[FRIAM] George on "Symmetry breaking"

[Nicholas Thompson]

 *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
nthompson at clarku.edu
https://wordpress.clarku.edu/nthompson
-------------- next part --------------
An HTML attachment was scrubbed...
URL: <http://redfish.com/pipermail/friam_redfish.com/attachments/20250723/9ddaad16/attachment.html>