October 20, 2011 § Leave a comment

Usually, growth is something “very” natural for us.

We assign growth to natural things, or at least to those things that we could accept as being quasi-natural. Examples for things that grow are plants, animals, but also cities, economies, or even mathematical structures like groups.  Cars, bridges, books and tools, but also symbols or words belong to things that—according to our expectations—do not (read: shall not) grow. While architectural laymen frequently tell that buildings grow, an architect in charge would never do so. We also are used to say that the amount of something, for instance data, is growing, but we do not speak about data itself as a growing entity. Would machines, technical artifacts, or abstract entities start to grow on itself, we’d soon feel deeply terrified. Just think about the topic of swarms in literature [1,2], the Golem saga and its modern equivalent, the Terminator.

Obviously, we use the concept of growth willingly in those cases where we do not have control over the entity, which is changing its morphology. Likewise, in all areas were we pretend to have the power to control we usually avoid to invoke growth as a concept. We usually expect that we should have complete control over machines, whether made from steel, silicon or symbols. If something we depend on is actually growing, we soon start to think about replacing “growth” by plans, building, constructing, cloning etc. This is true for cities, animals or plants, and even for the daily traffic swarms. There is also the phantasm of everlasting growth in certain flavors of capitalism, or the pessimistic expectation of Limits of Growth [3].

An interesting ambivalence to growth and control is taken by the concept of breeding, which is a successor of domestication. Breeding is an interesting play about variability and the associated surprise on the one hand and control on the other. Extending Heidegger’s notion of the Gestell, or also of “gestellt sein,” that he created to describe the relation of humans, or human culture, and technology, Peter Sloterdijk coined the concept of the “Menschenpark” as a kind of self-directed breeding.

Yet, the inherited standard language game about growth that is merely related to the controllability of morphological change is not only terribly outdated, it is primitive, inadequate and even dangerous, since it is creating quite extent blind spots. The problem with the usual form the game is that it is too representational, and by far not abstract enough. Our investigations will reveal that growth is just another name for a special flavor of differentiation. Later we will see (in the context of a theory of the Urban) how we may generalize both into what then we will call generic differentiation. Generic differentiation comprises four perspectives: growth, networks, associativity and complexity and also plays an important role by resolving the puzzle of theoreticity.

Since our envisioned epistemic machines shall not refer to explicitly programmed capabilities, these systems have to acquire new capabilities, in other words, they have to differentiate. If we do not understand these concepts of growth and differentiation on a very basic level, the system we are going to build will never be intelligent in any respect. Actually, what we need to build adaptive machines is an explicit and general theory of growth, which also would be a general theory of differentiation.Of course, we can not develop the whole theory here; yet, we may try to indicate some directions.

As it holds for all theories, this theory must be able to serve as a milieu for deriving—if not to say: growing—models. Such a general theory should thus not be restricted to a particular discipline. Only without disciplinary constraints we will be able to transfer the concepts into the field of epistemic machines and to investigate aspects of growth and differentiation with respect their adaptivity.


It is rewarding to check the neighborhood of the concept of growth. If something is growing we often also assign the notion of development. Development also has to do with  control, yet, in this case the control could be not only imposed to the entity, the control could be also a part of the entity itself. We say, that during ontogeny an organism develops. It changes its setup, concerning the morphology, the processes it is hosting, the internal relationships, and also its power and potential. Despite development takes place in exchange with the environment, the result is entity that clearly belongs to a particular class.  Caterpillars develop into butterflies, despite their morphology, internal organization and power gets drastically changed on the way. More important, the changes themselves belong to a particular class that we can identify as a set of orchestrated mechanisms. In short, their is an instance that we can call a plan. Indeed, biologists speak about the Bauplan typically for classes of organisms.

The transindividual change of morphology, power and potential of entities we usually call evolution. In contrast to development, evolution does not follow a plan, albeit their is are principles and tendencies. Evolutionary processes are the only class processes that is able to establish novelty. In that it is closely related to complexity, as we will see elsewhere. Evolutionary processes and complexity are thus also mandatory ingredients for any entity that is able to adapt to its environment. Particular forms of learning can be explained only through basic evolutionary processes, as Edelman demonstrated in 1993 [4].

