On Mechanism

[john.kineman]

A lot of the discussion on this forum centers around ideas about mechanisms and/or non-mechanisms. And yet it is clear to me that the scientific world has a very limited idea about this difference, or believes there is no significant distinction. So, I think it is worth discussing.

I have studied the work of mathematical biologist Robert Rosen for the past 20 years, in a very deep way and even extending his theories about life. MOST fundamental to his work is this distinction about what is a mechanism and what is not. He convincingly argued, using mathematical proofs in Category Theory along with biological empiricism (the conclusions require both), that life cannot be a mathematical machine. There have been mainly three kinds of response to this work. One is strong confirmation and support for it. In opposition tends to be arguments that it is irrelevant or that a mistake was made (generally not comprehending the work - these are mainly wild guesses wanting to be on the 'right' side of history defending the mainstream). The third response is to ignore it, a response that is facilitated by the difficulty in comprehending Category Theory (although that was only one line of reasoning). Rosen provided theorems and proofs but presented the claim in common language. He did not want to do a synthesis, however, which several after him have attempted. Part of his socio-political belief was that the knowledge was too early for acceptance, and I think he also felt it would hurt his career. He did well in professional life by keeping his statements highly technical, and I think that made it easy for people who understood to follow them, and easy for those who felt threatened to ignore them. Here is a plain-spoken piece he wrote as a commentary on other work: Rosen, R. (1991) Beyond dynamical systems. Journal of Social and Biological Structures, 14, 217–220.

In the above reference Rosen discusses some very obvious things about transcendent mathematical functions that can only be approached in the limit of computable (simulable) closed-form quantitative mathematics. The reason no closed-form solution is available is because the function does not exist within a closed syntax, which is what the positivistic classical science (Hilbert's Formalization program) was assuming and where we got the idea of a mechanism. In effect he demonstrates conclusively that mechanisms exist within contextual definitions that provide an external "semantics". We get away with a mechanistic view in classical physics by pushing the external semantics -- the origin problem -- outside the system of study. By doing that we thus study only simulable problems - mechanisms, and it works because a highly interactive dynamical system, such as our world and universe, will establish a common context - which we see as space-time. The exceptions exist as a result of causal boundaries within that context (quantum isolation as in Hameroff/Penrose model for consciousness, or super-luminal space-time expansion in cosmology, to name a few). The thing is that ANY space-time separation IS such a causal boundary. Even the distance between events - which is why uncertainty appears. If the scale of context-defining interactions is finer than the scale of observation, it looks solid. If the other way around, you must get multiple contexts - the appearance of relativity or multiple universes. Mechanisms are contextual and entailed with their contexts. Therefore, contextual relations with mechanisms must be studied to understand reality. Neither contexts nor mechanisms are 'wrong' or dismissable; they for a complementarity principle at the level of existence and operation as fundamentally immiscible knowledge. Immiscible means they cannot be reduced, but the relation, which is a holism, can be known. Maybe instead of the worn-out term 'holism' we should invent the term "relationism" as opposed to mechanism.

More generally, however, responses over his career (he passed in 1998) have been noticeably absent of any disproof or much counter argument except to dismiss the question. There have been some papers claiming he made a mistake, but they were quickly debunked (e.g.: Louie, A.H. (2007) A Living System Must Have Noncomputable Models. Artificial Life, 13, 293–297.)

I have posted references to this work on this list before, and I'll add some here. But I realize that the literature is overwhelming and none of us can manage to sort it ourselves without a compelling track to follow. Reading Rosen is a mind-opening experience - some say mind-blowing experience. I have compared its logic to the Veda, although Rosen himself did not have religious interests as such, nor, it appears, any inquiry into Eastern Philosophy. In essence he re-discovered Eastern philosophy de-novo (although his ideas were certainly informed by the early quantum physicists, many of whom were Vedic scholars). I have referred to him (in a commentary in the 2012 republication of his book on Anticipatory Systems) as "The Einstein of Biology". Those familiar with his work tend to agree.

A mathematical machine is what we SHOULD mean by mechanism. In the second reference above, Louie summarizes Rosen's main proof: I think it is worth taking seriously:

2 Rosen’s Theorems

In [5], Rosen defined the term simulable and several of its synonyms. A mapping is simulable if it is ‘‘definable by an algorithm.’’ It is variously called computable, effective, and evaluable by a mathematical (Turing) machine. In Chap. 8 of [5] he gave the following:

DEFINITION 2.1: A natural system N is a mechanism if and only if all of its models are simulable.
He then proved five propositions for a mechanism N. In particular, ‘‘Conclusion 4’’ is the

following:
THEOREM 2.2: Analytic and synthetic models coincide in the category C(N) of all models of N; direct sum 1⁄4

direct product.

n 2007 Massachusetts Institute of Technology Artificial Life 13: 293–297 (2007)

A. H. Louie A Living System Must Have Noncomputable Models And ‘‘Conclusion 5’’ is the following:

THEOREM 2.3: Every property of N is fractionable.

Immediately following this, in Chap. 9 of [5], Rosen, using these five just-proven properties, presented a detailed reductio ad absurdum argument that proves that certain modes of entailment are not available in a mechanism:

THEOREM 2.4: There can be no closed path of efficient causation in a mechanism. The contrapositive statement of Theorem 2.4 is

THEOREM 2.5: If a closed path of efficient causation exists in a natural system N, then N cannot be a mechanism.

