ENTROPY DIAGNOSIS PROCESS RELATED TO ENTROPY.

May 29, 2007 at 12:05 am · Filed under Uncategorized

DIAGNOSIS PROCESS RELATED TO ENTROPY Eduardo Alfredo Zevallos-Giampietri, M. D.Carlos Barrionuevo, M.D.Departamento de Patología, Instituto de Enfermedades Neoplasicas, Lima, Perú 

Vishnu
S. Shukla, M. D.Phoenix Cancer Help Group, Green Acres, ITC,
Bangalore, India                                                                                                Address correspondence:Eduardo A. Zevallos Giampietri, M.D.Instituto de Enfermedades Neoplásicas (INEN)Departamento de PatologíaAvenida Angamos Este, San Borja (Lima 34)Lima-PerúTel/Fax (51-1) 2171300 

E-mail: edzevallos@yahoo.com  Running head: Entropy diagnosis 

Abstract: Theories of knowledge based on internalism are basically anthropomorphic. Consequently fallacies and misinterpretations are produced because of the inherent subjectivity. Recent trends of conventional medicine strongly depend on internalism.  In this article we propose a concept of knowledge based on Entropy/Information. In this manner, we conjecture that subjectivity could be reduced. In addition we suggest a preliminary model of diagnosis in histopathology. 

Key words: entropy, evidence-based medicine, diagnosis, knowledge, medicine, pathology 

Introduction 

The scientific core of the diagnosis process is poorly understood. The diagnosis process can be placed in the context of Entropy/Information. We agree when Saridis says “However, other major cultural areas of thought, like social systems, religion, legal and governmental theories have not kept up with the technological achievements, and therefore are missing in benefits due to the lack of appropriate models for their study. The theory of Entropy, if introduced properly, in addition to its practical applications, has a philosophical foundation that has implications to the quality of life and the future of our planet” [1]. Medicine must be added to the list of disciplines that unfortunately have neglected the importance of Entropy. Most physicians inaccurately think that diagnosis is just finding the name of a disease that matches the patient’s problems. This type of practice is an overt reductionism, and as such promoted by “problem-based oriented approach” and “evidence-based medicine” (EBM). The physics and mathematics of the diagnosis process has been totally neglected by conventional medicine. Diagnosis, contrarily, is essentially an information process focused on a system. Therefore, diagnosis ultimately depends on the law of Entropy, and, consequently on Information Theory. Here, we introduced a preliminary model of diagnosis based on informatics. This model can be as well applied to several other areas. Since this model is rooted in Entropy/Information, it is dynamic, and predictably unbiased. The basic idea is that the process of diagnosis can be quantified using a pertinent model based on informatics, and disregarding as much as possible the anthropomorphic noise. A similar method based on artificial intelligence for visual learning has been published.  Indeed, in the last part of that article, the authors say, “Notably, it is the learning agent itself that judges its own performance based on training-set performance and residual entropy…The learning method contains few adjustable parameters, none of which is critical. Learning is incremental in two ways: First, training images are considered sequentially; second, continued “expert” learning produces increasingly better features and reduces any overfitting effects, resulting in improved test-set performance and a reduced number of features” [2].  

Our viewpoint is that the so-called teaching in conventional medical schools is not compatible with the natural learning process. Moreover, the so-called “continuing medical education” (CME) does not have realistic basis, since logical sequences are ignored. Organizations providing support to health-care institutions, despite an apparently good willingness, ultimately do not have solid scientific principles. There is no way or method to quantify if their policies and procedures have a real substantial impact in the outcome of a target population. For them, things may appear right, but this may be just an euphemistic exercise because their assessments are based on doubtful measurements established by the same providers. Therefore, under these circumstances they are close circles. In fact, it is well known that close circles are progressively contaminated by anthropomorphic biases [3]. Conventional linear statistics are used for large groups or population; therefore the degrees of freedom of the system are restricted, at such level. Contrarily, physician-patient relation is an individualized practice, and at this level the graining of the system is finer, therefore having much more degrees of freedom compared with that regarding statistical medicine. A level with more degrees of freedom has much more Entropy and Information compared with those of a system with less degrees of freedom. EBM pretends to  be applied to large group statistics  than to individual practice, thus we think this approach is inadequate. Bar-Yam using a multiscale complex system analysis, based on Ashby’s Law of Requisite Variety, reaches similar conclusions, and stated that  “The current health care system is an individualized system, and even when it provides care relevant to populations it typically provides them through one-to-one physician-patient model. Individualized care should be entrusted to a fine-scale, individual-care medical system, while a distinct system should be created for large-scale and efficient prevention and population health programs”. This author also points out the limitations of centralized control in the management of complex medical care, the limitations of automatization in improving health care, and the likelihood of medical errors in mismatched systems [4]. 