Hence, some forms of learning, namely structural learning, may also be conceived as a relative of growth. The adaptation of an entity to its environment in order to tune its responses and actions upon the environment requires at least a differentiation regarding its modeling capacities. It is thus not surprising to find an intensive trace of the concept of growth in the early pragmatists, namely Charles S. Peirce [5] and John Dewey [6]. Particularly the latter linked growth to learning and education. According to Dewey, growth can be conceived as the characteristic of experience wherein experience itself expands in richness. Yet, Dewey’s philosophical approach is restricted to human development. Peirce’s account, on the other hand, trying to invoke a whole cosmology, is too anthropomorphic as to be stable enough for its general claim. What we can see though is that it is reasonable to search for a general theory of growth.

Modes of Growth

Let us start with a small cartography of growth phenomena in nature.

We may distinguish :

  • – mineralic growth
  • – growth of coordinated swarms
  • – plant like growth
  • – animal like growth
Type Description
mineralic growth by accretion, the main example is given crystals, but also models of ligtnings, can be fractal, but often is also not;
coordinated swarms slime molds, traffic networks, social insects; the main principle is positive feedback, sometimes supplemented by negative forces, thereby establishing a kind of reaction-diffusion-system. The transition from order to organization is almost unregulated and mostly contingent.
plant-like growth is taking place almost exclusively at very limited areas, the meristeme, which consists only of a few cells. Differentiation is completely outward directed, i.e. new tissue appears always at the outside of the organism. Else, differentiation is regulated by a small set of counteracting hormones or regulation (e.g. auxin), which rules the branching and the setup of new leafs. This type of growth is largely the consequence of strong cell walls. Connectivity of cells is rather low and often outside the cells, cells are largely autark; due to these principles, plant-like growth has a strong tendency towards fractal growth.
animal-like besides ordinary growth by cell division (mostly actively coordinated), further principles are melting (destroying) and folding of tissues. This leads to an extremely variable and rich inner organization of the organism. The connectivity of animal tissue can be very different, from freely floating (immune system) to plant-like fixation (bones). Often, the cells are representatives of the connection itself (any kind of mesenchymatic fibres cells, neurons with axons)

We now may take a step away from the factuality of the described phenomena,  taking these modes of growth as abstract, structural templates. If we’d go abstract, we also would have to change our language. We then have to speak about relations and information, and about the dynamics unfolding in this abstract space.

Abstract Growth

In abstract space, we do not have to follow inherited constraints like organisms have to do. Animals can not grow like crystals, and rarely like plant. Also they have to maintain a well-defined and stable outer hull, at least the animals that we know from this earth.

As we have already mentioned above, growing does not only mean that the entity is becoming bigger. Usually, the entity also differentiates along with growth. Differentiation is more easy for larger organism, at least if they achieve a certain minimal size. Yet, if we compare plants and animals regarding the style of their growth we see that plants usually grow to the outside, while animals differentiate to the inside. During development, the system of blood vessels grow in a way that resembles to plant growth, despite the mechanisms are completely different. We have also seen that inward-directed differentiation is strongly based on an orchestration of unfolding and melting.

A common denominator of outward-directed growth and inward-directed differentiation is the creation of dedicated signal horizons, establishing thereby compartments. These compartments are also often instantiations for a particular “excitability” through the differential expression of a particular blend of receptors, e.g. for a particular hormone. Organs as representatives of particular functions are usually established through the placement of particular receptors.

In animal tissue this play between population of receptors and the anonymous “mass mailing” viz. secretion of hormones into the blood stream determines the condition for the operation of “sending” a message. “The” message is sent without attaching the address to it. Actually, we can not speak about a single message, since the “messenger” consists of a large population of really dull particles.The specificity of the message is established by a selective recoding into a differential materiality, which takes place on the surface of a particular organ, or tissue. In other words, in organisms there is no such thing as a single sender, a message in an envelope, a messenger, and a single receptor. we always will find populations. We suppose that this is not only true for the endocrinological system, but also for the data processing systems of a biological body. Furthermore, we consider this design principle as essential for the possibility of growth and differentiation, even if it comes to largely immaterial phenomena like learning.

In plants, there is rarely such a regulation through tissue-specific populations of receptors. In plants, it is mostly simply the distance between the areas which establishes a difference in the cocktail of anonymous messages. The reason that the flower is at the tip of the plant is just that it is at the tip of the plant: far away from the stem and even farther from the roots (exception: cauliflory in cacao).

In both cases, however, the result can be described as a qualitative change in the graph that links tissue apart from each other, let it be due to distance or due to compartmentalization. In abstract growth, complicated arrangements of compartments can be replaced by upend the inner structure to the outside. Since in the abstract space there is no such thing like mass, distance and code release almost the same effect: it establishes a signal horizon, or more appropriate, a signal intensity length.

