“Imagine we land a space probe on one of Jupiters’ moons, take up a sample of material, and find it is full of organic molecules. How can we tell whether those molecules are just randomly assembled goo or the outcome of some evolutionary process taking place on the planet?”
I have two potential COIs, one of which matters and one of which people might claim matters.
The one that matters is that I've collaborated with author Michael Lachmann for nearly 30 years, and we are close friends. This matters because if I didn't know Michael so well, I probably wouldn't have taken the time to figure this paper out.
The one that people might claim matters is that I’m currently funded by the Templeton World Charity Foundation.
I would disagree, because they’re an entirely separate organization from the Templeton foundation that funded some of the Assembly Theory research, they don’t care what I say, and I wouldn’t pander to them even if they did.
With that out of the way, what does the paper do? The heart of the paper is a simple and elegant exercise in discrete mathematics. Imagine a world of arbitrary objects that can be assembled, combinatorially, to produce additional objects.
You begin with a set of elemental objects that require no assembly at all, and you have a set of assembly rules for when two objects can be joined. This then gives you a set of objects that can be created in a single step.
Within this framework, we can take any object and calculate the minimum number of unique assembly steps that would have been required to produce it given our set of basic elements and our assembly rules.
Example below: The object at left has assembly index of four: 1) join C-D, 2) join two C-D pairs, 3) join two C-D quadromers at an interior D, 4) join two of the resulting octomers.
The one at right has assembly index of five: every link is a unique step.
(This previous example highlights an interesting relation between modularity / compositionally and the emergence of elaborate form. The structure at left is maximally modular and thus has low assembly index despite large size; the structure at right is minimally modular and so has the reverse.)
@ct_bergstrom I think I can feel with you. Only at age 12 I learned a (horribly complicated) trick to reliably distinguish left from right. Required half a second of focusing.
It's much better now, but I still wouldn't mind replacing left/right with a more "natural" concept…
In a system such as this, one can work out the mathematics of how the universe of possible objects increases with increasing assembly index. In general, it blows up super-exponentially. The Nature paper does this, though most of the details are hidden in the supplementary material.
But what happens if not all assembly rules are equally like to be applied, not all objects are equally likely to be incorporated into downstream objects, or not all objects are equally likely to survive?
One can treat that mathematically as well, and the space of observed objects can collapse.
@ct_bergstrom@wertercatt@tomtrottel Thanks for the review. I have always found it hard to see the main difference between assembly theory and algorithmic complexity (like Kolmogorov complexity), what is the main difference? Is it maybe the concept of the “copy number”?
@bjorn_hogberg@wertercatt@tomtrottel I don't fully understand this myself. My first thought was also that this was a reformulation of algorithmic complexity. Copy number is an important addition for sure. I look forward to a discussion emerging around this, which of course was my main motivation for writing the thread.
The authors have a short, dryly witty paragraph on this that I suspect will be lost on 99.99% of their audience; it was lost on me.
After further consideration, my interpretation of what they are saying is that until we get way down the evolutionary pathway toward complex life, what a universal Turing machine can do (KL complexity) is irrelevant because there are no universal Turing machines until very late in the process.
@ct_bergstrom ( forgive my unqualified comment, but that sounds like somekind of a chaos infused fuzzy compiler is needed , recompiling part of itself at runtime to compile new parts :-) )
@ct_bergstrom@wertercatt@tomtrottel I didn’t understand that. From that paragraph it sounds like AT is not to be used for actual biology, but rather for its “progenitor molecules”, i.e. stuff that would not require assemblers/constructors, like ribosomes and polymerases (Turing machine-like things)?
@ct_bergstrom@bjorn_hogberg@wertercatt@tomtrottel My understanding is the same as yours. Kolmogorov complexity assumes strong abstract computational powers (loops!), far beyond what we would expect from any real-world compositional mechanism. For instance, the K complexity of the sequences of natural numbers or of the cubes (say) is very small but we would be very surprised to see anything like this arising organically (either in the narrow sense of biology or the broader sense of chemistry).
@ct_bergstrom I think here Kolmogorov is just playing the customary complexity straw man, as if there's no third choice. Unfortunately, their attack that it "reflects nothing of the underlying process" largely applies to AT as well.
Their "conservative" assumption, taken seriously, requires an "underlying process" capable of performing constant effort searches of a hyperexponential space.
Rather than a third choice like, you know, looking at what reactions are actually happening in the 'goo'.
Moreover, with strong enough biases in how assembly proceeds, the objects that are produced in high multiplicity of “copy number”. This can occur even for objects that have high assembly index.
Notice that thus far we are still talking about a simple model in discrete mathematics.
If we see a world with a high diversity of objects with low assembly index, it suggests that objects are merely randomly assembling and/or disassembling with no particular preference among assembly rules nor much propensity for some forms to survive better than others.
If instead we see a world with a low diversity of objects with high assembly index, we then need some explanation for why we these objects instead of the many others that could exist. This explanation might involve biases in assembly — think catalysis — or in survival — think selection.
Here’s an example. Suppose we observe world 1 at left. The objects are low assembly index, low copy number. Much of the possibility space at observed assembly indices is filled out.
Suppose instead we observe world 2 at right. The objects are high assembly index, high copy number. There’s clearly something special about that AA-B-CC-DD structure; it’s either really easy to form, or really stable once formed, or both.
