Monday, June 05, 2023

Try Fitting Assembly/Constructor Theory Over Twistor Space

quantamagazine  |  Assembly theory started when Cronin asked why, given the astronomical number of ways to combine different atoms, nature makes some molecules and not others. It’s one thing to say that an object is possible according to the laws of physics; it’s another to say there’s an actual pathway for making it from its component parts. “Assembly theory was developed to capture my intuition that complex molecules can’t just emerge into existence because the combinatorial space is too vast,” Cronin said.

“We live in a recursively structured universe,” Walker said. “Most structure has to be built on memory of the past. The information is built up over time.”

Assembly theory makes the seemingly uncontroversial assumption that complex objects arise from combining many simpler objects. The theory says it’s possible to objectively measure an object’s complexity by considering how it got made. That’s done by calculating the minimum number of steps needed to make the object from its ingredients, which is quantified as the assembly index (AI).

In addition, for a complex object to be scientifically interesting, there has to be a lot of it. Very complex things can arise from random assembly processes — for example, you can make proteinlike molecules by linking any old amino acids into chains. In general, though, these random molecules won’t do anything of interest, such as behaving like an enzyme. And the chances of getting two identical molecules in this way are vanishingly small.

Functional enzymes, however, are made reliably again and again in biology, because they are assembled not at random but from genetic instructions that are inherited across generations. So while finding a single, highly complex molecule doesn’t tell you anything about how it was made, finding many identical complex molecules is improbable unless some orchestrated process — perhaps life — is at work.

Assembly theory predicts that objects like us can’t arise in isolation — that some complex objects can only occur in conjunction with others. This makes intuitive sense; the universe could never produce just a single human. To make any humans at all, it had to make a whole bunch of us.

In accounting for specific, actual entities like humans in general (and you and me in particular), traditional physics is only of so much use. It provides the laws of nature, and assumes that specific outcomes are the result of specific initial conditions. In this view, we must have been somehow encoded in the first moments of the universe. But it surely requires extremely fine-tuned initial conditions to make Homo sapiens (let alone you) inevitable.

Assembly theory, its advocates say, escapes from that kind of overdetermined picture. Here, the initial conditions don’t matter much. Rather, the information needed to make specific objects like us wasn’t there at the outset but accumulates in the unfolding process of cosmic evolution — it frees us from having to place all that responsibility on an impossibly fine-tuned Big Bang. The information “is in the path,” Walker said, “not the initial conditions.”

Cronin and Walker aren’t the only scientists attempting to explain how the keys to observed reality might not lie in universal laws but in the ways that some objects are assembled or transformed into others. The theoretical physicist Chiara Marletto of the University of Oxford is developing a similar idea with the physicist David Deutsch. Their approach, which they call constructor theory and which Marletto considers “close in spirit” to assembly theory, considers which types of transformations are and are not possible.

“Constructor theory talks about the universe of tasks able to make certain transformations,” Cronin said. “It can be thought of as bounding what can happen within the laws of physics.” Assembly theory, he says, adds time and history into that equation.

To explain why some objects get made but others don’t, assembly theory identifies a nested hierarchy of four distinct “universes.”

In the Assembly Universe, all permutations of the basic building blocks are allowed. In the Assembly Possible, the laws of physics constrain these combinations, so only some objects are feasible. The Assembly Contingent then prunes the vast array of physically allowed objects by picking out those that can actually be assembled along possible paths. The fourth universe is the Assembly Observed, which includes just those assembly processes that have generated the specific objects we actually see.

Merrill Sherman/Quanta Magazine; source:

Assembly theory explores the structure of all these universes, using ideas taken from the mathematical study of graphs, or networks of interlinked nodes. It is “an objects-first theory,” Walker said, where “the things [in the theory] are the objects that are actually made, not their components.”

To understand how assembly processes operate within these notional universes, consider the problem of Darwinian evolution. Conventionally, evolution is something that “just happened” once replicating molecules arose by chance — a view that risks being a tautology, because it seems to say that evolution started once evolvable molecules existed. Instead, advocates of both assembly and constructor theory are seeking “a quantitative understanding of evolution rooted in physics,” Marletto said.

According to assembly theory, before Darwinian evolution can proceed, something has to select for multiple copies of high-AI objects from the Assembly Possible. Chemistry alone, Cronin said, might be capable of that — by narrowing down relatively complex molecules to a small subset. Ordinary chemical reactions already “select” certain products out of all the possible permutations because they have faster reaction rates.

The specific conditions in the prebiotic environment, such as temperature or catalytic mineral surfaces, could thus have begun winnowing the pool of life’s molecular precursors from among those in the Assembly Possible. According to assembly theory, these prebiotic preferences will be “remembered” in today’s biological molecules: They encode their own history. Once Darwinian selection took over, it favored those objects that were better able to replicate themselves. In the process, this encoding of history became stronger still. That’s precisely why scientists can use the molecular structures of proteins and DNA to make deductions about the evolutionary relationships of organisms.

Thus, assembly theory “provides a framework to unify descriptions of selection across physics and biology,” Cronin, Walker and colleagues wrote. “The ‘more assembled’ an object is, the more selection is required for it to come into existence.”

“We’re trying to make a theory that explains how life arises from chemistry,” Cronin said, “and doing it in a rigorous, empirically verifiable way.”



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