Taking Definition 2.1 of mechanism into account, this is equivalent to
THEOREM 2.6: If a closed path of efficient causation exists for a natural system N, then it has a model that is

not simulable.

An iteration of ‘‘efficient cause of efficient cause’’ is inherently hierarchical. A closed path of efficient causation must form a hierarchical cycle. Both the hierarchy and the cycle (closed loop) are essential attributes of this closure.

In formal systems, hierarchical cycles are manifested by impredicativities, or the inability to replace these self-referential loops with finite syntactic algorithms. Impredicativities are simply part of the semantic legacy of mathematics as a language, in their expression of transcendental operations. Further elaboration on this concept may be found in abundance in [6]. The nonsimulable model in Theorem 2.6 contains a hierarchical closed loop that corresponds to the closed path of efficient causation in the natural system being modeled. In other words, it is a formal system with an impredicative loop of inferential entailment. Thus we also have:

THEOREM 2.7: If an impredicative loop of inferential entailment exists for a formal system, then it is not simulable.

A natural system that has a nonsimulable model is defined by Rosen as a complex system (Chap. 19 of [6]). A necessary condition for a natural system to be an organism is that it is closed to efficient causation (Chap. 1 of [6]). Theorem 2.7 then says an organism must be complex. The implication on the concept of artificial life is this:

THEOREM 2.8: A living system must have noncomputable models.

All Rosen’s theorems have been mathematically proven (although Rosen’s presentations are not in the ordinary form of definition-lemma-theorem-proof-corollary that one finds in conventional mathematics journals). Indeed, no logical fallacy in Rosen’s arguments has ever been demonstrated. Counterexamples cannot exist for proven theorems. For a detailed exposition of the underlying logic, the reader is encouraged to consult [2].

Note that Rosen’s conclusion is not that artificial life is impossible. It is, rather, that life is not computable: However one models life, natural or artificial, one cannot succeed by computation alone. Life is not definable by an algorithm. There is, indeed, practical verification from computer science that attempts at implementation of a hierarchical closed loop lead to deadlock, and hence are forbidden in systems programming [7]. 

Louie's references from the above:

[2] Louie, A. H. (2005). Any material realization of the (M,R)-systems must have noncomputable models. Journal of Integrative Neuroscience, 4(4), 423–436.
[3] Louie, A. H. (2006). (M,R)-systems and their realizations. Axiomathes, 16(1–2), 35–64.
[4] Mac Lane, S. (1998). Categories for the working mathematician (2nd ed.). New York: Springer-Verlag.
[5] Rosen, R. (1991). Life itself. New York: Columbia University Press.
[6] Rosen, R. (2000). Essays on life itself. New York: Columbia University Press. 

[N.Panchapakesan]

John
Thanks for intervening and explaining what Mechanism is all
about. It was certainly mystifying to the uninitiated.

At the cost of drastic oversimplification may I say that the
work of Robert Rosen and Louie seems to be a mathematical formulation
of ideas of many persons (probably including Roger Penrose) that
algorithmic or simulable formalisms can not explain or model Life.
While Penrose is waiting for quantum gravity to come in the future,
Rosen already has a provable formalism
. Persons like me,who believe, that at present , there is no
overlap between between intutive formalism and physical science and
they can only have co-existence (peaceful or otherwise), have a new
candidate (formalism) to consider.

Thanks and regards

Panchu

N. Panchapakesan

New Delhi, India

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[N.Panchapakesan]

[ignaciopeon .]

John Kineman reflections on Robert Rosen approach toward the understanding of life as open organic complex holodynamic and co-evolutionary systems for positivist scientists is difficult to understand. Many are trying to represent complex and dynamic living systems with algorithms, with models of closed systems. For the representation of complex and dynamic open living systems an heuristic approach is much better, as learning systems under the influence of dynamic contextual levels. Systems science with its open paradigm is difficult to understand for many  scientists who still use the closed systems paradigm. Open systems is also open to other forms of knowledge, toward the spiritual approach of different cultures on the mystery of life and consciousness under the transdisciplinary approach to knowledge

Ignacio Peon

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[Sungchul Ji]

Hi John, Pachu ji, et al.

Thank you , John, for the nice summary of Rosen's work.  I met Robert Rosen briefly in 1983 at the Second International Seminar on the Living State held in Bhopal, India, organized by Professor R. K. Mishra (1924-2009). To properly appreciate Rosen's work, it may be necessary to view it from a broader context than mathematics that addresses not only the formal sciences but also the natural (the study of the knowable) and spiritual sciences (the study of unknowable) as well.

 

As the American chemist, logician and philosopher Peirce (1839-1914) pointed out, we think in signs and communicate our thoughts and experiences in signs, signs being defined simply as anything that stands for something other than itself. (Think of an elephant, do you an elephant in your head?)

 

All the thoughtful posts we read on this forum, including those about Rosen's work, are signs.  So to understand these signs and what they stand for it may behoove us to inquire into the principles and regularities underlying the actions of the sign in general.  Peirce spent whole of his life studying signs, which is known as semiotics in America among the Peircean scholars and semiology in Europe among the Saussurean linguists.  One of the main differences between semiotics and semiology is that the former is triadic (sign-object-interpretant) while the latter is dyadic (signifier-signified), 'interpretant' being defined as the effect that a sign has on the mind of the interpretant. 

It seems generally agreed that the semiotic principles elucidated by Peirce is more general and can be readily applied beyond the human sign processes (also called semioses) to the sign processes in nature, including molecular, cellular and organismic semioses often referred to as 'biosemiotics'.

 

The main purpose of this post is to call your attention to the recent suggestion of mine that the Peircean semiotics can be extended to include the concept of the "signless" as the antonym of the sign.  It is my belief that all words have their opposites, including the word "sign".  I was led to the concept of "signless" or "nilsign" in 2016 [1, 2] as a logical consequence of applying one of the definitions of the sign given by Peirce to the quark model of the Peircean signs [3].  In addition, the category to which the nilsign belongs was referred to as the Zeroness  (in analogy to Peirce's famous triad of Firstness, Secondness, and Thirdness) which may be identifiable with the Zero of Rowlands [4], the Dao of Lao-tzu, and Brahman of Hinduism. 

 

It appears to me that there may be three kinds of Theory of Everything (TOE) –
(i) the mathematical TOE such as Rosen's and Rowland's,
(ii) the physical TOE such as the String Theory, and
(iii) the semiotic TOE such as illustrated in Figure 1 attached, which includes or presupposed (i) and (ii).

 

Any questions, comments or suggestions would be welcome.

 

 

 With all the best.

Sung

 

  

References:

   [1] Ji, S. (2017).  The Cell Language Theory: Connecting Matter and Mind.  World Scientific, New Jersey (in press).  Section 6.6.4.

   [2]  Ji, S. (2017). ibid. Section 6.6.

   [3]  Ji, S. (2004).  Semiotics of Life: A Unified Theory of Molecular Machines, Cells, the Mind, 

Peircean Signs, and the Universe based on the Principle of Information-Energy Complementarity.  

In: Reports, Research Group on Mathematical Iinguistics, XVII Tarragona Seminar on Formal Syntax

 and Semantics, Rovira i Virgili University, Tarragona, 23-27 April 2003. 

PDF at http://www.conformon.net/wp-content/uploads/2012/12/SOLManuscriptsubmitted_final_downloaded_from_Taragona_09032011_

modified_07282012.pdf 

   [4]  Rowlands, P. (2007).  Zero to Infinity: The Foundations of Physics. World Scientific, New Jersey. 

   

 

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[Diego Lucio Rapoport]

Dear Colleagues

It is interesting that we the issues here discussed came to be directed to Robert Rosen's work, and to see how depending on the mathematical background (or the lack thereof) of the interpreters the readings of his works can vary.

Indeed, Rosen  was perhaps the first to introduce the importance of semantics into theories of both physics and biology, and to stress the importance of "impredicativities", self-referential cognitive loops (a notion introduced by Poincare, on his condemnation of Cantor and the 

ensuing Hilbert-Frege attempt to construe a purely syntactic mathematics). 

However, his approach through category theory was such that it took several decades to construct the first and last example of his (M;R)

systems (Soto Andrade and Letelier). 

They remained in the realm of an unconstructable formalism, which remarkably he did not notice that this (his) framework suffered of the same drawback that the formalistic program had led to, not only to the stalemate at the foundations of mathematics but to a general revision of the logic of mathematics which Rosen assumed implicitly that it was Boolean logic, again in contradiction to the invocation of impredicativities.

He directed his attention to what he called would become a "revolution" namely it can be interpreted to surpass the duality posed by the CONTAIN image-schema which is basic to the formalistic program through set theory, by considering dynamical systems which would form a hierarchy of networks (depending on exterior control parameters) described by either exact or closed differential forms. 

This is the core of the topological approach, which instead of organizing the contextual activity of systems in space and time into Inside and Outside, it operates as the holistic contrast between GLOBAL and LOCAL. Of all this he kept completely silent, as well as he ignored that this had been started to be implemented in the 1920s in physics. Too much coarse ignorance if one is to launch a "revolution" (easily healed by taking a course of calculus on manifolds and differential geometry). 

In fact, he did mention that this approach would led to construct a rather universal example of his categorical (M,R) systems. He also even more surprisingly not only ignored that this was related to topology and particularly that of spacetime AND CONTEXTUAL at that, but also that already Chemistry in the 1960s and particularly studies on DNA were framed as topological structures, which today is the Topological Chemistry paradigm (Nobel prize, 2016) and physics of condensed matter (Physics Nobel, 2016).

Most surprisingly, his mentor, the founder of mathematical biophysics, Nicholas Rashevsky, had  stated in the 1930s that biology was to be understood in terms of topology, in contrast with physics to be understood in terms of the mainstream paradigm of spacetime geometries, while the case is that both appear naturally united in terms of torsion geometry of non-linearity pervasive to all material, semiotic and informational processes, and of the topology of  non-orientable surfaces such as Moebius strip and Klein Bottle. No Boolean logic at all.

So much for Rosen's "revolution".  

Diego Lucio Rapoport

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[Diego Lucio Rapoport]

With respect to Rowlands TOE mentoned below, the nilpotence fermionic structure is based on the Klein Bottle surface, as shyly briefly formulated in Rowlands' book, to be put aside conveniently assuming dualism all the way through.

It very much seems that, again, dualism operates as a blinder.

