*by Vera Bühlmann*

author’s manuscript.

In this article, I would like to discuss one of the key moments of reference in 20^{th} century information science, which arose from thermodynamics and which in fact links the latter to the former in many important aspects. Maxwell’s famous thought experiment explores how to think of heat, if we can conceive of it neither as a force nor in (metaphysical) substantial terms (–> negentropy). Before discussing how the stakes were formulated in this thought-experiment, and how these same stakes were re-articulated in famous discussions of it, it is important to understand that here, we have the beginning of a certain coinage of thinking about chance in purely operational terms: one which attributes probability to humanly imperfect faculties that need not, in principle, be taken into account if operations in the natural sciences be carried out by a “pure” agency like the particular intelligence which Maxwell set out to design in his thought experience. This very background links the concept discussed in this brief article to the discussions about artificial intelligence at large, also beyond the elected aspects that will be discussed here.[1]

James Clark Maxwell responded to the problem of thermodynamics’ irreversibility with a thought experiment designed to resolve the subjectivity which apparently inheres to experimental science when it involves heat balances (through probability). If heat is apparently not to be held identical with energy (irreversibility, 2^{nd} law) nor approached in metaphysical terms as a new kind of substance, then we can think of heat as the motion of molecules in populations, Maxwell maintained. Individually, so he formulated the belief of many of his contemporaries, the molecules must obey Newton’s Laws: Every action, every collision, must be measurable and calculable in theory. This assumption led him to invent a scenario that involves a perfect observer, one whose faculties were not to be flawed like the human imperfect ones, in short, a cognitive agency freed from all subjectivity, probability, and hence whose reasoning would be freed from irreversibility. Maxwell set up the ideally perfect experiment where the observer is to be capable of purifying the science of heat from the factual irreversibility at work in it (–> negentropy). For this observer, thermodynamics would be as determined and without need for the assumption of a final cause or any other agency that acts in non-reasonable manner from a distance, as Newtonian physics is.[2]

When Leó Szilárd attended to Maxwell’s thought experiment, he hoped to dissipate the rather metaphysical discussions that had emerged and gave rise to both animist as well as vitalist discussions of the possibility of a “perpetual movement” which Maxwell’s agency – if considered a legitimate concepts – would render real.[3] Instead he re-considered Maxwell’s purely mechanical agency at stake in computational terms and equipped it with the capacity to memorize and evaluate all the observations it makes, and hence be capable of making up for the inevitable expenditure of energy through understanding how it could be balanced again.[4] The core assumption of Szilárd[5] was that even this perfect observer’s faculties of observation would have to be accounted for in terms of measurement and calculation else – if observation is not formalized – the thought experiment’s value for justifying a classical notion of experimental science is nullified at once (since by definition such observation would transcend the conditions of experimentation). In order to account for the demon’s observation in those terms, Szilárd introduced “information” and “memory” into the set-up (although Szilárd did not speak of “information” properly, he spoke of the results of measurements which needed to be memorized in whatever “form”)[6]. He effectively transformed Maxwell’s original conception of a demon, acting mechanically like a thermostat, into a *deus ex machina*, an artificially intelligent being that can remember whatever experiences it makes while measuring.

But there were problems with faculties perfected in Szilárd’s manner as well: Once we assume that a system needs to be quantized in order to be measured and hence remembered, we are dealing with the unknown quantities of microscopic variables that “make it possible for the system to take a large variety of quantized structures”: stochastic definitions (Laplacean determinism) apply only to lower frequencies like those of a thermostat (in essence the kind of intelligence Maxwell conceived of), but not to higher frequencies like those of an oscillator (the re-devolpment of Maxwell’s intelligence by Szilárd); higher frequencies display no stochastic distributions; position and magnitude of the waves cannot be at once observed and hence such observation involves probabilities. Even if the perfect agent would apply his perfect faculties by measuring (objectively), it’s assumption would not lend itself to stigmatize probabilities to the side of subjectivity against a supposedly stochastic distribution of objective nature.