The “goal” of abstract growth could be described as creating an assemblage of various specializations (regarding the power to transform), linked by a whole bouquet of signal intensity lengths. This “bouquet” need not to be a continuous or smooth distribution.

Growth in Software Systems

These results we will now try to transfer into the domain of “software.” The question is:

How can a software-based system grow and/or differentiate autonomously?

Usually, software “grows” by writing code. As the use of the term “growth” already indicates, the development of software (admittedly also a common term in this context) is often a process, where the author does not have full control about it—irrespective the particular reason for that in a given case—, or if there are several programmers in a project rules at lest partially from the outside.

Anyway, somebody has to sit down in front of a computer that is equipped with an editor and a compiler for the programming language in use; then this person has to write code using this programming language. Self-programming computers have been an old dream of countless computer engineers since the inception of computers. Yet, for a particular reason not unknown to philosophers of language they did not succeed: it’s all about semantics and meaning, despite the fact, that computer programs are just “code.” Note that the failure has nothing to do with the impossibility to proof the correctness of software.

At this point we would like to switch the perspective. Instead of talking about programs and code, we will try to use the concepts of mechanisms and functions. Why should be perform such a move? It is pretty clear that a fully deterministic program will not extend its capabilities, even not if it is in contact to and exchange with its environment. What we are striving for is differentiation, even it is a kind of induced differentiation. The above question then can be extended: How should a software-based machine be arranged, or dealt with, such that it is justified to talk about mechanisms?

The first thing is that differentiation does not imply writing code. If we as humans learn, we do not invent new types of neurons all the time, or new ways to encode information, etc. These basic principles are pretty constant. Trying to write software programs that write software programs is much like creating a god which creates other gods. Even in ancient Greek mythology the primary gods (titans) had do die first…

Which mechanisms are available to extend the power of a given machine, whether it is an organic machine like a bacteria, or a Nematode, or one that is based on software? Interestingly enough, by just asking that it becomes clear that in the case of epistemic machine software takes a similar role like the matter in the case of worms. This also opens a highly interesting route for further investigations.

Back to the question of extending mechanisms: Again, nature provides a nice structural template. In order to find this, we have to take some steps into evolutionary biology. In the evolution of any kind of organism, at least here on earth, duplicating arbitrary partitions of “code” in the DNA seems to be the core mechanism. A famous case is the evolution of Cytochrome C, starting from mono-cellular organisms up to mammals like humans. Partitions on the DNA are not just whole genes, in the context of evolution it is just arbitrary, which snippet is getting duplicated. While the original part still continues to work as selected, the new part does not bear any functional role at all. Of course it could to just the same as the original. This strategy is taken often in those cases where the cell (or: organ, organism) needs a high metabolic power. No, the evolutionary significance of gene doubling is that the duplicate parts are free to be changed without endangering the survival of the whole thing. The principle of duplication followed by functional alteration is also deeply built in into the Bauplan of insects and mammals as well, known as metamericity. And finally, the evolutionary history of our brain knows a quite similar principle, known as “Überformung,” a transformation based on pullulation and equipped with functional shifts and differentiations. The morphological parts of the brain we use for smelling serves the rat as associative cortex for “abstract” reasoning.

All what we have to do then in order to get a growing machine is to find the right level of integration that is suitable to serve as a metamer (be sure we have a good candidate for that). Of course, for establishing appropriate signal intensity lengths the other principles of growth may be useful as well.

  • [1] Michael Crichton, Prey.
  • [2] Frank Schätzing, Der Schwarm.
  • [3] Dennis Meadows, Limits of Growth, Club of Rome, 1973.
  • [4] Gerald M. Edelman, 1993, Neural Darwinism: Selection and reentrant signaling in higher brain function. Neuron 10(2), 1993, p.115-125.
  • [5] Michael Ventimiglia (2008), Reclaiming the Peircean Cosmology: Existential Abduction and the Growth of the Self. Trans.C.S. Peirce Society: A Quarterly Journal in American Philosophy – Vol.44, No.4, pp. 661-680.
  • [6] John Dewey, “The Postulate of Immediate Empiricism” in: Jo Ann Boydston (ed.), The Middle Works of John Dewey 1899-1924. vol. 3. Southern Illinois University Press, 1977.



Leave a Reply

Fill in your details below or click an icon to log in: Logo

You are commenting using your account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

What’s this?

You are currently reading Growth at The "Putnam Program".


%d bloggers like this: