sign of progress. However, especially with the mounting costs involved in “fundamental” research, one can imagine scenarios in which science finds itself on a false limb from which it cannot retrace its path.


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reality lies in the (ephemeral) details more than in generalities or definitions.

“Because [according to Plato] mathematics reflected truth more perfectly than physics, Platonic science exploited it in the analysis of nature, with the ultimate goal of reducing physical reality to numbers and geometrical shapes. Aristotle rejected Plato’s mathematicism, believing that mathematics and physics study separate kinds of objects. For Aristotle, the quantities and shapes of mathematics were abstractions from physical entities. They captured certain qualities of material things but left unexplained their true natures, which could not be reduced to mathematics… For Aristotle the world had within it principles and powers of development. Natural things changed as a result of their inherent tendency to embody more perfectly the rational form or essence that defined them.” [Deason, in Lindberg and Numbers God and Nature, p167-8]

Plato identified his ideal “forms” with classes of things, as opposed to individual examples. A class has both an intension (the set of defining characteristics) and an extension (the set of those things that satisfy the definition). The class of dogs, for instance, is construed by noting features that dogs have in common. The notion of ‘dog’ is first an inductive generalization, the essence of something as gleaned from experience with specific individuals. It is then defined to consist in certain characteristics. Unlike the real exemplars, the ideal dog is a matter of definition. While real dogs are found, the class or category is made, albeit based on actual experience. It then becomes an archetype, corresponding only approximately to actual experience while precisely to the ideal. Common sense recognizes that the individual physical dog is the real thing, the ideal dog a fiction. Plato reversed common sense, however, by asserting the reality of the ideal, and the unreality of its material exemplars. The mental thing (the ideal) has a prior, objective, and higher existence, independent of the physical things that instantiate it. Aristotle disagreed, in effect holding that the reality of nature lies more in the extension than in the intension.


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…for example, deterministic chaos and complex self-similarity.

The fractal is a class of mathematical functions made (graphically) accessible by computer. Yet this idealization was soon further generalized to include the multifractal—with non-constant “fractal dimension”—making it possible to model yet deeper orders of natural complexity. Nevertheless, the basic intent remains to reduce complexity to an idealization. Multifractal functions are still algorithms, products of definition.


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Analysis involves the chunking of detail, a level of coarse graining.

Any modeling process implies idealization and streamlining, through which complexity is reduced. This can involve choice of scale or resolution of detail (coarse graining), isolation from context, or focus on particular behaviors. [Cf. ‘Artificiality’, from Encyclopedia of Science, Technology, and Ethics Macmillan Reference]. The very concept of system implies a division of natural reality into artificial compartments (such as experimental apparatus, environment, etc.) Even the divide between macroscopic and microscopic is somewhat artificial.


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…and both produce their favored ontologies.

While reification expresses the basic impulse of natural realism, it also serves to re-constitute natural phenomena as products of definition. When idealized, space and time, for example, are also viewed as objectively existing apart from their material constituents or markers. In classical physics, the notion of field was initially defined in terms associated with properties of matter (e.g., a temperature field), then later objectified as an independent entity. Cf. Elena Castellani “Gallilean Particles: An Example of Constitution of Objects” in Castellani Interpreting Bodies, p181-2: “Physics, classical or not, does not speak immediately of the objects that populate our external world. Classical mechanics, for example, is formulated in terms of mass points, which are obviously of quite another nature than everyday things. Mass points can be seen as ‘ideal objects’, taken to represent some main features of ordinary objects. How the properties symbolized through such ideal entities can actually be related to some ‘real’ macroscopic object has to be clarified… Arguments of this kind may lead to the following position: all the objects of physics, classical as well as non-classical, must be ‘constituted’.”


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Materialism and idealism foster divergent cosmologies and causal histories.

The materialist view is evolutionary: complex and sentient forms evolve from simple and insentient ones; matter pre-exists and gives rise to mental phenomena; “ideas” are iconic maps of complex realities and relationships. In contrast, the idealist view is involutionary: mind or spirit or idea preexists and gives rise to (or at least endures) the degenerate or illusory world of matter and appearances. A non-physical realm is hypostatized as more real than literal matter.


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The idealist goal of knowledge…whether the forms of Plato or the eternal transcendent mathematical laws of nature.

