Maturana and Quantum Measurement: possible links (or absence thereof)
Brief Review of Single Qubit Measurement (+ 1st part of Intro)
As discussed in class[1], exploring, understanding, and starting to live with quantum phenomena at hand constitutes a revolution in a broad spectrum of human endeavor. So-called natural language (in the context of social, historical, cultural, biological, human evolution) fails to express the complexities of such phenomena, in the sense that they bring about new ontological categories and disturb many of the notions that appear to be true and valid in our mid-sized world. I am only making these frivolous statements to annoy Kevin. Beware, there’s more on the way!
Natural language finds itself lagging behind the more abstract approach of mathematics. Math seems to be the more complete and general expression of quantum phenomena, due to the fact that empirical observations and measurements disrupt the systems and force them to materialize in certain ways.
At a given moment, a qubit is materialized in a specific state corresponding to any one of an infinite number of measurable properties (in the following diagram, the qubit |Ψθ> is in an eigenstate of the measurable property that goes along the MΦ measurement axis). In regards to its other properties, it maintains them in a state of superposition: it is neither in one state or the other, yet in both. Superposition is not a mixed state, as we would say of regular bits when faced with a lack of information. This is a pure state and represents the maximal amount of knowledge we can have about the system.
When we measure a property other than the one the qubit happens to be materialized in, the qubit pops out of existence in regards to its original property and materializes assuming one of the two eigen states of the newly measured property. It seizes to be in a state of superposition of the newly measured property, goes to a state of superposition of the former property, and maintains superposition in regards to all others. Just which eigen state the qubit will assume in regards to the newly measured property constitutes a truly random occurrence, in the most strict sense of the word. This is represented in the following way:
Born's Rule
Here, each point on the circle represents a measurable property. The vertical is a measurement of MΦ degrees. The eigenstates of that property are the points corresponding to 0 and 180 degrees along that measurement axis (in this case they actually correspond).
|Ψθ> is in a superposition in regards to MΦ, so to obtain the value of that measurement, we project the qubit onto the vertical and calculate the following way:
Prob of (+1) = α = 1/2 (1 + cosθ)
Prob of (–1) = 1 – α = 1/2(1 – cosθ)
With repeated measurements on single qubits from the same ensemble, we obtain a probabilistic idea of the initial state. In this case, the set of probabilities would also correspond to the initial state found if we reflected |Ψθ> along the vertical.
This mathematical representation, then, apparently carries with it more information about the nature of qubits than what could be attained through any individual observation on an actual qubit. “It represents something that doesn’t ordinarily present itself fully” through any known means, as Professor Imbo points out in class.
The only way to “observe” is actually imposing a measurement; a measurement being an interaction between two non-living things[2]. Up to now, and after over 80 years of experimentation, nothing has effectively eliminated, or even reduced, the alteration that a measurement imposes on a qubit. Mathematics is the language of choice when referring to these systems; some physicists argue that the true nature of qubits is purely mathematical.
This new category of entities that appear to inhabit this mathematical, non-spatial space also brings about a new domain of existence for the observer bringing forth these distinctions; a domain which is within science, which can be accessed from classical science (even though it lies outside the classical world), which can apparently be explained in terms of classical logic but that functions under an internal logic which is non-classical. Up to now, there are no mid-sized world analogies that seem to completely put the finger on what’s going on in the quantum world, not literally or metaphorically.
In order to explain things, we must bring them into language, and language is the domain of that which is known (or knowable). The fact that math can precisely describe a qubit’s behavior where all other language fails opens multiple fields for exploration.
We can look into language, its nature, the way it functions, the underlying principles behind the notions of representation, communication, etc, in math or any other language system. Nonetheless, language cannot happen independently from an observer. Everything said is said by an observer, and in our case, this observer observes from the domain of human existence, one that entails a broad range of dimensions, most of which are studied and/or arise with the use/aid of language and languaging.
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[1] Most of this section was developed from notes of the lectures given by Professor Imbo and the subsequent discussions
[2] Particles may effectively impose measurements on each other, background radiation can impose measurements as well (Polkinghorne, 2002). We won’t necessarily know when these measurements happen, though.
2nd Intro: A look at Maturana and what I plan to do in this paper
A lot of pages have been shed with numerous explanations regarding language. A few of these come from the pen of Humberto Maturana, a Chilean Neurobiologist who has dedicated more than 50 years of research into perception, cognition, and language. Anchored in the point of view of an experimental-biologist-epistemologist, he has systematically explored the implications of his findings in various fields including cybernetics, psychology, sociology, education, and philosophy of science.
In 1972, along with Varela, he comprised the theory of autopoiesis following the pathways of Bateson, Wittgenstein, the social ‘ricorso’ of Vico, the self-production notion of Paul Weiss, and many others[3]. I will attempt to concisely tackle a brief segment of his insights[4], and at some points make reference to Heidegger’s Various Ways of Questioning About the Thing[5], in order to look at the ontology of language and then at some analogies with the qubit measuring process.
All this, having in mind a complication that Maturana explicitly and recursively addresses: language is part of the problem to be explained, and for that, we have to stay within its bounds, and within the bounds of my being an observer (with a somewhat limited view) generating an explanation. Since explanations are usually generated in a metadomain in regards to that which they explain, this can be a bit problematic. Qubits refuse to come into natural language, and to explain natural language itself I am unable to step out of it. Some of the sentences may sound circular. My apologies.
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[3]According to a brief biography found on http://www.oikos.org/maten.htm. Another source for biographical data was found at http://en.wikipedia.org/wiki/Maturana
[4]I will mainly explore Maturana’s notions of language and its function, while touching on some of the operations that bring it about, focusing on his works “The Biology of Language: An Epistemology of Reality” as well as on “The Ontology of Observing: The Biological Foundations of Self Consciousness and the Physical Domain of Existence”. The latter is a more technical, condensed workbook he prepared for a conference at the American Society for Cybernetics.
