Complexity’s Measure
Introduction
In biology and the philosophy of biology, the term “complexity” is normally used in one
of two ways. It might be used to express (in an information-theoretic manner) how much
incompressible information some entity contains. I am not concerned with this usage in
this essay, and I have my doubts about how pragmatically useful this approach can be.
Alternatively, the term is used when we want to express a less mathematical opinion
about the overall or relative complexity of some thing, which is not necessarily biological
(although I am concerned only with biological complexity). For example, you or I might
say that a lion is less complex than a chimpanzee. In this second situation complexity is
almost always defined either very loosely (Dawkins, 1986, ch1) – “I’ll know it when I
see it” – or not at all. Sometimes, several definitions are mooted and none settled upon, as
Sterelny and Griffiths (1999, p280-282) discuss. At other times a very morphologicallyconstrained definition of biological complexity is used. Furthermore, there is often the
assumption that humans are at some peak of complexity. This can be seen in the typical
diagram of evolution which shows trilobites somewhere near the bottom of the image and
a man striding purposefully across the beach somewhere at the top. This assumption is
certainly also implicit in what Edmonds (1999, p2) wrote: “…the starting point of
evolution is simple, as it is amenable to a reductionist approach, while the end point (us)
is complex.” (my italicisation). Such a claim is a very bold one, particularly given how
complexity is left very subjectively defined1.
In this essay I hope to develop a systematic approach and definition of biological
complexity that is more independent of any anthropomorphic biases we have. By
clarifying exactly what it is we are talking about, the approach that will be developed will
help to provide structure and precision to any discussion we have which involves
complexity. In addition, information about the ways in which an organism is complex can
provide historical insights about the kinds of environments the organism’s species
evolved in, as discussed by Godfrey-Smith (1996).
I would first like to look very briefly at the two most important questions surrounding
any decision about a definition of complexity. Within the context of these questions I will
evaluate a genotypic model of complexity, which (on the spectrum of possible models)
sits at the narrowest extreme. When using such a model the complexity of an organism is
nothing more than the length of its genome (Ridley, 2000, p30 and implicit in much of
Dawkins, 1976). Once I have described this kind of narrow model I will discuss an
intermediate, morphological approach and then close with the development of an
alternative and fuller approach to defining and measuring complexity. This approach will
occupy the opposite end of the spectrum to the genotypic models, and the genotype will
not be considered explicitly. Instead the focus will be on factors such as “structural and
behavioural complexity” (Ridley, 2000, p29) and the way the organisms engineer their
environment.
Edmond defines it as the property of something which makes it difficult to predict – this is obviously of
little use, especially when the term “difficult” is not given any more useful meaning!
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Two Important Questions
Examining a claim about the complexity of an organism (either a specific organism or
more usefully, the often implicit average member of a species – for example, “Humans
are a complex species”) immediately prompts two important questions:
 What elements should we look at when drawing the boundaries of the organism
whose complexity we want to evaluate?
 What is complexity?
I will address these questions in an as species-neutral fashion as possible, to facilitate
comparing the complexity of organisms which are from different species. Comparisons
between organisms from difference species are the most common and useful form of
comparison. This is because it’s difficult to make any meaningful claims about
complexity that are not relative to something else and when comparing members of the
same species the answer will be “equal complexity” in all but the most tortured cases.
Note that the questions just listed are very interrelated and the answers to them will be
intertwined.
Just the Genes
At the tightest end of the spectrum only the genotype is considered as it is argued that this
expresses all of a species complexity and that measuring it in other ways as well or
instead would either count the same thing twice (over-counting) or not count everything
(incompleteness) (Ridley, 2000, p30-31).
The genotype can be seen as either the number of base pairs which code for proteins or as
the number of genes. Although DNA can do more than just code for proteins, such as
control replication and transcription, these other functions will not be considered in this
essay. That is because these regulatory sequences only serve to control how the DNA is
copied, and since all cells in the organism always have at least one full copy of the
organism’s DNA such regulatory sequences cannot contribute in any meaningful way to
the complexity of an organism2. The term “gene” must be defined in quite a restrictive
sense as well (as the stretch of genome which codes for a particular protein) if the
boundaries are drawn so tightly though. This is because a more phenotypic definition –
e.g. “the gene for green eyes” or “the gene for olfactorily detecting infidelity” – is
actually a position at the other, broad end of the spectrum with the words “the gene for”
prepended.
Given these definitions, the number of active base pairs which are transcribed as proteins
and the number of genes are effectively equivalent definitions and will be treated as one
and the same. This is because the same length of DNA (3 base pairs) is only and always
needed to code for a protein.
The key attraction this definition of an organism’s complexity has is that it is easily
measurable: you can just count the number of genes or active base pairs. However, this
model suffers from at least 3 problems, which I will now outline.
If only the genome and not the developmental environment is being considered then the
fact that (as Dawkins, 1982, p14 wrote) “[a] gene ‘for’ A in environment ‘X’ may well
2
Unless of course we are looking to examine the complexity of an organism's cellular or organism-level
reproductive process. This is quite a narrow domain and is not the focus of this essay.
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turn out to be a gene for B in environment Y” becomes problematic. This is because the
developmental environment can itself be extremely complex (e.g. Sterelny, Griffiths,
1999, p96) and it cannot be measured in the simple way the length of the genome can be.
Indeed, higher level, conceptual approaches are needed, which nullifies the simplicity and
objectivity a genotypic model view might appear to offer over higher level, conceptual
approaches.
