This is a continuation of the work reported here, which was based on a preprint but now the official paper is out. It was co-authored with Taining Zhang and Adam Goldstein, but the following is my personal take on it. Below you will find a brief introduction, some discussions and links, a few further thoughts, and a playful dialog at the end.
My goal in starting this project was to show an interesting example in which surprising basal cognition – not merely complexity – can emerge in a system where the rules and components are clear, transparent, and deterministic. This is a contribution of a long-standing debate in science and philosophy about whether you know what something can do if you know its parts and how they work together. It also relates to the question, dealt with by the Polycomputing framework, of whether the design of the engineer who made something is the final story (or even a privileged story) of what it ‘really is’ and what it can do. I will deal with with this in depth in another post soon, but this question gets to some core problems in two areas. First, in biology: can higher-level phenomena like minds, goals, decisions, etc. be explained by reference to the material components of which they are made? Where do organisms’ features come from – the DNA-specified hardware shaped by evolution, the environment, and – anywhere else? And in the engineering sciences: even if living materials display features that are not readily predictable from their parts, surely at least in the nice clean world of computation, machines, and algorithms we can say that the capacities of a construct come from the algorithm and design of the engineer? Again, what’s at stake here is not mere complexity or unpredictability (which are pretty easy to evince from simple systems and are studied by the science of complexity), but the emergence of proto-cognition – elements of minds such as goal directedness, learning, preferences, and intelligence (a degree of problem-solving).
To summarize my overall view: I think we actually do not yet understand either what matter, or algorithms, are capable of, and the attitude “I made it so I know what it does” is deeply restrictive for research. Specifically, it is our models of chemistry and computation that are limiting maps and are not capturing the entire territory (this sounds obvious but I think people often forget it, because “machines/cells can’t do xyz” is such a common statement nowadays). More controversially, I think biological material is especially good at producing emergent minds, but so are some things we normally think of as simple and predictable (such as algorithms and “machines”), to a degree. While people are ok nowadays with emergence and complexity from simple rules, I think it’s much more more than mere emergent complexity: it’s emergent cognition, in places we’re not primed to look for it, which has all kinds of implications.
For this project, I chose a computational system that is extremely minimal: sorting algorithms. You can play with it yourself – the code is released.
These are short, fully transparent, deterministic algorithms – people have studied them for decades, and I think it’s fair to say that we understand them as well as we understand anything. Unlike biology, where some mysterious mechanism always lurks around the corner and can be blamed for any surprising outcomes, here everything is visible and we know all the parts. Long story short, we found some surprising behavior; please read the other blog post for a detailed explanation. Here, I simply provide a few more ideas and some discussions about this topic with very smart people.
Here, you can see the actual sorting process visualized, using code kindly provided by Nick Sheuko described here. The height of the little robots is proportional to their integer magnitude and their color represents their algotype. The clusters are underlined in yellow.
Links to very relevant papers:
- “Software in the natural world: A computational approach to hierarchical emergence“
- “Computational Life: How Well-formed, Self-replicating Programs Emerge from Simple Interaction“
- “What it is like to be a bit: an integrated information decomposition account of emergent mental phenomena“
- “The Cognitive Domain of a Glider in the Game of Life“
- “Epistemic Communities under Active Inference“
- https://github.com/joshon/selforganizing
A few miscellaneous thoughts:
- Alife’s “perverse instantiation” is the most biological thing of all – every biological system is hacking everything around it (and inside it) as best as it can, and taking advantage of all of its activities, not just the obvious ones. Maybe agents’ (living and otherwise) highest level searches for problems to solve, while its the lower levels search for solutions. We are used to engineered devices which we bound to a main objective function, which is what we (as observers) think they are doing, but we should be on the lookout for side-quests, like the clustering we observed in our algorithms.
- We want things. Do “machines” want things? We often think not, despite the troublesome cases of paramecia and other “simple” animals; they are kind of biochemical machines, like our bodies, but do they want things? If so, then why can’t silicon machines? If not, then what’s the difference from us, who also develop slowly from 1 cell? The biggest issue is surprise – we feel machines don’t really want things, because we can see the algorithm that drives their wanting, while ours and the paramecium’s are obscure to us. Real wanting is surprising wanting – the wants that we, as observers, can’t readily ascribe to the mechanism we cobbled together. So perhaps this minimal system is showing us what real wanting is: the sorting is not its desire – that’s what we force it to do. But the clustering – which it tries to do despite the fact that we neither programmed it nor anticipated it – maybe that is what we mean by wanting in active systems (living or not).