The inner world of imagination can generate elements not presented by the outer world; this is why there is room for philosophy, as a discipline outside the bounds of science. On the other hand, physical reality typically contains elements not anticipated by imagination nor accounted for in thought. This is why the discoveries of physical science are of a different kind than those of logic, mathematics, or philosophy. While thought may be an abstract version of reality, one can hardly claim that reality is merely imagination or abstraction fleshed out with substance and qualities. Such might appear to be the case with material artifacts, which are realizations of a design or concept. Yet, even physical artifacts, made of real substances, have incidental properties independent of their defining concept. As Aristotle would say, they have material as well as formal cause.


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…the search for constancy beyond change and apart from perceiving subjects.

Any idealization is a qualitatively different thing than the untidy and changing reality from which it is drawn, just as a map is a different sort of thing from the territory it represents. Maps are above all symbolic and selective. Though based on reality, they are streamlined utilitarian products of definition. Thus, a road map may be proportional, while showing only the locations of different classes of roads and settlements and omitting topographic or other features. It is made to facilitate driving more than hiking, for example. It may be relatively up-to-date, but is not timeless, having been established at a particular date.

A two-dimensional map distorts the three-dimensional shape of the earth. The earliest maps of the world were distorted in other ways, too. They were based on incomplete information, of course; but also they incorporated religious symbolism that we would consider irrelevant to our purposes. They extrapolated features of the known world into unknown areas, even inventing imaginary continents. Of course, a map is also a thing in its own right, perhaps a work of art, a free-standing object apart from its representational function.


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… mathematics has a reality independent both of nature and of human minds.

For example, by showing how Cantor derived the set of natural numbers purely from the notion of ‘set’, Roger Penrose argues that mathematics is logically and psychologically independent of the real world. [The Road to Reality Knopf 2004, p64] But this begs the question, for the concept of set—while more abstract—hinges as much on experience of objects as does the concept of integer.


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Some have argued that…mathematics is the plausible basis for communicating scientifically with an alien civilization.

Max Tegmark, for example, argues that, since mathematics is free from cultural baggage, the universe itself must be mathematical. [“The Mathematical Universe” 2007] Penrose suggests that alien beings, even in an amorphous environment lacking definable “objects” (including their own physical selves), might nevertheless come upon an idea of integers. They could do so by carefully disregarding assumptions that seemed to them axiomatic in their situation. While this is how alternative geometries and algebras have been discovered by human mathematicians, it strikes me as one more reason for not assuming a fixed platonic mathematical world!


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It was a great creative leap of imagination…which we have come to accept as the reality of the solar system.

The deductive, Platonic, and Pythagorean traditions of the ancients impressed upon Christian thinkers the ideal of “perfection” of the celestial realm, with the loaded assumption that perfection corresponds to a simple product of definition. Thus Kepler tried to assimilate the planetary orbits to the five regular solids, and Galileo insisted on exactly circular orbits. Kepler had sought for years to account for the sizes and distances of the planets from the sun in terms of a simple geometrical scheme. This “harmony of the spheres” had the circular orbits of the planets inscribed on concentric spheres, each (apart from the earth) contained in one of the five regular polyhedra. Of course, it turned out that there are more than six planets. But such speculations were typical of Renaissance mysticism. Only in spite of this theoretical scheme did Kepler stumble upon his empirical laws, which have planets moving in “imperfect” elliptical rather than circular orbits.


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…Nancy Cartwright generically calls such artifacts nomological machines.

Cartwright describes nomological machines as “models in which we have a fixed arrangement of parts each with a known capacity operating together in a way that generates regular behaviour, so long as nothing interferes…” She cites the solar system as an example.

As a conceptual system, a machine can be defined apart from any environing context. It corresponds to a closed, isolated, reversible system. However, a real machine, such as an automobile, is a closed system only on the drafting board. In reality, it is open to an environment against which its non-reversible history can be charted. An engine might be made to reverse direction mechanically, but not thermodynamically. It suffers wear and tear in real operation, which marks its life with a direction in time.


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This is where Aristotle’s caveat still holds value in our day.