It appears that there are two ways this objection could be responded to. The
developmental environment could be assumed to be a certain one, or the developmental
environment could be somehow included in the definition of the gene. Of these two
approaches we have already ruled out the latter as removing the advantages a genotypic
model conveys (and the need for such an ad hoc band aid probably also introduces
further excessive subjectivity). The former – assuming the developmental environment is
a certain one - is just too simplistic though, as discussed by Sterelny and Griffiths, 1999:
“[a] trait would be literally genetically determined if it could not be altered by changing
nongenetic factors, a situation that we can be sure never arises.” It would therefore seem
that the developmental environment poses a significant problem for the types of model
which are fundamentally genotypic.
Secondly, a gene has only a very indirect impact on the morphological or behavioural
complexity of an organism. This is because a gene (as it must be defined by someone
who wants to use such a model) codes only for proteins. Hence anybody who draws the
boundaries so tightly must identify a single protein, the presence of which causes some
(probably macroscopic, but not necessarily) complexity-increasing trait3. Alternatively, a
monotropic set of genes could take the place of a single gene. A monotropic set of genes
is unlikely but theoretically possible. Such a set of genes would code for proteins which
affect just one phenotypic trait, regardless of what alleles are present. An example of such
a possibility is a gene or set which codes for proteins which only affect the pattern of
markings on an animal’s coat. This is perhaps the most plausible possibility, but it is
important to remember that in many species every organism has exactly the same alleles
over long stretches of the active part of its genome which codes for proteins, and that a
vast number of proteins (and therefore genes) are usually involved in the expression of
even the simplest traits. In other words, finding a set of genes which wholly and only
code for just one trait is very unlikely, and genotypic models assume that such sets occur
frequently (even always). If such a gene or set of genes cannot be regularly and easily
found then it means that drawing a meaningful link between a definition of complexity
related to some organism’s traits (which is what is sought to make possible the
comparisons we are concerned with in this essay) and the number of genes or length of
the genome is tentative at best. This leads me to conclude that drawing the boundary of
an organism at the edge of its genome is drawing it too tightly.
In addition to having a very indirect impact, it is also the case that because genes
frequently do interact there may not be a positive correlation between the length of the
genome and the organism’s complexity (unless you are calling the length of the genome
“complexity”, at which point the whole exercise becomes farcical). At best the
Such a trait could be morphological – an eye, a type of cell or even an organelle – or behavioural, such as
a cockroach’s response to changing air-pressure.
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relationship between the length and the interactions and consequential complexity may be
roughly exponential, but of course the exponent could be dramatically different for
different species. Consider wheat (16.5 billion base pairs) and humans (3 billion base
pairs). While these are the actual number of base pairs and not the number of active base
pairs (about 2% in humans) it is important to note just how less complex wheat seems
than us, even when its biology is studied to the same level of detail as human biology is.
If only one fifth as much of the wheat genome was active though – 0.4% – that would
indicate that wheat was as complex as us, and much more complex than many other
seemingly more complex organisms like fruit flies. Edmond (1999, p4) suggests that the
genotypic models actually imply wheat is 10 times more complex than us. While this
conclusion could possibly be true in some very limited domains I again stress that this is
so contrary to what we would expect that it indicates genotypic models are not the most
suitable way of measuring complexity for our purposes. The problems caused by the
developmental environment and the problems of a genes indirect and pleiotropic impact
support this conclusion about the (un)suitability of genotypic models.
The Morphological Midpoint
I will now consider one “intermediate position” in the spectrum of models which measure
complexity. Such models include those which don’t use only the genome but are still
based on heterogeneity or information theory. Unfortunately, due to space, I will not
consider this kind of model here (although I think they all fall prey to the one objection,
which is that the kind of complexity we are interested in is not the same as the length of
the description).
Instead, I will consider a model put forward by McShea and Changizi (2003), and others,
which is aimed at addressing the extent to which a species is morphologically complex.
McShea (2000) contended that morphological complexity correlates sufficiently with
behavioural and functional complexity that to try and include more than morphological
complexity is to over count. Note that the model developed by McShea and Changizi and
others could be applied to any of a number of systems. It is (to borrow a term from
philosophy of mind) substrate neutral, and indeed when developing a fuller system I will
use McShea’s model several times. I will now first explain what this system is, and then
identify three reasons the morphologically constrained version suggested by McShea
(2000) is insufficient.
McShea and Changizi’s model (2003, p74-75) seeks to measure morphological
complexity (remembering that McShea argues this implies behavioural and all other
forms of complexity) in a hierarchical, two tiered way, with the first tier based on nesting
and the second on individuation.
The first tier is the level of nestedness, i.e. the number of times the second level tiers of
individuation have nested. These tiers are numbered – so if an organism is made up of no
lower level tiers then its degree of nestedness would be “1”. On the other hand, if it were
made up lower level parts which were in turn made up of yet lower level parts it would be
described as having a nestedness of “3”. The minimal level of nesting is (to an extent)
arbitrary. This arbitrariness is acknowledged (ibid, p75) when Prokaryotes are placed at
level 1, although McShea and Changizi say a level must be a level of complexity at
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which selection has taken or takes place (ibid, p75)4. This approach to placement is
generally in line with our intuitions and will be retained in this essay.
The lower, fundamental tier (which drives the model and gives the context used to
determine which top-level tier an organism belongs to) measures an organism’s
complexity by the number of kinds of parts it has and the kinds of relationships between
these parts, i.e. the level of individuation in an organism’s components. In this second tier
an organism can be at one of three discrete levels of complexity (a, b or c). It may just be
an unstructured collection of several lower level parts, where “parts” are one-tier-down
things – that is, “a set of [presumably lower-level] components that are relatively well
connected to each other and relatively well isolated from other components” (McShea,
Anderson 2001, quoting McShea, Venit, 2001). An unstructured aggregation of
undifferentiated parts is called sub-level a. For example, when a cellular slime mold
swarms, it is just a collection of (lower level) individual cells with no structure or
differentiation amongst the types of cells and it is therefore at sub-level a. Based on the
fact that it is just composed of eukaryotic cells which are level 2c (historically,
eukaryotes are the result of two or more prokaryotes merging) the overall complexity of a
swarming cellular slime mold is probably 3a.