Diego Rapoport

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[Bruno Marchal]

On 13 May 2017, at 08:22, john.kineman wrote:

A lot of the discussion on this forum centers around ideas about mechanisms and/or non-mechanisms. And yet it is clear to me that the scientific world has a very limited idea about this difference, or believes there is no significant distinction. So, I think it is worth discussing.

I have studied the work of mathematical biologist Robert Rosen for the past 20 years, in a very deep way and even extending his theories about life. MOST fundamental to his work is this distinction about what is a mechanism and what is not. He convincingly argued, using mathematical proofs in Category Theory along with biological empiricism (the conclusions require both), that life cannot be a mathematical machine.

I am aware of the work of Robert Rosen, and I think that many of its saying is correct, but eventually I think such analysis confirms more mechanism than it attacks it. He weakened its conclusion by his critics on Church's thesis. He seems to have a reductionist conception of machine, but the machine themselves refutes already that form of reductionism.

There have been mainly three kinds of response to this work. One is strong confirmation and support for it. In opposition tends to be arguments that it is irrelevant or that a mistake was made (generally not comprehending the work - these are mainly wild guesses wanting to be on the 'right' side of history defending the mainstream).

The mainstream is more physicalist than it is possible with mechanism. Rosen also is physicalist, at least implicitly.

The third response is to ignore it, a response that is facilitated by the difficulty in comprehending Category Theory (although that was only one line of reasoning). Rosen provided theorems and proofs but presented the claim in common language. He did not want to do a synthesis, however, which several after him have attempted. Part of his socio-political belief was that the knowledge was too early for acceptance, and I think he also felt it would hurt his career. He did well in professional life by keeping his statements highly technical, and I think that made it easy for people who understood to follow them, and easy for those who felt threatened to ignore them. Here is a plain-spoken piece he wrote as a commentary on other work: Rosen, R. (1991) Beyond dynamical systems. Journal of Social and Biological Structures, 14, 217–220.

In the above reference Rosen discusses some very obvious things about transcendent mathematical functions that can only be approached in the limit of computable (simulable) closed-form quantitative mathematics. The reason no closed-form solution is available is because the function does not exist within a closed syntax, which is what the positivistic classical science (Hilbert's Formalization program) was assuming and where we got the idea of a mechanism.

But Hilbert confused provability and computability. Today, we know that Church thesis makes compuatbility into an absolute notion, at the price of making provability a relative, forever incomplete notion.

In effect he demonstrates conclusively that mechanisms exist within contextual definitions that provide an external "semantics".

Yes, but not necessarily a physical one. The arithmetical reality defines all the context possible, and indeed gives some role to non mechanical context, and imposes some non computability in the machine theology and in the machine physics. The problem might be that Rosen still use mechanism in a materialist context, which, I think (and can argue) are incompatible.

We get away with a mechanistic view in classical physics by pushing the external semantics -- the origin problem -- outside the system of study. By doing that we thus study only simulable problems - mechanisms, and it works because a highly interactive dynamical system, such as our world and universe, will establish a common context - which we see as space-time. The exceptions exist as a result of causal boundaries within that context (quantum isolation as in Hameroff/Penrose model for consciousness, or super-luminal space-time expansion in cosmology, to name a few).

But Hameroff seems to accept mechanism. Only Penrose is against Mechanism. Hameroff seems OK with the idea that the brain is a quantum computer, which do not violate Church's thesis. If the brain is a quantum computer, the immaterialist consequences of mechanism stiil go through, and we have to derive physics from the theology of numbers. Only Penrose is coherent with that respect. He keeps materialism, and so reject mechanism.

The thing is that ANY space-time separation IS such a causal boundary. Even the distance between events - which is why uncertainty appears. If the scale of context-defining interactions is finer than the scale of observation, it looks solid. If the other way around, you must get multiple contexts - the appearance of relativity or multiple universes.

The separation of the numbers is enough for that task. The problem with mechanism, is that we cannot invoke the "primarily physical" at all. This is not well known, and I can give reference, or explain this entirely. 

Mechanisms are contextual and entailed with their contexts. Therefore, contextual relations with mechanisms must be studied to understand reality. Neither contexts nor mechanisms are 'wrong' or dismissable; they for a complementarity principle at the level of existence and operation as fundamentally immiscible knowledge. Immiscible means they cannot be reduced, but the relation, which is a holism, can be known. Maybe instead of the worn-out term 'holism' we should invent the term "relationism" as opposed to mechanism.

I am not sure I understand. Mechanism is also a relationism, and by the first person indeterminacy (no machine can know which machine she is, nor whoch computations support it, it is an highly holist relationism which is in play. Rosen is right and well inspired, but what he says is a logical consequence of mechanism. I think that he misunderstood Church's thesis, perhaps also Gödel's theorem, which makes Mechanism into a sort of vaccine again reductionism.

More generally, however, responses over his career (he passed in 1998) have been noticeably absent of any disproof or much counter argument except to dismiss the question. There have been some papers claiming he made a mistake, but they were quickly debunked (e.g.: Louie, A.H. (2007) A Living System Must Have Noncomputable Models. Artificial Life, 13, 293–297.)

I have posted references to this work on this list before, and I'll add some here. But I realize that the literature is overwhelming and none of us can manage to sort it ourselves without a compelling track to follow. Reading Rosen is a mind-opening experience - some say mind-blowing experience. I have compared its logic to the Veda, although Rosen himself did not have religious interests as such, nor, it appears, any inquiry into Eastern Philosophy. In essence he re-discovered Eastern philosophy de-novo (although his ideas were certainly informed by the early quantum physicists, many of whom were Vedic scholars). I have referred to him (in a commentary in the 2012 republication of his book on Anticipatory Systems) as "The Einstein of Biology". Those familiar with his work tend to agree.

That is why I can appreciate some of Rosen conclusion, but again, they are enforced by "modern" (digital) mechanism. I show also the big price: we have to derive physics from arithmetic (through machine self-reference), and, up to now, it seems possible and partially working. 

A mathematical machine is what we SHOULD mean by mechanism.

Nice to hear that. 

In the second reference above, Louie summarizes Rosen's main proof: I think it is worth taking seriously:

2 Rosen’s Theorems

In [5], Rosen defined the term simulable and several of its synonyms. A mapping is simulable if it is ‘‘definable by an algorithm.’’ It is variously called computable, effective, and evaluable by a mathematical (Turing) machine. In Chap. 8 of [5] he gave the following:

DEFINITION 2.1: A natural system N is a mechanism if and only if all of its models are simulable.

Nice.OK.

He then proved five propositions for a mechanism N. In particular, ‘‘Conclusion 4’’ is the

following:
THEOREM 2.2: Analytic and synthetic models coincide in the category C(N) of all models of N; direct sum 1⁄4

direct product.

n 2007 Massachusetts Institute of Technology Artificial Life 13: 293–297 (2007)

A. H. Louie A Living System Must Have Noncomputable Models

The word "model" is  abit ambiguous here. Physicists and logicians use the word "model" in quite opposite sense. But mechanism entails this for the two sense of the word.

And ‘‘Conclusion 5’’ is the following:

THEOREM 2.3: Every property of N is fractionable.

Immediately following this, in Chap. 9 of [5], Rosen, using these five just-proven properties, presented a detailed reductio ad absurdum argument that proves that certain modes of entailment are not available in a mechanism:

THEOREM 2.4: There can be no closed path of efficient causation in a mechanism. The contrapositive statement of Theorem 2.4 is

THEOREM 2.5: If a closed path of efficient causation exists in a natural system N, then N cannot be a mechanism.

Taking Definition 2.1 of mechanism into account, this is equivalent to
THEOREM 2.6: If a closed path of efficient causation exists for a natural system N, then it has a model that is

not simulable.

Most properties and attributes of machine are not computable/simulable, including its material constitution which has to be a non computable sum of all computation going through its actual state of mind. Rosen argument is correct, as far as I can judge, but works in the mechanist frame.

An iteration of ‘‘efficient cause of efficient cause’’ is inherently hierarchical. A closed path of efficient causation must form a hierarchical cycle. Both the hierarchy and the cycle (closed loop) are essential attributes of this closure.

Not sure I understand this. I have to say that I am skeptical on the notion of cause. causality is a highly emergent notion, with Mechanism.

In formal systems, hierarchical cycles are manifested by impredicativities, or the inability to replace these self-referential loops with finite syntactic algorithms.

Here I disagree strongly. Kleene's second recursion theorem shows that Mechanism handles very well those self-referential loops. Indeed, so much that some want to forbid it in computer science, but then they lost the universal computer (which is not much disturbing for them, as the universal machine is the non controllable element which can crash unpredictably).

Impredicativities are simply part of the semantic legacy of mathematics as a language, in their expression of transcendental operations. Further elaboration on this concept may be found in abundance in [6]. The nonsimulable model in Theorem 2.6 contains a hierarchical closed loop that corresponds to the closed path of efficient causation in the natural system being modeled. In other words, it is a formal system with an impredicative loop of inferential entailment. Thus we also have:

THEOREM 2.7: If an impredicative loop of inferential entailment exists for a formal system, then it is not simulable.

Here I do agree with Rosen, and got a similar result from mechanism (the thesis that "I" am a machine, or that "my body" is a machine). It entails that both the soul of the machine (even in its most classical definition by Theaetetus) and its materials constitution is NOT simulable.

Mechanism in philosophy of mind should not be confused with Mechanism in physics. If we are machine, then the physical reality cannot be machine simulable, nor the psychological reality (and still less the theological reality). 

A natural system that has a nonsimulable model is defined by Rosen as a complex system (Chap. 19 of [6]). A necessary condition for a natural system to be an organism is that it is closed to efficient causation (Chap. 1 of [6]). Theorem 2.7 then says an organism must be complex. The implication on the concept of artificial life is this:

THEOREM 2.8: A living system must have noncomputable models.

I agree, in the sense "A living system must have non-computable realities".

Agains, that follows from the assumption of the existence of a level of description of my body such that I survive with a digital transplant done at that level. This entais that the physical is the sum of all computations in arithmetic going through my state, and that sum is not computable (up to the point of predicting some non computable element in physics).

All Rosen’s theorems have been mathematically proven (although Rosen’s presentations are not in the ordinary form of definition-lemma-theorem-proof-corollary that one finds in conventional mathematics journals). Indeed, no logical fallacy in Rosen’s arguments has ever been demonstrated. Counterexamples cannot exist for proven theorems. For a detailed exposition of the underlying logic, the reader is encouraged to consult [2].

Note that Rosen’s conclusion is not that artificial life is impossible. It is, rather, that life is not computable: However one models life, natural or artificial, one cannot succeed by computation alone. Life is not definable by an algorithm. There is, indeed, practical verification from computer science that attempts at implementation of a hierarchical closed loop lead to deadlock, and hence are forbidden in systems programming [7]. 

I agree, but it is a consequence of mechanism, and we can guess this, because I don't think Rosen invoked actual infinities in its argument. What Rosen (and many) missed is that mechanism makes the "body" part of the mind-body problem more problematic, and indeed, there is no other choice than to extract the physics from the machine or number  theology, and that provides a way to test mechanism. At first sight, physics looks too much computable, and local, but thanks to Quantum Mechanics, the natural world seems to obey to the necessary not entirely computable physics, and locally non localness imposed by the mechanist assumption in philosophy of mind/theology.

So, to sum up, I think Rosen is correct in his conclusion, but not t for its starting assumption. Its conclusion are close to what the ideally correct machine already can guess when introspecting itself deep enough.

Bruno Marchal

Louie's references from the above:

[2] Louie, A. H. (2005). Any material realization of the (M,R)-systems must have noncomputable models. Journal of Integrative Neuroscience, 4(4), 423–436.
[3] Louie, A. H. (2006). (M,R)-systems and their realizations. Axiomathes, 16(1–2), 35–64.
[4] Mac Lane, S. (1998). Categories for the working mathematician (2nd ed.). New York: Springer-Verlag.
[5] Rosen, R. (1991). Life itself. New York: Columbia University Press.
[6] Rosen, R. (2000). Essays on life itself. New York: Columbia University Press. 

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[john.kineman]

I want to acknowledge and make a few comments on the kind replies so far on this topic, from:

May 13 (14 hours ago)  nargispanchu

May 13 (14 hours ago)  ignaciopeon

2:18 AM (9 hours ago)  Sungchul Ji

5:22 AM (6 hours ago)  diego.rapoport

Ignacio correctly, I think, identified the relational systems approach as "life as open organic complex holodynamic and co-evolutionary systems, and also correctly, IMO, states that "for positivist scientists [this approach] is difficult to understand". Instead he recommends a "heuristic" approach, however recognizing that the relational holon approach is open to semantic knowledge in its formalism.  While I agree that heuristic approaches are needed, by view is that they are needed to establish the targets for more realist theory; that we need them to test for logical and empirical consistency in proposing a natural science. Largely, my work following Rosen is aimed at developing a natural science that would explain the heuristics. Many have given up on this (the "shut up and calculate" idea). Hawking's model dependent realism also misses this point in thinking that models are strictly human inventions, and that we are not to think, even in claiming that only models matter, that models are therefore natural aspects. In other words, when we thought it was only matter and energy, we studied matter and energy. Why, on discovering that it really models should we not then study natural models?

 

Panchu expressed some kind optimism that, as I believe, the relational view could be a presently available 'new formalism" amid may historical and current ideas that are waiting for something to complete them.  I think he correctly summarizes a premise of the theory, that "algorithmic or simulable formalisms can not explain or model Life. This is certainly a central point, and a departure from which relational theory then proposes non-simulable closed loops of causation as the way to explain or model life. I have an issue about this - if the non-simulability itself has a model, does that make it simulable, or would any attempt to specify it mean its destructive reduction? A preliminary conclusion is that, as Rosen himself said, it is not about being unable to open the system description, it is about how one does that - having the right kind of causal openness that is commensurate with nature. I think the holon does establish a reduction to 'open' wholes that, while necessarily expressing its own incompleteness nevertheless establishes a method of infinite analysis in terms of holistic components of nature. One thus can indeed keep the cake while eating it. We get the ability to look at any proximal wholeness without having to describe universal wholeness - and that I think is the true goal of analysis, to take out knowledge elements that are proximal to the questions of interest, in a way that ensures the more distal relations will have less relevant effects.

 

 Sung has given some very interesting history, even from personal encounter with Rosen (which unfortunately I missed in 1998 as he died just after accepting my invitation to meet at Asilomar). I later discovered that his daughter, Judith Rosen, keenly follows the work, though not its technical formalism so much. I have been working with her to have access to Rosen now lost personal semantics - which I see is always a major equivocation in continuing someone's work (we retain only their syntactic outputs as books, papers, lectures, etc. but we then have to re-invent the semantics). This has proven very illuminating and I think has served to help me decide which theoretical paths to follow up, as the mind can indeed go many places not necessarily consistent with the original insight.  I also appreciate the reference to Peirce, who's work I did look into a bit (it is so hard to be abreast of all the work in complexity because it literally involves all disciplines). I very much appreciate the proposal to extend Peircean semiotics to include "the concept of the "signless". I immediately thought of my own critique of Peirce, that it described three levels when according to R-theory, there must be four (in accord with Aristotle's causes and Vedic philosophy). The missing quadrant, I concluded earlier, was essentially unfettered existence itself - which I would associate with "sat" (there are many interpretations and labels, however). Peirce 1st, 2nd, and 3rd. seemed to miss the 'thing itself', being about what governs things. Of course material is not material, it is the realized, measurable view into a complex whole, so to us it is what appears to be the state of things as they presently manifest (the much criticized idea of a 'snapshot' of reality, but that is only the impression of it). Indeed, this added zero level would be signless - perhaps it is the "is-ness", Kant's "thing-in-itself", or Vedic 'infinite existence'. In relational space-time the universe necessarily has infinite extent.in space and time.  I have thought that with this addition Peirce's system can be aligned with the 4 causes, Jung's attempted holism, and of more recent interest to me, Chandogya's labeling of the causes in the conversation between Gautama and Sathyakama, which I interpret as a closed loop causal identity (showing up all through Vedanta) and involving the same idea as Aristotle later expressed (with some later confusion) in his four causes. The rightful order would be:

- Efficient (energetic cause) -- Prakasavat (light, shining, endowed with splendor),

- Material (sensible world) --  Anantavat (endless, or eternal existence),

- Final (contextual meaning) -- Ayatanavat (having a seat or home)

- Formal (systemic boundary) -- Jyotishmat (luminous source), 

- (Repeating) 

I think the closed identity loop comprising these four (the R-theory holon) is thus the same as the Vedic concept of "Rta" - cosmic order, which then also appears in the Varnas and later Vastu

 

Diego Rapoport points out semiotic origins of may of Rosen's ideas (Rosen often spoke in the language of syntax and semantics to get across what was missing in classical dynamics), and I think rightly states that Rosen's formalism has been very difficult to use. There are very few people who can work through the Category Theory logic of relations, Louie is probably the main one. Thus, the ideas have been rather stagnated and when dragged out of the closet there is often debilitating technical controversy. And yet, the technical foundation was probably necessary to establish for indeed, as Diego says, Rosen saw this as revolutionary, such that no equivocation would survive. He clearly said his intentions were to establish a foundation that others could follow, but strangely to avoid synthesis, even though he claimed to know how to "fabricate" life. The later was not demonstrated, and Rosen said it was beyond his intention to give any demonstration - he meant to lay out a series of fundamental clues that would not be assembled until the right time in human development. Admittedly that can sound like a conceit and his true motivation may be debated (although I defer to his daughter on that, as she knew him best). 

My conclusion is that it was a combination of factors (a) genuine concern at the time that the ideas would find their first use in some kind of social weaponization (which we may be seeing today), (b) a bit of self-preservation, as the theories were of the nature that one could get fired without some form of effective cover (mine is retirement), (c) a bit of disdain in the sense that he did not trust humanity very much with the ideas. He really was a theoretician without political ambitions and he wrote that he only published because his mentor, Rashevski, persuaded him that it was his professional duty.  Judith could correct this or add more. It is also true, as Diego says, that Rosen was not generous in citing predecessors (except for Rashevski and a few others he greatly admired). He cited Schrodinger and others he directly learned from. I think the general attitude toward pursuing a personal investigation into the matter of what causes life is the main explanation for this. We really don't know what he was aware of, except that he certainly knew traditions in mathematics, biology, and physics. His foray into the social dimension seems secondary to me. Participating in the Hutchins Institute in California was an honor, I think, and exception to his normal work. He was critical of strident pragmatists and constructivist as much as he criticized positivism and the limits of mechanism. That I found very interesting because once I had a workable synthesis, it was clear that it described a process of systemically self-constructing knowable syntax; and yet it is a formal description of that. So, I consider it a realistic approach to construction. And yet it does not contradict the statement that no formalism can be complete or without an non-syntactic, non-computable "semantic" residue. This is exactly what I was looking for - because in science we must reduce ideas to some descriptive logic, even if remembering that it is ultimately incomplete, like a series approximation. The key, then, is not IF one reduces, but HOW and to WHAT. He wanted a formalism that does not destroy natural relations between context and content.  I also suspect that the answer does indeed lie in some unity of these ideas.  Indeed the comments on topology are very relevant. It was part of the logical construction. There are indeed new applications of the M-R system that are now being published, but a great deal more theoretical work was needed to get there.  There are now examples of life forms consistent with the M-R formalism and even a testable new theory of space-time.  Category Theory is, of course, much broader than Boolean Logic.  It was used to get around the problem of determinism, as best I can see; to open the system to other kinds of causes besides efficient. However he only showed the effects on efficient maps, not the higher level influences, which tend to be buried in the math. The key, and most revolutionary aspect is the "inverse entailment". I try to bring that out in plain graphics, whereas relational biology keeps it hidden behind efficient maps. I think that was a major limitation, but probably a necessary one to allow some gradual absorption from present world views.  R-theory makes all four causes into explicit mappings and that gives a very parsimonious view of the whole. In contrast the relational algebra in Category Theory is indeed more difficult but mathematically provable, whereas I have to rely on that proof. So, we are only now getting the usable formalism. The language of "entailment" allows set relations that are not mere syntax, however I think we needed first to understand the holistic implications to have some order to impose on these greatly expanded possibilities. This kind of unity will not "fraction" nature as the idea of mechanism does. Similarly, torsion geometry and other ways of approaching non-linearity are relevant, but they are still approaching the problem from  syntax to semantics instead of the other way around. Rosen was adamant that "there is no syntactic bridge" to the natural world of relational complexity; however he did not say there is no semantic bridge in the other direction. Generalizing syntactic laws opens to infinite possibilities, but going in the other direction imposes a natural order on the relations that then becomes tractable.  Indeed "closed loops of causation" appear to be a tremendous generalization, but they are not the goal of analysis, they are the starting point - which is also why the approach is revolutionary and I think why Rosen knew it would not be accepted in his lifetime.