Moreover these mechanisms creating preferences for some objects over others are making it possible to create and explore more of the object space for high assembly index objects, instead of getting bogged down in the already massive space of low assembly index possibilities.
And this brings us to the money figure from the Nature paper, reproduced below. At the left of the figure we see a world like world 1 above. At right, a world like world 2.
At least at the metaphorical level, life on earth, of course, is like the world at right. Highly complex molecules, organisms, etc., at high assembly numbers, tightly clustered in possibility space. This paper helps us solidify what is special about the biological complexity we observe here.
Returning at long last to the question at the start of the thread, how do we know if our organic soup from a Jovian moon is the product of some evolutionary process:
If the discrete math model from the paper’s supplementary material can be ported to real-world chemical environments using e.g. mass spectroscopy, we basically know how to build an evolution-detector that we could put on a space probe.
But what I find even cooler is that this paper gives me a new way to think about how the complexity and compositionality of structures in the universe relates to the processes that led them to come into existence and persist long enough to be observed. At it’s core, that is assembly theory.
@bjeelka I'd say "the product of an evolutionary process" rather than "life", and defining "complex" is a bitch, but yeah, that's a pretty super tl;dr summary.
@ct_bergstrom Thanks for the careful review, Carl. I dreaded having to try to pierce the offputting writing and the negative reviews of this to understand its core value.
@ct_bergstrom
Reminds me a little of using Zipf's Law as a rough statistical test for language - for instance, in the case of the endlessly discussed Voynich manuscript.
@ct_bergstrom one problem with this is that it treats molecules as classical objects, i.e. based on independent point masses, which violates Heisenberg's assumption that the true system state is a higher-dimensional function dependent on all of the variables coupled together, simultaneously, and which is in principle unobservable. even the concept of a "particle" is just an approximation of this high dimensional function in the form of a factorization. it's unlikely that biology is so simple
@ct_bergstrom I feel like this is related to the Boltzmann brain thought experiment somehow, but I can't quite put my finger on how to connect them properly
(maybe this came up in the early feedback/critique, so apologies if this has already been discussed to (heat) death; I just learned of this paper through your thread)
@ct_bergstrom IIRC the consensus among cosmologists is more or less "current cosmology theories seem to suggest that we are statistically more likely to be Boltzmann brains than "normal" observers. We are assuming that that means there is an error in our theories yet to be discovered that explains this"
Who knows, maybe the maths in this paper is relevant to that?
On this regard – the processes that let complex structures come to be – I am reminded here of:
"On the statistical mechanics of life: Schrödinger revisited" by Jeffery, Pollack and Rovelli 2019 https://arxiv.org/abs/1908.08374
Where it says:
"We question some common assumptions about the thermodynamics of life and illustrate how, contrary to widespread belief, even in a closed system entropy growth can accompany an increase in macroscopic order."
These arise in several different scenarios, like condensation of solar systems. Solar systems become very stable within their dynamic activity when they "survive" whatever catastrophic (planetary crashing) was inherent in their formation, very difficult to predict.
So we can note that we ourselves, phenotypes of R/DNA genotypes, are very unlikely in general, but less unlikely under conditions at this location. There are several layers of assembly processes involved.
@ct_bergstrom This seems to assume two things - that life takes on the same form as life on earth, and that humans know what they are looking for.
I'm both cases, with infinite probability - what if we have "life" all wrong - we assume sentience in these cases? But what about basic conciseness + life, how could we spot something the universe has decided to try differently?
We so far have only one lab, and even then we're not entirely sure how it works.
@tanepiper If you look at the discrete math model, I think it does exactly the opposite. It doesn't make any effort to distinguish life and non-life, and certainly doesn't say anything about sentience. What it does do it tell us how we could spot assemblages that have arise through some sort of evolutionary process.
@ct_bergstrom Got it. It's a bit of a heavy read on holiday and I couldn't quite grok it, but from your description you make some clarity - life assembly doesn't require a specific set of preconditions other than a certain amount of repetition - where you see that, then it suggests that the further conditions for life are possible (hence why humans are humans, dogs are dogs, insects are insects, etc)
@ct_bergstrom
Hi Prof. Bergstrom
You might also find this work interesting (https://www.researchsquare.com/article/rs-3440555/v2), which is motivated by Francois Jacob's concept of tinkering and similar ideas, and falls within the broader category of Algorithmic Information Theory.
More importantly, it can characterize the hierarchical and nested relationships among repetitive substructures.
@ct_bergstrom Even if there is no cellular life in any of the outer system moons, there may be organic molecular structures that give us clues to how abiogenesis might have taken place.
@Walrus quite a profound comment as it turns out. The paper forced me to do a lot of rethinking of the difference between random goo and output of evolutionary processes.
It’s not a dichotomy but rather a matter of degree, and I never understood that before.
@ct_bergstrom
Amazing work and very well described theory where so many dimensions have been used to limit and or qualify the outcome to make it possible to calculate. For me as a simple beginner, this is great reading and I’m curious if this theory yet has been used on any exomaterial?
@Kaaswe not to the best of my knowledge, but my understanding is that the authors, or at least some of them, think that this would be almost immediately possible, using current mass spec technology.
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