[5]This will be based on an initial, fresh view of the paper of reference. I am by no means a specialist on Heidegger. Eventhough Maturana and Heidegger apparently share in the systematic approach, their starting points, vocabularies and frames of reference are quite different. Intertextualizing all of it would go beyond the scope of this paper, nonetheless, if we read into Maturana’s account on “composite unities”, we can see a certain resemblance with Heidegger’s “the thing as a bearer of properties”. Also, both authors put into question what is put into question and how it is put into question, before engaging their explanations. Their subject of analysis in regards to historicity, though, occurs at different domains: simply put, in the paper of reference, Heidegger questions what is a thing, and for the purpose of my paper, I will be referring to one of Maturana’s questions from the referenced books: how do we talk about things.
Language, Distinctions, Descriptions, Explanations…
Language, whether in its restricted or in its generalized form, can be considered as a system of arbitrary signals which communicate thoughts or feelings (Wikipedia, 2006). Maturana and Varela critique the broader definition of language as a denotative system of symbolic communication, composed of notations that denote entities regardless of the domain in which these entities may exist. We use language to refer to our everyday experiences full of objects, abstractions, emotions, language itself, etc., as well as things that don’t readily exist (like Goodman’s unicorn or Quine’s Pegasus). Mathematics is in itself a coherent language that constantly functions referring to things whose (material) existence could be questioned.
According to Maturana, understanding the evolutionary origin of natural language requires the acknowledgement of a basic biological process that could generate it. This understanding has been quite elusive, because of the very definition just announced: language is usually analyzed as a denotative system of symbolic communication. If language operated this way in a linguistic interaction, then its evolutionary origin would demand the preexistence of denotation for agreement on the symbolic values of the arbitrary components of the system of communication. Yet denotation[6] is the very function whose evolutionary origin should be explained.
Maturana (1978) states that denotation is not a primitive operation; it requires agreement consensus for the specification of the denotant and the denoted. He then goes on to say that if denotation is not a primitive operation, it cannot be a primitive linguistic operation, either. Language must arise as a result of something else that does not require denotation for its establishment, but that gives rise to language with all its implications as a trivial necessary result. This fundamental process, according to Maturana, is “ontogenic structural coupling,” which results in the establishment of a consensual domain (1978, p.24)
That last phrase is quite packed, though. So let’s start by saying, first of all, that Maturana and Varela, (1980) assert that living systems are autonomous entities[7] (this autonomy is the result of their organization as systems in continuous self-production, even though they depend on a medium for their concrete existence and material interchange). When different organisms interact recursively, each becoming a medium for the realization of the other, the result is mutual ontogenic structural coupling (Maturana 1978).
The various modes of conduct under their reciprocal interactions is established during the history of their interactions and through their interactions. These are arbitrary and contextual: Arbitrary, because they can have any form as long as they effectively affect the interactions; and contextual, because their participation in the interlocked interactions is defined with respect to the interactions that constitute the domain. Thus is born what Maturana (1975) calls the consensual domain.
So, for now, let us consider that language is a system of generative consensual interactions; and that denotation is a recursive consensual operation within language. As said above, denotation arises only in a metadomain as an a posteriori commentary made by the observer about the consequences of operation of the interacting systems.
According to all this, then, when linguistic behavior takes place recursively, in a second-order consensual domain, in such a manner that the components of the consensual behavior are recursively combined in the generation of new components of the consensual domain, a language is established.
With all this in mind, the fundamental operation that an observer can perform is that of a distinction: the specification of an entity by operationally cleaving it from a background (Maturana 1986). This has some resonance with the way Heidegger defines the function of naming, as belonging to “the most primordial way of speaking in general… not a substitution, not a second or latter order of expression.” (1968, p.25-26).
Maturana goes on to say: “that which results from an operation of distinction and can thus be distinguished is a thing with the properties that the operation of distinction specifies, and which exists in the space that these properties establish”[8] (1978, p.29). Heidegger would reply to this: “to go straight to the things cannot be carried out” the determinations and attributes which we relate to the thing –“space, time, and ‘this’– … present themselves as determinations which do not belong to the thing itself” (p.27). In Maturana’s terms, at the moment in which a community of observers refers to the thing as “this” thing, we establish a consensual domain in regards to the thing.
Heidegger, in his chalk example[9], follows an according approach. After seeing how spatial and temporal distinctions don’t belong to things in the sense that these distinctions change and the thing maintains its thingness, he goes on to say that if we maintain these distinctions as our truths, the closer we come to knowing what the thing is for itself. This maintaining of distinctions as our truths, corresponds to Maturana’s higher-order consensual domains.
It can only be our truth when we recognize our operation of naming the thing: in Heidegger’s example, the operation of writing it down and how the thing refers to the chalk and the written word denotes it (this time, in a second-order consensual domain).
Human beings can talk about things because they generate them by making distinctions that specify them in a consensual domain. Also, operationally, talking takes place in the same phenomenic domain in which things are defined. Human beings can only talk about that which they can specify through their operations of distinction. Of course, anything that can be distinguished by any means or operation accessible to us (perception, intuition, instruments, thought experiments, observations in regards to second- or n-order consensual domains…) counts. “We literally create the world in which we live by living it. If a distinction is not performed, the entity that this distinction would specify does not exist; when a distinction is performed, the created entity exists in the domain of the distinction only, regardless of how the distinction is performed” (1978, p. 34).
A description always implies an interaction by a member of a domain of consensus. The domain of descriptions is necessarily bounded by the ultimate possible interactions of the organism through its components. Nonetheless, language permits descriptions of entities in as many different domains as can be defined consensually, no matter how far from actual interactions they may seem to an observer. The domain of descriptions is treated as a metadomain that exists only in a consensual domain in reference to another domain.
Maturana treats explanations as “conceptual or concrete systems that are deemed as models of the systems that generate the observed phenomena” (Maturana, 1978, p.5); they are intended reproductions or reformulations of a system or phenomenon. We can see this more systematically by looking at his analysis of the scientific method, making its biological foundations explicit (see 1978, p.4-6; 1988, p.5). Briefly:
If all these criterions are “conjointly” met, then the explanation becomes a scientifically valid explanation. By following this method, the observer determines an appropriate domain in which the system or phenomenon exists, as well as the domain in which the explanation will be given and in which the reproduced system will exist. Of course, the explanation is in no way the thing itself: “it takes place in the praxis of living of the observer in a different phenomenal domain than the phenomenal domain in which the phenomenon to be explained is witnessed, and the latter as a consequence of the former stands in an operational metadomain with respect to it” (1988, p. 5).