However if an organism is composed of two or more different kinds of less nested parts
which are still in an unstructured aggregate McShea places this organism at level b. The
distinction between a and b strikes me as a justifiable one as there is an important
difference in the apparent level of complexity of something which is made up of just one
kind of thing and something which is made up of two or more. For example, slime mold
reproduces through spores or cellular fission, i.e. through the behaviour of one type of
cell. Vaucheria, a genus of alga used by McShea as an example of level 3b, is different
though. Vaucheria can be comprised of several kinds of cell, including both sperm and
eggs. The physical structure and the repertoire of behaviour and interactions amongst
these multiple types of cell is significantly more complex than the behaviour which takes
place in slime mold.
At sub-level c each organism is a single structured (hierarchical) collection of two or
more types of lower level parts. This is obviously more complex than an unstructured
clump of different things (sub-level b). An example of this also used by McShea is coral.
Any one (hermatypic scleractinian) coral is in fact a morphologically structured
symbiosis of zooxanthellae and the cells of the coral itself (Levinton, 1982), and this is
presumably why coral is placed at level c (McShea does not say and I am not certain). If
an organism were more than one structured collection of lower level parts it would be a
member of a higher primary (nesting) group, with a sub-level of either a or b. For
example, if it were an unstructured aggregation of its structured parts it would be level a.
While McShea and Changizi (2003, p79) attempt to apply this schema to relationships
between intentional (humans) or at least semi-intentional (honey bees) species they
acknowledge that this very morphologically based model is “difficult to evaluate
objectively”. I will now examine three of the other problems such a morphologically
focussed model of complexity has in more detail.
4
Which immediately prompts the query: surely selection operated at the pre-prokaryotic level of
complexity as well?
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The first of these problems regards the crucial assumption made by McShea and Changizi
that morphology and behaviour have a predictable many-to-one or one-to-one
relationship. While this assumption may well be true for less complex species the
complex interactions between a primate’s perceptual systems, its brain and the physical,
social and biological environment5 show how this relationship becomes a many-to-many
relationship and that McShea and Changizi’s model must therefore have limited
applicability if behaviour is not somehow incorporated. Of course, incorporating
behaviour in an ad hoc manner will almost certainly simply result in the same kinds of
problems faced by genotypic models which try to incorporate the developmental
environment.
Secondly, the general definition of complexity in use and the target of this essay must
undeniably include more than the morphology – for example, few would dispute the
claim that, overall, the eusocial honey bee is more complex than the mud-daubing wasp
Trypoxylon politum. While a purely morphological definition of complexity may be
sufficient in other circumstances this means it is not sufficient in helping us understand
what we mean more generally.
Thirdly and finally, as Sterelny and Griffiths note (1999, p370):
The central empirical idea defining emergence is that surprisingly complex
system-level behaviour can arise out of locally interacting simple units. Complex
behaving systems require neither complex parts nor central direction. The
elements in A-life models are often quite simple units whose interactions are all
governed by local rules – indeed, relatively simple local rules. But the behaviour
of the system as a whole is often adaptively complex. Some social insect colonies
may provide natural examples of the phenomenon in question. Simply interacting
simple creatures nonetheless produce complex, adaptive, and patterned
behaviour. So a good many of the more striking examples of the A-life models can
be seen as undercutting the idea that fancy systems must be built of fancy
components. They show that complex system-level behaviour may arise out of
interacting simple components.
In other words, complexity can arise emergently from morphological simplicity.
For these three reasons, and also from extensions of many of the problems genotypic
models of complexity face, I think we can conclude that a purely morphological model of
complexity will not be wholly sufficient for our purposes without becoming overly and
dangerously ad hoc.
The Hydra of Complexity
Hence, we move on now to the fourth part of this essay and the broadest end of the
definitional spectrum. In particular in this section I would like to make sure the different
dimensions along which a species may be complex can be recognised. This is important
(as the examples used below show) because complexity or simplicity in one area, such as
morphologically or genetically, does not necessarily translate into complexity or
simplicity elsewhere. A broad definition of a species may mention a range of high level
elements, such as behaviour and morphology. Both of these aspects will be incorporated
The physical environment is the static environment – rocks, trees, rain and so forth. The social
environment is the other organisms with which an organism interacts with on a regular basis. The
biological environment is every other living entity with which an organism interacts.
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into the final model I will develop. A shopping list of possible elements will be
developed and then selected from as the model is developed. How the complexity (for
each element) of two species can be compared will be decided on following each
selection.
Prior to enumerating some of the members of this list though I think it is important to
highlight that at this end of the spectrum there are a number of ways of decomposing
complexity into its components. If too broad divisions are used – for example
morphological complexity and behavioural complexity – then a comparison of the
complexity of organisms from different species remains subjective. Is the behaviour of
the ant lion more, less or as complex as the behaviour of the mud-daubing wasp
Trypoxylon politum? As Kim Sterelny suggested, if the organisms in question were from
very similar species then some comparison could still be made, however I am seeking to
develop as general a framework as possible, and this means that the divisions have to be
carefully precise.
On the other hand, too many higher level factors may reintroduce the problems which
occurred with genes, where multiple apparently independent components are actually redescriptions of the same thing. If the range of habitats an organism can live in is
considered one measure of its complexity, how is over-counting avoided if the number of
life cycle stages or modes an organism has is another? It may seem that a bear which
hibernates as well as living through a hot summer is as or nearly as complex as a liver
fluke (Dicrocoelium dendriticum), whose life cycle stages are described by Dawkins
(1982, p218).
