Assembling Abstract Objects in Abstract Spaces

The Expanse | Part 6

Nested Cognition in Assembly Space: Bridging a Boundary |1

The stage is set and the gear is packed. All the worn travel books have been read and all the recommended YouTube videos have been watched. Partaking in ritual preparation has never felt so good. If you have been here from the start you will know what we are looking for;¹ you understand why we are taking so many precautions. Don’t be afraid to have a look around and remember: it is the complex objects in abstract places that we are after.

Last time we looked at how philosophers in the Object-Oriented Ontology (OOO) camp believe that everyday objects (as well as more theoretical (hyper-)objects) exist at a base level of reality and deserve their own ontologically real status. Those in the opposing camp - Ontic Structural Realism (OSR) - view objects as secondary to the relational structures that allow them to exist in the first place. Objects, OSR claims, are created depending on the observer, not on a level fundamental to reality. In this sense, OSR proponents believe relational structures are more fundamental to reality than objects, whilst philosophers of OOO believe that objects and structure deserve equal merit. Using an example most of us can instantly recognise, (perhaps even reach out and grab), OOO sees the iPhone itself a real physical thing, fundamental to our reality, whereas OSR claims the causal relationship that led to the iPhone (e.g. advent of microprocessor technology, Steve Jobs and Apple's early ideation, the supply chain and infrastructure behind Apple and global smartphone manufacture and distribution) as more fundamental. I have previously stated my rather uncomfortable position as a fence-sitter. However, my precarious perch may not be in vain. A new theory based on object assembly may turn out to be a comfortable bridge to rest on.

Tit for tat aside one word keeps popping up. Considering all the possible configurations this word can take why don’t we stop messing about, narrow it down, stick a flag at the top of the bloody hill and finally define “object” as: 

a finite (has a “lifespan” or “span of existence”) thing that exists in our space-time (observable reality) in a certain quantity (theoretically the amount can be quantified). 

Examples of objects that fit this basic categorisation include a planet, a tree, a person, a rock, a house, a kettle etc etc. Whilst most of these objects are fairly “simple” and yes, it is true that we are looking for complex objects in order to smell out artificial lifeforms, starting simple and working our way up often proves to be the most efficient method of probing abstract spaces. So simple it is, for now.

Defining an object in this way, last year a witty chemistry professor and his team working out of Glasgow University produced Assembly Theory (AT). Proposed as a framework to understand how finite, complex objects have been assembled from matter over time in a certain space, a short introduction to Leroy Cronin’s brainchild is nigh-on impossible.² But, in the expansive realm of philosophical speculation, entertainment and general exploration of which this work resides, what I will proffer is that AT stands as a scaffolding to break into some unfairly gate-kept windows and whilst I don’t condone breaking and entering, I do condone exploration into unknown spaces. Balance is key.

A core component of the AT framework is “assembly space”. If we are speaking in terms of OOO and OSR, at first glance assembly space seems to sit in camp OSR. AT imagines a space of relational structure from which objects are assembled, suggesting that the space (which contains the relational structure) is more fundamental than the object itself. Put another way, the space is upstream of the completed object. However, when we stop and think about it the object becomes fundamental in understanding the structure of the space itself and as we shall see, to understand the space we often start with the object and work our way “back”. Put another way, we find our way upstream by following the path left by the object. AT appears to bridge both philosophical camps.

Attempting to understand the shape of object-containing spaces is not new to us. Historically speaking ancient philosophers including Aristotle, Democritus, Epicurus, and even Zeno’s infamous paradoxes have only served to highlight the complexity of the object-space relationship all around us. Astronomy and cosmology is perhaps the ultimate example of this. Take the question of the Earth’s position (as an object) in space. The history books have seen Ptolemy’s geocentric system³ be proved wrong by Nicolas Copernicus' heliocentrism.⁴ Placing the sun at the centre of our spatial system was a good horse to back but a dangerous one to ride. Copernicus incited a revolution which saw some burn, yet progress into shaping space remained slow until Kepler formalised the elliptical system and finally the way we look at our objective place in our surrounding space changed forever. We can now stop staring up, give our necks a rest, and finally see that this idea of understanding objects in space is a curiosity that cuts through the history of human observation. Exploring the relational structure that allows objects to evolve within various spaces may bring us one step closer to understanding the Expanse. Not the one above our heads - the one all around us.  

AT’s fundamental proposition is this: the universe cannot generate complexity; complex objects can only be created by living processes - all complex objects have been created within the “process of life”. When you think of life, perhaps “selection” comes to mind, closely followed by a figure with a long white beard poking out under a rimmed hat. Natural selection - championed by Charles Darwin - synthesised acute observations on biological life.⁵ Common adages like “survival of the fittest”, “adaptation” and “struggle for survival” are a 21st-century hangover and “Neo-Darwinism” has since morphed natural selection into a vessel for accommodating new studies into genetics and epigenetics, and mutations. But Cronin and his team run a chemistry-based lab, so you can imagine that they have a slightly different take on selection than your average neo-Darwinist. 

According to AT, selection is a “memory” chained within an object's assembly over long time frames. Back to our planetary example, it took around 9 billion years for the Earth to start forming after a very loud bang, and another 4.5 billion years for our planet to get to where it is today - teeming with life. Different parts were added and subtracted over aeons, slowly forming into the total objective mass that we laugh, cry, love and take power naps on to this day. If we were to disassemble the Earth, the various stages of its assembly would become clear: Ah, this part goes before this part, this part allows this part to exist, if we move that, this moves. Each stage of assembly is a memory in that object's existence, or a structure of relation between “parts”. Turning in a constant combinatorial motion, the assembly space appears to be continuously cranking out new objects across generations, geological millions and universal aeons. Lapses in time as you move up the scale of assembly cause the surrounding environmental conditions to change, fundamentally changing the possible relational structures that could form, eventually producing objects as a result. Changes in environmental conditions means changes to the objects assembly space (surrounding conditions/input) and changes to the assembly chain (resulting changes to object/output). Factors like this influence the amount of selection (or memory) held within an object's assembly chain. But can we predict when selection takes place?

Digging further into this mysterious space, Cronin’s team began to notice a causal relationship between two factors: how often an object is “discovered” (i.e. first assembled/ the assembly-chain is first produced) and how often an object is “reproduced” (i.e. made again and again in this assemblage). They found that a smaller gap in time between discovery and reproduction indicates some sort of part-selection has taken place.⁶ Aware this may sound a bit weird, hear me out. Newly imposed conditions (e.g. collision with space debris and new solar orbit) can lead to new objects (e.g. new planets) assembled at some point in time from that moment on. Draw circle 1 at that point. 

Just because a new object assembles does not mean that the new object is immediately assembled again. There may be a while between its first assembly and its second, such as the two billion years between the oldest known planet in our solar system and the second oldest. Or it may never be assembled again, like a bespoke, hand-finished engagement ring by a Swiss jeweller who just celebrated his 101st birthday, or life-bearing planet like Earth. Say, for argument's sake, this new object is assembled again, but later on in time. Draw circle 2 there. AT implies that the causal relationship between circle 1 and 2 - the space between them - is tantamount to understanding how much selection has taken place. If the gap is large, it is assumed the object has experienced low rates of selection. Conversely, a small gap implies that some type of selection has taken place because the same parts have been reproduced and reassembled quicker when compared to other objects and their parts in a similar assembly space. If two billion years stands between the oldest and second oldest  planet in our solar system, this suggests less selection has taken place when compared to, say, the single year between the assembly of the oldest and the second oldest Iphone. More selection took place in the Iphone assembly than the planetary assembly. Relational structures interconnected quicker - because life - us humans - were involved in the assembly chain. Thus the object with the smaller gap in time between production (1) and reproduction (2) may be more likely to exhibit emergent complexity in its final form. Slowly but surely we movin’.

There are two mechanisms underlying how an object is first assembled and how it is reproduced: time (a forward, kinetic force, moving us on⁷) and space (location the physical assembly is taking place). Location is important because of “historical contingency”.⁸ Imagine that the coloured circles above are objects, the arrows indicating the distance in time between the production of the first objects (1) and their subsequent reproduction (2). You can see that the object at the top has a larger gap than the one below. The dotted rings surrounding the objects and their stages of production (1) and reproduction (2) constitute the boundary of the particular object's assembly space. Notice how they overlap; assembly spaces can run adjacent to each other, or remain in isolation. Networks of relation combine matter as building blocks to produce various objects. Occasionally this matter creates “agential material” - both smart material that is artificially produced by us and smart material that produced us. Agential material is material that can be goal directed, able to observe the environment and change behaviour based on achieving collective goals. Shape memory alloys - metals that "remember" their original shape are a good example. So are the cells that make us. 

Outside these boundaries of self is another boundary, this one relating to the surrounding context for which the assembly space - and thus the objects being assembled - exist within. Our planet Earth - our biosphere - is one example of such a contextual boundary in which multiple overlapping assembly spaces exist within, forming life. The causal relationship between the assembly space and the contextual space in which assembly exists inside of becomes intimately linked. Not only does morphospace - the space of all possible configurations of a particular structure - connect the two spaces, we can also think of historical contingencies - the events that occur within a given location over a period of time and how these events affect the causal structure of the assembly space - as connecting the two spaces as well. In “AT historical contingency is intrinsic with the space built compositionally, where items are combined recursively… [which] substantially constrains the number of possible objects”.⁹ It seems historical contingencies are built into the fabric of assembly spaces. Historical contingencies can cause the union of parts that had never had a chance to interact before, creating a new “pathway” in the objects assembly chain. An example could be a meteoric impact. Under a new set of constraints (e.g. a tilted axis, atmospheric changes, morphed geology or ecology) the structure of the planets assembly space and thus that which can evolve within pivots towards a different set of building blocks and conditions compared to if that event did not occur, or occurred at a different time. This new direction leads to new part unions, until the object is fully assembled in its observable state at the time of observation.¹⁰ 

Historical contingency is conceptually intriguing. First of all, how much do we actually know about history? We are often so concerned with the shape of space, but I cannot think of a bigger space more meaningful to us than the one left behind by history. Yet how much time do we spend thinking about the structure of history? By talking about the structure of history we must step into the structure of the past. And it would be next to impossible to discuss the structure of the past without at least dipping our toes into time. But that is a lot of stepping and dipping, and whilst this article series is called The Expanse, the water we are currently waist deep in kind of gives me the creeps - we are not staying for long. Just long enough to understand that - from Minkowski’s famous diagram of spacetime and quantum-mechanics-derived notions of retro-causality, to fringe-lurking concepts like the “arc event of time” and less fringe but equally dismissed ancient wisdom from the Vedic Yugas, the Chinese Dynastic Cycles, the Mayan Long Count Calendar, the Aztec Five Suns, Hesiod’s Ages of Man or Nietzche’s Theory of Eternal Recurrence - history, as an object  (Camp OOO), becomes something we can objectively grasp at and see and feel and manipulate. The object of history appears “hyper” in its relations to every other object that has been through the past, made it to the present and hopefully will make it out into the future. Despite the causal nature of history driving events across time, yells from Camp OSR ring out, adamantly stating that calling history an object is wrong. Yet calling history anything less than structure also feels not quite right. History appears to float somewhere between the two philosophical camps. History imposes conditions onto object assembly, influencing whether or not selection ever takes place. Whatever structure you think history takes, whether linearly steaming ahead into the sweet-smelling inferno like Francis Fukuyama’s End of History,¹¹ eternally cyclical like Ray Dalio’s Changing World Order, somewhere in between or not on the option sheet at all, the point still remains: history has a fundamental structure. (And that structure is hard to quantify - neigh-on impossible to observe 100% accurately.) Whether or not we take history itself as a (hyper-)object or historical contingency as the fundamental causal structure behind object assembly, we can agree on one thing: objects exist, and are assembled in space connected by history. 

Back to selection. Evidence that an object has undergone selection within the assembly space can be identified first by ascertaining whether the given object has a high “copy number”. More copies means more of that object exists i.e. igneous rocks, leaf-cutter ants or common juniper trees. But a high copy number alone does not indicate selection nor complexity. Evidence that an object develops complexity through such part-selection is suggested through the addition of a high assembly index. For an object to have a high assembly index there must be a high number of steps between the object as a whole and its smallest reducible part i.e. there are less steps between igneous rock and its smallest reducible part when compared to a human and our smallest parts - thus we have a higher assembly index. The more steps it takes to make an object, the higher the assembly index. This can be understood by moving backwards in the chain of creation from the top-down. What is the outermost layer? Then subtract to the next outermost, until the most fundamental building blocks, often molecular structures, are hypothetically reached. Using a comparative example of inanimate object¹² (i.e. an igneous rock) and biological life (i.e. a human), whilst drastically over-simplified, we might see a hypothetical top-down assembly chain like:

Igneous rock  >  minerals/compounds  >  ionic compounds/anions/molecular chains  >  ions/native elements/elements  >  atoms…

And the following for biological life:

Lifeform  >  organs  >  tissue  >  cells  >  organelles  >  proteins/DNA/RNA  >  compounds  >  molecular chains  >  elements/ions  >  atoms…

Igneous rock arrives at an assembly index of 5, whilst a general biological lifeform comes in at 10. To imagine what the assembly process of complex objects like life looks like (because imagining what something looks like is a step towards understanding how it functions at a deeper level), we can elicit the following panarchical-like structure:¹³

Think of each level as a stage in an object's assembly space. Moving up the levels reflects the natural passage through time. Moving down the levels represents the feedback loop from the top level back to the bottom level (if the system is functioning well). Stage 1 represents the smallest building blocks - atoms - and all their infinite possible combinations beginning to form the core atomic elements. Stage 2 is where combinations begin assembling without any “contingencies” - think random molecular chains, eventually combining into a compound, then forming a longer protein and DNA and RNA structures. Stage 3 is where historical contingencies (e.g. the human genome guiding proteins) help select for combinations of “parts” in a very deliberate order, creating the substructure of organelles, cells and eventually tissue and organs. Stage 4 ends in the physical object we can observe - the whole - like humans, and the quasi-physical qualities that make us human, like our consciousness and (part-time) collective intelligence. 

