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Journal ArticleDOI

A Category Theoretical Argument against the Possibility of Artificial Life: Robert Rosen's Central Proof Revisited

01 Jan 2006-Artificial Life (MIT Press)-Vol. 12, Iss: 1, pp 117-134

TL;DR: The essence of Rosen's ideas leading up to his rejection of the possibility of real artificial life in silico are reviewed and the conclusion is that Rosen's central proof is wrong.

AbstractOne of Robert Rosen's main contributions to the scientific community is summarized in his book Life itself. There Rosen presents a theoretical framework to define living systems; given this definition, he goes on to show that living systems are not realizable in computational universes. Despite being well known and often cited, Rosen's central proof has so far not been evaluated by the scientific community. In this article we review the essence of Rosen's ideas leading up to his rejection of the possibility of real artificial life in silico. We also evaluate his arguments and point out that some of Rosen's central notions are ill defined. The conclusion of this article is that Rosen's central proof is wrong.

Topics: Argument (53%), Artificial life (52%)

Summary (3 min read)

1 Introduction

  • One of the stated goals of artificial life is the implementation of living systems in silico and their simulation over an entire life cycle [5].
  • So far this undertaking has been at best partially successful.

2 Models

  • In this section the authors will introduce Rosen’s notion of synthetic and analytic model.
  • Rosen focused his discussion entirely on models; he largely avoided writing about systems.
  • The reason for this is that as observers the authors do not have direct access to real systems in the physical world Q1 Artificial Life Volume 12, Number 12 A Category Theoretical Argument against the Possibility of Artificial LifeD. (the Welt an sich).
  • Throughout the remainder of this article, the word ‘‘system’’ will always refer to formal systems unless explicitly stated otherwise.
  • An exhaustive discussion of this topic would of course go beyond the scope of this article; the reader who wishes to explore category theory in any depth is referred to textbooks [19, 10].

2.1 Categories

  • Objects (sets, or anything else; in their case: models).
  • For every object X, an identity morphism idX. !.
  • In the simplest case, the objects of a category are sets and the morphisms are mappings between the sets.
  • Throughout this article the concept of duality will not be explored in any depth, but it will be used to indicate relations between definitions and categories; specifically, the concepts of direct sum and direct product are dual; the reader might compare the definitions in Figures 1 and 3.
  • The reason the direct product and sum need to be introduced here is that Rosen essentially identifies them with analytic and synthetic models respectively.

2.2 Analytic Models

  • While the concepts of analytic and synthetic model are crucial to the entire argument, Rosen only hinted at a mathematical definition.
  • Rosen’s notion of model might to some appear somewhat counter-intuitive at first.
  • Not only might it be that the observables used are inaccurate, measuring the system only crudely; it might also be that the set of observables used is not sufficient to give a full description of the system.
  • The objects of the category are the models, and the morphisms are the refinement relations between them .
  • The mutual refinement of two models that are based on unlinked observables is formally the direct product in the category AðSÞ.

2.3 Synthetic Models

  • The second kind of models are synthetic models.
  • The poset has exactly one top element, that is, one element that is not itself included.
  • Like analytic models, synthetic models also form a category, YðSÞ .
  • The state space of the compound system is fourdimensional, describing the momenta and the positions of both particles.
  • Also, the process of taking the direct sum of analytic models is a purely syntactic (or algorithmic) process.

2.4 Relation between Analytic and Synthetic Models

  • Rosen defines mechanisms as the class of systems of which all analytic and synthetic models are equivalent; according to Rosen, this is the case when direct product and direct sum coincide.
  • Artificial Life Volume 12, Number 18 A Category Theoretical Argument against the Possibility of Artificial LifeD. Chu and W. Kin Ho.
  • Not every analytic model is a synthetic model.
  • Firstly, the authors assume that subtrees in the category of analytic models are always disjoint.
  • Replace all linear branches in AðSÞ with the most refined model in the linear branch.