Maturana states that “many scientists and philosophers of science believe that without the independent existence of an objective reality, science could not take place”. He goes on to say that scientific explanations do not require the assumption of objectivity because scientific explanations do not explain an independent objective reality, they explain a set of operational coherences set forth by a community of scientists (or “standard observers”). Its operational effectiveness as a cognitive domain rests mainly on the fact that the modes of operation of this particular consensual domain have been well outlined, studied, systematically critiqued and improved. “Science is not a manner of revealing an independent reality, it is a manner of bringing forth a particular one bound to the conditions that constitute the observer as a human being”. (1978, p.4-6)
The extent of what an organism can do is determined by its organization and structure, and all that an organism can do constitutes its cognitive domain. Our cognitive domain is bounded and unlimited in the same manner in which our domain of reality is bounded and unlimited. Varela would later add: “cognition consists not of representations but of embodied action. Correlatively, the world we know is not pregiven, it is enacted through our history of structural coupling” (p. 336, article provided by Ellen).
Knowledge implies interactions, and we cannot step out of our domain of interactions, which is closed. We live, therefore, in a domain of subject-dependent knowledge and subject-dependent reality. That there is an external, objective, independent reality, in coordination with which we construct our consensual domains, granted. That we can access it, or speak about it in strictly objective terms, seems rather bleak at this point, for currently, we speak from language and this necessarily implies interactions.
Our consensual domains carry the weight of history, and all new distinctions we make are inevitably bounded by that which is known. The greater portion of our history as human beings is entangled with the so-called natural language, with the distinctions made remotely and the structures set in place to describe a reality coherently in terms of those living in it.
The quest for objectivity and the true nature of things has taken us a long way, and the operational coherences set forth in this search have been fruitful. The subatomic level of things, the foundational particles that comprise our physical world, tell an interesting story.
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[6]We saw in Goodman (1968), in the case of pictorial representation, that a picture can denote x in order to represent it, but needs not denote anything to be an x-representation.
[7]The foundations of autopoiesis, briefly stated, would go something like this: Living systems are autonomous, self-referring and self-constructing closed systems, which set out to the task of continually producing themselves no matter the circumstances. If this fails, the system disintegrates or dies. In the words of Cohen and Wartofsky (1979), “Maturana and Varela propose a theoretical biology which is topological, and a topology in which elements and their relations constitute a closed system, which is entirely self-referential and has no ‘outside’, Leibnizian for our day”. (p. v)
[8]Here, I will define the observer (by implication) as the system which can make distinctions and specify that which it distinguishes as something different from itself. Maturana’s treatment of the observer focuses specifically on living systems, and is broadly developed in all of the cited works. He also goes into the source of “self-counsciousness” as strongly correlated to the observer (1988, p.44). While this is a very important point of his work, that particular distinction is not all that relevant for us in the present paper.
[9]Heidegger (1968) pp. 27-31: After ascertaining the spatial ‘truth’ that the distinction “this” imposes on his chalk, in order to avoid loosing this “great valuable”, Heidegger writes it down on a piece of paper (“here is the chalk”) which is eventually blown away (from the chalk). A person finds the paper in the hallway and claims the statement to be false. So Heidegger then claims that the truth was entrusted to an unstable piece of paper, and that it was actually a half truth. He goes on to write “Here is the chalk and right now – and now is the afternoon”, on the blackboard, getting at the temporal ‘truth’ too, and making sure it won’t be blown away. After class is over someone comes in and claims the statement to be false, it is no longer the afternoon. The chalk is always a “this”; through his examples, he made this an independent truth by writing it down, and then considers it better to keep the truth with us, either dropping or enduring the fear of subjectivism.
So what about Qubits?
That our access to the nature of an objective, independent reality is apparently shaken by quantum mechanics and the role of observation, is not what I wish to discuss (even though it was one of the directions I explored before ending up here). In effect, one can’t objectively know the properties of a qubit without objectively altering them. One cannot know what is happening in the subatomic world unless one observes, and, as stated at the beginning, an observation is a measurement in this realm of existence, as we now know it.
Nonetheless, it is not the observer who yanks the qubit in and out of existence or who collapses the wave function, it is the measurement. Measurements are imposed in the absence of an observer, in the absence of consciousness (as it is ordinarily understood, and yes I will leave it at that :) ). Presumably, measurements have been happening (and still do) in places far removed from our ordinary consciousness. That we have access to these things that happen outside of our consciousness and outside of our imagination and outside of our language is another story.
In order for an observer to look into the quantum world, a measurement has to be done, a qubit is forced out of a potential superposition and materializes in an eigen state of the property being measured. What effectively happens in absence of our observations is something that still requires more study, and that presently, appears to be quite hard a question to objectively answer.
So, finally..: the Mix!
Human beings can only talk about that which they can specify through their operations of distinction. The operations of distinction involving the distinctions of qubits are new of their kind. Language, logic, and most of our knowledge of the world and our systems of interacting with it (including experimental apparatus in quantum physics) rest in the classical domain of existence.
The quantum reality is accessible to us only by a combination of second- and third-order distinctions in consensual domains: namely mathematical abstraction, experimental apparati, and quantum physics.
As quoted above, “we literally create the world in which we live by living it. If a distinction is not performed, the entity that this distinction would specify does not exist; when a distinction is performed, the created entity exists in the domain of the distinction only, regardless of how the distinction is performed.” (Maturana, 1978, p. 34)
Following this phrase in this context, we can attempt an M-move: Language is the “measurement apparatus” with which we specify entities by operationally cleaving them from a background. Before we actually do this, the entities may virtually be there, nonetheless, there is not much we can know or say about them. We drag them into existence making way along our a priori categories (which might be morphed to function as eigenstates?) and then progressively adjusting them into new ones, always in a consensual domain, in a sense that coordinates actions and behaviors in a coherent way.
