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Saturday 4 November 2017

Information Flow: The Concept that just wont let go...

Barwise, Jon. 1983. “Information and Semantics.” Behavioral and Brain Sciences 6 (1):65–65.
Barwise, Jon, Dov Gabbay, and Chrysafis Hartonas. 1996. “Information Flow and the Lambek Calculus.” In , 49–64.
Barwise, Jon, and John Perry. 1983. Situations and Attitudes. Cambridge, Mass: MIT Press.
Barwise, Jon, and Jerry Seligman. 1993. “Imperfect Information Flow.” In , 252–60.
Bremer, Manuel, and Daniel Cohnitz. 2004. Information and Information Flow: An Introduction. Vol. 3. Book, Whole. Berlin/Boston: De Gruyter.
Cacciatore, Michael A., Juan Meng, and Bruce K. Berger. 2017. “Information Flow and Communication Practice Challenges: A Global Study on Effective Responsive Strategies.” Corporate Communications 22 (3):292.
Clifford, A. H., Samson Abramsky, Michael W. Mislove, and Tulane University Department of Mathematics. 2012. Mathematical Foundations of Information Flow: Clifford Lectures Information Flow in Physics, Geometry, and Logic and Computation, March 12-15, 2008, Tulane University, New Orleans, Louisiana. Vol. 71. Providence, R.I: American Mathematical Society.
Daly, Angela, and ProQuest (Firm). 2016. Private Power, Online Information Flows and EU Law: Mind the Gap. Vol. 15. Portland, OR;Oxford;London; Hart Publishing, an imprint of Bloomsbury Publishing Plc.
Gao, L., CM Song, ZY Gao, AL Barabasi, JP Bagrow, and DS Wang. 2014. “Quantifying Information Flow During Emergencies.” SCIENTIFIC REPORTS 4:3997.
Ghobrial, John-Paul A. 2014. The Whispers of Cities: Information Flows in Istanbul, London, and Paris in the Age of William Trumbull. Oxford: Oxford University Press.
Hackett, Troy A. 2011. “Information Flow in the Auditory Cortical Network.” Hearing Research 271 (1):133–46.
Horowitz, JM, and M. Esposito. 2014. “Thermodynamics with Continuous Information Flow.” PHYSICAL REVIEW X 4 (3):031015.
Humphrey, Curtis M., and Julie A. Adams. 2013. “Cognitive Information Flow Analysis.” Cognition, Technology & Work 15 (2):133–52.
Kane, J., and P. Naumov. 2014. “Symmetry in Information Flow.” ANNALS OF PURE AND APPLIED LOGIC 165 (1):253–65.
Kassir, Abdallah. 2014. “Communication Efficiency in Information Gathering through Dynamic Information Flow.”
Leeper. 2011. Foresight and Information Flows. National Bureau of Economic Research.
Nielson, HR, and F. Nielson. 2017. “Content Dependent Information Flow Control.” JOURNAL OF LOGICAL AND ALGEBRAIC METHODS IN PROGRAMMING 87:6–32.
Rabinovich, Mikhail I., Valentin S. Afraimovich, Christian Bick, and Pablo Varona. 2012. “Information Flow Dynamics in the Brain.” Physics of Life Reviews 9 (1):51–73.
Siegel, M., TJ Buschman, and EK Miller. 2015. “Cortical Information Flow during Flexible Sensorimotor Decisions.” SCIENCE 348 (6241):1352–55.
Silva, Flávio Soares Corrêa da, and Jaume Agustí i Cullell. 2008. Information Flow and Knowledge Sharing. Amsterdam;Boston; Elsevier.
Stojmirović, Aleksandar, and Yi-Kuo Yu. 2007. “Information Flow in Interaction Networks.” Journal of Computational Biology 14 (8):1115–43.
Tkačik, Gašper, Curtis G. Callan, and William Bialek. 2008. “Information Flow and Optimization in Transcriptional Regulation.” Proceedings of the National Academy of Sciences of the United States of America 105 (34):12265–70.
Wu, Ze-Zhi, Xing-Yuan Chen, Zhi Yang, and Xue-Hui Du. 2017. “Survey on Information Flow Control.” Ruan Jian Xue Bao/Journal of Software 28 (1):135–59.
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Thursday 2 November 2017

My Next Minor Presentation: Informationist Philosophy of Mathematics at The Victorian Postgraduate Workshop

"I present an informationist alternative to Platonist, in re realist, and nominalist appraisals of the nature of mathematical entities and structures, and their explanatory power. Informational conceptions of the nature of mathematical entities are considered conceptually taxing due to problems with conceptions of information. I argue that, even given this difficulty, the causal informationist about mathematical entities can offer a story that is just as coherent as that given by the Aristotelian in re realist about mathematical entities, is more plausible than soft Platonism, and that debunks the Platonist petitio-principii-cum-strawman charge that intractable nominalism is Platonism's only viable alternative."

 https://vppw.wordpress.com/keynote-speaker/
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Wednesday 1 November 2017

The Metaphysical question of the nature of Information: A problem as intractable and interminable as the nature of mathematical entities? Update No. 1.

There are myriad competing conceptions of information across the hard and special sciences, and across philosophy. Here I am developing a cache of some of the key historical and contemporary proposals.

I will be progressively updating this post, and then adding a table of contents to it...


Algorithmic Information Theory: Complexity and Program Description Length

 

Chaitin efforts a unification of algorithmic and classical Shannonian information concepts, and of the concepts and machinery of complexity theory and statistical information theory:
An attempt is made to apply information-theoretic computational complexity to metamathematics. The paper studies the number of bits of instructions that must be a given to a computer for it to perform finite and infinite tasks, and also the amount of time that it takes the computer to perform these tasks. This is applied to measuring the difficulty of proving a given set of theorems, in terms of the number of bits of axioms that are assumed, and the size of the proofs needed to deduce the theorems from the axioms. This paper attempts to study information-theoretic aspects of computation in a very general setting. It is concerned with the information that must be supplied to a computer for it to carry out finite or infinite computational tasks, and also with the time it takes the computer to do this. These questions, which have come to be grouped under the heading of abstract computational complexity, are considered to be of interest in themselves.
(Chaitin 1974)

Information in Biology and Molecular Bioscience




Scientific metaphysician Collier points out the intractability of the field and dentifies the root of many metaphysical quandaries as situated in the pragmatic scientific expediencies of applied mathematical sciences: 
Information is a multiply ambiguous notion. Since it is unlikely that information is just one thing, it is more useful to characterize various aspects of information and its use in ways that are open-ended and general enough to allow linking together information and information related concepts in various disciplines and specialties… The central idea of this paper is a physical information system, in which the information bearing capacity rests in the dynamical possibilities of the elements of the system, and on the closure conditions of the system itself. I will argue that such a system is minimally required for the expression of information, as opposed to merely being subject to the application of one or another information theoretic formalism. Information expression itself is a dynamical (and perhaps semiotic) process that cannot be fully described in purely formal terms. This is because formal descriptions can apply just as well to accidental relations, which do not convey information, as they can to dynamical connections that can convey information. The great tragedy of formal information theory is that its very expressive power is gained through abstraction away from the very thing that it has been designed to describe. 
(Collier 2003, 102)


