Essay Abstract

The Universe appears to be inherently unpredictable, not just for fundamental reasons from the limits of mathematical proof, or the consequences of quantum mechanics, but also due to how complex systems express or develop new rules at higher levels which emerge independently of their lower levels. However, most of these complex systems are still simple, and have few constraints which places limits on the nature of the unpredictability of the dynamics shown by these systems. Living systems are not only able to exhibit more unpredictable behaviors, but these are intrinsically more novel than the unpredictable behaviors associated with the abiotic universe. In this essay I discuss how a new theory I have been developing, assembly theory, can be used to identify if a given object has been constructed or not by exploring the constraints required for the object to form from undirected or random processes. I try to explain that the more assembled a given a system is, the more of the possible state space is accessible, and hence how both unpredictable and capable of generating novelty the system is. Finally, I argue that living systems are also intrinsically unpredictable in terms of their ability to express novelty and outline a scale of assembly which might provide a way to distinguish living systems from non-living systems.

Author Bio

Leroy (Lee) Cronin is the Regius Professor of Chemistry in Glasgow. His research has four main aims 1) the construction of an artificial life form / work out how inorganic chemistry transitioned to biology / searching for new life forms; 2) the digitization of chemistry; and 3) the use of artificial intelligence in chemistry including the construction of 'wet' chemical computers and to self-assemble a chemical brain; 4) The exploration of complexity and information in chemistry. He runs a team of around 60 people funded by grants from the UK EPSRC, US DARPA, Templeton, Google.

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4 days later

Hello Lee --

Very nice to see your essay in the mix this year!

I really, really like pathway assembly. This may have been something you were telling me about the last time we met in DC--if so, I finally understand it! It is, indeed, computable--and, OK, fine, it's in NP, I think (just because it's a shortest path problem), but the way in which it is computed is quite simple.

If I understand correctly, you also have some AIT-like stories, where you consider also maps between assembly spaces, and how these lead to relative lower bounds. This reminds me of the (uncomputable) material in Kolmogorov Complexity, and translating between machines.

I know you developed these for molecular biology, but I am wondering how they can be equally well applied to human systems. If I think about a sentence, for example, I should be able to find repeated subunits. In those cases, however, the subunits are often with variable placeholders, e.g., ["the". [NOUN]] gets repeated in different places, but then you have to sub-in for the noun. So I can't just immediately stack it on. But there are lots of other places I can, e.g., if I'm looking at the topology of a social network, where I can see subunit motifs being repeated.

Indeed, what happens if you try to apply these methods to a metabolic network, for example? I feel like there's some material on "graph grammars", but I kind of gave up on it because it seemed like the problem was too hard. But perhaps you have deeper insights here.

Do you have a sense of where pathway grammars fall in the Chomsky hierarchy? Meaning, what kinds of processes they can model well. Is it possible, for example, to capture a context-free language like mathematical syntax? Again, I don't have a sense for the class of patterns your methods can capture well.

(That brings up another thought, which is that one can consider pathway assembly across multiple patterns; now you have, I think two things--you want to get the right subunits for a particular pattern, but also reuse of those subunits across different patterns. This would perhaps be equivalent to the difference between the Kolmogorov Complexity of a distribution, and of a sample from that distribution. This could be quite easy to do, if you considered toy examples, like the pathway assembly of a sequence of coin tosses, where the coin follows different Markov processes--you may even discover a nice relationship between the entropy of the process and the pathway complexity.)

In short, it would be lovely to have a (big, long) introduction to these ideas, perhaps in a journal like J Roy Soc Interface, which is often really open to these kinds of things.

Yours,

Simon

    Hi Lee!

    Awesome essay! I really loved learning about this new idea, especially when it comes to thinking about proteins and how they fold. Speaking of proteins, do you think this framework is general enough to structures with that change the landscape of possible transformations over time? Using proteins as an example, most of them fold in such a way that makes it physically more difficult for other objects to attach to certain regions. So in a sense, as a structure grows, transformations are no longer equally as likely as occurring as they were before. The reason why I think this is potentially interesting is because it suggests that structures change their space of possible transformations as they evolve. Then by the time you arrive at a final structure to measure the Assembly Complexity, you might have to take this into account. I wonder if it's not actually possible to estimate that, since you'd need to know the available state space at every time step in the assembly, and if that state space changes at every step, then it could be very difficult to calculate in practice. For proteins, you'd have to know how the protein folds to do this, which is a whole other problem in itself. What are your thoughts on this?

    Also, I'd be really curious to know what your thoughts are on my essay, since I focus on how state spaces change over time, and how an observer could switch to one state space to another to solve a particular problem. I think there's a lot of potential overlap between these ideas and Assembly Theory!

    Cheers!

    Alyssa

      Dear Lee,

      I learned a lot things of the entropies in your essay. Thank you so much. In my past essay to be published from the book, I pointed out when the entropy is used. This condition is "macroscopic". I would like to ask you when the "macroscopic" context is adapted. The biology is always in "macroscopic", itn't it??

      In this time, I wrote the essay on the unpredictability on computation.

      Best wishes,

      Yutaka

      6 days later

      Dear Simon,

      Thanks for these comments. You are right. I'm developing assembly theory to go way beyond biology but look at the intrinsic historhy associated with a given configuration in a state space. This will apply to everything; quantum states; letters; social systems and so on. I'm working up a general representation of the theory and I aim this will replace our confused notion of 'complexity' rather looking at hwo assembled the universe is and how much assembly information is required to get to that configuration. I'm writing up the theory now and we have one or two experimental results that show how this theory can lead to new insights, understanding and predictions.

      Thanks,

      Lee

      Dear Alyssa,

      Thanks for your comments. Assembly theory will work for proteins and protein folding - indeed the evolved infrastructure of biology that takes advantage of the current trajectories in 'folding space' can be traced using assembly theory. I'm working on the framework that this will fit into with my team from genes and protein sequences, then 3D structures.

      Assembly theory explains how you can get access to new structures based on the history of previous structures - there is no free lunch - the future is constrained by the past. Assembly theory already takes this into account.

      I enjoyed your essay BTW and I'm interested how you make the decision, as an observer, to switch space. When you switch a physical space you need to ensure you have the history of that space correctly accounted for since you will be exploring one structure with another and the contexts / origins will be wrong. We can of course observe common paterns in complex systems but I think this is because the assembly spaces are similar and similar dynamics are expressed, but that is the extent of the overlap.

      I hope this helps! Great to hear from you!

      Lee

      8 days later

      Dear Leroy,

      I greatly appreciated your work and discussion. I am very glad that you are not thinking in abstract patterns.

      "Living systems are not only able to exhibit more unpredictable behaviors, but these are intrinsically more novel than the unpredictable behaviors associated with the abiotic universe. In this essay I discuss how a new theory I have been developing, assembly theory, can be used to identify if a given object has been constructed or not by exploring the constraints required for the object to form from undirected or random processes".

      While the discussion lasted, I wrote an article: "Practical guidance on calculating resonant frequencies at four levels of diagnosis and inactivation of COVID-19 coronavirus", due to the high relevance of this topic. The work is based on the practical solution of problems in quantum mechanics, presented in the essay FQXi 2019-2020 "Universal quantum laws of the universe to solve the problems of unsolvability, computability and unpredictability".

      I hope that my modest results of work will provide you with information for thought.

      Warm Regards, `

      Vladimir

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