2.4.1 Analytic-Synthetic Means S Is Defined on a State Space

  • It is straightforward to show that for all state-space-based systems S, analytic and synthetic models will always be equivalent:.
  • Thus there are a finite number of unlinked observables that specify the system completely; this in turn means precisely that the systems is defined on a finite state space.
  • In Life itself, Rosen makes the connection between the equivalence of synthetic and analytic models and the equivalence of direct sum and direct product.
  • Since the concepts of direct product and direct sum are dual to each other, the following is always true:.
  • This, however, does not translate directly into a theorem about the equivalence of analytic and synthetic models, because, as the preceding discussion has made clear, the relation between synthetic and analytic models is only partially a relation of duality:.

3 Mechanisms and Machines

  • In this section the authors will now finally define the notion of mechanism.
  • Mechanisms are an important class of systems, because Rosen defines them as the class of systems that are simulable; the question whether life in silico is possible is thus essentially the question whether or not at least some living systems are mechanisms.
  • Thus, all mechanisms can be exhaustively defined as state-based systems.
  • The best way to convince oneself that Turing machines are indeed mechanisms is to consider implementations of Turing machines in cellular automata (such as in the Game of Life [1]).
  • F0; 1g k Rosen points out that models of machines in terms of states are not particularly instructive, and introduces an alternative representation, so-called relational models .

4.1 The Proof

  • Or more precisely, that the relational model in Figure 7 cannot be reconstructed from a state description.the authors.
  • The authors would now like to know whether it is possible to recover the original component f from this state description; more specifically, Artificial Life Volume 12, Number 1 13 A Category Theoretical Argument against the Possibility of Artificial LifeD.
  • Let us consider two possibilities: Continuing the argument will lead to no closure.
  • According to Rosen this possibility is not compatible with the assumption of a machine.
  • In the context of machines, where synthetic models are equivalent to analytic models, one would expect that ‘‘functions are always localized into corresponding organs’’ [23, p. 212].

5 The Concept of Implementation

  • There are two main possible criticisms of Rosen’s proof.
  • This requirement of localization says that in machines the authors can at any time precisely specify which parts of the system implement a particular mapping and which parts do not.
  • In the next few paragraphs the authors will explain this in more detail.
  • While that may be true, the authors will now show that even in machines those properties are not compatible.
  • Because all he has shown is that closed systems share this property with machines; this does not tell us whether or not closed systems are mechanisms; thus the authors still do not know whether artificial life in silico is possible.

5.1 Syntax and Semantics

  • The discussion in the last section indicated already that there is a problem with the notion of the implementation of a mapping.
  • It can thus acquire new properties from the larger system with which it associates.
  • From the above quotation it seems that the concept of a mapping and its implementation are semantic; this does not fit very well with the idea of a mechanism as an inherently syntactic system (syntactic in the sense that all aspects of the machine can be derived from the complete description of its parts).
  • It is in this context that one often observes that components acquire new properties that also might change according to the context.
  • Relational models might be valuable in certain contexts to describe both machines and organisms, yet in the context of Rosen’s ‘‘proof ’’ they are misplaced.

6 Discussion and Conclusion

  • The authors have mainly concentrated on a comprehensive outline of the mathematical concepts to clarify the mathematical background of the most important notions underlying Rosen’s work.
  • The main conclusion of this is that relational models rely on an understanding of the system and its context and function, while state-space-based models only reflect purely formal aspects of systems.
  • Biologically important notions, such as ‘‘function’’ (an inherently semantic concept) can therefore trivially never be recovered from such descriptions.
  • The authors believe that Rosen’s circles of ideas contain valuable contributions to those big questions, and their reevaluation will help to bring us closer to an understanding of life and artificial life.

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Citation for published version
Chu, Dominique and Ho, W. (2006) A Category Theoretical Argument Against the Possibility
of Artificial Life. Artificial Life, 12 (4). pp. 117-135. ISSN 1064-5462.
DOI
https://doi.org/10.1162/106454606775186392
Link to record in KAR
https://kar.kent.ac.uk/14519/
Document Version
UNSPECIFIED

Author proof---not final version!
A Category Theoretical Argument
against the Possibility of Artificial
Life: Robert Rosen’s Central
Proof Revisited
Dominique Chu
Computing Laboratory
University of Kent
Canterbury
United Kingdom
and
School of Computer Science
University of Birmingham
Birmingham B15 2TT
United Kingdom
D.F.Chu@kent.ac.uk
Weng Kin Ho
School of Computer Science
University of Birmingham
Birmingham B15 2TT
United Kingdom
W.K.Ho@cs.bham.ac.uk
Abstract One of Robert Rosen’s main contributions to the
scientific community is summarized in his book Life itself. There
Rosen presents a theoretical framework to define living systems;
given this definition, he goes on to show that living systems are
not realizable in computational universes. Despite being well known
and often cited, Rosens central proof has so far not been evaluated by
the scientific community. In this article we review the essence of
Rosens ideas leading up to his rejection of the possibility of real
artificial life in silico. We also evaluate his arguments and point out
that some of Rosens central notions are ill defined. The conclusion
of this article is that Rosen’s central proof is wrong.
1 Introduction
One of the stated g oals of artificial life is the implementation of living systems in silico and their
simulation over an entire life cycle [5]. So far this undertaking has been at best partially successful.
Several researchers have built computational systems that display lifelike behaviors. Very famous
examples are Ray’s Tier ra [21] and Adami’s Avida [2]; those systems consist of adaptive computer
programs that compete for limited resources, displaying interesting evolutionary effects reminis-
cent of living systems. Other examples of living systems in silico are Ono and Ikegami’s self-
assembling cells [18, 17], McMullin’s SCL model [3, 15, 14], and Rasmussen et al.’s self-assembling
lipid bilayers [20].
Probably the most famous of artificial life creatures is John von Neumann’s self-reproducing
machine [6, 7]. The center piece of this machine is the so-called universal constructora machine that,
given enough sup plies and a description of a machine D, can build D. Together with a control unit
that regulates the sequence of events and a description of all parts of the von Neumann machine, the
universal constructor is an essential element allowing self-reproduction of the entire machine (for an
in depth discussion of the intricacies of von Neumann’s design see [13]).
Those and many other systems show interesting lifelike behavior; nevertheless, few researchers
would call any of them ‘‘living.’’ It is widely acknowledged that the problem of research into artificial
life forms is not only of a technical nature (how to design an artificial organisms) but at least equally
of a conceptual nature: We do not know what life is; at least, we do not have a set of criteria that can
be applied to a given system to decide whether or not it is alive.
There have been some attempts to formulate a general theory of life. One of the best-known
approaches in this context goes back more than thirty years in time and has culminated in Maturana
n 2006 Massachusetts Institute of Technolog y Artificial Life 12: 1 18 (2006)