Here’s a potential laugh for you guys: Perhaps it would be interesting to analyze some of the passages in Genesis with this in mind. The Earth was formless and empty and dark, then God pops up and starts saying (using language?) “let there be light”, and light appears (photons?), and so on…
Having binary logic brought forth in our classical, mid-sized world, and using it to effectively interact with it, reinforces this logic. When languaging and bringing things into existence, we bring them into a domain that functions with these a priori distinctions, and thus the things we distinguish exist in this domain as well.
Qubits don’t obey this. Physicists have had to struggle with math, logic and natural language in order to be able to explain what is going on. They force us into new domains. As noted at the beginning, they are accessible through classical science and with our classical notions. Yet, their internal functioning is non-classical. Having made these distinctions in the actual physical world is outstanding, it brings us to reconsider all that is known. Perhaps if we could somehow function following the logic of qubit systems things would be different. Perhaps this goes beyond logic, or logic is something that belongs in this broader picture that qubits paint. Speculations, speculations….
The M-move falls short though, and I will pose some questions which can perhaps be more thoroughly looked into at another time. Of course, we would have to set out to the task of defining terms homologous to those treated at the beginning (as well as for many other terms and mathematical entities that are worked with in quantum physics), as well as their implications, in the natural language linguistic domain.
Are things actually superposed before language “measures” them? If I measure something with language, in regards to a given property, do I send the other properties to a superposition? Will the measured property assume an eigen state? The superposition principle holds together “alternative, and eventually mutually exclusive, possibilities right until the last moment, when suddenly one of them alone surfaces as the realized actuality” (Polkinghorne, 2002, p.44) on a given occasion. Is this the case with things as they are being measured with language?
Do we know what we’ll get after we ‘measure’ with language? With qubits, Born’s rule tells us we can expect stochastic outcomes, it delimits them as a range of probabilities. In language, elements of choice are present, and we don’t necessarily follow strict, scientific, rules. The community of observers who establish language has not set forth a set of coherent, scientific procedures to do so; it has not been utterly necessary safe in very specific domains.
Speculations (and more frivolous statements)
We have ‘created’ qubits, in linguistic terms, by bringing them forth as distinctions. The domain of this distinction is in math and that is where the qubits actually live. Natural language hasn’t captured all of these distinctions.
In order to bring qubits to life in other ways, we need to make new distinctions, not only on the qubits themselves, but also on the world ‘around’ us. Eventhough the mid-sized and quantum worlds are currently treated as non-intersecting phenomenal domains in our day to day existence, employing quantum reasoning or concepts in the former (even if initially in a somewhat loose way, as I am doing here) will bring forth distinctions that will progressively lessen the gap between math and natural language. As these new classes of distinctions become more engraved in our world, they can eventually be posed back upon the quantum reality. We can also look for distinctions in other disciplines from the mid-sized world and see if they fit the quantum one.
There are still mysteries in regards to how reality is “actualized” through our senses, physically encoded into cognition, or vice versa (how our senses encode the reality we live in). The world is apparently infinite, we are finite beings that apparently interact with it through a biological structure which is not completely understood. If all matter/energy can indeed be described by the wavefunction, stimuli would tend to be rather continuous, nonetheless some studies and philosophical positions suggest that we perceive reality in discrete chunks. It is a neurological fact that there is no way (internally) for us to distinguish between illusions, hallucinations, and “real” things; these notions obey social consensus, consensual operations of distinguishing, and the comparison of our ‘perceptions’ to those of others or of a consensual source. Goodman and Allen both touch on this.
One last frivolous statement…
We do not exist in a pre-existing domain of physical existence; we bring it forth and specify it as we exist as observers. The experience of the physicist, be this in classic, relativistic or quantum physics, does not reflect the nature of “the universe”; it reflects the ontology of the observer as a living system as he or she operates in language bringing forth the physical entities and the operational coherences of their domains of existence.
Bibliography
Imbo, Tom; Huggett, Nick; and Grimes, Ellen. Entangled Identities: Systems in Physics, Philosophy, and Architecture. (Oral) Class Lectures. Summer 2006. University of Illinois at Chicago.
Maturana, H.R.; and Varela, F.G (1972 and 1980). De máquinas y seres vivos, Editorial Universitaria, Santiago, Chile, 1972 (in Spanish).
Autopoiesis and Cognition: the realization of the living, Boston Studies in the Philosophy of Science, Vol 42, Reidel Publishing, 1980 (in English).
Maturana, Humberto R. (1978) Biology of language: The epistemology of reality, Chapter 2 in Miller, George A., and Elizabeth Lenneberg (eds.), Psychology and Biology of Language and Thought: Essays in Honor of Eric Lenneberg, New York: Academic Press, pp. 27-63.
Maturana, Humberto (1988). Ontology of Observing, The biological foundations of self consciousness and the physical domain of existence, Conference Workbook: Texts in Cybernetics, American Society For Cybernetics Conference, Felton, CA. 18-23 October, 1988.
Maturana, Humberto (1999) Autopoiesis, Structural Coupling and Cognition, (draft version in: http://www.isss.org/maturana.htm)
Heidegger, Martin (1968) What is a thing? Regnery Publications.
Goodman, Nelson (1968). An Approach to the Theory of Symbols. Bobbs-Merril.
Varela, Francisco. Article provided by Ellen.
Humberto Maturana (biography). Ecology of Mind Website. http://www.oikos.org/maten.htm.
Humberto Maturana. Wikipedia Free Encyclopedia Article. http://en.wikipedia.org/wiki/Maturana
Polkinghorne, John (2002). Quantum Theory, A Very Short Introduction. New York: Oxford University Press.
Natural language finds itself lagging behind the more abstract approach of mathematics. Math seems to be the more complete and general expression of quantum phenomena, due to the fact that empirical observations and measurements disrupt the systems and force them to materialize in certain ways.
