The Life & Mind Seminar Network

The Role of the Spatial Boundary in Autopoiesis

Posted in Seminars by matthewegbert on August 21, 2008

At the Life & Mind Seminar on Tuesday we very briefly discussed the importance of a spatial (physical) boundary in the context of autopoietic systems. I am interested in this topic, so here is my attempt to rekindle a discussion of it. Here is my view on the importance of a spatial boundary in autopoietic systems.

Much of the conversation on Tuesday focused on the idea of `boundary’ in the context of autopoiesis. There are two boundaries with which we are concerned: the spatial (yesterday often refered to as `the physical’) and the organisational.

A spatial boundary is a delimitation of a contiguous region of space. Examples of spatial boundaries include a soap bubble, a cardboard box and a cell membrane.

An organisational boundary is less easily visualized. It is a delimitation of a set of influential factors. From all of the influential factors involved in a car moving down a road, we can select a certain subset of factors – say those factors that keep the car on the road. However, the organizational boundary from autopoietic theory is a more restrictive concept than just a selection of influential factors. Unlike the selection described above, an autopoietic organizational boundary delimits a contiguous set of enabling processes. If we consider figure 1, this may become clear.

Figure 1: Two types of boundary. End points of arrows represent processes while the arrows themselves represent `enable’.

Let us imagine that this diagram represents all of the processes involved in an abstract system that we are studying. Each processes is represented as a vertex, and each arrow represents the concept of `enables’1. Furthermore, the system includes a physical boundary (described here by a dashed line) that spatially (physically) surrounds certain reactions. Autopoiesis theory suggests that we consider networks of mutually enabling processes. If process P is not enabled by any process P in the network than P is not part of the network. Similarly if there exists no process P within the network that is enabled upon process P then process P can not be part of the network. There is exactly one such network in figure 1; it is the subset enclosed by the organizational boundary (the dotted line). It is easy to deduce that such networks must be reentrant and contiguous. The property of contiguousness allows us to consider the idea of a boundary around such a selection of processes more seriously than we could for a more arbitrary selection of processes (such as the car example above in which the selection of different processes may be non-contiguous and therefore require several distinct boundaries to enclose all of the selected processes).

I believe autopoiesis to be concerned with the organizational boundary as described above, but let us now consider the spatial boundary. A spatial boundary delimits a contiguous region of space. Some autopoietic organizations may produce such spatial boundaries and others may not2. For a variety of reasons (e.g. spatial boundaries are easy to visualize, computational models of autopoiesis tend to include a spatial boundary, the concept of boundary quickly invokes the notion of spatial boundary, etc.), this spatial boundary has been confused with the operational boundary. The spatial boundary has been confused with the boundary fundamental to autopoietic theory. The importance of the spatial boundary has been falsely inflated. I believe that the role of a spatial boundary is simply a spatially-bounding process that enables other processes. For example, by constraining reactants to be in close proximity, the cell membrane enables reactions that would otherwise not be possible. The spatial boundary spatially-encloses certain processes – but this does not give the enclosed processes greater importance or causal value than those processes that occur outside of the spatial-boundary.

In case the above verbal description is not clear, I will try to restate the point diagrammatically. There are two ways to incorporate the concept of the physical boundary into the figure discussed above. The first is to do as I have done in figure 1, to draw a box around certain processes, proclaiming them “inside the physical boundary”. But this is actually incorrect! I have switched the space in which I am diagramming the system. The spatial boundary delineates physical-space, not organizational space. This way of diagramming the spatial boundary is incorrect and may lead to unfortunate lines of inquiry such as “What is special about those mechanisms on the inside of the spatial membrane?”

Figure 2: The spatial boundary here is more accurately represented as a process that enables other processes (dashed arrows).

The more appropriate way to include the spatial boundary in this diagram is depicted in figure 2. Here, the spatial boundary is more accurately represented as a process (vertex) that enables other processes (all of the dashed arrows).

