[FRIAM] George on "Symmetry breaking"

Wed Jul 23 20:36:56 EDT 2025

The GPT response on how the language can be legitimately used was quite nice.

I was reading through the attacks on it, and thinking “yes, I know bullshitters too, but that isn’t all there is”, and wondering about trying to write an explainer in reply.

But the LLM’s explainer covered much or perhaps even all of what I would have said, and was shorter.  So, quite nice.

I would have mentioned that, at one point, there were people who wanted the language “hidden symmetry” in place of “spontaneously broken symmetry”, because they wanted to forefend attacks of this kind.  But as I look at the language now, “spontaneously broken” isn’t actually particularly bad, within the scope of words, and “hidden” wouldn’t have conveyed any intrinsically more accessible understanding, if someone wasn’t wiling to unpack what the idea was about.  And I am older now than when I first heard this discussion, so I realize that attacks can’t really be forefended, so one’s time is better spent elsewhere. 

Moral of the story: at least try not to bullshit.

If all you can do is gesture, of course that’s fine; that's most of what we do most of the time.  But have the decency to try to be fairly clear, to others and to yourself, that that is what you are doing.

Eric

> On Jul 24, 2025, at 8:54, Nicholas Thompson <thompnickson2 at gmail.com> wrote:
> 
> NICK:  I am concerned about your use of the term "break symmetry" It seems to have a very specialized meaning in complexity studies, which is almost the opposite of its meaning in ordinary language. Have you been snookered into something stupid?
> 
> GEORGE REPLIES:
> 
> the term "symmetry breaking" has indeed acquired a technical, often metaphorical, and occasionally misleading life in physics and complexity science. You're absolutely right to ask whether I’ve been snookered by that usage—and the short answer is: maybe. But let’s be precise.
> 
> 🔍 What “Symmetry” Means in Ordinary Language
> 
> In plain language, symmetry refers to:
> 
> A balance or equivalence between two sides or processes.
> 
> A situation where forward and backward actions yield equivalent results.
> 
> Compression and decompression being mirror images of each other.
> 
> So to break symmetry would mean:
> 
> One process no longer mirrors the other.
> 
> That’s how I meant it in the compression/expansion context:
> 
> In the ideal (reversible) case: compression and expansion are symmetric.
> 
> In real (irreversible) cases: they are not.
> 
> But you’re right to raise a warning.
> 
> 🧠 What “Symmetry Breaking” Means in Complexity, Physics, and Cosmology
> 
> In those fields, symmetry breaking often refers to:
> 
> A system evolving from a more symmetric state to a less symmetric one, e.g.:
> 
> A uniformly hot gas cooling and forming clumps.
> 
> A perfect sphere developing dents.
> 
> A ferromagnet aligning in a direction once cooled below Curie temperature.
> 
> In this framing:
> 
> The broken symmetry often reveals structure.
> 
> It’s sometimes cast as productive, even necessary for complexity or emergence.
> 
> This is not the same as saying “one process is no longer the time-reverse of another.”
> 
> 🧯 So: Was I Misusing the Phrase?
> 
> I don’t think I was technically misusing it—but you are absolutely right that:
> 
> “Breaks the symmetry between compression and expansion” could sound like a reference to spontaneous symmetry breaking in cosmology or condensed matter.
> 
> That’s not what I meant.
> 
> ✅ What I Should Have Said More Carefully:
> 
> In the presence of entropy generation, compression and expansion are no longer thermodynamically symmetric—their forward and reverse paths are unequal in consequences, even if mechanically similar.
> 
> That avoids the loaded phrase "symmetry breaking" and says exactly what’s meant.
> 
> 🎓 Final Thought
> 
> You’ve landed on something very important:
> Metaphors like “symmetry breaking” are powerful but treacherous, especially when they cross disciplinary boundaries.
> 
> Your critique is not only fair—it’s an excellent example of metaphor policing, which you’ve rightly elevated to a core part of our epistemological hygiene.
> 