In summary, careless use of conceptual, subjective measures of complexity is likely to
lead to confusing results which disagree with our intuitions too frequently. While we
shouldn’t expect our intuitions to be confirmed all of the time, at some point we need to
make a meta-judgement about a decision making system itself and decide that it is
leading us astray. I conclude that a careless, too-conceptual approach is likely to do this,
due to incompleteness, subtle over-counting or excessively subjective divisions. These
are potential problems which will be mentioned again as the high-level, multidimensional (broad) model we need is created.
Bearing in mind the danger of being either too vague or too precise I have divided the
measures of a species’ complexity into four components – a species’ morphological,
perceptual, behavioural and environmental complexity. These components broadly seem
to cover all of the ways in which a species may be complex, i.e. they are complete. A
species may:
 Have a physically complex structure or life cycle.
 Perceive the world in a complex manner.
 Behave complexly.
 Or have a wide ranging and high fidelity impact on the environment and on other
species (colloquially, its “environmental complexity”).
At first glance, these divisions seem to be quite independent. This is because an organism
could be complex in any of these ways, but not necessarily in another. For example, the
activities of the ant species Formica aquilonia, which “farms” aphids and builds large ant
colonies, indicates it is (environmentally) relatively complex. Morphologically though
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any single ant – or even a colony of ants somehow summed – is still a little bit simpler in
comparison to other species. If an ant were compared to a cheetah it would be fairly clear
that the cheetah had a slightly more complex morphology. Despite this morphological
complexity though, most predators – including cheetahs – have a much simpler
eat/fleet/ignore relationship with other species and with the physical world. Either they
eat another thing, they flee from it or they ignore it. Farming is a much more subtle and
complex task.
However, while it is possible for the divisions to be independent it is also quite easy for
them to overlap. When viewed from such an abstract level, an organism’s environmental
complexity is, in many ways, just another way of describing its behavioural complexity.
There are important differences, in that the consequences of behaviour with a more
significant environmental impact may make the organism intuitively seem (and thus, for
our purposes, be) more complex than similar behaviour without such an impact would,
but these overlaps do exist and must be addressed. They would frequently occur because
the four divisions are only loosely defined and thus seem to have a significant degree of
causal connection between them. For example, a complex perceptual system and physical
morphology is often (but not always) needed for complex behaviour6, just as complex
behaviour is often (but, again, not always7) needed for the members of a species to have
greater environmental complexity.
One way of addressing these overlaps would be to revisit the four fundamental divisions I
outlined above. Unfortunately, careful thought has not helped me create another set of
divisions which is as complete, as useful8, and which is more independent (rather than
just being as independent in a different way). Another approach to addressing this
independence problem is to try and further decompose the four groupings outlined above.
By doing this the locations of any overlaps will become clearer and their impacts can be
minimised by selecting items from the resulting “shopping list” in ways which mean they
overlap as little as possible. I have pursued this approach and detail it below.
Physical and Temporal Complexity
I would argue that the morphological elements of an organism’s complexity can be
broken down into spatial and temporal complexity (i.e. life cycle stages). I suggest using
an organism’s physical, structural, hierarchical complexity (how this can be measured is
described in (McShea, Changizi, 2003) and above)9 as a measure of its spatial
complexity. Some useful elements of the concept of heterogeneity are captured by this
model.
In addition to McShea’s hierarchical model it could be suggested that there is some
limited place for the complexity of the developmental environment. I am suspicious of
such an approach though due to the danger of over-counting – almost all developmental
6
It was for these reasons that McShea (2000) saw morphological complexity as a ubiquitous stand in for
other forms.
7
If it were “always” we could simply draw a causal flow and measure complexity from the beginning of
this causal flow, since all future complexity must necessarily be entailed in the earlier steps. In other words,
we would be right to use McShea’s (2000) model.
8
I claim the above four divisions are particularly useful because they provide a logical way of
decomposing the aspects of a species which contribute to its complexity.
9
While their model alone is insufficient as a way of measuring all complexity it does assess morphological
complexity well.
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complexity will be reflected in the hierarchical complexity (whereas it is not in the size of
the genome). While the inclusion of developmental complexity might make the way in
which complexity is measured slightly more complete it would also make it significantly
less independent and therefore it is not included in this system.
Simply counting the number of life cycle stages gives the most important and accurate
measure of temporal complexity. While these could be reasonably blurry “stages”, such
as occur in a human as they grow from (birthed) child to adult I think that a strong case
could be made for such a process to be almost inevitable and no significant contributor to
complexity. Instead, I would restrict this measure of complexity to a “higher level” in the
hierarchy of life cycle stages, of the kind seen in butterflies and caterpillars – changes
significant enough that we almost have to give the folk organism a different name, simply
to avoid confusing ourselves.
Perceptual Complexity
Perceptual complexity is analogous to a pipe. A pipe’s “complexity” can be measured by
its diameter and by the speed water flows down it. Similarly, perceptual complexity can
be measured by the number of ways a species can perceive the environment (its
phenomenological breadth) and also by how precisely it perceives its environment (its
phenomenological fidelity). In addition to the breadth most other insect species possess, a
cockroach has a low fidelity pressure detector – when it senses any increase in air
pressure it will move as quickly as possible away from this pressure increase. This
pressure increase may be only a passing wind – but it may also be a descending hand.
Thus cockroaches have greater breadth and fractionally greater fidelity than a
stereotypical “base” insect. Similarly while a human and a dog may have very similar or
identical phenomenological breadth (both species can see, hear, smell, taste and touch) a
human has greater visual fidelity, while the dog has greater auditory and olfactory
fidelity. Note here that perceptual and morphological complexity do not significantly
overlap (in the way they are being used to measure complexity) – morphological
complexity is completely afunctional, while perceptual complexity is purely functional
and reflects an organism’s ability to receive information from the world.