Sorry if this has been long - I wanted to collate the comments and think about their implications. Please let me know what I have missed.

Yours,

John 

 

 

[Diego Lucio Rapoport]

Dear John

thanks for your reply. Indeed, category theory as topoi goes beyond dual logic, however it was not applied nor by Rosen nor his continuators.

The point is that the unconstructibility of examples of his categories invalidate his valid own criticism of simulation (however abstract his approach was)

rather than the "real mathematical object", but this shared with all mathematical analysis !!!.

I fully agree with Rosen that there is no purely syntactic "bridge" to contextualize, however i fully disagree that this is the case of  nonlinearity which generically has torsion as its physical AND SEMIOTIC embodiment and origin, The closed loops that Rosen precisely invoked, but extended to multiple contextualization as HyperKlein bottle.

As for Rosen's "revolution" he referred to that part of his theory in which he wanted to  construct one universal example of his categories, through consideration of differentials that precisely lead to the topologies of torsion!!

Rosen should have, at least, taken a basic pregraduate course on calculus on manifolds; his ignorance of the basic maths of his own proposal was, to say the least, appalling. His manifesto for this "revolution" in terms of differential forms he copied and pasted in almost all of his books verbatim, with no elaborations. He actually did not heed his mentor's, Rashevsky, insights.

(I discussed this in Part I of my latest trilogy and the whole background, you may see you my "Klein bottle Logophysics, Self-reference, Genomic Topologies, Harmonics and Evolution").

Not to mention his ignorance that his own proposal had been started to be elaborated in physics already 50 years before him, and in biology 20 years before him, that both were being ellaborated contemporarily to him !!

For all his hype and shortcomings, i agree with some of his insights, and consider to have elaborated related ideas in my own work on the Klein bottle logophysics. As for the issue of computability, genomes appear to be algorithmically generated from the Klein bottle and very simple automata, incorporating contextuality in the Klein bottle logic, from its very form !

Sincerely,

Diego Lucio Rapoport

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[Bruno Marchal]

Hi John,

I think you missed my point, perhaps. Let me sum up. Robert Rosen misunderstood, I think, the "Church-Turing" thesis, also called "Church's thesis by him and most (old enough)  logicians. But he get correct conclusions, and is well inspired in his use of category theory. 

My point is that such an argumentation is already made by the universal machine (the Gödel-Löbian kind, that is those who knows that they are universal, like the so-called "sufficiently rich universal system). So, would Rosen be correct in his conclusion, that would be a confirmation of the post Gödel form of mechanism. 

The (psychological, conscious) life of the machine cannot be mechanical, nor can its physics be, indeed, even up to a point that mechanism might be refuted by the current physics for the reason that our physics inferred by observation would look too much mechanical, nevertheless, up to now, the quantum phenomenon confirms classical mechanism in philosophy of mind (I can give references on this if you are interested).

In fact, thanks to incompleteness, we can argue that Mechanism is quasi literally a powerful vaccine against the reductionist conception of numbers, machines and then of all relative life forms a fortiori.

Best Regards,

Bruno Marchal

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[john.kineman]

Hi Diego,

This is an older discussion, but one I stumbled upon just now and I think I never followed up on these comments. I'd like to take it up in a bit more detail if you are willing.

Instinctively I am skeptical about your criticisms of Rosen's intelligence and training - many who knew him considered him a genius, as do I. However, there are major gaps that I tried to fill by following the tracks he laid down. Mainly, he refused to do a synthesis, claiming it was too soon for that. Of course one has to suspect if he really knew how, or was just intuiting it, but in any case I have not found a single error in his logic but for not following it to its holistic conclusion. I think the times were not right and job security was an issue. He specifically said all the pieces of a complete theory are there in his publications, but he did not want to be the one to do the synthesis, preferring, I think, to present a puzzle like Fermat's last theorem. His command of calculus and higher quantitative math is not in question here, I'm fairly sure.

That leads me to think there is some other issue involved in giving the impression that he missed something or merely reinvented current work. I don't think either is the case. Certainly what he was saying had been proposed in physics. He has a whole chapter in Essays saying so and citing Schrodinger. However, as he also points out, Schrodingers profound point was ignored and is to this day. There is a collective myopia about final and formal cause and it is not easy to correct it because people will attack the philosophy without following the logic. So, he went to great pains to prove the assertions, and his life's work was mainly to provide an irrefutable proof, not to claim that the ideas were first thought of by him but to show how they were expunged from modern science intentionally and on false grounds. He was bringing back discarded ideas and giving them a mathematical underpinning. It was the proof that was new, not the concept.

I am curioius, however, about your reference to "Tortion" -- I have heard that a lot in paranormal research - Claud Swanson has books claiming that torsion has been the missing 5th element and basis for subtle energy phenomena. But I don't understand tortion. I know it is not the classical definition of torque forces, but rather a twisting in space-time of some sort. Can you explain it?

My own synthesis of Rosen's work results in definition of a holon which is a circular causality moving between local and non-local domains - I'm now wondering if in some way that itself could correlate with this idea of torsion??

Any thoughts?

John

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