Systems [sic] Biology

The correct term is ‘system biology’.  Note the singular form system: not “systems biology”.  This last usage is a solecism that became accepted when it had been repeated often enough, a very example of ‘accumulated wrongs become right’.

System biology may be defined as the study of life using the tools of system theory (not ‘systems theory’).  Ludwig von Bertalanffy’s 1968 masterwork is called General System Theory.  (In some of his later writings, the term “systems theory” did occasionally appear.  I have in my collection some copies of his original typescripts, in which he had written “system theory”, but in the published versions they mysteriously mutated to “systems theory” — evidence of the handiwork of an over-zealous copy editor, perhaps…)

Consider the everyday terms ‘vegetable soup’, ‘ten-foot pole’, ‘train station’; NOT ‘vegetables soup’, ‘ten-feet pole’, ‘trains station’.  In mathematics, one says ‘set theory’, ‘group theory’, ‘number theory’, ‘category theory’, ‘system theory’, etc; NOT ‘sets theory’, ‘groups theory’, ‘numbers theory’, ‘categories theory’, ‘systems theory’, ….  Likewise, in biology, one uses ‘cell biology’, ‘population biology’, ‘system biology’; NOT ‘cells biology’, ‘populations biology’, ‘systems biology’.  One may also note ‘computer science’, ‘plant science’, ‘system science’; NOT ‘computers science’, ‘plants science’, ‘systems science’.

Of course one studies more than one object in each subject!  Indeed, one would say in the possessive ‘theory of sets’, ‘biology of populations’, …; one says ‘theory of systems’ and ‘biology of systems’ for that matter.  But the point is that when the noun of a mathematical object (or indeed any noun) is used as adjective, one does not use the plural form.

Grammatically, a noun-used-as-adjective in a compound is called a noun adjunct (also attributive noun or noun premodifier).  So in ‘system biology’, ‘biology’ is the noun and ‘system’ (singular!) is the noun adjunct.  The rule is that in a noun adjunct, the singular form is used.

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Relational Biology

A. H. Louie


This is a brief introduction to the Rashevsky-Rosen school of relational biology.

Relational biology is the study of biology from the standpoint of ‘organization of relations’.  It was founded by Nicolas Rashevsky in the 1950s, thence continued and flourished under his student Robert Rosen.   And I was Rosen’s student.


Nicolas Rashevsky
(1899–1972)


Robert Rosen
(1934–1998)

The Modelling Relation

Causality in the modern sense, the principle that every effect has a cause, is a reflection of the belief that successions of events in the world are governed by definite relations.  Natural Law posits the existence of these entailment relations and that this causal order can be imaged by implicative order.

A modelling relation is a commutative functorial encoding and decoding between two systems.  Between a natural system (an object partitioned from the physical universe)  and a formal system (an object in the universe of mathematics) , the situation may be represented in the following canonical diagram:

The encoding ε maps the natural system N and its causal entailment c therein to the formal system F and its internal inferential entailment i ; i.e.,

ε : NF     and     ε : ci .

The decoding δ does the reverse.  The entailments satisfy the commutativity condition

c = εiδ .

Stated graphically, this equality says that, in the diagram above, tracing through arrow c is the same as tracing through the three arrows ε , i , and δ in succession.  Thence related, F is a model of N, and N is a realization of F.  In terms of the modelling relation, Natural Law is a statement on the existence of causal entailment c and the encodings ε : NF and  ε : c i .

A formal system may simply be considered as a set with additional mathematical structures.  So the mathematical statement ε : NF , i.e., the posited existence for every natural system N a model formal system F , may be stated as the axiom

Everything is a set.

A mapping is an inference that assigns to each element of one set a unique element of another set.  In elementary mathematics, when the two sets involved are sets of numbers, the inference process is often called a function.  So ‘mapping’ may be considered a generalization of the term, when the sets are not necessarily of numbers.  (The use of ‘mapping’ here avoids semantic equivocation and leaves ‘function’ to its biological meaning.)

Causal entailment in a natural system is a network of interacting processes.  The mathematical statement ε : c i , i.e., the functorial correspondence between causality c in the natural domain and inference i in the formal domain, may thus be stated as an epistemological principle, the axiom

Every process is a mapping.

Together, the two axioms are the mathematical formulation of Natural Law.  These self-evident truths serve to explain “the unreasonable effectiveness of mathematics in the natural sciences”.