Probability enters the picture of Laplacean determinism in that the movement of molecules has to be measured and calculated *in populations (rather than individually)*. This implies a foregrounding of a certain role of code in this measuring and calculating.[7] The methods of probabilistics differ from those of stochastics with regard to this role of encryption. From this perspective, entropy is a term to measure the dissipation of heat by means of encrypting “a large amount”– large enough to count the totality of possible transformation in an ideal state in which every next step is equally likely (entropy). The core assumption of thermodynamics is that the amount total of energy in the universe be invariant, that nothing can be added or subtracted to it (First Law of Thermodynamics). Entropy is the name for that number, and its extension (largeness of this number) is subjected to encryption in algebraic code (–> equation). Like this, to think of energy in terms of entropy does not depend upon a semantic or substantial interpretation of energy, and it does not need to know just how much energy there really is in the universe (–> invariance). Every system that real (empirical) science can identify is *one that factors in* in this only cryptographically knowable invariant amount total of energy in the universe.

Léon Brillouin, building upon the work of Szilárd, went a step further. Familiar with Turing’s[8] and Shannon’s[9] and Wiener’s[10] work on a mathematical notion of information and their dispute with regard to whether information can be measured in terms of the experimental entropy notion applied to physical systems (Shannon), or whether it needs to be accounted for in Schrödinger’s terms of negentropy import in biological systems[11], Brillouin foregrounded the role of “code” in such “intelligent” computation and applied a *double* notion of negentropy and entropy – one to energy, one to information, under the assumption that both be linked by code: free (entropic) information to him is the maximum amount of apriori cases formulated in a code. The apriori cases can be computed by combinatorics, and each of them must be regarded as equally likely to happen in entropic information. Bound (negentropic) information is empirically measured information (in experiments with any particular manifestation of such a code). This transcendental in the measurement of information allows for thinking of information as a kind of currency that through circulating is capable of transforming energy into information and vice-versa. This is how Brillouin could affirm the ultimate failure of Maxwell’s thought experiment: Not even an observation can be obtained gratuitiously, he maintained, and all information has its price.

The implications of such an economy, one that transforms information into energy and vice versa, has only rarely been explored so far. It is mainly pursued in the work of Michel Serres, which I want to point to in conclusion to this article. Thus we want to ask with Michel Serres: “What does this demand for an absolutely exact measurement mean?” He resumes:

“In a famous theorem, Brillouin proofed that a perfect experiment can absolutely not be realized, because it would produce an infinitely large amount of information and, in addition to this, an infinitely large amount of negentropy would have to be expended. […] the classical physicist believed that he could go to the very limits, and observe what would happen if all mistakes in observation could be reduced to zero; today we know that this margin is impossible, because the costs for this observation would rise to infinity. Absolute determinism is a dream, for perfect precision with regard to the initial conditions cannot be achieved. In other words, this demand [for the perfect experiment, VB] exceeds the limits of a possible experiment, it transcends its own postulates. It is possible to proof that one can never know exactly all the parameters of an experiment. There remains a rest of chance, a remainder of the unknown […].[12]