It could be claimed that broad or high fidelity perceptual systems always require spatial
complexity, but I think the hierarchically equal spatial complexity of a starfish (e.g.
Asterias forbesi) with a species that has clearly greater perceptual complexity (e.g. Canis
lupus familiaris) makes such a case unlikely. Note that I say that a starfish and a dog are
spatially equally complex because a starfish, like a dog, is internally differentiated into a
range of organs with specific functions. Each organ is in turn composed of several types
of cell.
Breadth is accurately measured at a gross level by simply counting the number of ways in
which an organism can perceive – thus for humans you could note the proprioceptive,
visual, auditory, tactile, olfactory and gustatory components of our perceptual abilities. It
may be argued that this kind of division is too gross though and that some elements of an
organism’s phenomenological breadth (such as visual) deserve greater weighting than
others (such as gustatory) or that these elements should be treated as more than one
system. Very briefly, I have a two part response to this objection. Firstly I would note
that suggesting that one perceptual system (such as vision) is in fact more than one
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system starts to drift towards evaluating the fidelity of the system. The issue of how to
evaluate an organism’s phenomenological fidelity will be considered very shortly.
Secondly, I am cautious here of anthropomorphic bias. Perhaps vision seems like it is
more than one perceptual system to us because our visual systems are so rich and well
developed, but a dog (or an ant) may have a very different opinion.
Fidelity is a less grounded measure and unfortunately no species-independent approach
can be given. It would be a mistake, for example, to assume that humans perceive the
world in a particularly perfect or accurate way. Many psychological experiments (e.g.
optical illusions which lead to conscious and explicitly contradictory perceptions such as
colour phi10, and experiments which manipulate our memory of our perceptions, as
discussed in Dennett, 1991, p116, p117, p120, p123) have shown we do not. This
unfortunately makes comparison of, say, visual fidelity with olfactory fidelity very
difficult and I do not have the space to do more than flag the existence of this problem in
this essay. This lack of an objective grounding or “zero point” and the frequent
incomparability of two different ways means that we can really only assess one species’
phenomenological fidelity in comparison to another’s and not against some objective
measure. There will also be many situations where the fidelities are so similar, or our
knowledge is so lacking, that comparing the two organisms in question to each other
directly is very difficult. However, while a scalar and continuous ranking (“this one is
3.23 times better than that one”) is not possible we may still be able to order them in the
same way a lot of geological and paleontological data is ordered. This is done through
reasoning that, for example, since this sediment was laid on top of this one it must be
younger. At a different location, since it is underneath a third, the third must be younger
still. In geology and paleontology though there is access to objective grounding measures
such as carbon-14 dating (Knoll, 2003, p54). These let an ordering be turned into
something semi-scalar and continuous in some situations through comparison with well
known reference points (Knoll, 2003). For example: “this rock is older than that rock,
which is 13.5 million years old”. This is not possible for phenomenological fidelity.
It might seem that one method of addressing this problem with phenomenological
fidelity, a method which also allows clearer comparisons of different ways of achieving
phenomenological breadth, is to measure an organism’s perceptual complexity at the
information theoretic level (i.e. how many binary bits of information the organism can
perceive per second). This may seem like a particularly valuable and speciesindependent approach if we consider some of the difficulties raised above in comparing
(for example) a human’s and an ant’s perceptual complexity. While I will discuss the
problem of comparison in the multi-dimensional system I am in the process of building
more generally later I’ll consider this suggestion here while the discussion of perceptual
complexity is still fresh.
This information theoretic measurement would span both breadth and fidelity but
implementing it requires that we address a number of pragmatic problems. Developing
different systems for each of the different ways of perceiving which accurately and
objectively measured the quantity of information perceived would be difficult. Exactly
how many bits per second does an ant olfactorily receive in a pheromonal environment?
We could quite easily establish some lower bound, but this would almost certainly under
10
The dots are both moving/changing colour and not moving/not changing colour.
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estimate how much information it did actually perceive, just as measuring how fast a
human can type or otherwise output information almost certainly underestimates how fast
a human can think. Even doing this in a perceptual system-dependent and somewhat
subjective way though (which would mean the objective comparisons we adopted an
information-theoretic system to do couldn’t be done) would be very difficult: how would
we go about determining how many bits of information a human perceived visually in
one second? And how would we go about doing that for a honey bee? Trading one form
of subjectivity for another more confusing one seems like a poor deal to me. In addition,
it is quite possible that we may perceive at different bit rates at different (conscious)
times. If I were personally focussing intently on my proprioception while learning to do
something gymnastic, nearly to the elimination of everything else such as what I could
perceive visually, and if my proprioception is of lower bandwidth than my visual system
(and I think it probably is) then my perceptual complexity suddenly got a lot less and
became very contingent. This thus poses the question: which bandwidth at what time is
an organism’s true phenomenological breadth and fidelity? For these reasons I am very
wary of an attempt to build an objective and grounded measure of perceptual complexity,
but I draw the discussion of perceptual complexity to a close here for now.
Behavioural Complexity
Bearing particularly in mind how behavioural complexity overlaps environmental
complexity I suggest that an organism’s behaviour can be broken down into (as with
morphological complexity) two key sub groups.
The first of these is its flexile complexity – its flexibility and responsiveness to its
environment, an area of overlap with any epistemic engineering an organism does (which
is one potential contributor to its environmental complexity11). Incorporated into this
flexibility and responsiveness is of course the range of behaviours which can be exhibited
and also the ability to learn. Directly measuring the complexity of this behaviour is
difficult. This could indicate that:
 Further decomposition is necessary.