Just like doing calculus during a pub quiz, each stage of the assembly space for life might best be described as “fractally complicated” - that is objective “life” can be broken into small pieces each just as complicated and complex on their own as the whole is in its entirety. All observable objects have arrangements of subatomic particles (e.g. protons, neutrons and electrons) as a base, but because the assembly space within the quantum realm still spooks top tier lab-coated physicists worldwide, atoms would be the next logical step to represent the smallest reducible parts of an object. However, atoms are also problematic when quantifying an object's assembly index. Imagine you have a book - an index - and on the first page is the object's first building block: a singular atom. On each consecutive page after there is the next building block within the assembly chain i.e. 2 atoms. When we realise there can be around 20-100 atoms in an amino acid, over 10,000 atoms within one protein and over 100 trillion atoms in a single cell, our book would quickly become impractically long. Thus consecutive jumps in the types of building blocks within the assembly index, from an atom to a larger block of structure like different molecular chains and so on, is simply more workable. Just ask yourself how many pages it would take to get from the finished product to the earliest state and you will have a rough idea of the assembly index. 

If both yes’s are combined (yes to high copy number and yes to high assembly index), AT’s framework implies the object, in its completed form, exhibits complexity. And if the object is complex, it implies a “selection” has taken place over time within the assembly space. It is true that “complexity” is a fuzzy, overused term, notoriously difficult to define in any actionable way. Instead of entering the maze with no clear exit, Cronin’s team focussed on the process within which complexity emerges. I see this process as a non-linear chain of causal relations, something like this:

Here, time and its inherent kinetic force (kinetic in that it makes things move) leads to “symmetry breaking”. Imagine you have a glass on the shelf. Over time the likelihood of that glass breaking increases. Times effect on symmetry breaking is a bit like that. We will see the importance of symmetry breaking later, but it must be understood that this breaking process takes place at each link of an object's assembly chain, and the object is not assembled until this has occurred recursively. Breaking of symmetry leads to temporary chaos, stochastically produced by environmental and contextual conditions. Over time this repetitive chaos leads to a new stage in the object's assembly state, represented by a “balance” or “new equilibrium”. Imagine the “union” of new parts that we spoke about earlier. If self-organisation occurs, a new order of combinations may be assembled and different, novel object combinations become “selected” for within the assembly space, From here it may then be recombined with other matter and start the process of evolution once more. Selection provides direction within the assembly process, leading to a higher number of complex parts and eventually, emergence through convergence: complex objects are assembled into existence. We are now deep within an abstract place, and we won’t be leaving for a while. Keep an eye out for any sudden movements. 

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Appendix 1

1. If so I applaud you - we are only about a third of the way in - I told you it would be a hell of a journey.

2. Consequently I implore you to read the full Nature article to get a proper feel for the theory yourself (See also: Constructor Theory; Kolmogorov Complexity & Algorithmic Information Theory).

3. Which most likely took direct influence from the Platonic School continued in part by Aristotle (Shape of Space, Pp.12-17 )

4. This was not necessarily novel to Copernicus, but he was the first that we know of to introduce a comprehensive model of how heliocentrism could function as a central tenet of our solar system.

5. Including variation, inheritance, overproduction, differences in survival and reproduction.

6. Part-selection literally refers to the process of selecting different parts to assemble an object from.

7. Is time fundamental? What is retrocausality in quantum mechanics? For our debate, leaving these big open questions aside, let’s at least see kinetic movement as one aspect of whatever “time” is.

8. Cronin et al, 2023 (see also: Boojari, 2020).

9. Cronin et al, 2023.

10. Ibid.

11. Which was directly influenced by Hegel’s linear procession of epochs. See Appendix 1 for my own interpretation of the Fukuyama-Hegel Historical Structure.

12. Inanimate and not sentient or conscious as far as we can tell...although some “believe that consciousness is part of the fundamental nature of matter – of all matter” including rocks…(see: David, 2016)

13. Structure adapted from research surrounding panarchies (see: Sundstrom et al, 2023; What is panarchy? & Wahl, 2017).