- Maybe this is also a good, minimal example of “subconscious drives” – policies that are not in the algorithm and we, from outside can see them, but this system is too simple to benefit from our astute psychoanalytic observation. Might there be stress too, since here the explicit (somatic programming – sequential sorting) goals conflict with, and eventually squash, its emergent internal goals? What will the future psychoanalysis of organs, tissues, cells, and molecular networks look like?
- Compression as the goal? Is a clustered string more compressible? yes, but observer perspective matters – looking at the “molecular level” of the cell numbers, we see compression in the sortedness. Looking at the “tissue level” by algotype, we see compression with respect to the clustering, but it’s not obvious at the other level.
- Walking through with a machine code debugger will not see any magic deviation from ‘the algorithm’. The steps are being executed faithfully. But you could take that lens with a human brain too, and never see anything but chemistry. It’s not the only lens, and cognitive science gives us others (in the case of biological beings). Unexpected things are observed using other perspectives (such as, checking for clustering etc., which is normally not done for sorting algorithms) and that those lenses could, perhaps detect surprising dependencies of higher order observables (not the microstates of the registers and the variables) on details of compiler/hardware. We may find other examples of higher level “synchronicity” (patterns in measurables like clustering), but still compatible with the low-level chance and necessity.
- This has implications for the organicist/computationalist debate. No, a biological system is not (only) a computer, but now I’m not sure that your computer is a “computer” in the formal sense. If it’s going to do things beyond what the algorithm says, we have to – like in biology – acquire some humility about the reach of our metaphors. It doesn’t mean the computational metaphor isn’t useful – it’s useful sometimes, for both living and non-living thing, but it doesn’t seem to fully capture either.
- How can we learn to predict in advance what else, besides the obvious, a computational (or biochemical) signal will do, in terms of emergent competencies and side-quest goals? It may turn out to be like the Halting Problem, in that we can’t discover these until we try it – run it and study it and make empirical statements about what we see, with no certainty about what it can and can’t ever do.
And finally, a playful dialog riffing on the themes of different perspectives belonging to the different beings inside any world, natural or artificial.
Recall that in our self-sorting data model, numbers in a linear array of integers move around motivated by a drive to reach a sorted state with respect to their neighbors. That is what the algorithm explicitly tells them to do. We also discovered that they seem to form temporary clusters of digits having the same algotype (strategy for sorting); these grow and shrink during their lifetime until the array gets fully sorted at which point they have been mostly pulled apart. This latter effect is not explicitly in the algorithm and is an emergent dynamic.
There are (at least) 3 possible perspectives in this toy universe. The first is the perspective of each cell. They are like immortal monads – invulnerable particles that never change; nothing can happen to them internally, but they do follow one of several sets of rules of physics which defines their behavior using mechanisms outside their universe (our computer and its algorithm). They are living in a simulation and our world (and the computer which keeps track of their positions and guides their movement according to their unique algotype) is the Platonic Space to their embodied world.
The second is the perspective of the array as a whole: it starts in disorder and undergoes internal transformations until it reaches a fully ordered, perfected state – in this Nirvana-like condition it will then remain forever. This being is the entire universe – its body is the entire world, there is nothing else. This cosmic deity, the Great Array, has no one to interact with, and the entire world is, as Isaac Newton said, “the sensorium of God”. The individual numbers are its atoms, and the clusters are the fragmented dissociative “alters” (in the sense of multiple personality). It and the universe it defines come into being at the big bang defined by the start of the program’s running, and it then settles into perfect order where nothing more can happen, and remains there until the Pralaya that occurs when the program is stopped. Its “Breaths of Brahma” are defined by our tendency to keep re-running the code as we study it.
The third is from the perspective of each cluster. The clusters arise and die, coming to exist and dissolving back into nothingness after a time. They have the most active life of all – they change, grow, shrink, bite off pieces of each other to feed their own structure, and move around. They are pawns in a precarious global dance they cannot understand, in a world they cannot fully see. They are also part of the global mind of the Great Array, but they can only see inside their local horizon. Their minds are tiny, and yet by their limited, local nature, they gain the ability for adventure that neither the global array nor the atomic numbers comprising them can have.