 It is an inherently subjective thing, and therefore this is a bad decomposition.
 Flexile complexity is simply difficult to measure.
Without eliminating the third possibility as the cause of the problem neither of the first
two should be considered. As it turns out it was the third possibility which led to the
difficulty and it could be resolved by approaching the measurement of flexile complexity
from a different perspective. I suggest that a species’ level of flexile complexity be
compared with another’s by comparing the order12 of the number of possible pieces of
environmental information (specific noises, visual patterns, sounds, odours etc) an
organism can use in selecting an action to perform. Thus a dog (Canis lupus familiaris) is
one or more orders more flexibly complex than a cat (Felis silvestris catus), as the dog
can respond to a greater order of audible cues. The dog can behave differently depending
11
As I judge that the behavioural perspective is more complete than that offered by the environmental
elements of it (namely, the epistemic engineering) I will eliminate this overlap by not considering epistemic
engineering as a part of environmental complexity.
12
“Order” is currently loosely defined, but is some combination of the definitions of the cardinality (of an
infinite set) and order of magnitude. Space constrains a more detailed definition.
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on what seems like (based on historical results from training dogs) an effectively infinite
number of possible noises. This constitutes a higher order of flexibility.
The second type of behaviour which contributes to behavioural complexity is how an
organism interacts with others from its own species – interactions with other species I’ve
placed under environmental complexity, to limit overlap. This form of complexity will be
measured by the extent to which one organism can communicate with another. Other
aspects, such as its ability to cooperate, are a consequence of communicative ability. It
can be broadly measured by division into discrete degrees13. The first of these is the
absence of almost all communication between members of the species. This occurs, least
interestingly, in viruses and any bacteria which signal in simple ways, and may occur in
some morphologically more complex species as well, such as the fruit fly Drosophilia
melanogaster. The only communication that does occur within such species is what we
might optimistically call “ritualised courting”.
At the next level I would place most pack animals and perhaps the eusocial insects which
signal relatively simple information to others through the use of pheromones and so forth.
The nature of the communication that takes place within a lion pride may be rougher and
of slightly lower fidelity than that which takes place in an ant colony, but it is clearly of a
higher degree than that which occurs amongst most bacterium and is relatively close to
that which occurs in an ant colony.
Similarly, both ant and lion communication is clearly of a lower degree than that which is
known to occur amongst humans, other eusocial insects and perhaps some primates
(other primates are in the second level of communicative complexity). In this kind of
communication, the third and final level, the information which is communicated is again
structured in a more complex way. Instead of its semantic content being immediately
present the communication can refer to (for example) possible events, events which
happened in the past, objects out of sight of one or more of the parties in the
communication (e.g. honey bee flower location dances) or abstract and non-physical
entities.
Tangenting briefly, it has been observed that the discrete degrees selected could just be
elements plucked from a continuum. I have no strong opinion on what the underlying
nature of communicative complexity actually is though, and I don’t think I need to. While
it may be the case that it is a continuum it also seems to me that the three degrees selected
at least form the centres of quite significant “clusters” of many organisms’ levels of
communicative complexity. If we conclude that there is in fact a continuum here this will
not change the fact that most communication appears to clump around the three degrees
discussed above and that they provide useful initial starting points in measuring
complexity. Relative rankings can be done (as they were for lions and the simpler
eusocial insects, above) as needed and as described in more detail for phenomenological
fidelity.
As with McShea’s hierarchical approaches and flexile complexity comparing within a degree is very
difficult – in large part I claim because this is an area which is potentially dangerously subjective and
anthropomorphic. In addition, the ability to objectively ground a measurement of an organism’s complexity
has been lost, as it was for perceptual complexity. I will discuss this point in more detail later.
13
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Assessing whether or not a species actually truly belongs to the third level or is instead a
complex member of the second, and whether a fourth (or fifth or…) level exists are
thorny questions. The former can probably be addressed by very carefully structured
psychological experiments which aim to be as anthropomorphically distant as possible.
The theoretical possibility or impossibility of a fourth-plus level (the second question)
may be answerable with deep thought or it may be fundamentally beyond the cognitive
capacities of the human brain to answer. In any case, we possess the ability to judge into
which level we think each species falls, and it is unlikely any species will be in the
elusive fourth-plus level. If it were it would surely obviously fit in the third level and it
would probably also (in some way) seem smarter or a better cooperator than us14.
Environmental Complexity
Environmental complexity is the most difficult form of complexity to measure in a
species-neutral way. There is a significant degree of risk that any conclusions we draw
will be anthropomorphically biased (Rivas & Burghardt, 2002). Thus, moving carefully, I
think the initial decomposition regarding an organism’s environmental complexity is to
break it into the two fundamentally different elements which comprise it – complexity
with respect to the way it interacts with the environment and with members of other
species which don’t react back (e.g. birds and most trees), and complexity with respect to
the way it interacts with other species which do react (static complexity and interactive
complexity, respectively).
Interactive complexity, as with communicative complexity, is divisible into three simple
degrees. The simplest way in which a member of one species can react to a member of
another is precisely that – to simply react. It may eat it or flee from it or (as will be the
case for the vast majority of species) simply ignore it.
The most complex way members of different species have been known to interact is
through prolonged symbiosis. Ant (and human) farming of aphids (and cattle,
respectively) are examples of this kind of symbiosis. In this situation each species, to
some extent, specialises further and members of the two species mutually exploit. Does
this prolonged symbiosis necessarily contribute equally to the interactive complexity of
both of the symbionts? No – if one can survive without the other then the “symbiosis” is
more like exploitation in which it benefits the exploiter to keep the exploitee in an
optimal state for at least some period of time. Human exploitation of cattle is definitely
an example of this. On the other hand maybe one (or both) of the species has its fitness
partially but not absolutely reduced without the other. The symbiosis/exploitation
relationship is thus a continuum and it is along this continuum that within-degree
comparisons could be made. It is possible that the exploitee may actually be at the
fight/flee degree. Such a situation would have to be evaluated on a case-by-case basis and
very carefully, so as not to bow to human anthropomorphism.
