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Rob Sheldon on “constructor theory”

Dr Sheldon
Rob Sheldon

Physicist Sheldon kindly writes to discuss the latest attempt to make a dollar out of fifteen cents: That is, to address design in nature according to purely physical principles that leave out information.

It’s a poorly written article, but the concepts are coming from “Category Theory”, which was highlighted in Jonathan Wells recent article on the sugar code. Richard Sternberg is also keen on it.

Recapping what I said earlier on the topic, set theory was developed in the late 1800’s, and combined with Georg Cantor’s work, enabled the explosion of mathematical creativity of the early 20th. One book that deeply impressed me was “Naming Infinity–A True Story of Religious Mysticism and Mathematical Creativity.” The story relates how Cantor went crazy trying to understand infinity, and three French mathematicians tried but failed to continue his work, when three Russian orthodox mathematicians were able to solve the riddle, briefly founding the intensely creative “Lusitania” ship of faith in the heart of Leninist Moscow. If you ever wonder whether academia is worth all the suffering, this book will be an encouragement, albeit unintentionally.

Set theory can be used to construct the natural numbers, and from there, all of number theory. So what Euclid’s axioms were to geometry, is what set theory is for algebra. Set theory was founded on the handful of Zermelo-Frankel axioms plus the “Foundational Axiom” that removed self-referencing sets–Russell’s paradox: the set of all sets that do not contain themselves, or the colloquial version, “a barber in a little town shaves all the men who do not shave themselves. Who shaves the barber?” This verboten set, however, removes all sorts of useful arguments and math constructions from the Modernist toolkit. For example, St Paul quotes Epimenides the Cretan, who said “All Cretans are liars” with the inspired commentary, “what he says is true” and now Modernists can’t make any sense of that verse.

But we don’t need to be so drastic, and eliminate recursive sets. Category theory says that we can draw pictures of graphs or trees or Venn diagrams that don’t behave like sets, but they still have fixed properties. If we call these things “classes”, then they also include sets. And from category theory, comes an alternative axiom known as the Anti-Foundation Axiom, says that “Of all classes that can be diagrammed as a tree or a graph, if they have the same picture, are the same class.” For example, if you have a diagram that is infinite, and it looks just like this other infinite diagram, then they are the same. So strangely, as classes get bigger, they also get fewer, and ultimately, they are one. So if set theory starts out with the null set, and builds up toward infinity, then category theory starts with a large number of classes and builds toward one. It solves Cantor’s infinity problem.

This approach is very similar to Plato’s apophatic method. If you can’t describe something, can you at least describe what it isn’t? And after enough or infinite isn’ts, perhaps there is only one thing left that is? More generally, recursive loops (like finding what isn’t) usually converge to a fixed state. If you put a mike in front of a speaker, it makes the same screech independent of background noise, volume setting on speaker, etc. Infinity need not be scary if it is predictable and unique. Category theory handles many recursive sets and infinite loops because infinity doesn’t bother it.

Constructor theory is applying this same approach to the problem of life. If we can’t describe how to make life from non-life, can we at least describe what non-life isn’t? After enough isnts, perhaps we have learned something about life?

Unfortunately, the Aeon article decides to combine “Constructor theory” with “deconstructor theory” aka Darwinism, and that makes the whole effort worthless. That is, after saying what physics cannot do (design), the author says evolution can do design, which makes evolution non-physical. This is what the buzzword “emergent” means — a Bergsonian vitalism that enables non-design to design. The author starts out on the category theory path, but thinks he has gotten over the hard part, and swaps in Darwinism. It’s bait-and-switch, and that’s what makes Deutsch both famous and unremarkable. What a pity.

A pity. But it’s all that can be expected from Darwinism.

As noted earlier, if we wanted to be sure the origin of life people wouldn’t get anywhere, we would say, bring on more and more Darwin. But we aren’t the ones saying that, so … ?

No theory will get anywhere with origin of life if it does not deal with information realistically.

See also: A serious and non-magical look at The Science Fictions series at your origin of life research


Suzan Mazur’s The Origin of Life Circus

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