At a given moment, a qubit is materialized in a specific state corresponding to any one of an infinite number of measurable properties (in the following diagram, the qubit |Ψθ> is in an eigenstate of the measurable property that goes along the MΦ measurement axis). In regards to its other properties, it maintains them in a state of superposition: it is neither in one state or the other, yet in both. Superposition is not a mixed state, as we would say of regular bits when faced with a lack of information. This is a pure state and represents the maximal amount of knowledge we can have about the system.
When we measure a property other than the one the qubit happens to be materialized in, the qubit pops out of existence in regards to its original property and materializes assuming one of the two eigen states of the newly measured property. It seizes to be in a state of superposition of the newly measured property, goes to a state of superposition of the former property, and maintains superposition in regards to all others. Just which eigen state the qubit will assume in regards to the newly measured property constitutes a truly random occurrence, in the most strict sense of the word. This is represented in the following way:
Born's RuleHere, each point on the circle represents a measurable property. The vertical is a measurement of MΦ degrees. The eigenstates of that property are the points corresponding to 0 and 180 degrees along that measurement axis (in this case they actually correspond).
|Ψθ> is in a superposition in regards to MΦ, so to obtain the value of that measurement, we project the qubit onto the vertical and calculate the following way:
Prob of (+1) = α = 1/2 (1 + cosθ)
Prob of (–1) = 1 – α = 1/2(1 – cosθ)
With repeated measurements on single qubits from the same ensemble, we obtain a probabilistic idea of the initial state. In this case, the set of probabilities would also correspond to the initial state found if we reflected |Ψθ> along the vertical.
This mathematical representation, then, apparently carries with it more information about the nature of qubits than what could be attained through any individual observation on an actual qubit. “It represents something that doesn’t ordinarily present itself fully” through any known means, as Professor Imbo points out in class.
The only way to “observe” is actually imposing a measurement; a measurement being an interaction between two non-living things[2]. Up to now, and after over 80 years of experimentation, nothing has effectively eliminated, or even reduced, the alteration that a measurement imposes on a qubit. Mathematics is the language of choice when referring to these systems; some physicists argue that the true nature of qubits is purely mathematical.
This new category of entities that appear to inhabit this mathematical, non-spatial space also brings about a new domain of existence for the observer bringing forth these distinctions; a domain which is within science, which can be accessed from classical science (even though it lies outside the classical world), which can apparently be explained in terms of classical logic but that functions under an internal logic which is non-classical. Up to now, there are no mid-sized world analogies that seem to completely put the finger on what’s going on in the quantum world, not literally or metaphorically.
In order to explain things, we must bring them into language, and language is the domain of that which is known (or knowable). The fact that math can precisely describe a qubit’s behavior where all other language fails opens multiple fields for exploration.
We can look into language, its nature, the way it functions, the underlying principles behind the notions of representation, communication, etc, in math or any other language system. Nonetheless, language cannot happen independently from an observer. Everything said is said by an observer, and in our case, this observer observes from the domain of human existence, one that entails a broad range of dimensions, most of which are studied and/or arise with the use/aid of language and languaging.
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[1] Most of this section was developed from notes of the lectures given by Professor Imbo and the subsequent discussions
[2] Particles may effectively impose measurements on each other, background radiation can impose measurements as well (Polkinghorne, 2002). We won’t necessarily know when these measurements happen, though.
2nd Intro: A look at Maturana and what I plan to do in this paper
A lot of pages have been shed with numerous explanations regarding language. A few of these come from the pen of Humberto Maturana, a Chilean Neurobiologist who has dedicated more than 50 years of research into perception, cognition, and language. Anchored in the point of view of an experimental-biologist-epistemologist, he has systematically explored the implications of his findings in various fields including cybernetics, psychology, sociology, education, and philosophy of science.
In 1972, along with Varela, he comprised the theory of autopoiesis following the pathways of Bateson, Wittgenstein, the social ‘ricorso’ of Vico, the self-production notion of Paul Weiss, and many others[3]. I will attempt to concisely tackle a brief segment of his insights[4], and at some points make reference to Heidegger’s Various Ways of Questioning About the Thing[5], in order to look at the ontology of language and then at some analogies with the qubit measuring process.
All this, having in mind a complication that Maturana explicitly and recursively addresses: language is part of the problem to be explained, and for that, we have to stay within its bounds, and within the bounds of my being an observer (with a somewhat limited view) generating an explanation. Since explanations are usually generated in a metadomain in regards to that which they explain, this can be a bit problematic. Qubits refuse to come into natural language, and to explain natural language itself I am unable to step out of it. Some of the sentences may sound circular. My apologies.
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[3]According to a brief biography found on http://www.oikos.org/maten.htm. Another source for biographical data was found at http://en.wikipedia.org/wiki/Maturana
[4]I will mainly explore Maturana’s notions of language and its function, while touching on some of the operations that bring it about, focusing on his works “The Biology of Language: An Epistemology of Reality” as well as on “The Ontology of Observing: The Biological Foundations of Self Consciousness and the Physical Domain of Existence”. The latter is a more technical, condensed workbook he prepared for a conference at the American Society for Cybernetics.
[5]This will be based on an initial, fresh view of the paper of reference. I am by no means a specialist on Heidegger. Eventhough Maturana and Heidegger apparently share in the systematic approach, their starting points, vocabularies and frames of reference are quite different. Intertextualizing all of it would go beyond the scope of this paper, nonetheless, if we read into Maturana’s account on “composite unities”, we can see a certain resemblance with Heidegger’s “the thing as a bearer of properties”. Also, both authors put into question what is put into question and how it is put into question, before engaging their explanations. Their subject of analysis in regards to historicity, though, occurs at different domains: simply put, in the paper of reference, Heidegger questions what is a thing, and for the purpose of my paper, I will be referring to one of Maturana’s questions from the referenced books: how do we talk about things.
Language, Distinctions, Descriptions, Explanations…
Language, whether in its restricted or in its generalized form, can be considered as a system of arbitrary signals which communicate thoughts or feelings (Wikipedia, 2006). Maturana and Varela critique the broader definition of language as a denotative system of symbolic communication, composed of notations that denote entities regardless of the domain in which these entities may exist. We use language to refer to our everyday experiences full of objects, abstractions, emotions, language itself, etc., as well as things that don’t readily exist (like Goodman’s unicorn or Quine’s Pegasus). Mathematics is in itself a coherent language that constantly functions referring to things whose (material) existence could be questioned.
According to Maturana, understanding the evolutionary origin of natural language requires the acknowledgement of a basic biological process that could generate it. This understanding has been quite elusive, because of the very definition just announced: language is usually analyzed as a denotative system of symbolic communication. If language operated this way in a linguistic interaction, then its evolutionary origin would demand the preexistence of denotation for agreement on the symbolic values of the arbitrary components of the system of communication. Yet denotation[6] is the very function whose evolutionary origin should be explained.
Maturana (1978) states that denotation is not a primitive operation; it requires agreement consensus for the specification of the denotant and the denoted. He then goes on to say that if denotation is not a primitive operation, it cannot be a primitive linguistic operation, either. Language must arise as a result of something else that does not require denotation for its establishment, but that gives rise to language with all its implications as a trivial necessary result. This fundamental process, according to Maturana, is “ontogenic structural coupling,” which results in the establishment of a consensual domain (1978, p.24)
That last phrase is quite packed, though. So let’s start by saying, first of all, that Maturana and Varela, (1980) assert that living systems are autonomous entities[7] (this autonomy is the result of their organization as systems in continuous self-production, even though they depend on a medium for their concrete existence and material interchange). When different organisms interact recursively, each becoming a medium for the realization of the other, the result is mutual ontogenic structural coupling (Maturana 1978).
The various modes of conduct under their reciprocal interactions is established during the history of their interactions and through their interactions. These are arbitrary and contextual: Arbitrary, because they can have any form as long as they effectively affect the interactions; and contextual, because their participation in the interlocked interactions is defined with respect to the interactions that constitute the domain. Thus is born what Maturana (1975) calls the consensual domain.
So, for now, let us consider that language is a system of generative consensual interactions; and that denotation is a recursive consensual operation within language. As said above, denotation arises only in a metadomain as an a posteriori commentary made by the observer about the consequences of operation of the interacting systems.
According to all this, then, when linguistic behavior takes place recursively, in a second-order consensual domain, in such a manner that the components of the consensual behavior are recursively combined in the generation of new components of the consensual domain, a language is established.
With all this in mind, the fundamental operation that an observer can perform is that of a distinction: the specification of an entity by operationally cleaving it from a background (Maturana 1986). This has some resonance with the way Heidegger defines the function of naming, as belonging to “the most primordial way of speaking in general… not a substitution, not a second or latter order of expression.” (1968, p.25-26).
Maturana goes on to say: “that which results from an operation of distinction and can thus be distinguished is a thing with the properties that the operation of distinction specifies, and which exists in the space that these properties establish”[8] (1978, p.29). Heidegger would reply to this: “to go straight to the things cannot be carried out” the determinations and attributes which we relate to the thing –“space, time, and ‘this’– … present themselves as determinations which do not belong to the thing itself” (p.27). In Maturana’s terms, at the moment in which a community of observers refers to the thing as “this” thing, we establish a consensual domain in regards to the thing.
Heidegger, in his chalk example[9], follows an according approach. After seeing how spatial and temporal distinctions don’t belong to things in the sense that these distinctions change and the thing maintains its thingness, he goes on to say that if we maintain these distinctions as our truths, the closer we come to knowing what the thing is for itself. This maintaining of distinctions as our truths, corresponds to Maturana’s higher-order consensual domains.
It can only be our truth when we recognize our operation of naming the thing: in Heidegger’s example, the operation of writing it down and how the thing refers to the chalk and the written word denotes it (this time, in a second-order consensual domain).
Human beings can talk about things because they generate them by making distinctions that specify them in a consensual domain. Also, operationally, talking takes place in the same phenomenic domain in which things are defined. Human beings can only talk about that which they can specify through their operations of distinction. Of course, anything that can be distinguished by any means or operation accessible to us (perception, intuition, instruments, thought experiments, observations in regards to second- or n-order consensual domains…) counts. “We literally create the world in which we live by living it. If a distinction is not performed, the entity that this distinction would specify does not exist; when a distinction is performed, the created entity exists in the domain of the distinction only, regardless of how the distinction is performed” (1978, p. 34).
A description always implies an interaction by a member of a domain of consensus. The domain of descriptions is necessarily bounded by the ultimate possible interactions of the organism through its components. Nonetheless, language permits descriptions of entities in as many different domains as can be defined consensually, no matter how far from actual interactions they may seem to an observer. The domain of descriptions is treated as a metadomain that exists only in a consensual domain in reference to another domain.
Maturana treats explanations as “conceptual or concrete systems that are deemed as models of the systems that generate the observed phenomena” (Maturana, 1978, p.5); they are intended reproductions or reformulations of a system or phenomenon. We can see this more systematically by looking at his analysis of the scientific method, making its biological foundations explicit (see 1978, p.4-6; 1988, p.5). Briefly:
- Observation of a phenomenon, that, henceforth, is taken as a problem to be explained. Here, the observer specifies (either explicitly or implicitly) a procedure of observation (and the provision of the operations to be performed) in order to observe the problem. This in turn specifies the phenomenon to be explained. The better this is done, the more replicability can be assured.
- Proposition of an explanatory hypothesis in the form of a deterministic system that can generate a phenomenon isomorphic with the one observed. Here the observer proposes a conceptual or concrete system, that when operating, gives rise (as a consequence of its operation) to the phenomenon to be explained. In other words, the observer elaborates a model of the system that he or she assumes generates the phenomenon wished to explain.
- Proposition of a computed state or process in the system specified by the hypothesis as a predicted phenomenon to be observed. Here the observer uses the proposed model to compute a state or a process that he or she should be able to witness (in his or her domain of experience, may ultimately be a reading from a dial) as a result of the operation of the specified model.
- Observation of the predicted phenomenon. Here, he or she attempts to observe the predicted phenomenon as a case in the modeled system. If this observation is successful the observer maintains that the explanatory model has been validated and that the system under study is in that respect isomorphic to it and operates accordingly. There are of course necessary constraints for the specification of the model, as well as necessary attempts to deny that the second observations are actually controls.