Sahotra Sarkar calls for a physicalist unification and revision that minimises abstractive sequence accounts and incorporates dynamical and conformational elements into the concept of information in biology:
The failure of explanations involving codes and information and the success of the usual reductionist explanations in molecular biology together gether suggest a rather striking possibility: abandon the notions of codes and information altogether and pursue a thoroughly physicalist reductionist account of the interactions between DNA, RNA and protein (and explain away the conceptual framework from the 1950s as an artifact of the coincidental colinearity of DNA and protein). In principle, this does not present any real difficulty. We would treat the DNA-RNA-protein system as a network of chemical reactions, and write down a system of linear differential ential equations to describe the process. 
The main difficulty with such an account is that this model would have a rather large number of variables. These variables would have to keep track of the concentrations of each different type of DNA, RNA and protein that could potentially arise in the cell, not just the ones that emerge during normal gene expression, but also those that could arise through errors. 
Nevertheless, in most contexts, this level of complexity is not beyond what can be quite easily numerically analyzed. The coefficients describing the formation of a particular RNA type from a given DNA type and for forming a protein type from an RNA type would incorporate the specificity of the code. Moreover, these coefficients could quite naturally incorporate all that is known to happen to an RNA segment in a particular environment including editing, as well as nonstandard translation. Moreover, such a model would be dynamic and actually allow the exact description of the concentration changes of the various components over time. 
Why not abandon "codes" and "information" and pursue this possibility? There is no fully convincing reason not to do so. One possible reason why it has so far not been pursued is that only what might be called the "statics" of gene expression has usually been studied in any context. Molecular biology, especially molecular genetics, has not yet gone very far even in characterizing what genes are expressed in what part of an organism, let alone the finer details of the temporal regulation of genes within a cell except, of course, for Escherichia coli. In this static context, the coding account still serves some organizing function and, in spite of its increasing failures, it is being retained while few explanations are actually being pursued sued in this kind of work in genetics. Thus, the inability of the code to provide significant explanations is no major handicap. Another possible reason is that there is a useful sense in which "coding," "information," "translation" and related notions make the relations between DNA, RNA and protein transparent, which no dynamical account involving reaction coefficients can. The intuition, here, is that the code is "natural" in a sense that these coefficients are not. Perhaps lurking behind this usefulness there is some insight to be grabbed, which the conventional information-based account of molecular biology has grasped even if, so far, very shakily.
Nevertheless, what does seem obvious is that a dynamical account, whether it is physicalist, informational, or whatever, will eventually be necessary if even approximate accounts of gene expression, interaction and cellular behavior, let alone the development of complex organisms, are to be pursued at the molecular level. There is, moreover, one development whose importance even the most conventional molecular biologists have recognized, which implicitly relies on such a dynamical model and has no concern whatsoever for coding and information even though it deals with DNA. This is the polymerase chain reaction (PCR), which permits the rapid amplification of a given (double-stranded) DNA segment. The process begins by creating complementary single strands of DNA by heating the double-stranded segments to temperatures close to boiling. Using primers, which are a few nucleotides long to start the reaction, entire double stranded segments are created from each of the single stranded segments. This results in two copies of the original double-stranded segment. After n cycles of this process, there are (on average, that is, ignoring stochastic effects) 2" such copies and they can be used for any purpose. It has been claimed with some justice that the PCR technique has "revolutionized molecular genetics" (Watson et al. 1992, p. 79). There is no concern for coding or information in this process. What is at stake is that a particular single-stranded DNA sequence catalyzes the formation of another specific sequence, namely, the one that is complementary to it. The dynamical equations to model this process are formally those for DNA replication in general. These can be solved to calculate the rate of DNA formation. This is reductionist reasoning, through and through, and this is what molecular biologists using PCR are relying on, even if only implicitly, when they predict dict the time required to produce a certain amount of DNA. "Codes" and "information" are irrelevant in this context.
It appears, therefore, that we are faced with a quandary. The conventional account of information as sequence is of little explanatory value in the novel contexts we are beginning to encounter. The alternative physicalist account of rate equations is, at present, of use in only very few contexts. I wish to suggest that we are faced with a situation that will require a rather radical departure from the past. For a coherent account of the relations between tween DNA, genes and biological behavior that has significant explanatory value, we will have to avoid both these accounts. Not adopting the physicalist calist account is neither controversial nor difficult since it has so far never been invoked in this context except, implicitly, in the development of PCR technology. However, because of the extent to which the idea of coding has been central to how molecular biology has been conceptualized, abandoning doning the idea of information as sequence will have important consequences. sequences. Let me list some of these and argue that they are, in fact, desirable: 
(i) If biological "information" is not DNA sequence alone then, trivially, other features of an organism can also characterize information. And this is precisely what recent developments in molecular biology indicate. In particular, ticular, the developmental fate of a cell might be largely a result of features such as methylation patterns of DNA that are not, as far as we know today, even ultimately determined only by DNA sequences. These "epigenetic" patterns can be inherited for several cell generations. Different cells in the same organism, presumably with identical DNA sequences, can be epigenetically genetically different. Because of these differences, cell specialization and differentiation, the usual prelude to developmental changes, can take place. Epigenetic specifications are also critical in generating those differences in offspring (of sexually reproducing organisms) which depend on whether an allele is inherited from the mother or the father. Epigenetic specifications tions can sometimes be transmitted across organismic generations. It would be highly unintuitive not to regard these determinations as "transfers fers of information" if "information" is to have any plausible biological significance.
Each of these consequences is desirable. Nevertheless, before the notion of information as sequence and the picture of molecular biology that comes with it are abandoned, some alternative is necessary. Let me end by noting two possibilities, the first would be a return to the old concept of specificity and develop it further, beyond the stereochemical theory whose limitations are, in any case, gradually becoming apparent. For instance, in the immunological context, it has already become clear that not all residues dues that are in contact between antibodies and antigens contribute equally to the free energy of the interaction (see Sarkar 1998). Of about twenty residues that are in contact at the interaction site, only four or less dominate the interaction. This is not a total failure of the stereochemical model. Rather, it is a modification of that part of it which asserts that only molecular shape matters.
Perhaps a similar account can be given that will explain the specific interaction teraction between complementary base paris during DNA replication and transcription, and all this will be incorporated in a general systematic account count of specificity. Coding will be retained only as a short-hand description tion of the usual triplet specification of amino acid residues, but it will not be assumed to have any explanatory value. Nevertheless, the special role played by DNA triplets would be incorporated in the account of specificity that would be developed. Finally, the differential equations that I mentioned above would be incorporated to provide a dynamical account of the entire DNA-RNA-protein and other interactions in the cell. The new account of specificity would remove the taint of artificiality that the reaction coefficients had. Perhaps the most interesting feature of such an account would be that it would be purely physicalist and, consequently, reductionist in the strongest sense, in sharp contrast to the informational account that is currently prevalent. So far little, if any, effort has been expended towards the elaboration of such a picture, probably because there is, as yet, no plausible candidate for such a generalized theory of specificity.
The second possibility is the elaboration of a new informational account in which "information" is construed to be broader than just DNA sequence. quence. For instance, Shapiro (1991, 1992) has argued that the entire genome should be viewed as "a dynamic information storage system that is subject to rapid modification" (1992, p. 99). From Shapiro's point of view, there exists not only the usual genetic code relating amino acid residues to DNA base triplets, but an additional coding relation for sequences that serve regulatory and other roles. The latter code is clearly not triplet, and is not even symbolic in any conventional sense since it would be "interpreted" preted" as a process rather than some other entity. The hierarchical organizanization of the entire genome determines the behavioral repertoire of a cell. "Information" is no longer determined by local sequence alone, nor is it linear, since these hierarchies can show considerable complexity. Though Shapiro is not explicit on this point, "information" in such a picture need not be constrained to DNA sequences-patterns of methylation and other heritable features of the genome could well carry information. 
There is little doubt that such a picture is intriguing because it automatically cally retains those insights that the conventional view has, such as the existence istence of a peculiar triplet relationship between DNA and amino acid residues, while extending this view to incorporate recent discoveries in molecular biology. However, as Shapiro (1991) has acknowledged, no testable able claim has yet emerged from this picture. Whether, eventually, any will, I cannot say. I am willing to acknowledge that "testability," as it is usually understood-that is, demanding new predictions-might well be too strong a criterion for most biological contexts. However, for a theory to be worth admission into serious discourse, it should at least allow the systematic tematic and clear organization of known facts. Shapiro's approach has not yet even been developed to that extent. However, should an admissible theory emerge, it would, as in the case of the comma-free code, be a theory based on assumptions about information storage and utilization. It would be manifestly nonphysicalist. It would also give a new lease of life to information-oriented mation-oriented thinking in biology and, perhaps, even finally begin to explain what "biological information" actually happens to be. 
Sahotra Sarkar. Molecular Models of Life: Philosophical Papers on Molecular Biology (pp. 247-248). Kindle Edition. 



Sahotra Sarkar introduces a semiotic and non-semantic unified conception of information for biology:


According to the Oxford English Dictionary, the term "information" (though spelled "informacion") was first introduced by Chaucer in 1386 to describe an item of training or instruction. In 1387, it was used to describe the act of "informing." As a description of knowledge communicated by some item, it goes back to 1450. However, attempts to quantify the amount of information contained in some item date back only to R. A. Fisher in 1925. In a seminal paper on the theory of statistical estimation, Fisher argued that "the intrinsic accuracy of an error curve may ... be conceived as the amount of information in a single observation belonging to such a distribution" (1925, p. 709). The role of the concept of information was to allow low discrimination between consistent estimators of some parameter; the amount of "information" gained from a single observation is a measure of the efficiency of an estimator. Suppose that the parameter to be estimated is the mean height of a human population; potential estimators can be other statistical "averages" such as the median and the mode. Fisher's theory of information became part of the standard theory of statistical estimation, but it is otherwise disconnected from scientific uses of "information." The fact that the first successful quantitative theory of "information" is irrelevant vant in scientific contexts outside its own narrow domain underscores an important feature of the story that will be told here: "information" is used in a bewildering variety of ways in the sciences, some of which are at odds with each other. Consequently, any account of the role of informational thinking in a science must pay careful attention to exactly what sense of "information" is intended in that context.  

Shortly after Fisher, and independently of him, in 1928 R. V. L. Hartley provided a quantitative analysis of the amount of information that can be transmitted over a system such as a telegraph. During a decade in which telecommunication came to be at the forefront of technological innovation, tion, the theoretical framework it used proved to be influential.' Hartley recognized that, "as commonly used, information is a very elastic term," and he proceeded "to set up for it a more specific meaning" (1928, p. 356). Relying essentially on a linear symbolic system of information transmission (for instance, by a natural language), Hartley argued that, for a given message, sage, "inasmuch as the precision of the information depends upon what other symbol sequences might have been chosen it would seem reasonable to hope to find in the number of these sequences the desired quantitative measure of information" (p. 536). Suppose that a telegraphic message is n symbols long with the symbols drawn from an alphabet of size s. Through an ingenious argument, similar to the one used by Shannon (see below), Hartley showed that the appropriate measure for the number of these sequences is n log s. He identified this measure with the amount of information mation contained in the message. 
Using the same framework as Hartley, in 1948, C. E. Shannon developed an elaborate and elegant mathematical theory of communication that came to be called "information theory" and constitutes one of the more important developments of applied mathematics in the twentieth century. The theory of communication will be briefly analyzed in section 10.2 below, with an emphasis on its relevance to genetics. The assessment of relevance will be negative. When, for instance, it is said that the hemoglobin-S gene contains information for the sickle-cell trait, communication-theoretic information cannot capture such usage. (Throughout this chapter, "gene" will be used to refer to a segment of DNA with some known function.) To take another example, the fact that the information contained in a certain gene may result in polydactyly (having an extra finger) in humans also cannot be accommodated by communication-theoretic information. The main problem is that, at best, communication-theoretic information provides a measure of the amount of information in a message but does not provide an account of the content tent of a message-its specificity, what makes it that message. The theory of communication never had any such pretension. As Shannon bluntly put it at the beginning of his paper: "These semantic aspects of communication are irrelevant to the engineering problem" (1948, p. 379).  
Capturing specificity is critical to genetic information. Specificity was one of the major themes of twentieth-century biology. During the first three decades of that century, it became clear that the molecular interactions that occurred within living organisms were highly "specific" in the sense that particular molecules interacted with exactly one, or at most a very few, reagents. Enzymes acted specifically on their substrates. Mammals produced antibodies that were highly specific to antigens. In genetics, the ultimate exemplar of specificity was the "one gene-one enzyme" hypothesis esis of the 1940s, which served as one of the most important theoretical principles of early molecular biology. By the end of the 1930s, a highly successful theory of specificity, one that remains central to molecular biology ogy today, had emerged. Due primarily to L. Pauling (see, e.g., Pauling 1940), though with many antecedents, this theory claimed: (i) that the behavior of biological macromolecules was determined by their shape or "conformation"; and (ii) what mediated biological interactions was a precise "lock-and-key" fit between shapes of molecules. Thus the substrate of an enzyme had to fit into its active site. Antibodies recognized the shape of their antigens. In the 1940s, when the three-dimensional structure of not even a single protein had been experimentally determined, the conformational formational theory of specificity was still speculative. The demonstration of its approximate truth in the late 1950s and 1960s was one of early molecular ular biology's most significant triumphs.  
Starting in the mid-1950s, assumptions about information provided an alternative to the conformational theory of specificity, at least in the relation tion between DNA and proteins (Lederberg 1956). This relation is the most important because proteins are the principal biological interactors at the molecular level: enzymes, antibodies, molecules such as hemoglobin, molecular lecular channel components, cell membrane receptors, and many (though not most) of the structural molecules oforganisms are proteins. Information, tion, as F. H. C. Crick defined it in 1958, was the "precise determination of sequence, either of bases in the nucleic acid or of amino acid residues in the protein" (Crick 1958, p. 153; emphasis in the original). Genetic information tion lay in the DNA sequence. The relationship between that sequence and the sequence of amino acid residues in a protein was seen to be mediated by the genetic "code," an idea that, though originally broached by E. Schrodinger in 1943, also dates from the 1950s. The code explains the specificity cificity of the one gene-one enzyme relationship elegantly: different DNA sequences encode different proteins, as can be determined by looking up the genetic code table. Whatever the appropriate explication of information tion for genetics is, it has to come to terms with specificity and the existence tence of this coding relationship. Communication-theoretic information neither can, nor was intended to, serve that purpose. 
Surprisingly, a comprehensive account of a theory of information appropriate propriate for genetics does not exist. In the 1950s there were occasional attempts by philosophers-for instance, by R. Carnap and Y. Bar-Hillel (1952)-to explicate a concept of "semantic" information distinct from communication-theoretic information. However, these attempts were almost most always designed to capture the semantic content of linguistic structures tures and are of no help in the analysis of genetic information. Starting in the mid-1990s, there has been considerable skepticism, at least among philosophers, about the role of "information" in genetics. For some, genetic information is no more than a metaphor masquerading as a theoretical concept (Sarkar 1996a,b; Griffiths 2001). According to these criticisms, even the most charitable attitude toward the use of "information" in genetics netics can only provide a defense of its use in the 1960s, in the context of prokaryotic genetics (i.e., the genetics of organisms without compartmentalized mentalized nuclei in their cells). Once the "unexpected complexity of eukaryotic genetics" (Watson, Tooze, and Kurtz 1983, chapter 7) has to be accommodated, the loose use of "information" inherited from prokaryotic otic genetics is at least misleading (Sarkar 1996a). Either informational talk should be abandoned altogether or an attempt must be made to provide a formal explication of "information" that shows that it can be used consistently sistently in this context and, moreover, is useful. 
Section 10.3 gives a sketch of one such attempted explication. A category of "semiotic" information is introduced to explicate such notions as coding. ing. Semiotic information incorporates specificity and depends on the possibility sibility of arbitrary choices in the assignment of symbols to what they symbolize as, for instance, exemplified in the genetic code. Semiotic information mation is not a semantic concept. There is no reason to suppose that any concept of biological information must be "semantic" in the sense that philosophers use that term. Biological interactions, at this level of organization, are about the rate and accuracy of macromolecular interactions. They are not about meaning, intentionality, and the like; any demand that such notions be explicated in an account of biological information is no more than a signifier for a philosophical agenda inherited from manifestly nonbiological contexts, in particular from the philosophy of language and mind. It only raises spurious problems for the philosophy of biology.

Sahotra Sarkar. Molecular Models of Life: Philosophical Papers on Molecular Biology (pp. 263-265). Kindle Edition. 

Sahotra Sarkar. Molecular Models of Life: Philosophical Papers on Molecular Biology (pp. 261-263). Kindle Edition. 


Bergstrom and Rosvall's proposal for the adaptation of Shannonian theory for a 'transmission sense of information' for ontogeny and genotype to phenotype feature signalling:

Biologists rely heavily on the language of information, coding, and transmission that is commonplace in the field of information theory developed by Claude Shannon, but there is open debate about whether such language is anything more than facile metaphor. Philosophers of biology have argued that when biologists talk about information in genes and in evolution, they are not talking about the sort of information that Shannon’s theory addresses. First, philosophers have suggested that Shannon’s theory is only useful for developing a shallow notion of correlation, the so-called ‘‘causal sense’’ of information. Second, they typically argue that in genetics and evolutionary biology, information language is used in a ‘‘semantic sense,’’ whereas semantics are deliberately omitted from Shannon’s theory. Neither critique is well-founded. Here we propose an alternative to the causal and semantic senses of information: a transmission sense of information, in which an object X conveys information if the function of X is to reduce, by virtue of its sequence properties, uncertainty on the part of an agent who observes X. The transmission sense not only captures much of what biologists intend when they talk about information in genes, but also brings Shannon’s theory back to the fore. By taking the viewpoint of a communications engineer and focusing on the decision problem of how information is to be packaged for transport, this approach resolves several problems that have plagued the information concept in biology, and highlights a number of important features of the way that information is encoded, stored, and transmitted as genetic sequence.
(Bergstrom and Rosvall 2011) 


Nicholas Shea Proposes his Infotel-Semantic conception of information in biology:

The success of a piece of behaviour is often explained by its being caused by a tru representation (similarly, failure falsity). In some simple organisms, success is ju survival and reproduction. Scientists explain why a piece of behaviour helped t organism to survive and reproduce by adverting to the behaviour's having be caused by a true representation. That usage should, if possible, be vindicated b an adequate naturalistic theory of content. Teleosemantics cannot do so, when it applied to simple representing systems (Godfrey-Smith 1996). Here it is argued that the teleosemantic approach to content should therefore be modified, not aba doned, at least for simple representing systems. The new 'infotel-semantics' ad an input condition to the output condition offered by teleosemantics, recognising that it is constitutive of content in a simple representing system that the tokening of a representation should correlate probabilistically with the obtaining of it specific evolutionary success condition.

The most important insight of teleosemantic theories of content is to identify the significance of output conditions. Such theories emphasise that a representation's content is fixed by the way a consumer system reacts to it. They eschew reliance on the circumstances in which it is tokened. Informational theories' exclusive focus on how a representation is produced led them into a corner. Teleosemantics reversed out of the corner by turning its attention to the outputs caused by representations. But can teleosemantics depend entirely on output conditions for content determination, or does it need an input condition too? The present paper argues that it does, at least as applied to simple representing systems. For Godfrey-Smith (1996) has raised a telling objection against fully output-oriented teleosemantics. From the objection flows an adequacy condition: a theory of content for simple representing systems should be compatible with the fact that content attribution is used to explain successful behaviour - that is, behaviour that contributes to the survival and reproduction of the representing system. That adequacy condition is met if, in addition to the teleosemantic output condition, representations are required to carry correlational information about their contents. Although the teleosemantic literature often discusses correlational information, its significance has not been identified precisely. This paper argues that the importance of correlational information lies in meeting the adequacy condition. Thus, carrying information is a necessary condition for representation in simple systems: a representation has the indicative content that p only if it carries the correlational information that p obtains

Section 2 explains my approach to the project of naturalising content and section 3 sets out the core of teleosemantics. Section 4 argues that there should be a substantive explanatory connection between true representation and successful behaviour and shows how that adequacy condition relates to Godfrey-Smith's objection to teleosemantics. Section 5 formulates a theory of content for simple representing systems by supplementing teleosemantics with correlational information (§5.1), showing how the supplemented theory meets the adequacy condition (§5.2), and explaining that standard teleosemantic theories do not contain a tacit input condition (§5.3). Section 6 shows that the resulting 'infotel-semantics' also has the merit of ruling out the possibility that tokens generated entirely at random in a simple system should count as intentional.
(Shea 2007)




Jeremy Green and James Sharp suggest unification of positional information and computational patterns (Wolpert and Turing) for genetics:

'One of the most fundamental questions in biology is that of biological pattern: how do the structures and shapes of organisms arise? Undoubtedly, the two most influential ideas in this area are those of Alan Turing’s ‘reaction-diffusion’ and Lewis Wolpert’s ‘positional information’. Much has been written about these two concepts but some confusion still remains, in particular about the relationship between them. Here, we address this relationship and propose a scheme of three distinct ways in which these two ideas work together to shape biological form. The problem of patterning the embryo is almost synonymous with developmental biology itself. One can trace controversies about how embryonic pattern arises back to Aristotle, but in the late nineteenth and early twentieth centuries the problem was revisited by such greats as Boveri, Roux, Driesch, Spemann and Morgan. They recognised that cell fates in embryos are somehow spatially coordinated into ‘patterns’ and that some continuously varying properties or substances that form ‘gradients’ might achieve this coordination. They also recognised that information could be physically, or more likely chemically, transmitted from one part of an embryo to another (see Lawrence, 2001). However, vagueness as to what these chemicals might be and how they might work persisted. It was advances in biochemistry in the 1920s and 1930s that began to inspire increasingly concrete thinking about the physico-chemical nature of pattern formation. Then, in 1952, Alan Turing (see Box 1), the great mathematician, code-breaker and computer scientist, published The Chemical Basis of Morphogenesis (Turing, 1952). In the highly readable introductory part of this paper, he laid out in crystalline prose a perfectly formal statement of the problem of embryonic pattern formation, distinguishing it, for example, from ‘mechanical morphogenesis’. He provided a conceptual solution – that of reaction-diffusion (RD) – but one that remained relatively obscure for a further 20 years. It took Lewis Wolpert (see Box 2), another non-biologist (who originally trained as a civil engineer), to again bring a hard edge to the problem in the late 1960s and early 1970s. In a series of eloquent theoretical review articles, Wolpert distilled and synthesised much that was known and theorised regarding pattern formation, brilliantly focusing the term ‘positional information’ (PI) and providing, almost literally, a graphical icon for the field: ‘The French Flag’ (Wolpert, 1969, 1971). 
The test of time has shown that, of the many theories regarding pattern formation, Turing’s and Wolpert’s remain pre-eminent. Wolpert’s, being the conceptually simpler, is most often found in textbooks and courses, while Turing’s is currently enjoying a resurgence. Wolpert, typically, proposed his concepts in a robust and contrarian way (the quotation below from his 1971 review is characteristic) and so it is often thought that the two ideas are mutually exclusive. In this Hypothesis article, we aim to overturn this impression and show that these two big ideas in developmental biology, despite indeed being conceptually distinct, are in fact wonderfully complementary and often collaborate to establish the complexity of developmental forms that we see. We first discuss the background behind Turing’s and Wolpert’s ideas, then introduce some real examples of each, before moving on to list the three main ways in which the two proposed patterning mechanisms might work together. “This [positional information-based] view of pattern formation must be contrasted with those views which explicitly or implicitly claim that in order to make a pattern it is necessary to generate a spatial variation in something which resembles in some way the pattern… [Such a] view of pattern formation is characterised by the work of Turing (1952) [and others] and is the antithesis of positional information.” Lewis Wolpert (1971)'
(Green and Sharpe 2015)



Marcello Barbieri offers a primarily anti-materialist or non-physicalist conception: 
The discovery of the double helix suggested in no uncertain terms that the sequence of nucleotides is the information carried by a gene (Watson and Crick 1953). A few years later, the study of protein synthesis revealed that the sequence of nucleotides in genes determines the sequence of amino acids in proteins, with a process that amounts to a transfer of linear information from genes to proteins. In both types of molecules, therefore, biological information was identified with, and defined by, the specific sequence of their subunits.
This idea was immediately accepted into the Modern Synthesis because it provided the molecular basis of both heredity and natural selection. Heredity became the transmission of information from one generation to the next, the short-term result of molecular copying. The long-term repetition of copying, on the other hand, is inevitably accompanied by errors, and in a world of limited resources not all copies can survive and a selection is bound to take place. That is how natural selection came into being. It is the long-term result of molecular copying, and can exist only in a world of informational molecules. Information has become in this way the key concept of modern biology, but also the object of a fierce controversy. The reason is that information, heredity and natural selection simply do not exist in the world of chemistry, and this creates a contrast with the idea that “life is chemistry”. This view was proposed for the first time by Jan Baptist van Helmont (1648), and has been re-proposed countless times ever since. One of the most recent formulations has been given by Günther Wächtershäuser (1997) in these terms “If we could ever trace the historic process backwards far enough in time, we would wind up with an origin of life in purely chemical processes”.
Wächtershäuser claimed that “information is a teleological concept”, and that science does not really need it: “On the level of nucleic acid sequences it is quite convenient to use the information metaphor… and apply teleological notions such as ‘function’ or ‘information’… but in the course of the process of retrodiction the teleological notions, whence we started, fade away. And what remains is purely chemical mechanism”. This amounts to saying that biological information, the most basic concept of modern biology, is nothing more than a verbal expression. The same charge has been made by the supporters of physicalism, the view that all natural processes are completely described, in principle, by physical quantities.
 The specific sequence of genes and proteins and the rules of the genetic code cannot be expressed by physical quantities, so what are they? According to physicalism, they are mere metaphors. They are linguistic terms that we use as shortcuts in order to avoid long periphrases. They are compared to those computer programs that allow us to write our instructions in English, thus saving us the trouble to write them in the binary digits of the machine language. Ultimately, however, there are only binary digits in the machine language of the computer, and in the same way, it is argued, there are only physical quantities at the most fundamental level of Nature.
 This conclusion, known as the physicalist thesis, has been proposed by various scientists and philosophers (Chargaff 1963; Sarkar 2000; Mahner and Bunge 1997; Griffith[s] 2001; Boniolo 2003) and is one of the most deeply dividing issues of modern science. Most biologists are convinced that information and the genetic code are real and fundamental components of life, but physicalists insist that they are real only in a very superficial sense and that there is nothing fundamental about them. Clearly, we must face this charge, and we must discuss it on its own grounds, i.e., in terms of physical theory.
...
Mechanics, thermodynamics, electromagnetism and nuclear physics, have all been built on the discovery of new fundamental observables, and now we realize that this is true also in biology. Life began when the first molecular machines appeared on the primitive Earth and started manufacturing genes and proteins by copying and coding, i.e., by processes that necessarily require two new observables. The nature of these observables has so far remained elusive because biologists have not yet come to grip with the idea that life is artifact-making. As soon as we realize that genes and proteins are manufactured molecules, we immediately see that sequences and coding rules are real observables. This conclusion, in turn, has three major consequences.
(1) The first is that the physicalist thesis is not valid because an observable is an objective tool of science, not a metaphorical entity.
(2) The second is that information is not a teleological concept, but a descriptive one. There is no more teleology in information and in the genetic code than there is in the quantities of physics and chemistry, because all of them are observables.
(3) The third consequence is a new understanding of information. Biological information is indeed the sequence of genes and proteins, but the nature of these sequences has so far eluded us. Now we realize that they are objective and reproducible but non-computable observables. They are nominable entities, a new type of fundamental observables without which we simply cannot describe the world of life.
(Barbieri 2012)



Arnon Levy proposes a specific fictionalism about biological information:

In thinking about development, professionals and laymen alike commonly treat genes as providing the information for adult form. In contrast, other factors are usually thought of as raw materials or as background conditions. Susan Oyama’s book The Ontogeny of Information (1985), prompted a number of philosophers to argue that this dichotomy is untenable and that there is no distinct sense in which genes carry developmental information. There seems to be a general agreement that genetic coding, the mapping of DNA base triplets onto the amino acids that constitute proteins, is a legitimate and important theoretical concept. The critics’ claim is that a richer, semantic sense of genetic information cannot be rescued from biological usage, nor is it necessary for explaining development. Indeed critics generally think that appeals to information are detrimental. Sarkar (1996) and Griffiths (2001) have argued that lack of care in the use of informational concepts leads to widespread misunderstandings of the explanatory structure of molecular biology: It encourages the belief that phenotypes can be “read-off” genes in a bottom-up manner. Furthermore, some hold that attributing an informational role to genes lends spurious support to genetic determinism (Griffiths, 2006). 
There exists a highly developed mathematical theory of information, pioneered by Claude Shannon (1948). But most authors who have written on the topic agree that Shannon’s notion is not the relevant one here. It is worth recounting – briefly and non-technically – why. Shannon’s theory allows that anything can be a source of information so long as it has a range of distinct states. One state carries information about another provided that the two are correlated. Information theorists then say that the two states are connected by a channel along which signals are transmitted. Intuitively, an information channel allows the receiver to learn about the state of the sender by consulting the signal. Information theory provides quantitative measures for the amount of information contained in a signal, the capacity of channels, the efficiency of particular coding and transmission schemes and related matters. These tools can be useful in biology, especially in bioinformatics, where large amounts of data pertaining to genes and proteins are analyzed. But in these contexts the apparatus of information theory is used as a data analysis tool: Bioinformaticians treat an available data set as carrying information about some process or structure of interest – the structure of a protein, for instance, or the topology of a regulatory network. They are not using information in an explanatory account, as a way of saying what genes do or how they do it. And for good reason: Genes carry Shannon information but so does any other factor that reliably affects protein structure (such as temperature). Genes may carry more information, but if information is understood along Shannon lines, their role isn’t qualitatively different. In contrast, the use of informational terminology that is under debate is meant to distinguish genes from other developmental factors. Genes are said to carry developmental information whereas food, also a crucial ingredient in development, doesn’t. In accounting for this explanatory use Shannon’s notion is of no avail.