Cf. Heideggar: “Because physics, already as pure theory, requests nature to manifest itself in terms of predictable forces, it sets up the experiments precisely for the sole purpose of asking whether and how nature follows the scheme preconceived by science.” [M. Heideggar The Question Concerning Technology Harper & Row 1977, p20] Ilya Prigogine makes a similar point: “The phenomenon studied must be prepared and isolated until it approximates some ideal situation that may be physically unattainable but that conforms to the conceptual scheme adopted.” [Prigogine and Stengers Order Out of Chaos, p41 (italics theirs)]


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Laws of nature involve an act of faith, originally informed by religious and deductive traditions…

Paul Davies “On the Multiverse” conference on time, 2011: “The concept of an externally imposed set of infinitely precise transcendent immutable time-symmetric mathematical relationships (‘laws of physics’), together with their attendant mathematical entities such as real numbers, is an idealization with no justification in science, and represents an act of faith that is a hangover from European medieval theology and Platonic philosophy… The asymmetry between the laws and the states of the world is a direct reflection of the asymmetry between creature and creator.”


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A system is physically closed when there is no material exchange with an environment.

It may also be isolated, with no exchange of energy or information either, which renders it epistemically closed (e.g., black holes). In order to be considered real, by the canons of physics and common sense, a system must be observable; and if observable, then not completely isolated. The concept of isolated system is an idealization permitted on the macroscopic scale insofar as observation is a matter of a negligible interaction with impinging quanta—a situation obviously different on the micro scale.


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…a background…against which processes can appear irreversible and asymmetric.

Symmetry, like reversibility, is a property of deductive systems; the real world cannot be fundamentally symmetrical because no part of it truly stands on its own. Symmetry is a result of idealization and isolation. Cf. Smolin Time Reborn, p 117-18: “Symmetries arise from the act of treating a subsystem of the universe as if it were the only thing that existed… It doesn’t matter [if we rotate the system under study] because we ignore the interactions between that subsystem and the rest of the universe… If these symmetries are approximate, then so are the laws of conservation of energy, momentum, and angular momentum.”


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Irreversibility is fundamental even at the quantum level, as demonstrated by the “collapse of the wave function.”

Reversibility is often associated with wave motion. As a natural phenomenon, wave motion is generally not reversible, however. A water wave, for example, emanates from a point outward and does not normally re-converge on that same point. A light wave does converge on a (different) point of absorption, which suggests the behavior of particles rather than waves. This discrepancy is the basis of the measurement problem.

While the Schrödinger wave equation is time-reversible as a mathematical construct, as soon as a measurement is made, it “collapses” irreversibly to a particular value. This can be thought of as decoherence, introduced by the measurement process, which couples a nominally isolated system with an environment. However, according to Ellis, irreversibility is not tied specifically to decoherence as an explanation, but follows from other quantum approaches as well. Moreover, reversibility is approximated in exceptional circumstances, which are just the situations upon which science has classically focused. [George F. R. Ellis “On the flow of Time” 2008]


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Reversibility thus depends on a generally unrealizable definition of precise instants.

Cf. George F.R. Ellis “Physics in the Real Universe: time and space”: “The time reversible picture of fundamental physics… does not take cognizance either of the progress of time in quantum measurements, or of how complex phenomena arise from the underlying micro-physics, with the emergence of the macroscopic arrow of time as a major feature of chemistry, biology, and human life. It does not take seriously the physics and biology of the real world but rather represents an idealised view of things which is reasonably accurate in certain very restricted situations (for example laboratory experiments where all external influences except that of the experimenter are excluded).”


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It only appears so when measured against artificial, a-historical reference frames.

For similar reasons, symmetry breaking seems spontaneous when the “space” in which it occurs provides no information that could account for a preferred direction or choice. Like Buridan’s Ass, the classic example of a pencil perfectly balanced on its point is an idealized artificial situation.


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…but the universe itself is not static, nor a mere product of definition.

While playing a film of perfect frictionless billiard balls backwards cannot be distinguished from playing it forwards, the world is not a film or digital recording running in a projector. The film (or the data set of the digital recording) is a closed system with no environment. Its reversibility presumes a “gods-eye” view from the camera, with constant illumination, and no reference to events happening off the billiards table or off the screen. In contrast, the very arrival of photons from a changing light source off the table would provide a basis for distinguishing the direction of the film. Reversibility is thus a matter of arbitrarily limited context, and a property of the film as an artifact.

Similarly the “baker’s transformation” as a mathematical operation is reversible; but as a physical process, it will involve minute deviations from the mathematical ideal, so that actual irreversible mixing occurs. As with the billiard table, to reverse a film of this process treats actual interactions as though perfectly defined at each frame. The change of frame is a logical operation, and hence reversible.


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How a theoretically reversible system becomes irreversible has been considered a serious problem in thermodynamics.

The irreversibility of thermodynamics seems to contradict the reversibility of classical dynamics, so that the theoretical problem arose, in the 19th century, of how to derive irreversibility from dynamics. Cf. H. C. v. Baeyer Warmth Disperses and time Passes Modern Library 1999, p136-7: “How does the obvious irreversibility of the world emerge from its reversible building blocks?… This question has dogged physicists ever since Ludwig Boltzmann discovered the meaning of entropy in the atomic constitution of matter. Actually Boltzmann himself suggested an answer, and most scientists believe it, but a rigorous mathematical proof of the second law, starting with a reversible description of individual atomic process, has not yet been achieved… Whether such a proof will ever be found… is not known.”


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…sub-volume of the container…from which to release the gas into a larger space.

The equivalent constraint on the billiards table (or perhaps snooker or pool table) is the initial “racked” configuration, from which the scattering balls spread out over the table. It is amusing to speculate how the notion of “billiard ball physics” might have developed differently if the model had involved nine or twenty-two balls rather than three! The three-body problem is difficult enough; the mechanics of many more might have led more quickly to the recognition of “deterministic chaos.”

Compare the irreversible mixing of paints with the reversible mixing of immiscible liquids, such as oil and water. The difference is due to microscopic (i.e. chemical) differences in the substances, making reversibility contingent upon microscopic order.


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…but in how we conceive the initial entropy state of the universe.

As Roger Penrose [Cycles of Time Vintage, 2010, p76-9] has aptly put it, the mystery does not lie in the fact that “Humpty Dumpty” couldn’t be put together again, but that he found himself on a high wall in the first place. Life (and Humpty) are possible on earth because the sun supplies a low-entropy form of energy; and this is ultimately possible because of the low-entropy state of the universe at the Big Bang, before “gravitational degrees of freedom” were activated.

Moreover, to say that entropy in the Universe must always increase misstates the 2nd Law, which pertains only to thermally isolated systems. Cf. Lee Smolin The Unique Universe June 2, 2009: “If our scientific methodology only makes sense when applied to subsystems of a vaster universe, then it is tempting to react to the problems that arise when we try to extend it uncritically to that whole universe by positing that our universe is in fact a subsystem of an even vaster multiverse. We get to do physics as we have been trained to, but this is a trap because to do this we must employ structures that have no operational significance. Better, in our view, to regard the Newtonian schema as inapplicable to cosmology, and to look for another notion of law that can make sense when applied to our entire, but single, universe.”


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Such an ideal …may be perfectly determinate and reversible by definition.

However, even if it were closed, a physical system might be irreversible because it departs in some other way from an ideal definition. P. W. Bridgman [The Nature of Thermodynamics Harper Torchbook, 1961, p150] gives the example of a source of radiation enclosed in a perfectly reflecting sphere, to illustrate how emission is reversible: the source reabsorbs the reflected radiation. Unlike such a thought experiment, however, nature does not seem to benefit from such a perfectly symmetrical mirror. In the real world, an emitted particle (or wave) does not return to its source. He also makes the point that the issue is not literal reversal of a process, but return to an initial state, regardless of the details of the path. It is better, therefore, to speak of recoverability than reversibility in thermodynamics. Jos Uffink [“Bluff your way in the Second Law of Thermodynamics”, 5th July 2001, p90-91] makes the same point: “The second meaning of ‘reversible’ is the notion of a process whose initial state can be completely restored by some other process… Discussions on irreversibility and the second law in the philosophy of physics seem to have largely overlooked this distinction.” Bridgman [ibid p123] makes the further point that a simple (reversible) device can be made irreversible by adding a ratchet of some sort. However, this renders the mathematics enormously more complicated—an example of mathematics dictating the kind of systems studied.


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no shielding from quantum tunneling or gravitational influence.

Thermodynamic entropy measures the proportion of energy unavailable to do work in a system. This, however, is relative to how the system is defined and partitioned. If nature has more levels than presently recognized, there could be far more energy bound in a “system” than is presently recognized.

Entropy is not an entirely coherent concept, in part because of its historical development in terms of energy available for human purposes, at a particular stage of technological development (steam engines). The definitions of the simple systems involved do not lend themselves to consideration of complex systems, or in terms of cosmic systems in which additional forces such as gravity or dark energy come into play at various epochs.


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…leads to a characteristically different statistical accounting for quantum entities.

The usual interpretation of the Bose statistics is that the particles are indistinguishable and so must be tallied differently. But such a statistics could also result if the particles were distinguishable but connected by some force that tends to put them all in the same state. Hence, the contrasting Fermi statistics may assume distinguishable particles, which then appear to have a repelling force acting between them, such that no two can occupy the same state within an atom. [Reichenbach in Castellani Interpreting Bodies, p71]


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…an object must be compared…at least to some record…or to another of its kind.

According to the Stanford Encyclopedia of Philosophy [“Identity and Individuality in Quantum Theory”]: “A more thoroughgoing criticism of this property-based approach to individuality insists that it conflates epistemological issues concerning how we distinguish objects, with issues concerning the metaphysical basis of individuality. Thus, it is argued, to talk of distinguishability requires at least two objects, but we can imagine a universe in which there exists only one.” However, “imagination” is based on actual experience, as is logic. What is metaphysically distinct is what can be so conceived. Though we may be convinced of the logical propriety behind what is conceivable, this sense of conviction is based on generalized experience of the actual world. In the quantum realm, however, there are physical limits to what can be cognized as distinct, deriving from the finite speed of light and finite quantum of action. Moreover, to imagine a universe consisting of a single thing is already a contradiction, since it ignores the presence of the imaginer!


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(It would seem that God made particles identical, and this has become the industry standard!)”

Within limits, the parts of a mass-produced machine must be functionally identical, from one exemplar to the next, since they must be interchangeable. Yet, however perfect a ball bearing, ways can be devised to distinguish one from another—for example by marking them with paint or a scratch, or by a careful photographic record of their movements in relation to other things. In spite of such minor variations required to establish individual identity, ball bearings remain sufficiently interchangeable for their purpose, because they conform closely enough to a definition and minor variations don’t affect their performance. One may wonder, by comparison, what can it mean to interchange two natural things of a kind, such as protons or even leaves of a tree. Leaves may be functionally identical, yet it is no simple matter to replace one with another. This is because the tree, not the human observer, must recognize and accept one leaf grafted in the place of another. Similarly, organs from two bodies may be functionally identical, yet not necessarily interchangeable. For, leaves and organs, even as functioning parts, are more than products of human definition and intent.


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Hence, even the idea of an atom…or in the unification of forces at high energy.

Symmetry breaking is a name given to the processes through which the primal theoretical unification of forces (at the Beginning) gives way to the world we know, effectively as phase changes due to cooling. More abstractly, it is a name for the process whereby a member of a kind acquires individual identity. [See: Hans Reichenbach “Genidentity in Quantum Particles” in Castellani Interpreting Bodies, p63] To mark a billiard ball, for example would break its symmetry. But there is also “spontaneous” symmetry breaking, which results from an unstable equilibrium (e.g., a pencil balanced on point). Some net force or direction wins out in a momentary stalemate of forces, thereby going from a more symmetrical (but unstable) to a less symmetrical (but more stable) situation. Given only the endpoint, the particular path to stable equilibrium cannot be predicted any more than the particular path away from unstable equilibrium when given only the initial point.

Breaking symmetry can be related to the principle of sufficient reason—insofar as it has to do with choices instead of causes or forces such as gravity. In the case of Buridan’s Ass, for example, it is the hunger of the donkey that propels it toward one resolution or another of the impasse. There is a process of positive feedback involved in cases like the unstable equilibrium of the balanced pencil; the further the pencil has departed from vertical, the stronger the net force acting on it. Processes of negative feedback, in contrast, create stable equilibrium (e.g., a ball at rest in a bowl or basin). In the case of Buridan’s Ass, imagine that the donkey has already satiated itself and now finds the smell of hay revolting. It will maintain the maximum distance from both bales of hay, which means equidistant. What appears as indifference (lack of sufficient reason) is actually an active choice.