Author proof---not final version!
and Varela’s celebrated no tion of autopoiesis [25, 12]. An autopoietic system is characterized by two
main properties:
!
It is separated from its environment by a boundary.
!
It has an inter nal org anization that is capable of dynamically sustaining itself (including
its boundary); this internal sufficiency of the productional processes is often referred to
as closure [4].
While autopoiesis has had considera ble influence on various sciences (notably not including biolog y),
there is no stringent theory of autopoiesis that formulates its contents in an unambiguous way (see
Nomura [16] for an attempt).
A more mathematical approach to the topic, also emphasizing closure prope rties, is due to Robert
Rosen and is comprehensively laid ou t in his book Life itself [23]; also see [24, 22, 7, 8, 26, 9].
Rosens work defines a living system as closed with respect to ‘‘efficient causation.’’ This is often
understood to be roughly equivalent to the closure property of autopoietic systems [11]. However,
the two concepts are not identical. Maturana and Varela themselves illustrated the concept of
autopoiesis by means of a computational model [25]; this model has since been re-implemented by
McMullin and Varela [15, 14, 3]. Rosens central message, on the other hand, is precisely that closed
systems are fundamentally different from computing machines. Rosen takes one further step by
claiming that living systems cannot even be implemented in computationa l systems. If he were right,
this would mean that attempts to construct life in silico are futile. Altogether, Rosen’s central
conclusion is that life in silico is impossible.
A detailed presentation of the argument supporting his conclusion is laid out in Rosen’s book Life
itself; a central part of this book is a semi-formal proof for this assertion. Life itself was published in
1991 and has since attracted quite considerable interest, reflected in numerous citings of it. This
interest is not surprising, given that if the proof (and the conclusion) were correct, then this would
have deep implications for the field of artificial life and even our view and understanding of life.
Unfortunately, a clean assessment of the argument is hampered by the inaccessibility of Rosen’s
writing. Its free mixing of mathematical allusions, formal arguments, and comments on the history
and philosophy of science, in addition to poor editing, makes it very hard for the reader to distill the
essential argument from the text, let alone critically assess it. Rosens idiosyncratic style is not helpful
in this effort.
In this article we aim at two objectives. Firstly, we wish to clarify a number of concepts that are
essential for Rosens proof but not clearly presented by Rosen himself. In order to achieve this we
will (in Section 2) review the notions of synthetic and analytic models. Those concepts are central to
Rosens idea of machine versus living system, and thus essential for his central proof. An important
part of this section will also be to clarify the relations between those two models and certain concepts
from category theory. This relation is only hinted at in Rosens original work. Having clarified those
basic concepts of synthetic and analytic models, we will then go on to define ‘‘mechanisms’’ (and
‘‘machines’’) in Section 3. The notion of mechanism is of particular importance in that it is
coextensive with the set of systems that can be simulated in computers. In Section 4 we will recap
Rosens central proof stating that living systems are not mechanisms, hence not simulable.
The second main goal of this article is to give a critical assessment of Rosen’s central proof. We
will do this in Section 5, where we also show that Rosen’s own concept of machine is flawed. We will
provide a brief discussion and conclusion in Section 6.
2 Models
In this section we will introduce Rosen’s notion of synthetic and analytic model.
Rosen focused his discussion entirely on models; he largely avoided writing about systems. The
reason for this is that as observers we do not have direct access to real systems in the physical world
Q1
Artificial Life Volume 12, Number 12
A Category Theoretical Argument ag ainst the Possibility of Artificial LifeD. Chu and W. Kin Ho

Author proof---not final version!
(the Welt an sich). Knowledge about the real world is thus necessarily incomplete; at the very least,
whatever we know about real system s, we can never be sure what the status of this knowledge
actually is.
This diffi culty disappears when we restrict the discussion to formal systems instead; in con-
trast to real systems, formal systems are accessible. Throughout the remainder of this article, the
word ‘‘system’’ will always refer to formal systems unless explicitly stated otherwise. For all practical
purposes, thus, the notion of system is interchangeable with the notion of model, only that we tend
to use the word ‘‘system’’ to denote given formal systems and their very accurate models.
Rosens argument fundamentally rests on the distinction between two types of models, namely
synthetic and analytic models [23, 22]. The main purpose of this section is to introduce them and to
clarify their relation to certain concepts from category theory. Since we do not assume that the
reader is familiar with this branch of mathematics, we will give a brief introduction to some con-
cepts of category theory. An exhaustive discussion of this topic would of course go beyond the
scope of this article; the reader who wishes to explore category theory in any depth is referred to
textbooks [19, 10].
2.1 Categories
We start by defining the notion of category.
A category is a construct that consists of the following:
!
Objects (sets, or anything else; in our case: models).
!
Morphisms between objects; not every object needs to be the doma in or codomain of
a morphism.
!
For every object X, an identity morphism id
X
.
!
For each pair of morphisms f : A ! B, g : B ! C a composite morphism fg : A ! C.
!
Furthermore, we require associativity [( fg)h = f( gh)] and that morphisms can be
combined with the identity map (given a morphism f : A ! B, we have f id
A
= f and
id
B
f = f ).
In the simplest case, the objects of a category are sets and the morphism s are mappings between the
sets. In the more general cas e the objects might be anything, including categories themselves.
Categories are often graphically represented as points (objects) of which some are conn ected by
directed gra phs (the morphisms), usually indicated as arrows. The strength of category theory is that
it allows one to formulate relations between the objects and also relations between categories.
A pervasive concept in category theory is the idea of duality. Two concepts in category theory are
dual if one is like the other but with all arrows reversed. For example, if A is a category, then the
opposite category A
op
is A with all arrows reversed. A and A
op
are then dual to each other.
Throughout this article the concept of duality will not be explored in any depth, but it will be used to
indicate relations between definitions and categories; specifically, the concepts of direct sum and
direct product are dual; the reader might compare the definitions in Figures 1 and 3.
The reason the direct product and sum need to be introduced here is that Rosen essentially
identifies them with analytic and synthetic models respectively. The concepts of analytic and synthetic
model in turn are essential to the concept of mechanism the class of systems that can be simulated
in computers.
2.2 Analytic Models
While the concepts of analytic and synthetic model are crucial to the entire argument, Rosen only
hinted at a mathematical definition. The purpose of this section is to make the notion of analytic
model precise.
Artificial Life Volume 12, Number 1 3
A Category Theoretical Argument against the Possibility of Artificial LifeD. Chu and W. Kin Ho

Author proof---not final version!
Before doing so, however, we will briefly discuss the informal idea behind analytic models.
Rosens notion of model might to some appear somewhat counter-intuitive at first. A typical model
in science formulates a dynamic relationship between entities, as for example a differential equation.
Rosens idea of model is fully compatible with this conventional view, yet somewhat different in
emphasis. Instead of focusing on the dynamics of components of a system, a model in Rosen’s sense
is a certain way to measure properties of the system. Given a system S, an analytic model of S is a set
of observables that describe the system. Clearly, the quality of the description depends on the
accuracy with which the observables are measured. An observable that can have say, 100 different
values, is better, or at least of higher resolution, than an obser vable that can have only two values.
Increasing the resolution of an observable thus leads to a refined model.
Besides an increase of resolution of an observable, there is a second type of refinement: Not only
might it be that the observables used are inaccurate, measuring the system only crudely; it might also
be tha t the set of observables used is not sufficient to give a full description of the system. In this
situation adding a new observable will also refine the model. One might for example describe a car in
terms of its speed and the number of passeng ers it takes; this description would, in Rosen’s sense, be
a simple analytic model. Another model of a car would describe it in terms of its milage and how
much fuel it carries. Putting those two models together, thus describing the car in terms of speed,
number of passengers, milage, and fuel content, will give a more accurate picture of the state of the
car than either of the models and thus refine both of them.
For every system S there will usually be many different models that are in a partial order
relationship with each other, generated by the refinement relationships between them. Note that, while
models in Rosens sense do not explicitly take into account the dynamics of the system, the y never-
theless are complete descriptions of the system. This reflects the assumption that a complete de-
scription of a system at a specific time already determines all future behavior (although possibly only
in a statistical sense). In esse nce, an analytic model is a set of observables with a given resolution.
Formally, an observable is a mapping f from a system S (the system to be modeled) to a set
(usually R
n
). The observable f induces an equivalence relation on S: Two elements s
1
, s
2
2 S are
equivalent (s
1
" s
2
) if f (s
1
) = f(s
2
). The size of the equivalence classes thus indicates how well f
discriminates between states of the system; the smaller the equivalence classes, the better is the
corresponding observable. An analytic model M of S is the partition of S into equivalence classes
generated by some f.
One and the sam e system S will typically have many different analytic models corresponding to all
possible observables f ; those models will be related to each other and can be compared by the way
they partition S into equivalence classes. The relevant concept here is that of refinement: Given a
model M
1
, the model M
2
is a refinement of M
1
if all equivalence relations induced on S by M
2
are
subsets of the equivalence relations induced by M
1
on S. Intuitively, this means that M
2
can distinguish
between at least as many states of S as M
1
. Given two models M
1
, M
2
of S, those models need not be
in a refinement relation to each other, but may be unlinked.
1
This will be the case if the observables
measure unrelated aspects of the system. If there is no specific refinement relation between M
1
Figure 1. Direct product: If S, M
1
, M
2
are objects of the category C, then S is the direct product if we can find an
object X and morphisms k
1
: S ! M
1
, k
2
S ! M
1
, f : X ! M
2
, and c : X ! M
2
such that there is a unique morphism
u : X ! S. The direct product is a generalization of the familiar concept of the Cartesian product of two sets to arbitrary
categories.
1 It is an important technicality that observables and hence models may be partially linked. This is not of fundamental importance, though,
and will be ignored in the present discussion; the reader interested in this aspect is referred to Rosen’s discussion in [22].
Artificial Life Volume 12, Number 14
A Category Theoretical Argument ag ainst the Possibility of Artificial LifeD. Chu and W. Kin Ho

Figures (5)
Citations
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Journal ArticleDOI
TL;DR: This paper provides a critical review of the major assumptions which guide the development of modern computer science and engineering towards emulating biological systems and explores the potential and the virtues of biology to reshape contemporary science.
Abstract: This work is an attempt for a state-of-the-art survey of natural and life sciences with the goal to define the scope and address the central questions of an original research program. It is focused on the phenomena of emergence, adaptive dynamics and evolution of self-assembling, self-organizing, self-maintaining and self-replicating biosynthetic systems viewed from a newly-arranged perspective and understanding of computation and communication in the living nature. The author regards this research as an integral part of the emerging discipline of nature-inspired or natural computation, i.e. computation inspired by or occurring in nature. Within this context, he is interested in studies which represent a significant departure from traditional theories about complex systems and self-organization, emergent phenomena and artificial biology. In particular, these include non-conventional approaches exploring the aggregation, composition, growth and development of physical forms and structures, autopoiesis along with the associated abstract information structures and processes. This paper provides a critical review of the major assumptions which guide the development of modern computer science and engineering towards emulating biological systems. For this purpose, the author explores the potential and the virtues of biology to reshape contemporary science. The goal of this survey is to discuss the present state of natural and engineering sciences in the light of a necessary paradigm change in the structure and methodology of research and deliver some insights for developing a new kind of integral science based on the principles for dynamic interdependence of the constituting disciplines and on the evolving relationships among them.

72 citations


Cites background from "A Category Theoretical Argument aga..."

  • ...The formalization of autopoiesis and the engineering of living systems represent two non-trivial problems in modern science (Rosen, 1999; Chu & Ho, 2006; Nomura, 2007)....

    [...]

  • ...Although his proof was incomplete, Chu and Ho identified the importance of Rosen's idea....

    [...]

  • ...The author does not discuss the implications of Darwin’s indubitable contribution to biology, because a detailed review of this subject goes beyond the scope and the focus of this paper....

    [...]

  • ...Another category theoretical argument and revision of Rosen’s theorem was provided by Chu and Ho (Chu & Ho, 2006)....

    [...]


Journal ArticleDOI
TL;DR: The definition of life has excited little interest among molecular biologists during the past half‐century, and future advances, for example, for creating artificial life or for taking biotechnology beyond the level of tinkering, will need more serious attention to the question of what makes a living organism living.
Abstract: The definition of life has excited little interest among molecular biologists during the past half-century, and the enormous development in biology during that time has been largely based on an analytical approach in which all biological entities are studied in terms of their components, the process being extended to greater and greater detail without limit. The benefits of this reductionism are so obvious that they need no discussion, but there have been costs as well, and future advances, for example, for creating artificial life or for taking biotechnology beyond the level of tinkering, will need more serious attention to be given to the question of what makes a living organism living. According to Robert Rosen's theory of metabolism-replacement systems, the central idea missing from molecular biology is that of metabolic circularity, most evident from the obvious but commonly ignored fact that proteins are not given from outside but are products of metabolism, and thus metabolites. Among other consequences, this implies that the usual distinction between proteome and metabolome is conceptually artificial -- however useful it may be in practice -- as the proteome is part of the metabolome.

67 citations


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TL;DR: Within this framework, the advent of systems biology as a new and more integrative field of research is described, along with the form which has taken on the debate of reductionism versus holism.
Abstract: Reductionism has largely influenced the development of science, culminating in its application to molecular biology. An increasing number of novel research findings have, however, shattered this view, showing how the molecular-reductionist approach cannot entirely handle the complexity of biological systems. Within this framework, the advent of systems biology as a new and more integrative field of research is described, along with the form which has taken on the debate of reductionism versus holism. Such an issue occupies a central position in systems biology, and nonetheless it is not always clearly delineated. This partly occurs because different dimensions (ontological, epistemological, methodological) are involved, and yet the concerned ones often remain unspecified. Besides, within systems biology different streams can be distinguished depending on the degree of commitment to embrace genuine systemic principles. Some useful insights into the future development of this discipline might be gained from the tradition of complexity and self-organization. This is especially true with regards the idea of self-reference, which incorporated into the organizational scheme is able to generate autonomy as an emergent property of the biological whole.

63 citations


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TL;DR: It is shown here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation.
Abstract: A living organism must not only organize itself from within; it must also maintain its organization in the face of changes in its environment and degradation of its components. We show here that a simple (M,R)-system consisting of three interlocking catalytic cycles, with every catalyst produced by the system itself, can both establish a non-trivial steady state and maintain this despite continuous loss of the catalysts by irreversible degradation. As long as at least one catalyst is present at a sufficient concentration in the initial state, the others can be produced and maintained. The system shows bistability, because if the amount of catalyst in the initial state is insufficient to reach the non-trivial steady state the system collapses to a trivial steady state in which all fluxes are zero. It is also robust, because if one catalyst is catastrophically lost when the system is in steady state it can recreate the same state. There are three elementary flux modes, but none of them is an enzyme-maintaining mode, the entire network being necessary to maintain the two catalysts.

57 citations


Cites background from "A Category Theoretical Argument aga..."

  • ...A controversial aspect of Rosen’s analysis is his contention that a system closed to efficient causation cannot have computable models [11–14]....

    [...]


Journal ArticleDOI
TL;DR: While Robert Rosen's work is the main focus of this article, an attempt is made to advance a perspective for the broad field of studies that developed around the notion of anticipation, including the circumstances of epistemological and gnoseological significance, leading to the articulation of the early hypotheses regarding anticipatory processes.
Abstract: Anticipation relates to the perception of change. Therefore, dynamics is the context for defining anticipation processes. Since preoccupation with change is as old as science itself, anticipation-related questions go back to the first attempts to explain why and how things change. However, as a specific concept, anticipation insinuates itself in the language of science in the writings of Whitehead, Burgers, Bennett, Feynman, Svoboda, Rosen, Nadin and Dubois, i.e. since 1929. While Robert Rosen’s work is the main focus of this article, an attempt is made to advance a perspective for the broad field of studies that developed around the notion of anticipation. Of particular interest are the circumstances of epistemological and gnoseological significance, leading to the articulation of the early hypotheses regarding anticipatory processes. Of no less interest to the scientific community are questions pertinent to complexity, adaptivity, purposiveness, time and computability as they relate to our understanding of anticipation.

52 citations


Cites background from "A Category Theoretical Argument aga..."

  • ...Chu and Ho (2006) correctly noticed that, in Rosen’s view, ‘living systems are not realizable in computational...

    [...]

  • ...Chu and Ho (2006) correctly noticed that, in Rosen’s view, ‘living systems are not realizable in computational universes’....

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References
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Book
01 Jan 1966
TL;DR: This invention relates to prefabricated buildings and comprises a central unit having a peripheral section therearound to form a main residential part defined by an assembly of juxtaposed roofing and facing trusses.
Abstract: This invention relates to prefabricated buildings and comprises a central unit having a peripheral section therearound to form a main residential part. This peripheral part is defined by an assembly of juxtaposed roofing and facing trusses; the roofing trusses rest on said central unit and also on the facing trusses which themselves rest on a peripheral support wall. The facing trusses are of triangular section and have an inclined outer wall extending downwardly and beyond the said peripheral support wall.

4,649 citations


Book
01 Jan 1980
Abstract: Editorial Preface General Table Of Contents Foreword Introduction (by Professor Maturana) Biology Of Cognition Dedication Table of Contents I. Introduction II. The Problem III. Cognitive Function in General A. The Observer B. The Living System C. Evolution D. The Cognitive Process IV. Cognitive Function in Particular A. Nerve Cells B. Architecture C. Function D. Representation E. Description F. Thinking G. Natural Language H. Memory and Learning I. The Observer V. Problems in the Neurophysiology of Cognition VI. Conclusions VII. Post Scriptum Autopoiesis: The Organization Of The Living Preface (by Sir Stafford Beer) Introduction I. On Machines, living and Otherwise 1. Machines 2. Living Machines II. Dispensability of Teleonomy 1. Purposelessness 2. Individuality III. Embodiments of Autopoiesis 1. Descriptive and Causal Notions 2. Molecular Embodiments 3. Origin IV. Diversity of Autopoiesis 1. Subordination to the Condition of Unity 2. Plasticity of Ontogeny 3. Reproduction, a Complication of the Unity 4. Evolution, a Historical Network 5. Second and Third Order Autopoietic Systems V. Presence of Autopoiesis 1. Biological Implications 2. Epistemological Implications 3. Cognitive Implications Appendix: The Nervous System Glossary Bibliography Index Of Names

4,304 citations


BookDOI
01 Jan 1980

3,585 citations


Additional excerpts

  • ...and Varela’s celebrated notion of autopoiesis [25, 12]....

    [...]


Journal ArticleDOI
TL;DR: Notwithstanding their diversity, all living systems must share a common organization which the authors implicitly recognize calling them “living,” but there is no formulation of this organization, mainly because the great developments of molecular, genetic and evolutionary notions in contemporary biology have led to the overemphasis of isolated components.
Abstract: Notwithstanding their diversity, all living systems must share a common organization which we implicitly recognize calling them “living.” At present there is no formulation of this organization, mainly because the great developments of molecular, genetic and evolutionary notions in contemporary biology have led to the overemphasis of isolated components, e.g., to consider reproduction as a necessary feature of the living organization and, hence, not to ask about the organization which makes a living system a whole, autonomous unity that is alive regardless of whether it reproduces or not. As a result, processes that are history dependent (evolution, ontogenesis) and history independent (individual organization) have been confused in the attempt to provide a single mechanistic explanation for phenomena which, although related, are fundamentally distinct.

1,489 citations


"A Category Theoretical Argument aga..." refers methods in this paper

  • ...and Varela’s celebrated notion of autopoiesis [25, 12]....

    [...]

  • ...Maturana and Varela themselves illustrated the concept of autopoiesis by means of a computational model [25]; this model has since been re-implemented by McMullin and Varela [15, 14, 3]....

    [...]


Book
01 Jan 1991
TL;DR: It's important for you to start having that hobby that will lead you to join in better concept of life and reading will be a positive activity to do every time.
Abstract: basic category theory for computer scientists What to say and what to do when mostly your friends love reading? Are you the one that don't have such hobby? So, it's important for you to start having that hobby. You know, reading is not the force. We're sure that reading will lead you to join in better concept of life. Reading will be a positive activity to do every time. And do you know our friends become fans of basic category theory for computer scientists as the best book to read? Yeah, it's neither an obligation nor order. It is the referred book that will not make you feel disappointed.

458 citations


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Q1. What are the contributions in this paper?

A detailed presentation of the argument supporting his conclusion is laid out in Rosens book Life itself this paper.