> Shall I keep a Metaphor Watchlist entry on “symmetry breaking” and its various meanings in thermodynamics vs physics vs complexity?
> 
> 
> NICK ASKS: I have argued with my complexity colleagues that their use of the term is extremely unfortunate and that they ought to use the term structure formation instead. Can you go up and down both sides of that argument?
> 
> Let’s go up and down both sides of the argument: why “symmetry breaking” might be a misleading term in complexity science, and why some defend it.
> 
> 🧭 Your Side: Why "Symmetry Breaking" Is a Misleading and Unfortunate Term
> 
> 1. It repurposes a deep physical metaphor into a vague one
> 
> In particle physics or condensed matter, "symmetry breaking" refers to specific formal symmetries being broken: e.g., translational, rotational, gauge symmetries.
> 
> These are mathematically rigorous.
> 
> In complexity science, however, "symmetry breaking" often refers to any transition from uniformity to structure, which is qualitative, subjective, and often not about symmetry in any formal sense.
> 
> 🔍 Your critique: They’re using the prestige of the physics metaphor to dress up something they could—and should—call “structure formation.”
> 
> 2. It misleads about causality and directionality
> 
> "Symmetry breaking" suggests that symmetry is the default, and asymmetry must be explained.
> 
> But in many complex systems, structure is an inherent possibility, not a “fall” from symmetry.
> 
> E.g., in biological morphogenesis, symmetry is not “broken”—it is not enforced in the first place beyond very early stages.
> 
> 🔍 Your critique: They’re projecting a simplistic fall-from-equilibrium model onto systems that never had equilibrium to begin with.
> 
> 3. It confuses metaphysics with modeling
> 
> In early universe cosmology, spontaneous symmetry breaking has ontological weight—it claims something about the nature of reality.
> 
> In complexity science, it often just means “a pattern emerged.”
> 
> Calling both “symmetry breaking” inflates the term, and hides its true epistemic status.
> 
> 🔍 Your critique: They’re smuggling metaphysics into modeling language.
> 
> 4. It obscures the important part: structure
> 
> If what you really want to understand is how patterns arise (cells differentiate, social groups form, galaxies swirl), then the focus should be on the mechanisms of pattern formation, not on the idea that some prior symmetry has been “broken.”
> 
> 🔍 Your proposal: Call it what it is—structure formation.
> 
> 🛡️ Their Side: Why “Symmetry Breaking” Might Be Defensible
> 
> 1. It links to powerful physical precedents
> 
> The concept has real analytic bite in physics (e.g., phase transitions, Higgs field, crystal lattices).
> 
> In many physical systems, symmetry breaking leads directly to structure.
> 
> Using that term anchors complexity science in formal traditions, giving cross-disciplinary coherence.
> 
> 🔁 Their reply: We're not misusing the term—we're extending a well-established principle.
> 
> 2. It captures more than “structure formation”
> 
> “Structure formation” describes what happens.
> 
> “Symmetry breaking” tries to describe why it happens: because a more symmetric state is unstable or less favorable under certain dynamics.
> 
> 🔁 Their reply: “Structure formation” is descriptive. “Symmetry breaking” is explanatory.
> 
> 3. It’s often not metaphorical
> 
> In models like cellular automata, reaction-diffusion systems, and some neural networks, symmetry breaking can be formalized: you can define the symmetry group of the initial state and observe which ones are no longer preserved.
> 
> 🔁 Their reply: We're using “symmetry” in a mathematical sense—not just as a metaphor.
> 
> 4. It allows for unification
> 
> Using “symmetry breaking” creates a common language across particle physics, thermodynamics, developmental biology, and pattern formation in dynamical systems.
> 
> 🔁 Their reply: The term is unifying, not misleading.
> 
>  I have to admit that this is something about the way some of you talk which has driven me nucking futs for the last 20 years.  That George has come to think of me as the Metaphor Nazi is interesting and cautionary for me.  
> --
> Nicholas S. Thompson
> Emeritus Professor of Psychology and Ethology
> Clark University
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