Accepting that Shannon-information isn’t the way to go, “advocates” of information have mostly opted for a teleosemantic account (Sterelny, Smith Information in Biology: A Fictionalist Account and Dickison, 1996; Maynard Smith 2000; Sterelny 2000; Shea 2007). This view seeks to ground inherited information in natural selection. It relies on the idea that we can think of products of natural selection as having a function, and furthermore that under certain conditions functions can ground ascriptions of content. On the teleosemantic view, genes carry information about (or for) the structure they encode in virtue of being selected for producing that structure. … [Conclusion] My fictionalist proposal is motivated by the idea that even if we treat information non-literally we may still take it seriously and assign it a real role in biological understanding. But we shouldn’t take it too seriously. If information is a metaphor then it is, after all, untrue that cells and molecules bear semantic content. Let me comment on two contexts in which this makes a difference. The “metaphysics” of information. 20th-century molecular biology is sometimes described as having made a fundamental ontological discovery, namely that genes and other informational factors constitute a distinct kind of entity populating the world.
(Levy 2011)


Scientific Realism, Ontic Structural Realism, Entropy, and Information



Ladyman, Ross, and Collier Analyse The Relationship Between Physical Entropy and Information (the discussion is several pages long, and one of the most detailed and coherent available in the context of scientific realism):
The eminent physicist Wojciech Zurek (1990b) agrees with Peres in identifying so‐called ‘physical entropy’, the capacity to extract useful work from a system, with a more abstract entropy concept—in this case, the idea that entropy is the complement of algorithmic compressibility, as formalized by Chaitin (1966).24 Zurek also regards the formal similarity of von Neumann entropy and Shannon–Weaver entropy as reflecting physical reality, so in his treatment we get formal reification of three entropy/order contrasts. Let us refer to this as ‘the grand reification’. Zurek expresses the physical entropy of a system as the sum of two parameters that sets a limit on the compressibility of a set of measurement outcomes on the system. These are the average size of the measurement record and the decreased statistical entropy of the measured system. He then argues (p.214) that if the latter is allowed to be greater than the former, we get violation of the Second Law. In regarding this as a constraint on fundamental physical hypotheses, Zurek thus implicitly follows Peres in treating thermodynamics as logically fundamental relative to other parts of physical theory.
      We have referred to concepts of information and entropy from communications and computational theory as ‘abstract’ because they measure uncertainty about the contents of a signal given a code. Zurek substantivalizes this idea precisely by applying it to the uncertainties yielded in physical measurements and then following standard QM in interpreting these uncertainties as objective physical facts. However, biologist Jeffrey Wicken (1988) contests the appropriateness of this kind of interpretation.25 Following Brillouin (1956, 161) and Collier (1986), Wicken (1988, 143) points out that Shannon entropy does not generalize thermodynamic entropy because the former does not rest on objective microstate/macrostate relations, whereas the latter does. Entropy, Wicken argues, doesn't measure ‘disorder’ in any general sense, but only a system's thermodynamic microstate indeterminateness. He claims that it increases in the forward direction in time in irreversible processes, but that this cannot be presumed for ‘disorder’ in general. ‘Everything that bears the stamp says Wicken, ‘does not have the property of increasing in time. Irreversibility must be independently demonstrated’ (144). He argues that algorithmic complexity as formalized by Chaitin is the proper target concept at which Shannon and Weaver aimed when they introduced their version of ‘entropy’.26 Wicken's general view is that both thermodynamic information and what he calls ‘structural’ information (as in Chaitin) are relevant to the dynamics of biological systems (as leading instances of ‘self‐organizing’ systems), but that they are essentially different concepts that play sharply distinct roles in the generalization of the facts.
(Ladyman et al. 2007, 214)

 An early offering from Harms, in an attempt to clarify and disambiguate concepts of information derived from the classical statistical Shannonian conception... 
This paper takes the position that one can usefully clarify what one means by “information” in terms of three general categories of information concepts. I shall dub these statistical information, semantic/conventional information, and physical information. Statistical and semantic information concepts can typically be located with respect to Shannon’s information theory and naturalistic semantic theory, respectively. Both sorts of information involve (statistical or historical) relationships between systems, and though controversies may exist, the nature of the relationships under consideration are generally understood, or at least widely discussed. Physical information concepts on the other hand consist largely of the residue of intuitions about information once relational information has been accounted for. The looming question shall be whether there is a coherent concept of physical, intrinsic, or structural information that can be grounded in a productive and defensible theory of such.

The distinction between the three broad kinds of information concepts is easy enough to see in the case of gene-pool examples. Consider an individual in some population who carries the sickle-cell gene. There are several senses in which we might want to say that there is information in this fact. In the first place, supposing we could assign probabilities to the general occurrence of such a gene in general as well as conditional on various external environments (like those in which malaria is a significant risk) then we might want to say that the occurrence of this gene carries information about the environment, in the sense that its discovery in some randomly chosen individual changes the probability that malaria is a risk in the local environment. This sort of probabilistic environment-indication is fundamentally a matter of statistical relationships between two systems (gene pools and environments), rather than anything intrinsic in the gene itself. Information theory calls this kind of information “mutual information,” and if that is all one means by “information,” one is on firm ground. As we shall see, information theory also grounds other kinds of information, such as the information “generated” by an occurrence. One might think, for instance, that less likely events generate more information, or are intuitively more informative than more common events. The tools of information theory allow one to quantify such notions.

On the other hand, one might be instead interested in the information contained more properly in the gene itself. One form our intuitions often take is that the gene contains the information how to produce (in context) the particular sickle-cell deformity. Part of this kind of information seems to consist in the particular sequence of nucleotides making up the gene. But the instructional information as to how to produce the particular effect also depends, quite essentially, on the transcribing and decoding conventions of the genetic machinery. These arrangements are a matter of historical “convention” (in a sense that will be made precise later) and as such are not fully intrinsic. Instead, they bear close similarity with the interpreted meaning of words, such that we can say quite literally what the gene “means” in the context of the interpretive machinery is that a hemoglobin cell is to be sickled. This sort of information cannot be cashed out merely in terms of probabilities but instead depends crucially on certain historically established arrangements involving the interpretation of nucleotide strings. Other sorts of semantic informational relationships such as reference (as distinct from statistical indication) share this dependence on established conventions and as such deserve to be grouped together as those which depend on established rules or conventions regarding proper usage. (Harms 2006) 




Information and Semantic Information 



Carlo Rovelli Efforts an Evolutionary-cum-functional conception of Semantic Information:
The second is the notion of ‘information’, which is increasingly capturing the attention of scientists and philosophers. Information has been pointed out as a key element of the link between the two sides of the gap, for instance in the classic work of Fred Dretske [3]. 
However, the word ‘information’ is highly ambiguous. It is used with a variety of distinct meanings, that cover a spectrum ranging from mental and semantic ("the information stored in your USB flash drive is comprehensible") all the way down to strictly engineeristic ("the information stored in your USB flash drive is 32 Giga"). This ambiguity is a source of confusion. In Dretske’s book, information is introduced on the base of Shannon’s theory [4], explicitly interpreted as a formal theory that "does not say what information is".
In this note, I make two observations. The first is that it is possible to extract from the work of Shannon a purely physical version of the notion of information. Shannon calls its "relative information". I keep his terminology even if the ambiguity of these terms risks to lead to continue the misunderstanding; it would probably be better to call it simply ‘correlation’, since this is what it ultimately is: downright crude physical correlation. 
The second observation is that the combination of this notion with Darwin’s mechanism provides the ground for a definition of meaning. More precisely, it provides the ground for the definition of a notion of "meaningful information", a notion that on the one hand is solely built on physics, on the other can underpin intentionality, meaning, purpose, and is a key ingredient for agency. The claim here is not that the full content of what we call intentionality, meaning, purpose - say in human psychology, or linguistics - is nothing else than the meaningful information defined here. But it is that these notions can be built upon the notion of meaningful information step by step, adding the articulation proper to our neural, mental, linguistic, social, etcetera, complexity. In other words, I am not claiming of giving here the full chain from physics to mental, but rather the crucial first link of the chain. 
(Rovelli 2016) 
Christopher Timpson enlists J.L. Austin's appraisal of truth theory and the philosophy of language in an attempt to disambiguate and disentangle concepts of information, and sets out to propose a kind of pragmatic (in the Peircian/scientific sense) nominalism about information:
Distinctions are drawn between a number of different information concepts. It is noted that ‘information’ in both the everyday and Shannon-theory setting is an abstract noun, though derived in different ways. A general definition of the concept(s) of information in the Shannon mould is provided and it is shown that a concept of both bits (how much) and pieces (what) of Shannon information is available. It is emphasised that the Shannon information, as a measure of information, should not be understood as an uncertainty; neither is the notion of correlation key to the Shannon concept. Corollaries regarding the ontological status of information and on the notion of information’s flow are drawn. The chapter closes with a brief discussion of Dretske’s attempt to base a semantic notion of information on Shannon’s theory. It is argued that the attempt is not successful. 

The epigraph to this chapter is drawn from Strawson’s contribution to his famous 1950 symposium with Austin on truth. Austin’s point of departure in that symposium provides also a suitable point of departure for us, concerned as we are with information. Austin’s aim was to de-mystify the concept of truth, and make it amenable to discussion, by pointing to the fact that ‘truth’ is an abstract noun. So too is ‘information’. This fact will be of recurrent interest during the course of this study. 
‘ “What is truth?” said jesting Pilate, and would not stay for an answer.’ Said Austin: 
‘Pilate was in advance of his time.’
As with truth, so with information:
 
For ‘truth’ [‘information’] itself is an abstract noun, a camel, that is of a logical construction, which cannot get past the eye even of a grammarian. We approach it cap and categories in hand: we ask ourselves whether Truth [Information] is a substance (the Truth [the information], the Body of Knowledge), or a quality (something like the colour red, inhering in truths [in messages]), or a relation (‘correspondence’ [‘correlation’]).  
But philosophers should take something more nearly their own size to strain at. What needs discussing rather is the use, or certain uses, of the word ‘true’ [‘inform’]. (Austin, 1950, p. 149)
A characteristic feature of abstract nouns is that they do not serve to denote kinds of entities having a location in space and time. Typically it is added that these are nouns which do not denote entities which may be objects of perception, or seats of causal power. ‘Wisdom’, ‘justice’, ‘terror’, ‘honesty’ are abstract nouns, as are ‘number’, ‘set’, and ‘policy’. An abstract noun may be either a count noun (a noun which may combine with the indefinite article and form a plural) or a mass noun (one which may not). ‘Information’ is an abstract mass noun, so may usefully be contrasted with a concrete mass noun such as ‘water’; and with an abstract count noun such as ‘number’.6 Very often, abstract nouns arise as nominalizations of various adjectival or verbal forms, for reasons of grammatical convenience.7 Accordingly, their function may be explained in terms of the conceptually simpler adjectives or verbs from which they derive; thus Austin leads us from the substantive ‘truth’ to the adjective ‘true’. Similarly, ‘information’ is to be explained in terms of the verb ‘inform’. Information, we might say, is what is provided when somebody is informed of something. If this is to be a useful pronouncement, we should be able to explain what it is to inform somebody without appeal to phrases like ‘to convey information’, but this is easily done. To inform someone is to bring them to know something (that they did not already know)… 

Now, I shall not be seeking to present a comprehensive overview of the different uses of the terms ‘information’ or ‘inform’, nor to exhibit the feel for philosophically charged nuance of an Austin. 
It will suffice for our purposes merely to focus on some of the broadest features of the concept, or rather, concepts, of information. The first and most important of these features to note is the distinction between the everyday concept of information and technical notions of information, such as that deriving from the work of Shannon (1948) [(Shannon and Weaver 1949)]. The everyday concept of information is closely associated with the concepts of knowledge, language, and meaning; and it seems, furthermore, to be reliant in its central application on the prior concept of a person (or, more broadly, language user) who might, for example, read and understand the information; who might use it; who might encode or decode it. 
A technical notion of information might be concerned with describing correlations and the statistical features of signals, as in communication theory with the Shannon concept, or it might be concerned with statistical inference (e.g., [(Fisher 1925)]; [(S. Kullback and Leibler 1951)]; Savage, 1954; (Solomon Kullback 1959)). Again, a technical notion of information might be introduced to capture certain abstract notions of structure, such as complexity (algorithmic information, [(Chaitin 1966)] Chaitin (1966); (Kolmogorov 1968, 1963); Kolmogorov (1965); Solomonoff (1964)) or functional role (as in biological information perhaps, cf. [(Jablonka 2002)] Jablonka (2002) for example).
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So as a measure of uncertainty, H(X) [Shannon's measure] is not unique; however, as a measure of Shannon informationt  — of compressibility — it is unique (this follows from the noiseless coding theorem). Hence H(X) as a measure of uncertainty is distinct from H(X) as a measure of informationt and the concepts measure of uncertainty and measure of informationt are distinct.

Let us take up a different question. We may grant that Shannon’s informationt quantity is not an amount of uncertainty, but what of the intuitive link between uncertainty and information with which we began this section? Doesn’t that still stand? Indeed it does—so far as it goes—and this tells us that whatever information in the sense delivered by the link to uncertainty might be, it is not the informationt of the Shannon theory. It is something else instead. What is it?

In some degree, we evidently have a link to the everyday notion of information, as uncertainty seems to be an appropriately epistemic concept: The more uncertain I am about the outcome, the less I know; the less I know, the more information I gain when I learn what the outcome is. But these equations are rather tortuous and shouldn’t be admitted without further ado. To begin with, we need to handle the question ‘How much do I know about the outcome?’ with care. We are supposing that the experiment is genuinely probabilistic; and all one knows is the probability distribution. Thus, strictly speaking, all one knows about what outcome will occur is that any of the outcomes assigned non-zero probability can occur (and conversely, that none of those assigned zero probability will occur); and that is consistent with continuum-many different probability distributions, many of which will receive different values of uncertainty. So when we say that one knows more when one has a more peaked probability distribution (lower uncertainty distribution), we are providing a new sense for ‘how much does one know?’, equating ‘how well can I predict?’ (how spread is the distribution) with ‘how much do I know?’ in this new sense. This should be contrasted, for example, with a case in which I have partial knowledge about some predetermined fact about what the outcome will be—I know something, but not everything about it: that would be a quite different sense of how much I know about the outcome. 
But what information have I gained as the result of the experiment? The information that the outcome was thus-and-so, rather than being any of the other outcomes consistent with the probability distribution. This is a bona fide piece of information in the everyday sense. But does the uncertainty measure H(X) or equally one of the other [formulae] then tell me how much information in the everyday sense I have gained from acquiring this piece of information? That is, is a measure of amount of information in the everyday sense? It would seem not; at least not without heavy qualification.

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We began by noting some elementary features of the everyday notion of information: that ‘information’ is an abstract (mass) noun derived from the verb ‘inform’; that the notion of informing and thus of information itself is to be made out in terms of the prior concept of knowledge; that there is a distinction between possessing information and containing it, while the latter category admits a further distinction between containing information propositionally and containing it inferentially; that one should be wary of the trap of trying to explain possession of information simply as containing it; that pieces of information must be truths. Above all, the aim was to sharpen our appreciation of the differences between the aim was to sharpen our appreciation of the differences between the everyday notion of information and that of information information and that of informationt theory. The everyday notion is a semantic and an epistemic concept linking centrally to the notions of knowledge, language, and meaning; to that of a person (language user) who might inform or be informed.
The Shannon concept, by contrast, we saw to be concerned with the behaviour of various physical systems characterized abstractly, at a level at which no semantic properties are in play, nor even any epistemic ones. The noiseless coding theorem defines the concepts both of the quantity of informationt produced by a source and also that of the pieces of Shannon informationt produced. Drawing from this case, a general definition of what informationt in a Shannon-type theory actually is was presented: informationt is what is produced by a source that is required to be reproducible at the destination if the transmission is to be a success. This led us to distinguish between the piece of informationt produced on an occasion—an abstract type, a particular sequence of states—and the concrete object or objects which instantiate it: the token of the piece of informationt. Thus we concluded that ‘information’ in Shannon’s theory was an abstract noun too. 
It is sometimes thought (as noted in the introduction) that the Shannon concept is merely a quantitative one, defining an amount of information only; but at least the amount it quantifies is the amount of everyday information that might be about in a given situation. However, we have seen that this is an error on both counts: Shannon’s analysis does provide us with a notion of what is produced (pieces of informationt), but it certainly does not in general quantify information in the everyday sense. To reinforce this point I argued that the common interpretation of the Shannon quantity H(X) in terms of uncertainty did not capture the Shannon concept of informationt proper (measure of informationt and measure of uncertainty are distinct concepts) while an amount of uncertainty as given by a measure like H(X) will typically not measure the amount (or even average amount) of information in the everyday sense to be gained. Similarly, we noted that the primary interpretation of the mutual informationt H(X: Y) was in terms of the noisy coding theorem, even though this same mathematical quantity can be useful as a measure of uncertainty in inference. 
(Timpson 2013)
  Olimpia Lombardi attempts a disambiguation on the basis of pluralism and conceptual analysis:

The main aim of this work is to contribute to the elucidation of the concept of information by comparing three different views about this matter: the view of Fred Dretske’s semantic theory of information, the perspective adopted by Peter Kosso in his interaction-information account of scientific observation, and the syntactic approach of Thomas Cover and Joy Thomas. We will see that these views involve very different concepts of information, each one useful in its own field of application. This comparison will allow us to argue in favor of a terminological ‘cleansing’: it is necessary to make a terminological distinction among the different concepts of information, in order to avoid conceptual confusions when the word ‘information’ is used to elucidate related concepts as knowledge, observation or entropy.
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This discussion suggests that there is a severe terminological problem here. Usually, various meanings are subsumed under the term ‘information’, and many disagreements result from lacking a terminology precise enough to distinguish the different concepts of information. Therefore, a terminological cleansing is required in order to avoid this situation. My own proposal is to use the word ‘information’ only for the physical concept: this option preserves not only the generally accepted links between information and knowledge, but also the well-established meaning that the concept of information has in physical sciences. I think that this terminological choice retains the pragmatic dimension of the concept to the extent that it agrees with the vast majority of the uses of the term. But, what about the semantic and the syntactic concepts? Perhaps Dretske’s main goal of applying the concept of information to questions in the theory of knowledge can be also achieved by means of the physical concept, without commitments with non-physical information channels. Regarding the syntactic view, it would be necessary to find a new name that expresses the purely mathematical nature of the theory, avoiding confusions between the formal concepts and their interpretations. Of course, this terminological cleansing is not an easy task, because it entails a struggle against the imprecise application of a vague notion of information in many contexts. Nevertheless, this becomes a valuable task when we want to avoid conceptual confusions and futile disputes regarding the nature of information.


(Lombardi, 2004)
Christoph Adami deploys a 'revivalist' contemporary interpretation of classical formalism for biological information:
Information is a key concept in evolutionary biology. Information stored in a biological organism’s genome is used to generate the organism and to maintain and control it. Information is also that which evolves. When a population adapts to a local environment, information about this environment is fixed in a representative genome. However, when an environment changes, information can be lost. At the same time, information is processed by animal brains to survive in complex environments, and the capacity for information processing also evolves. Here, I review applications of information theory to the evolution of proteins and to the evolution of information processing in simulated agents that adapt to perform a complex task.
 
But there is a common concept that unifies the digital and the biochemical approach: information. That information is the essence of “that which evolves” has been implicit in many writings (although the word “information” does not appear in Darwin’s On the Origin of Species). Indeed, shortly after the genesis of the theory of information at the hands of a Bell Laboratories engineer,15 this theory was thought to ultimately explain everything from the higher functions of living organisms down to metabolism, growth, and differentiation.16 However, this optimism soon gave way to a miasma of confounding mathematical and philosophical arguments that dampened enthusiasm for the concept of information in biology for decades. To some extent, evolutionary biology was not yet ready for a quantitative treatment of “that which evolves:” the year of publication of “Information in Biology” coincided with the discovery of the structure of DNA, and the wealth of sequence data that catapulted evolutionary biology into the computer age was still half a century away.
Colloquially, information is often described as something that aids in decision making. Interestingly, this is very close to the mathematical meaning of “information,” which is concerned with quantifying the ability to make predictions about uncertain systems. Life—among many other aspects— has the peculiar property of displaying behavior or characters that are appropriate, given the environment. We recognize this of course as the consequence of adaptation, but the outcome is that the adapted organism’s decisions are “in tune” with its environment—the organism has information about its environment. One of the insights that has emerged from the theory of computation is that information must be physical—information cannot exist without a physical substrate that encodes it.17 In computers, information is encoded in zeros and ones, which themselves are represented by different voltages on semiconductors. The information we retain in our brains also has a physical substrate, even though its physiological basis depends on the type of memory and is far from certain. Context appropriate decisions require information, however it is stored. For cells, we now know that this information is stored in a cell’s inherited genetic material, and is precisely the kind that Shannon described in his 1948 articles. If inherited genetic material represents information, then how did the information carrying molecules acquire it? Is the amount of information stored in genes increasing throughout evolution, and if so, why? How much information does an organism store? How much in a single gene? If we can replace a discussion of the evolution of complexity along the various lines of descent with a discussion of the evolution of information, perhaps then we can find those general principles that have eluded us so far. 
In this review, I focus on two uses of information theory in evolutionary biology: First, the quantification of the information content of genes and proteins and how this information may have evolved along the branches of the tree of life. Second, the evolution of information-processing structures (such as brains) that control animals, and how the functional complexity of these brains (and how they evolve) could be quantified using information theory. The latter approach reinforces a concept that has appeared in neuroscience repeatedly: the value of information for an adapted organism is fitness, and the complexity of an organism’s brain must be reflected in how it manages to process, integrate, and make use of information for its own advantage. 
To define entropy and information, we first must define the concept of a random variable. In probability theory, a random variable X is a mathematical object that can take on a finite number of different states x1 · · · xN with specified probabilities p1, . . . , pN. We should keep in mind that a mathematical random variable is a description—sometimes accurate, sometimes not—of a physical object. For example, the random variable that we would use to describe a fair coin has two states: x1 = heads and x2 = tails, with probabilities p1 = p2 = 0.5. Of course, an actual coin is a far more complex device—it may deviate from being true, it may land on an edge once in a while, and its faces can make different angles with true North. Yet, when coins are used for demonstrations in probability theory or statistics, they are most succinctly described with two states and two equal probabilities. Nucleic acids can be described probabilistically in a similar manner. We can define a nucleic acid random variable X as having four states x1 = A, x2 = C, x3 = G, and x4 = T, which it can take on with probabilities p1, . . . , p4, while being perfectly aware that the nucleic acid molecules themselves are far more complex, and deserve a richer description than the four-state abstraction. But given the role that these molecules play as information carriers of the genetic material, this abstraction will serve us very well going forward.  
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Information is the central currency for organismal fitness,80 and appears to be that which increases when organisms adapt to their niche. Information about the niche is stored in genes, and used to make predictions about the future states of the environment. Because fitness is higher in well-predicted environments (simply because it is easier to take advantage of the environment’s features for reproduction if they are predictable), organisms with more information about their niche are expected to outcompete those with less information, suggesting a direct relationship between information content and fitness within a niche (comparisons of information content across niches, on the other hand, are meaningless because the information is not about the same system). A very similar relationship, also 


(Adami 2016)

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