Biology Extends Physics

A living system is a material system, so its study shares the material cause with physics and chemistry.  Reductionists claim this, therefore, makes biology reducible to ‘physics’. Physics, in its original meaning of the Greek word φύσις, is simply (the study of) nature.  So in this sense it is tautological that everything is reducible to physics.  But the hardcore reductionists, unfortunately, take the term ‘physics’ to pretentiously mean ‘(the toolbox of) contemporary physics’.

Contemporary physics that is the physics of mechanisms reduces biology to an exercise in molecular dynamics.  This reductionistic exercise, for example practised in biochemistry and molecular biology, is useful and has enjoyed popular success and increased our understanding life by parts.  But it has become evident that there are incomparably more aspects of natural systems that the physics of mechanisms is not equipped to explain.  The overreaching reductionistic claim of genericity is thus a misrepresentation and renders it into a falsehood.

Biology is a subject concerned with organization of relations.  Physicochemical theories are only surrogates of biological theories, because the manners in which the shared matter is organized are fundamentally different.  Hence the behaviours of the realizations of these mechanistic surrogates are different from those of living systems.  This in-kind difference is the impermeable dichotomy between predicativity and impredicativity.

Relational Biology

The essence of reductionism in biology is to keep the matter of which an organism is made, and throw away the organization, with the belief that, since physicochemical structure implies function, the organization can be effectively reconstituted from the analytic material parts.

Relational biology, on the other hand, keeps the organization and throws away the matter; function dictates structure, whence material aspects are entailed.

In terms of the modelling relation, reductionistic biology is physicochemical process seeking models, while relational biology is organization seeking realizations.  Stated otherwise, reductionistic biology begins with the material system and relational biology begins with the mathematics.  Thus the principles of relational biology may be considered the operational inverse of (and complementary to) reductionistic ideas.

Any question becomes unanswerable if one does not permit oneself a large enough universe to deal with the question.  The failure of presumptuous reductionism is that of the inability of a small surrogate universe to exhaust the real one.  Equivocations create artefacts.  The limits of mechanistic dogma are very examples of the restrictiveness of self-imposed methodologies that fabricate non-existent artificial ‘limitations’ on science and knowledge.  The limitations are due to the nongenericity of the methods and their associated bounded microcosms.  One learns something new and fundamental about the universe when it refuses to be exhausted by a posited method.

The above is a necessarily terse introduction to relational biology.  The enthusiasts may want to explore the subject further.  A good place to start is my 2009 book More Than Life Itself: A Synthetic Continuation in Relational Biology.

A. H. Louie: Publications

[38]   Louie, A. H. (2017) [monograph]
       Intangible Life: Functorial Connections in Relational Biology
       xxiii + 264 pp. (Anticipation Science, Vol. 2) Springer, New York. ISBN 978-3-319-65408-9
       http://link.springer.com/book/10.1007/978-3-319-65409-6

[37]   Louie, A. H. (2017)
       Mathematical Foundations of Anticipatory Systems
       Roberto Poli (ed.), Handbook of Anticipation. Springer, New York. 
       link.springer.com/referenceworkentry/10.1007/978-3-319-31737-3_21-1

[36]   Louie, A. H. (2017)
       Relational Biology
       Roberto Poli (ed.), Handbook of Anticipation. Springer, New York. 
       link.springer.com/referenceworkentry/10.1007/978-3-319-31737-3_17-1

[35]   Louie, A. H. and Poli, R. (2017)
       Complex Systems
       Roberto Poli (ed.), Handbook of Anticipation. Springer, New York. 
       link.springer.com/referenceworkentry/10.1007/978-3-319-31737-3_3-1

[34]   Albertazzi, L. and Louie, A. H. (2016)
       A Mathematical Science of Qualities: A Sequel
       Biological Theory, 11(4), 192–206 
       link.springer.com/article/10.1007/s13752-016-0248-0
       [Louie Qualities 2016 pdf]

[33]   Louie, A. H. (2015)
       The Imminence Mapping Anticipates
       Anticipation Across Disciplines.   
       Mihai Nadin (ed.), (Cognitive Systems Monographs, Vol. 29). Springer, New York. ISBN 978-3-319-22598-2, pp. 163-185. 
       link.springer.com/chapter/10.1007/978-3-319-22599-9_11
       [Louie Imm Map Anticip 2015 pdf]

[32]   Louie, A. H. (2015)
       A metabolism–repair theory of by-products and side-effects
       International Journal of General Systems, 44(1), 26-54
       tandfonline.com/doi/full/10.1080/03081079.2014.937433

[31]   Louie, A. H. (2013) [monograph]
       The Reflection of Life: Functional Entailment and Imminence in Relational Biology
       xxxii + 243 pp. (IFSR International Series on Systems Science and Engineering,
       Vol. 29) Springer, New York. ISBN 978-1-4614-6927-8
       link.springer.com/book/10.1007/978-1-4614-6928-5/page/1

[30]   Louie, A. H. (2013)
       Explications of functional entailment in relational pathophysiology
       Axiomathes 23(1), 81-107
       link.springer.com/article/10.1007/s10516-012-9189-9    
       [Louie Pathophysiology 2012 pdf]

[29]   Louie, A. H. (2012)
       Anticipation in (M,R)-systems
       International Journal of General Systems, 41(1), 5-22
       tandfonline.com/doi/abs/10.1080/03081079.2011.622088
       [Louie AMR 2012 pdf]

[28]   Louie, A. H. (2011)
       Essays on More Than Life Itself
       Axiomathes 21(3), 473-489
       springerlink.com/content/71200q3v2867642h
       [Louie Essays on ML 2011 pdf]

[27]   Louie, A. H. and Poli, Roberto (2011)
       The spread of hierarchical cycles
       International Journal of General Systems, 40(3), 237-261
       tandfonline.com/doi/abs/10.1080/03081079.2010.550579
       [LouieP Hierarchical Cycles 2011 pdf]

[26]   Louie, A. H. (2010)
       Artificial claims about synthetic life: the view from relational biology
       Journal of Cosmology 8, June 2010
       journalofcosmology.com/ArtificialLife100.html#19
       [Post html]
       [Louie Venter 2010 pdf]

[25]   Louie, A. H. (2010)
       Relational biology of symbiosis
       Axiomathes 20(4), 495-509
       springerlink.com/content/h481521x7264626l
       [Louie Symbiosis 2010 pdf]

[24]   Louie, A. H. (2010)
       Robert Rosen's anticipatory systems
       Foresight 12(3), 18-29
       emeraldinsight.com/journals.htm?issn=1463-6689&volume=12&issue=3&articleid=1864160
       [Louie Rosen's AS 2010 pdf]

[23]   Louie, A. H. (2009) [monograph]
       More Than Life Itself: A Synthetic Continuation in Relational Biology
       xxiv + 388 pp. (Categories Series, Vol. 1) ontos verlag, Frankfurt. 
       ISBN 978-3-86838-44-6
       degruyter.com/view/product/208476

[22]   Louie, A. H. (2008)
       Functional entailment and immanent causation in relational biology
       Axiomathes 18(3), 289-302
       springerlink.com/content/k7gh4648h6w5m636
       [Louie Entailment 2008 pdf]

[21]   Louie, A. H. and Kercel, Stephen W. (2007)
       Topology and life redux: Robert Rosen's relational diagrams of living systems
       Axiomathes 17(2), 109-136
       springerlink.com/content/x17xx1734w82674w
       [LouieK Topology 2007 pdf]

[20]   Richardson, I. W. and Louie, A. H. (2007)
       A phenomenological calculus of Wiener description space
       Chemistry and Biodiversity 4(10), 2315-2331
       onlinelibrary.wiley.com/doi/10.1002/cbdv.200790189/abstract
       [RLouie Wiener 2007 pdf]

[19]   Louie, A. H. (2007)
       A Rosen etymology
       Chemistry and Biodiversity 4(10), 2296-2314
       onlinelibrary.wiley.com/doi/10.1002/cbdv.200790188/abstract
       [Louie Etymology 2007 pdf]

[18]   Louie, A. H. (2007)
       A living system must have noncomputable models
       Artificial Life 13, 293-297
       mitpressjournals.org/doi/abs/10.1162/artl.2007.13.3.293?journalCode=artl
       [Louie ALife_Noncom 2007 pdf]

[17]   Louie, A. H. and Richardson, I. W. (2006)
       A phenomenological calculus for anisotropic systems
       Axiomathes 16(1-2), 215-243
       springerlink.com/content/x2p11tg1984wq858
       [LouieR Anisotropy 2006 pdf]

[16]   Louie, A. H. (2006)
       (M,R)-systems and their realizations
       Axiomathes 16(1-2), 35-64
       springerlink.com/content/e1503x8876611743
       [Louie MR 2006 pdf]

[15]   Louie, A. H. (2005)
       Any material realization of the (M,R)-systems must have noncomputable models
       Journal of Integrative Neuroscience 4, 423-436
       worldscinet.com/jin/04/0404/S0219635205000926.html
       [Louie JIN_Noncomp 2005 pdf]

Act Two : [2005, ▲ )

► Entr’acte : [1985,2005) ◄

Act One : ( ▼ ,1985)

[14]   Richardson, I. W. and Louie, A. H. (1992)
       Membranes and meters
       Journal of Theoretical Biology 154, 9-26
       sciencedirect.com/science/article/pii/S0022519305801845
       [RLouie Meters 1992 pdf]

[13]   Richardson, I. W. and Louie, A. H. (1988)
       The metric structure of irreversible thermodynamics
       Journal of Theoretical Biology 132, 125-126
       sciencedirect.com/science/article/pii/S0022519388801978
       [LouieR Metric 1988 pdf]

[12]   Louie, A. H. and Richardson, I. W. (1986)
       Dissipation, Lorentz metric, and information: 
         a phenomenological calculus of bilinear forms
       Mathematical Modelling 7, 227-240
       sciencedirect.com/science/article/pii/0270025586900497
       [LouieR Bilinear 1986 pdf]

[11]   Richardson, I. W. and Louie, A. H. (1986)
       Irreversible thermodynamics, quantum mechanics, and intrinsic time scales
       Mathematical Modelling 7, 211-226
       sciencedirect.com/science/article/pii/0270025586900485
       [RLouie Irreversible 1986 pdf]

[10]   Louie, A. H. (1985) [tierce in the "Red House Book"]
       Categorical System Theory
       Theoretical Biology and Complexity: 
         Three Essays on the Natural Philosophy of Complex Systems
       (Robert Rosen, ed.), Academic Press, Orlando FL, pp.69-163 (out of print)
       amazon.com/Theoretical-Biology-Complexity-Natural-Philosophy/dp/0125972806
       [Louie CST 1985 pdf]

 [9]   Louie, A. H. and Somorjai, R. L. (1984)
       Stieltjes integration and differential geometry: 
         a model for enzyme recognition, discrimination, and catalysis
       Bulletin of Mathematical Biology 46, 745-764
       springerlink.com/content/20p754jk71815331
       [LouieS Stieltjes 1984 pdf]

 [8]   Louie, A. H. (1983)
       Categorical system theory and the phenomenological calculus
       Bulletin of Mathematical Biology 45, 1029-1045
       springerlink.com/content/m301h563w12v2wv7
       [Louie CSTPC 1983 pdf]

 [7]   Louie, A. H. (1983)
       Categorical system theory
       Bulletin of Mathematical Biology 45, 1047-1072
       springerlink.com/content/635736782532364m
       [Louie CST 1983 pdf]

 [6]   Richardson, I. W. and Louie, A. H. (1983)
       Projections as representations of phenomena
       Journal of Theoretical Biology 102, 199-223
       sciencedirect.com/science/article/pii/0022519383903600
       [RLouie Projections 1983 pdf]

 [5]   Louie, A. H. and Somorjai, R. L. (1983)
       Differential geometry of proteins: helical approximations
       Journal of Molecular Biology 168, 143-162
       sciencedirect.com/science/article/pii/S0022283683803271
       [LouieS DGP Helical 1983 pdf]

 [4]   Louie, A. H. and Richardson, I. W. (1983)
       Duality and invariance in the representation of phenomena
       Mathematical Modelling 4, 555-565
       sciencedirect.com/science/article/pii/0270025583900155
       [LouieR Duality 1983 pdf]

 [3]   Louie, A. H. and Somorjai, R. L. (1982)
       Differential geometry of proteins: 
         a structural and dynamical representation of patterns
       Journal of Theoretical Biology 98, 189-209
       sciencedirect.com/science/article/pii/0022519382902582
       [LouieS DGP Patterns 1982 pdf]

 [2]   Louie, A. H., Richardson, I. W., and Swaminathan, S. (1982)
       A phenomenological calculus for recognition processes
       Journal of Theoretical Biology 94, 77-93
       sciencedirect.com/science/article/pii/0022519382903307
       [LouieRS Recognition 1982 pdf]

 [1]   Richardson, I. W., Louie, A. H., and Swaminathan, S. (1982)
       A phenomenological calculus for complex systems
       Journal of Theoretical Biology 94, 61-76
       sciencedirect.com/science/article/pii/0022519382903290
       [RLouieS Complex 1982 pdf]