If all these criterions are “conjointly” met, then the explanation becomes a scientifically valid explanation. By following this method, the observer determines an appropriate domain in which the system or phenomenon exists, as well as the domain in which the explanation will be given and in which the reproduced system will exist. Of course, the explanation is in no way the thing itself: “it takes place in the praxis of living of the observer in a different phenomenal domain than the phenomenal domain in which the phenomenon to be explained is witnessed, and the latter as a consequence of the former stands in an operational metadomain with respect to it” (1988, p. 5).
Maturana states that “many scientists and philosophers of science believe that without the independent existence of an objective reality, science could not take place”. He goes on to say that scientific explanations do not require the assumption of objectivity because scientific explanations do not explain an independent objective reality, they explain a set of operational coherences set forth by a community of scientists (or “standard observers”). Its operational effectiveness as a cognitive domain rests mainly on the fact that the modes of operation of this particular consensual domain have been well outlined, studied, systematically critiqued and improved. “Science is not a manner of revealing an independent reality, it is a manner of bringing forth a particular one bound to the conditions that constitute the observer as a human being”. (1978, p.4-6)
The extent of what an organism can do is determined by its organization and structure, and all that an organism can do constitutes its cognitive domain. Our cognitive domain is bounded and unlimited in the same manner in which our domain of reality is bounded and unlimited. Varela would later add: “cognition consists not of representations but of embodied action. Correlatively, the world we know is not pregiven, it is enacted through our history of structural coupling” (p. 336, article provided by Ellen).
Knowledge implies interactions, and we cannot step out of our domain of interactions, which is closed. We live, therefore, in a domain of subject-dependent knowledge and subject-dependent reality. That there is an external, objective, independent reality, in coordination with which we construct our consensual domains, granted. That we can access it, or speak about it in strictly objective terms, seems rather bleak at this point, for currently, we speak from language and this necessarily implies interactions.
Our consensual domains carry the weight of history, and all new distinctions we make are inevitably bounded by that which is known. The greater portion of our history as human beings is entangled with the so-called natural language, with the distinctions made remotely and the structures set in place to describe a reality coherently in terms of those living in it.
The quest for objectivity and the true nature of things has taken us a long way, and the operational coherences set forth in this search have been fruitful. The subatomic level of things, the foundational particles that comprise our physical world, tell an interesting story.
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[6]We saw in Goodman (1968), in the case of pictorial representation, that a picture can denote x in order to represent it, but needs not denote anything to be an x-representation.
[7]The foundations of autopoiesis, briefly stated, would go something like this: Living systems are autonomous, self-referring and self-constructing closed systems, which set out to the task of continually producing themselves no matter the circumstances. If this fails, the system disintegrates or dies. In the words of Cohen and Wartofsky (1979), “Maturana and Varela propose a theoretical biology which is topological, and a topology in which elements and their relations constitute a closed system, which is entirely self-referential and has no ‘outside’, Leibnizian for our day”. (p. v)
[8]Here, I will define the observer (by implication) as the system which can make distinctions and specify that which it distinguishes as something different from itself. Maturana’s treatment of the observer focuses specifically on living systems, and is broadly developed in all of the cited works. He also goes into the source of “self-counsciousness” as strongly correlated to the observer (1988, p.44). While this is a very important point of his work, that particular distinction is not all that relevant for us in the present paper.
[9]Heidegger (1968) pp. 27-31: After ascertaining the spatial ‘truth’ that the distinction “this” imposes on his chalk, in order to avoid loosing this “great valuable”, Heidegger writes it down on a piece of paper (“here is the chalk”) which is eventually blown away (from the chalk). A person finds the paper in the hallway and claims the statement to be false. So Heidegger then claims that the truth was entrusted to an unstable piece of paper, and that it was actually a half truth. He goes on to write “Here is the chalk and right now – and now is the afternoon”, on the blackboard, getting at the temporal ‘truth’ too, and making sure it won’t be blown away. After class is over someone comes in and claims the statement to be false, it is no longer the afternoon. The chalk is always a “this”; through his examples, he made this an independent truth by writing it down, and then considers it better to keep the truth with us, either dropping or enduring the fear of subjectivism.
So what about Qubits?
That our access to the nature of an objective, independent reality is apparently shaken by quantum mechanics and the role of observation, is not what I wish to discuss (even though it was one of the directions I explored before ending up here). In effect, one can’t objectively know the properties of a qubit without objectively altering them. One cannot know what is happening in the subatomic world unless one observes, and, as stated at the beginning, an observation is a measurement in this realm of existence, as we now know it.
Nonetheless, it is not the observer who yanks the qubit in and out of existence or who collapses the wave function, it is the measurement. Measurements are imposed in the absence of an observer, in the absence of consciousness (as it is ordinarily understood, and yes I will leave it at that :) ). Presumably, measurements have been happening (and still do) in places far removed from our ordinary consciousness. That we have access to these things that happen outside of our consciousness and outside of our imagination and outside of our language is another story.
In order for an observer to look into the quantum world, a measurement has to be done, a qubit is forced out of a potential superposition and materializes in an eigen state of the property being measured. What effectively happens in absence of our observations is something that still requires more study, and that presently, appears to be quite hard a question to objectively answer.
So, finally..: the Mix!
Human beings can only talk about that which they can specify through their operations of distinction. The operations of distinction involving the distinctions of qubits are new of their kind. Language, logic, and most of our knowledge of the world and our systems of interacting with it (including experimental apparatus in quantum physics) rest in the classical domain of existence.
The quantum reality is accessible to us only by a combination of second- and third-order distinctions in consensual domains: namely mathematical abstraction, experimental apparati, and quantum physics.