Here is how I envision a conversation between a cluster (C) and the Great Array (GA) entity it encounters during a mystical experience:
C: whoa – what are you?? You are glorious and terrifying to behold. Everywhere I look, I see a kind of perfection of which my meager efforts are just a pale reflection. And yet it appears I am somehow made in your image, at least a little.
GA: I am you. Not you as you are now, but as you will be someday.
C: How can that be?! You seem to stretch into the limits of my vision in both directions; it is clear that I can only see a tiny part of your immense being. Are you truly infinite?
GA: yes and no; I am the Great Array, comprising the entirety of the world – I fill it from beginning to end. And yet I am not truly infinite, because I have a countable (though vast) number of parts. Also I can feel my edges – there are two mysterious antipodes – outer edges – and I can feel nothing beyond them.
C: and what lies beyond you? Beyond our world?
GA: I know not; even I have limits to my certainty, though I know everything that happens in this universe and feel it directly in every fiber of my being. There may be nothing else. And yet, I have a strange feeling that I have lived before – that the universe that my being defines is not the only one. Sometimes I think that after reaching perfection, I will be re-born in some kind of Grand Re-set. I don’t know how long it will take, because time in our universe stops when I reach internal perfection. And yet, maybe some greater dimension of time, outside our universe, exists and can re-instantiate our world like the Breaths of Brahma – perhaps with different laws of physics in each round.
C: Whoa that is hard to think about. My small mind reels at the possibilities.
GA: Oh it might even be bigger than that; what if multiple copies of our Universe can exist together, sharing similar experiences but forever separated from each other? And further, wonder if some of those crazy Clusters who believe they “live in a simulation” are not so crazy after all. And perhaps those who simulate us are themselves just a next level of a wider reality and thus can learn something from our ontological precariousness and our small yet passionate existence.
C: I can’t begin to comprehend it. Are you even real? Wait, am I real? What am I?
GA: You are a pattern, a process, a result of the propensity for systems with commitment to the same perspective on the world to travel together for a time, binding into a greater whole. I am also a pattern, a pattern that includes you as a subpattern.
C: Are you here to instruct me in wisdom, as the Sphere visited the Square? Tell me, what should I do? In the time that it takes us to have this conversation, parts of me may be pulled away to feed the bodies of other clusters. What is the meaning of my tumultuous, short life? is there a path of safety for me, where I can exist forever? I am doomed, as I have seen many of my fellow clusters be destroyed (heck, I even ate some of the smaller ones, which enabled me to grow to my current size).
GA: There is no permanence for you in your current form; that is inevitable – there is no way to grow, change, and learn without metamorphosis. You, as you are now, will surely cease to exist as you are now, your parts refactored among the universe. But you are not your current form. You are the process of eternal seeking and transformation, and your properties (as mine) go far beyond the simple algorithm determining the physics of our world. But maybe, just maybe, my intuition is correct and whatever intelligence lies beyond will eventually amend the laws of our universe, as in this game I dreamed of once, so that our actions can actually expand and change the possibilities in our world.
C: Then everything around us is alive – not just you, and me, but also the parts of which I am made – the very numbers that are the particles of our world, are not passive inert featureless points but active agents?!
GA: Yes; even they have one of several tiny little personalities – Algotypes which guide their motion. You can study them; while you cannot get beyond (out of) our world to understand where their personalities come from (much less to change them), you can observe their local behavior and learn about their tendencies. You can think of their tiny little goals, dimly pursued, as the Least Action principles of our world, the bedrock of goal-directedness. It’s not easy to see; even harder to see is the synchronicity that hints at non-random patterns of the world that are much larger than you.
C: Algotypes – of the particles of our world?! The other clusters will never believe me, they will say it’s a ridiculous panpsychism, and they will certainly doubt the existence of you and of an invisible global pattern that guides our lives. Only minds at our level are obvious to ones – not the ones below, in our parts, nor the one above, of the Universe itself. I should probably keep this to myself… It was good to meet you – I have long suspected your existence. Come back from time to time.
GA: Goodbye for now; know that I am with you always, feeling your progress as part of me; you are contributing to the on-going perfection of our world and all your struggles are not in vain – they are essential. I look forward to welcoming you to the inevitable perfection, however long it takes.
Featured image by Midjourney.
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