In the past, because it is easily visualizable, because terminology was confusing, because it is common, we have seen the spatial boundary as especially important. But here we see the spatial boundary takes its place among the other enabling processes – not special except perhaps in the great number of processes that it enables.

Does anyone disagree? Does anyone think that the spatial boundary is more important than suggested here?


1For example, say chemical reaction R can only happen within a certain temperature range. If chemical reaction R’ acts as a feedback reaction that maintains total system temperature within the range needed for R to occur, we say R’ enables R.

2On Tuesday, Ezequiel said that he only refers to spatial boundary producing organizations as `autopoietic’ while the more general class of mutually-enabling-networks as described above he considers `autonomous’. Throughout this paper I use the word autopoiesis to refer to this latter, more general class of operationally closed, mutually enabling networks of processes.


7 Responses

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  1. Tom Froese said, on August 22, 2008 at 3:31 pm

    Hi Matt,

    Thanks for this post – diagrams always help! I mostly agree with your argument, and it is making me think more carefully about how I understand autopoiesis.

    I found the most useful contribution arising from the seminar was indeed the distinction, proposed by Nathaniel I think, between physical boundary and organizational limit. It might be even clearer if we always call the former “semi-permeable membrane” when talking about single cell organisms.

    Two quick comments:

    1: If we treat the semi-permeable membrane of a single cell organism as being nothing but another enabling process, then we change the definition of autopoiesis to being just another closed set of enabling conditions (a broader class of systems – more what I would understand as “organizationally closed”, or “constitutively autonomous”).

    Since the notion of one process enabling another is a relational term, we cannot locate this term spatially. Accordingly, this would mean that we cannot talk anymore about the constitution of a unity in the space in which those processes exist. This autonomous unity is not spatial, it is systemic.

    2: This semi-permeable membrane is still special in that it directly enables most (if not all) other processes of the autopoietic system, since these would otherwise (under precarious conditions) diffuse away and disintegrate. This special role is also indicated in Figure 2, as a vertex giving rise to multiple arrows. The physical boundary and the organizational limit might thus be more closely connected than at first expected.

    I’ll have to think about this more…

  2. Nathaniel Virgo said, on August 22, 2008 at 4:33 pm

    Thank you Matt for this post. I think it’s very clear and a good summary of the sort of thing we were discussing in the seminar. It’s very important that we spell out as clearly as possible this distinction between the two types of bounds an autopoietic system has. I do have a comment to make, though: I do think the spatial boundary does have an important role in autopoiesis, but it’s a different role from that played by the organisational limits.

    Tom has just posted a reply making a similar point so I’ll edit mine down to try and avoid repetition.

    As Tom said I think the word “limits” has better connotations than “boundary” for describing the extent of the system in operational terms (see Ezequiel’s reply to my blog post), and has the benefit of reinforcing the distinction between these two really quite different concepts. I think we should encourage this change in nomenclature as widely as possible.

    Keeping the two terms as distinct as possible is especially important because I think both the spatial boundary and the organisational limits are important for an understanding of autopoiesis, but they play very different roles so important not to make them sound like similar types of entity.

    A cycle of “enabling” arrows looks like a definition of operational closure, which is an important part of autopoiesis, but the other important side of autopoiesis (for me) is that it results in the constitution of a spatially distinct individual (“a unity in the space in which it exists”). Without this additional requirement the definition of autopoiesis would be too general and would include, for instance, the abiotic reaction cycles that always form when a chemical system is held out of thermodynamic equilibrium.

    The spatial boundary is usually seen as important because it allows us to say what is part of this “unity” and what isn’t. But this is confusing because if the unity is defined as what’s inside the spatial boundary then the unity which the autopoietic system constitutes is not the same as the autopoietic system itself; it’s probably quite a small part of it in fact. I am not quite sure if this way of expressing this is correct or useful; I’m a bit lost when it comes to disentangling the language surrounding this concept. If anyone has any ideas about how to properly conceptualise the relationship between the spatially bounded part of the autopoietic system and the rest of it, it would be really good to hear them.

    But this spatial boundary does not, in my opinion, have to be very distinct. It just has to allow the individual to be located in a particular region of space. This is one reason why I prefer your phrase “spatial boundary” to the phrase “physical boundary” which we were using in the seminar: the notion of a “physical boundary” suggests to me that the boundary has to be a physically constructed thing, like a wall, rather than simply the bounds of a region of space that contains the individual.

    Of course, in a the case of a cell there is a physically constructed wall-like thing – the membrane – which has resulted in the word “membrane” sometimes being used to refer to the spatial boundary. I think the membrane is a third concept which should be kept distinct from the other two (the spatial boundary and the organisational limits). A membrane is simply one of a number of conceivable ways in which a system can remain spatially distinct. The reaction diffusion spots that I’m using as a model maintain their spatial identity without a membrane, through a balance between diffusion and reaction processes. (also, just as a side note, “semi-permeable” doesn’t really do justice to the nature of a cell membrane: it doesn’t just let some things through, it’s actually covered in molecular pumps that actively transport stuff across it continuously)

    Incidentally, I like Matt’s clear diagrams and the notion of arrows representing processes ‘enabling’ each other is a good way to visualise these ideas, but in biology, membranes (including the cell membrane but also membranes inside the cell and larger membranes inside multi-cellular organisms) are often more about preventing deleterious reactions than enabling good ones. A process can enable another process sometimes and detract from it at others – a process that raises the temperature can enable an enzymatic reaction if it’s cold but disable it if it’s hot. I wonder if there is a way that this could be indicated on this sort of diagram. It seems as if the notions of positive and negative feedback must fit into this picture somehow as well, though I’m not sure how at the moment.


    Finally I’d like to make one more point about autopoiesis. It’s not especially related to Matt’s post, but it’s very relevant to the discussion in the seminar.

    The theory of autopoiesis as originally written had two purposes: to define life and to attempt to ground the concept of cognition, and this dual purpose gives rise to two different directions from which one can be interested in the theory. The theory has been summed up by the equation


    [I’m not sure of the origins of this phrase by the way – I think it is not from M&V – if anyone can give me a reference for it I would be happy] This hypothesis can be broken down into two separate claims:




    I think this leads to interest in autopoiesis from two distinct groups of people: those interested primarily in defining life and those interested primarily in defining cognition. Many of these people share the intuition that the two things are equal (and both equal to autopoiesis), but when it comes to extending the definition or resolving ambiguities, most people will either have a bias towards making it a better definition of life or a better definition of cognition.

    Those who are interested in defining life are likely to concentrate on issues such as a lipid membrane with active transport; those interested in cognition are much more likely to focus on how the system can react and adapt to its environment and on the related issue of normativity. [see footnote]

    But if we want autopoiesis to remain relevant to both we must be careful to tread a middle path. Unless we believe that the theory of autopoiesis has already been sown up with no gaps and can prove beyond doubt both equations 2 and 3 (I do not believe this) then there is no a priori reason to believe that life does in fact equal cognition, and making autopoiesis a better definition of life will not necessarily make it a better definition of cognition, and vice versa.

    As an example, I can see how lipid membranes were important for the emergence of cognition as we know it on planet Earth; but we surely need to be be very careful indeed if we want to go from there to making such a specific type of molecular mechanism a definitional part of what it means to be cognitive.


    [footnote] My personal bias is very much towards the latter, mostly because I think that


    i.e. autopoiesis is necessary but not sufficient for life. I think life is autopoiesis plus quite a lot of other specific things, and we probably won’t be able to pin them all down satisfactorily until we have some more examples (such as life that has arisen other planets, separately from that found on Earth)

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  4. andreashager said, on February 28, 2013 at 10:13 pm

    Reblogged this on Andreashager's Blog.

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