The consequences Michel Serres draws from the failure are as original as daring: chance is to be regarded as the object of science, he maintains, not nature! Michel Serres sees in information theory a philosophy of physics that is inherent to the domain of physics. It is remarkable, he points out, that Brillouin titled his book *La Science et La **théorie de l’information. *This book contains, so Serres, an epistemology of the concept and the praxis of experimentation, formulated in the language of physics, exhaustively descriptive, quantified, normalized and constitutive. This epistemology is at once one of natural laws, precise and approximational insight, hence all of classical philosophy, as well as, in the theory of code, language, script and translation it contains, this epistemology is all of modern philosophy as well. “Philosophers ought no longer search for an epistemology of experimental reason, nor write schoolbooks about it; it exists already.” [13] The theory of information is the philosophy of nature inherent to physics precisely in that it acknowledges this remainder of chance, which insists in all that can be known as substantial to any concept of understanding and knowledge. It is this remainder upon which Serres’ “logiciel intramatériel” operates. The subjectivity or agency of this logiciel constitutes “l’objective transcendentale”, a transcendental objectivity whose forms of intuition are not, as in Kant, constituted by physics notions of time and space, but by Brillouin’s “a priori probabilities” – the maximum and finite (albeit, depending on the code at stake, very large) number of equally likely cases which the combinatorics of a code may compute. To Brillouin and to Serres, the codes in terms of which information can be measured – as the currency that circulates in energetic expenditure – are to be regarded as different levels of negentropy in a manner analog to the energy levels in quantum mechanics, where bound particles can take on only certain discrete values of energy (rather than any energy, as is the view for particles in classical mechanics). Codes, as levels of negentropy, provide the sufficient reason for a certain disposition of knowing or “architectonic speculation” (–> *architectonic disposition*).

[1] The point I want to highlight is that against all enthusiasms of this outlook (non-anthropocentric cognition and reason) stands a certain complication in how we think of chance: from a quantum-science point of view, there appears the need to complement the operational definition with one that considers also a certain “substantiality” of chance itself – not in order to relativize the objectivist paradigm of science, but quite contrarily, in order to maintain its centrality for a non-dogmatic, scientific understanding of knowledge (–> invariance).

[2] “A being whose faculties are so sharpened that he can follow ever molecule in is course, and would be able to do what is at present impossible to us. […] Let us suppose that a vessel is divided into two portions, A and B by a division in which there is a small hole, and that a being who can see the individual molecules opens and closes this hole, so as to allow only the swifter molecules to pass from A to B, and only the slower ones to pass from B to A. He will, thus without expenditure of work raise the temperature of B and lower that of A, in contradiction to the second law of thermodynamics,” cited in Leon Brillouin, (J. H. Jeans, “Dynamical Theory of Gases”, 3^{rd} ed. p. 183, Cambridge UP New York, 1921)

[3] second perpetual motion of a second kind …

[4] As Gleick points out, Szilouin thereby anticipated Turings famous thought experiment by some years.

[5] In his 1928 Habilitation entitled *Über die Entropieverminderung in einem thermodynamischen System bei Eingriffen intelligenter Wesen.*

[6] cf. gleick

[7] The systems of real physics can count as universal only in the mediate sense that they obey the laws of thermodynamics. But the entropic, thermodynamic universe itself cannot be thought of as a physical system properly, because the universe’s entropy itself is an assumed ideality – an ideality which is to serve as a support to the experimental paradigm of science, with the least possible semantical (biased) import.

[8] Turing…

[9] Shannon, Claude E., “A Mathematical Theory of Communication”, *Bell System Technical Journal* 27 (3): 379–423 (1948);

[10] Norbert Wiener: *Cybernetics: Or Control and Communication in the Animal and the Machine*, 1948

[11] Shannon discusses the term negative entropy, but considers its distinction negligible for information as a mathematical quantity notion. It was Norbert Wiener, who via the work by John von Neumann, Alan Turing, Claude Shannon and Leo Szilard maintained against Shannon that negentropy is in fact crucial, rather than negligible for a mathematical theory of information; it is largely due to this dispute that until today, different notions of mathematical information are in usage: (1) information as a measure for order in terms of entropy, and (2) information as a measure for order as negentropy; while both speak of information as a measure, and hence capable of establishing order, the two concepts of order are actually inverse to each other: order as negentropy means minimal entropy (maximal amount of bound energy, minimal of free or available energy in Schrödinger’s terms), while order as entropy means minimal negentropy (maximal amount of free and available energy, minimal amount of bound energy in Schrödingers terms). Much confusion in the understanding of “information” arises from this still today.

[12] Michel Serres, my own translation … from the German version:

[13] Michel Serres, my own translation … from the German version: