The World As Ever Breaking Symmetries : 13.7: Cosmos And Culture We have so wanted a deductive theory from which all that specifically arises in the universe follows as a set of theorems.  In this post, I want to give a (contrived) hypothetical example that it need not be so.
NPR logo The World As Ever Breaking Symmetries

The World As Ever Breaking Symmetries

We have so wanted a deductive theory from which all that specifically arises in the universe follows as a set of theorems.  In this short blog post, building on the past two blog posts (post 1 / post 2), I want to give a (contrived) hypothetical example that it need not be — and virtually certainly is not — so.

No "Theory of Everything" will explain it all.

Picture a human construction to make my point:  A quite massive square cross sectional  "tier 1" beam running due north-south, between two massive compression plates at the north and south ends of the beam. Halfway along this beam, tier 1, imagine two slightly smaller cross section, "tier 2" beams at right angles, one running east from beam 1 and attached to beam 1 by the West end of the tier 2 beam. The second of these "second tier beams,"  is attached to beam 1, midway along beam 1's length, and points west, attached to beam 1 by the east end of this tier two beam. Both of these tier two beams end butted against massive steel plates at their "free ends."

Now consider four, slightly smaller, cross section "third tier" beams, each attached to the  mid point of either of the two second tier beams, and pointing either north or south from each of the second tier beams. Again, all four third tier beams abut at their "free end" a massive steel plate.

Continue with successive fourth, fifth ... tier beams, 8, 16, 32 ... in number, all attached at the midpoints of the beams a tier earlier, and all successively smaller in cross section and all ending abutting massive steel plates.

For fun, let there be 10 such tiers of beams in a very large room, the last tier with 2 to the 10th power — or 1028 — rather small cross section beams abutting, again, massive steel plates.

Confine all these beams between a lower and an upper very strong horizontal surface that must be slightly stepped to fit the decreasing cross section of the beams.

Well, its a bit of an odd construction, but watch:

Let's compress the first beam, running North South, abutting two massive steel plates which are, in this ONE case, also powerful compression devices.  All the rest of the plates are merely rigid massive steel plates.

So, let's do the experiment: We compress beam 1.  It will buckle, making a bow shape.  Thanks to the horizontal surfaces confining the beam from above and below, the beam will buckle EITHER TO THE EAST OR THE WEST, NOT BOTH.  This is a clear symmetry breaking and there IS NO LAW FOR WHICH WAY THE BEAM WILL BUCKLE.

But suppose it buckles to the east. This puts a compression load on only one of the tier two beams, the one running East from the tier 1 first beam, and ending in a massive steel rigid plate. So only one of the tier two beams, the now compressed east running beam, will buckle to the north or south. It will buckle only in one direction, say north. Again, there is NO LAW for this symmetry breaking.

In a cascade of successive lawless symmetry breaking "choices" a succession of 10 of the total 2048 beams will buckle, each in a specific, fully random, lawless, direction.

We see a simple example of a lawless cascade of broken symmetries, afforded by one compression force and a very non-random arrangement of beams of successively smaller cross section.

Is there a law that ENTAILS the SPECIFIC SET of which 10 beams among the total 2048 beams will buckle and their direction of buckling?


More, is this cascade of bucklings a history dependent process? Yes. There is no law for which way each beam in turn buckles when it breaks symmetry.  The entire lawless cascade is both lawless and history dependent. Once beam 1 buckles to the east, the tier 2 beam running to the west from beam 1's midpoint, will never buckle, nor will its beam descendants to tier 10.   Each lawless symmetry breaking sets the stage for what CAN HAPPEN NEXT.

A new structure among the beams comes to exist in the universe, whose detailed becoming is lawless, history dependent and contingent.

Note that, in a easily understood sense, when beam 1 buckles and breaks its symmetry, that symmetry breaking generates a NEW FORCE, the new compression force on the two tier two beams attached to its midpoint and each ending abutted to a massive steel plate. Of course, in a deeper sense, the “new force” is a propagation of the initial compression force on beam 1.

But in the more general case, for example of the geological history of the earth, with core, mantle with convective cells carrying continental plates that crush into one another heaving up mountains on which rain falls to carve river drainage basins, the "form" of the ever new forces, each begotten by a prior force and often a symmetry breaking, is more subtle than the case of the beams above.  And where these involve symmetry breakings, there is no law for the historically contingent becoming of planet Earth.

Of course, the example above is very simple and WE constructed the beam lattice structure that behaves,as idealized, as described. The deep questions include:

  1. In the becoming of the universe, what roles do such successive symmetry breakings play with no "designer’s hand?"
  2. Where, if anywhere, are there cascades of such symmetry breaking? Two blogs ago I discussed such successive symmetry breakings in a vast chemical reaction graph hypopopulated by matter. The emergence of new chemical species is a symmetry breaking which create the conditions for yet more new chemical species, often more than one, is a form of such "generalized" symmetry breaking that branches into the chemical Adjacent Possible, perhaps in outer space chemistry, perhaps in the biosphere. The same is true for the evolving biosphere, where new species create niches for yet more new species, often more than one, again branching into the Adjacent Possible of the evolution of the biosphere. The same is true for our evolving technological economy where each new invention creates economic niches, often for more than one new complement or substitute, so the economy has exploded in the branching diversity of new goods  in the past 50,000 years.  These new goods, like new complex molecules on the vast reaction graph, are symmetries being broken in the becoming of the universe too, but far more subtle than the lattice of beams above.
  3. How do the broken symmetries, beams above, complex chemical reactions wandering on a vast reaction graph, biological evolution, economic evolution, create the NEXUS of enabling constraints — eg biological niches and economic niches — that allow the next novelties to arise? These enabling constraints are the embodied information arising due to broken symmetries that I think is our most useful definition of what "Information IS." No, not Shannon, nor Kolmogorov, with no semantics and no becoming of the information since the Big Bang.
  4. What of the complex geological cascades that form all the diverse minerals on the earth, each in specific locations and sometimes in specific adjacent chemical/mineral conditions.   Are these cascades of broken symmetries and not deducible in detail beforehand?
  5. Are these cascades of broken symmetries present in stellar and galactic evolution?  In space dust cloud evolution?

Understanding the emerging complexity of the universe may well involve the partially lawless cascading broken symmetries in the above odd room, writ large, as well as  what seems a rather unexamined role of "natural law."  Without, roughly, Newton's laws, the behavior of the beams in the room in their cascade of partially lawless broken symmetries could not occur.  In a way that it seems we have not thought much about, the laws themselves seem to serve also as "enabling conditions" that enable the sequences of broken symmetries in the room, mineral formation in situ, and the evolution of the biosphere.

Perhaps what we look for is not a deductive theory of everything that happens in detail. Perhaps we seek some broader framework of laws, boundary conditions that come to exist via broken symmetries — lawless in detail — that create those boundary conditions. Then those newly formed boundary conditions can constitute "embodied information" enabling a specific process to occur via constrained release of energy — constrained by the very boundary conditions.  And simultaneously the broken symmetry and new boundary conditions can create the new source of the the energy to do the constrained release of energy that therefore constitutes the work — not heat — to carry out the enabled process. And more, cascades of such lawless-in-detail broken symmetries in which what occurs in the universe opens up ever new possibilities in an ever expanding Adjacent Possible, that can come to be actualized.

The lattice beams, and partially lawless broken symmetries as some 10 of them bow, are a very simple example of all this.

If so, this vision is not what we have expected since Newton and Einstein.  But Darwin might nod "Yes."