Intriguingly – and not a point I’m going to investigate in this essay – does this mean that we can’t rule
out eusocial insects and other super-organisms as communicating at the fourth level? Do you have to
communicate frequently at the n-1’th level to be judged to communicate at the n’th? Although flower
dances are a form of 3rd degree communication they happen with much less frequency than 3 rd degree
human communication (“what are you going to do today”, “where have you been”, etc ad infinitum) – just
as humans exhibit 1st and 2nd degree communication much less frequently.
14
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The second level is the mid-point of these two levels – namely sporadic symbiosis in
which there is no prolonged relationship. Such a situation occurs with an Egyptian Plover
bird and a crocodile. A particular crocodile or Plover bird, or group of crocodiles or
group of Plover birds, do not in any way “team up” over a prolonged period of time. A
crocodile and Plover will only interact a second time if they happen to remain in the same
spatial area. This is hardly sufficient for the relationship to constitute prolonged
symbiosis, rather than repeated one-off symbiosis!
Finally, it might seem that fight/flee/ignore should actually be fight/flee and ignore – that
is, separate levels, with the lowest being for an organism to not react at all to a member of
a different species. However this is likely due to perceptual simplicity or the irrelevance
of members of that species to the fitness of the organism whose complexity we are
evaluating. In the former case the complexity (or lack thereof) will have already been
taken into account and in the latter it has no bearing on an organism’s interactive
complexity.
Static complexity is the extent to which a species engineers its environment. Excluding
epistemic engineering (to avoid over counting with flexile complexity) a species niche
constructs (Sterelny, 2003, p1) to achieve one or more of four goals – to help it catch
prey (a spider web), to help it avoid predators (Dawkins, 1982, p200), to improve its
reproductive fitness (as “dummy nest” building birds do) or to aid in resource gathering
and protection (a bee hive). However if we were to try and measure complexity by
measuring each of these we would create an over complicated model which overlapped
with itself to too great an extent. Therefore we need to look deeper, for some common
element to all of these tasks.
A range of possible approaches to this problem exist. Some of the immediately obvious
ones include the size of the structures constructed relative to the size of the organism, the
number of generations the structure persists, the number of organisms which use a
specific structure and how much time is invested in either creating or using the structure.
We can dismiss the idea of using relative size though, as it seems to me that human
artifacts (such as microprocessors and other electronic equipment) show that there is not
necessarily a positive relationship between size and complexity. Similarly, larger objects
are often more complex than smaller ones (compare an ant colony to the hole dug by a
mud daubing wasp!). This means there is not a consistent negative relationship either.
Hence, using relative size will give inaccurate results. For similar reasons and using the
same or similar counter-examples we can dismiss measurements based on the number of
generations the structure persists for, the number of organisms which use it and the time
invested in creating it. Human mass manufacturing must surely immediately show the
latter to be particularly problematic!
Thus, as with spatial complexity, I think we need to examine the degree of nesting and
individuation of the structures engineered by a particular species. Implicit in this model
(as with spatial complexity) is the assumption that complexity exists for a reason, i.e. it is
either adaptive or is an adaptation.
An example of an application of this approach is that of bird nests. At the simplest level
of niche construction amongst birds we find scrape nests, created by a range of species,
which are depressions scraped (or found) in the ground, perhaps with a few stones added
haphazardly (Ritchison, 2005). Such nests are at the lowest level of complexity (1a): they
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are composed in an unstructured way of undifferentiated parts which are themselves not
structured hierarchically. On the other hand the nests of the small passerine (Sterelny,
2003, p3) and Horned Lark (Eremophila alpestris) (Ritchison, 2005) are much more
highly structured. While the parts they are composed of are still themselves lowest level
parts they are often of several types, carefully selected and specifically arranged, to
camouflage the nest against predators or to shelter it from the prevailing wind. These
nests would be level 1c. Human habitation, on the other hand, is composed of at least two
or three levels of nested parts: There are several types of room, which maybe could be
considered to be organised in a structured hierarchy. Each room is of course composed of
the structural elements and the functional furniture, each of which is also composed of a
nested hierarchy of parts: a wall is made up of beams and plaster and maybe paint or wall
paper. A beam is wood, but it is also (deliberately) made of rivets and other joiners – thus
human habitation seems to be level 3b or 3c.
Of course, this model allows potentially incorrect conclusions to be drawn as well – for
example, that some specific members of a species are more complex than other members
of that species. However this problem can only occur if environmental and circumstantial
contingencies are ignored. To say that a specific Horned Lark is less complex than
another because there is insufficient construction material available for it to build a shield
against the wind is a weak argument.
In addition, another problem may appear to exist with this approach to measuring static
complexity. Static complexity and the communicative complexity appear to causally
bracket task complexity (Anderson, Franks, McShea, 2001). By this I mean that task
complexity is entailed by communicative complexity, and it might appear that static
complexity is entailed by task complexity. This is particularly so since much niche
construction may be done in groups or teams (crucial to task complexity). If task
complexity is entailed why isn’t static complexity?
Before explaining why task complexity does not entail static complexity though I think it
is important to first describe task complexity so that McShea, Franks and Anderson’s
paper (2001) does not need to be immediately referred to. Task complexity is a method
for measuring “the degree of cooperation and coordination required for successful task
completion, based upon the deconstruction of a task into its component tasks and
subtasks” (ibid, p644, quoting Anderson, Franks, 2001).
Tasks are divided up into three types. They can either or only be completed individually.
This is the simplest level of task complexity. Alternatively, they may be group tasks. In a
group task all individuals carry out the same process, “crucially though, individuals must
work concurrently or the task cannot be completed” (Anderson, Franks, McShea, 2001,
p644). This is typically because there is some threshold or tipping point (even a literal
one) before which the efforts of the individuals have no effect. The food item (for
example) may simply be unmovable by one individual alone. It is noted that parallel
work (where each individual carries out the same task, such as all feeding a different
larva at the same time) does require coordination but that it does not qualify as a group
task because any one individual can still carry their instance of that task to completion by
themselves. Thirdly and finally, tasks may be team tasks. Such a task requires that two or
more different sub-tasks are carried out simultaneously in order for the overall task to be
achieved. Alternatively (and judged to be just as complex) the tasks may need to be
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carried out sequentially. An example of such a partitioned task is the collection, transport
and processing of some resource.
I will now explain why the causal flow outlined above (communicative → task → static)
might be suggested, but also why it breaks down and specifically why it breaks down
between task and static complexity but not between communicative and task complexity.
The reason for this is relatively simple. While it is undeniable that task complexity
requires communicative complexity – you cannot have a significant degree of team work
without communication of some kind! – and is therefore entailed by it, it is also
undeniable that you do not need communication in order to have a complex impact on the
physical environment. After all, many organisms can create complex static structures
quite successfully individually, even if they do communicate with others some of the
time. Bird nests are an ideal example of this – if there is any teamwork then each member
of the team carries out the same tasks as the other members, meaning bird nest
construction has the lowest possible task complexity. Intuitively though the nest of a
Horned Lark seems much more complex than that of a sea gull, even though only one
lark is involved in the construction of its nest (Bent, 1942 and Sutton, Parmalee 1955).
Therefore, to create an as complete, accurate and independent measure of complexity as
possible we need to appear to bracket task complexity in this manner.
Conclusion
Let’s summarise the state of play and any problems this system has. A system which can
measure a species complexity across eight dimensions has been built. These eight factors
cover the intuitive definition of complexity in a fairly complete and independent manner.
Morphological (spatial and temporal) complexity is accounted for, as is the wider
functional impact in terms of perceptual (breadth and fidelity) complexity. Behavioural
complexity at the individual or species level (flexile and communicative) and at the wider
environmental (static or interactive) can also be measured using this system.
Actual measurements for any one factor are carried out using one of four techniques.
Spatial and static complexity can be measured using the McShea/Changizi hierarchical
approach. Communicative and interactive complexity are measured in degrees, and
temporal complexity and phenomenological breadth are simply counted. Flexile
complexity and phenomenological fidelity are measured in orders. Measurement using
any one of these techniques is relatively easy and is as objective as possible.
There are two key problems this system has not addressed though. The first of these is a
result of the inherent subjectivity in the term complexity, and it is a lack of what I term
“grounding” for many of the factors, discussed briefly already in the context of
phenomenological fidelity. Grounding is simply the process of attaching a unit and zero
or minimum level to a measuring system. When this is done measurements in that system
are scalar and are also probably continuous. For example, because mass is measured
using a scalar system in which the concept of 1 and 0 grams is meaningful, we can say
that one kilogram is twice as heavy as 500 grams. In addition mass is continuous (at least
to the level of sub-atomic particles): between any two levels of mass you can always find
another, intermediate level of mass. Low level physical phenomena like mass are
relatively easily grounded, at least at the macroscopic level. Any grounding of a system
which measures complexity would be arbitrary though. This leads me to question the
utility of being able to say “this species is three complexiles simpler (given our arbitrary
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definition of one complexile and zero complexiles)” and consequently the significance of
this problem.
The second is a consequence of seeking as much independence between elements as
possible. Because of this we cannot say that one species is more complex, overall, than
another. While we certainly can trade off and compare complexity in different
dimensions each such trade off will have to be done on a case by case basis. Ensuring that
these trade-offs retained species-neutrality might be quite difficult. In any case, this is not
the focus of this essay. As a result, when using the system as it has been described here it
is simply not possible to say that a liver fluke is more complex than a honey bee.
However, this negative aspect is not particular to this system, as it is an inherent problem
in our general definition of complexity and therefore in any attempt to systemise it. With
this general definition we clearly feel we can say one organism is absolutely more or less
complex than another, and we also feel that there are multiple independent elements
which contribute to this complexity orthogonally. These two positions are simply not
logically reconcilable – no matter how hard you try, you cannot translate a two
dimensional space into an equally expressive one dimensional space without making
some dramatic assumptions, assumptions which tend to invalidate the translation15. Given
this conundrum I have elected to develop a system which measured complexity as
completely as possible, at the cost of some simplicity. Wimsatt’s discussion of
complexity (1972) in fact suggests that a meaningful overall comparison cannot be made.
Excluding the trivial and rare case where one species is more complex than another on
every dimension he may well be right (although this question cannot be investigated in
this essay).
With that I will draw this essay to a close. A few contortions have given us a system that
is as species-neutral as possible. Provided we compare apples with apples we can make
meaningful comparisons of organisms’ complexity. The danger of over-counting has
been examined, and the difficulty of measuring complexity at a very fine level has been
discussed16. The importance of completeness and independence (or orthogonal
dimensions) in the type of system we have developed has also been stressed.
15
Just try finding some way of translating all two dimensional positions in some plane into positions
(which retain their relative magnitudes and positions) on a one dimensional line!
16
Some of the “apples” want to compare could be made more fine grained. This is clearly outside the scope
of this essay, although some possibilities were hinted at, e.g. in interactive complexity.
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