As quoted above, “we literally create the world in which we live by living it. If a distinction is not performed, the entity that this distinction would specify does not exist; when a distinction is performed, the created entity exists in the domain of the distinction only, regardless of how the distinction is performed.” (Maturana, 1978, p. 34)
Following this phrase in this context, we can attempt an M-move: Language is the “measurement apparatus” with which we specify entities by operationally cleaving them from a background. Before we actually do this, the entities may virtually be there, nonetheless, there is not much we can know or say about them. We drag them into existence making way along our a priori categories (which might be morphed to function as eigenstates?) and then progressively adjusting them into new ones, always in a consensual domain, in a sense that coordinates actions and behaviors in a coherent way.
Here’s a potential laugh for you guys: Perhaps it would be interesting to analyze some of the passages in Genesis with this in mind. The Earth was formless and empty and dark, then God pops up and starts saying (using language?) “let there be light”, and light appears (photons?), and so on…
Having binary logic brought forth in our classical, mid-sized world, and using it to effectively interact with it, reinforces this logic. When languaging and bringing things into existence, we bring them into a domain that functions with these a priori distinctions, and thus the things we distinguish exist in this domain as well.
Qubits don’t obey this. Physicists have had to struggle with math, logic and natural language in order to be able to explain what is going on. They force us into new domains. As noted at the beginning, they are accessible through classical science and with our classical notions. Yet, their internal functioning is non-classical. Having made these distinctions in the actual physical world is outstanding, it brings us to reconsider all that is known. Perhaps if we could somehow function following the logic of qubit systems things would be different. Perhaps this goes beyond logic, or logic is something that belongs in this broader picture that qubits paint. Speculations, speculations….
The M-move falls short though, and I will pose some questions which can perhaps be more thoroughly looked into at another time. Of course, we would have to set out to the task of defining terms homologous to those treated at the beginning (as well as for many other terms and mathematical entities that are worked with in quantum physics), as well as their implications, in the natural language linguistic domain.
Are things actually superposed before language “measures” them? If I measure something with language, in regards to a given property, do I send the other properties to a superposition? Will the measured property assume an eigen state? The superposition principle holds together “alternative, and eventually mutually exclusive, possibilities right until the last moment, when suddenly one of them alone surfaces as the realized actuality” (Polkinghorne, 2002, p.44) on a given occasion. Is this the case with things as they are being measured with language?
Do we know what we’ll get after we ‘measure’ with language? With qubits, Born’s rule tells us we can expect stochastic outcomes, it delimits them as a range of probabilities. In language, elements of choice are present, and we don’t necessarily follow strict, scientific, rules. The community of observers who establish language has not set forth a set of coherent, scientific procedures to do so; it has not been utterly necessary safe in very specific domains.
Speculations (and more frivolous statements)
We have ‘created’ qubits, in linguistic terms, by bringing them forth as distinctions. The domain of this distinction is in math and that is where the qubits actually live. Natural language hasn’t captured all of these distinctions.
In order to bring qubits to life in other ways, we need to make new distinctions, not only on the qubits themselves, but also on the world ‘around’ us. Eventhough the mid-sized and quantum worlds are currently treated as non-intersecting phenomenal domains in our day to day existence, employing quantum reasoning or concepts in the former (even if initially in a somewhat loose way, as I am doing here) will bring forth distinctions that will progressively lessen the gap between math and natural language. As these new classes of distinctions become more engraved in our world, they can eventually be posed back upon the quantum reality. We can also look for distinctions in other disciplines from the mid-sized world and see if they fit the quantum one.
There are still mysteries in regards to how reality is “actualized” through our senses, physically encoded into cognition, or vice versa (how our senses encode the reality we live in). The world is apparently infinite, we are finite beings that apparently interact with it through a biological structure which is not completely understood. If all matter/energy can indeed be described by the wavefunction, stimuli would tend to be rather continuous, nonetheless some studies and philosophical positions suggest that we perceive reality in discrete chunks. It is a neurological fact that there is no way (internally) for us to distinguish between illusions, hallucinations, and “real” things; these notions obey social consensus, consensual operations of distinguishing, and the comparison of our ‘perceptions’ to those of others or of a consensual source. Goodman and Allen both touch on this.
One last frivolous statement…
We do not exist in a pre-existing domain of physical existence; we bring it forth and specify it as we exist as observers. The experience of the physicist, be this in classic, relativistic or quantum physics, does not reflect the nature of “the universe”; it reflects the ontology of the observer as a living system as he or she operates in language bringing forth the physical entities and the operational coherences of their domains of existence.
Bibliography
Imbo, Tom; Huggett, Nick; and Grimes, Ellen. Entangled Identities: Systems in Physics, Philosophy, and Architecture. (Oral) Class Lectures. Summer 2006. University of Illinois at Chicago.
Maturana, H.R.; and Varela, F.G (1972 and 1980). De máquinas y seres vivos, Editorial Universitaria, Santiago, Chile, 1972 (in Spanish).
Autopoiesis and Cognition: the realization of the living, Boston Studies in the Philosophy of Science, Vol 42, Reidel Publishing, 1980 (in English).
Maturana, Humberto R. (1978) Biology of language: The epistemology of reality, Chapter 2 in Miller, George A., and Elizabeth Lenneberg (eds.), Psychology and Biology of Language and Thought: Essays in Honor of Eric Lenneberg, New York: Academic Press, pp. 27-63.
Maturana, Humberto (1988). Ontology of Observing, The biological foundations of self consciousness and the physical domain of existence, Conference Workbook: Texts in Cybernetics, American Society For Cybernetics Conference, Felton, CA. 18-23 October, 1988.
Maturana, Humberto (1999) Autopoiesis, Structural Coupling and Cognition, (draft version in: http://www.isss.org/maturana.htm)
Heidegger, Martin (1968) What is a thing? Regnery Publications.
Goodman, Nelson (1968). An Approach to the Theory of Symbols. Bobbs-Merril.
Varela, Francisco. Article provided by Ellen.
Humberto Maturana (biography). Ecology of Mind Website. http://www.oikos.org/maten.htm.
Humberto Maturana. Wikipedia Free Encyclopedia Article. http://en.wikipedia.org/wiki/Maturana
Polkinghorne, John (2002). Quantum Theory, A Very Short Introduction. New York: Oxford University Press.
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posted by ۞ D at 10:08 AM
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