On the other hand, non-conventional Medicine (the one not taught in medical schools) is surprisingly in the route of accruing scientific principles. New currents such as Systemic Medicine have more scientific basis compared with the conventional medicine. Indeed, Systemic Medicine has postulated that Entropy is a cornerstone in health and disease [5]. Traditional Medicine, paradoxically, may have much more scientific basis than conventional medicine, as it considers the human body as a dynamical non-linear system. It is very likely that Traditional Medicine is ultimately focused in the modulation of the body’s Entropy. Unveiling this relationship will open a vast new field in diagnosis and therapy. This is a consistent philosophy that can be traced back to cultures such as China,
India, and Perú. Conventional medicine and EBM, taught in medical schools, are basically reduction “problem solving” exercises, which depends on gross non-dynamic linear methods and statistics. Reductionism is completely inadequate to understand complex systems, because complexity carries impredicativility, which means that definitions are spurious. Actually, definitions for complex systems are against well-established concepts such as Gödel’s Incompleteness Theorem [6], and Popper’s Principle [7]. Complex systems can be conceptualized (not defined) by approaching not only to their elements, but also to their function. It has been well demonstrated that nature is not linear, and it behaves in non-linear and dynamical manner. Therefore, using linear methods and linear statistics is utterly unnatural. Conventional medicine and its drill EBM are sort of “local” approaches, but when they are stretched into different situations they usually fail, indeed, because their lack of non-locality. The criticisms to conventional medicine would be the topic of forthcoming article (manuscript on preparation). 

The estimated brain computational power is 1013 to 1016 operations/sec [8]. While, the lifetime human memory, according to Landauer, is in the order of 109 bits, and “The remarkable result of this work was that human beings remembered very nearly two bits per second under all the experimental conditions. Visual, verbal, musical, or whatever—two bits per second” [9]. Amazingly, the human brain holds much more bits per second than those that can accumulate in a lifetime. Human learning process, therefore, may depend more on the brain’s operational capacity than on the memory. The human eye observation is bounded by a “maximum visual resolution/transmission” about – log2 1/7 = 2.807 bits [10], which means that the amount of information plateaus at about 7 parts over a continuum, and at this level there is a substantial interobserver agreement with correlation coefficients k between 0.61 – 0.80. However, in practice the effective amount of information transmitted from a continuum is about or less than 2 bits or – log2 1/4 (or one choice out of four), because some information is lost at the boundaries between categories. This maybe related to interobserver disagreements.  Francis Bacon’s induction model postulated that scientific theories came out to explain pre-existent data, and verified the theories gathering additional confirmatory evidences. Skeptical philosophers such David Hume seriously doubted that a series of “objective” observations might establish the validation of a general theory or law, since there is always a future possibility of observations refuting the law. Positive observations confirming a theory are easy to find or make, but contradictions are more difficult to find and are usually not welcome. This skeptical assertion turned to be a reality when Einstein’s General Relativity falsified the apparently invulnerable Newtonian physics. Relativity arises from pure theoretical basis, thus, for this reason it contradicts the essence of classical empiricism. In science, usually, the hypothesis or the theory is first and subsequently followed by experiments, observations, and collection of data to test the theory. In 1943, Karl Popper with his classical publication “The Logic of the Scientific Investigation” changed the scope of science philosophy. According to Popper “observation is always selective. It needs a chosen object, a defined task, an interest, a point of view, a problem”. [11].  

The issue of Knowledge

What is knowledge? One of the most common assertions is Plato’s definition that knowledge is “a true justified belief” [12]. This definition restrictively differentiates belief from knowledge. A belief may or not may be true, at the same time may or not may be justified. For instance, we can say that I believe that small dwarfs that live inside the PC run computers, and they make all the calculations and scripts that appear on the screen. This statement is a belief, and even our belief is apparently justified, and it has an structural syntactic logic, but this is not enough. To turn our belief into knowledge, we have to demonstrate that in fact dwarfs run the computer. Since objectivity depends on the disturbing metaphysical concept of counterfactual definiteness, this belief may still be a potential knowledge. Similarly, all other beliefs could be potential knowledge. But, intelligently speaking not being able to demonstrate the contrary does not necessarily raise a belief to the category of knowledge. Indeed, this is similar to Popper’s falsifiability. Thus, it is very easy for human mind to confuse between what is merely a belief from what is a real knowledge. If we analyze in depth Plato’s definition of knowledge we found that it has a tremendous flaw: it is purely anthropomorphic. Therefore, it is not impartial with itself. Even worse, it can be consciously and unconsciously contaminated or manipulated by the background (anthropomorphic) noise. Moreover, it is blind itself to differentiate between the core message and the anthropomorphic noise. The concept of what constitutes knowledge has to be constructed inside the Mathematical Theory of Information [13], which by default is non-anthropomorphic. A falling tree in the forest equally produces information with or without “intelligent observers”. An event received in our brain constitutes a piece of knowledge if mathematically can be traced back (decoded) to its source without distortion. This means that the measured event (message or data) have consistency in both senses and directions. Of course the code/decode and the transmission correction have to be appropriately performed. This concept of knowledge is sustained by the hierarchical model of human communication proposed by R. M Losee [14]. Eventually, even the inputs entering into the system may be traced back. The Mathematical Theory of Information can be used in both directions. The mental functions, after all, are based on spiking of transmembrane potentials. This spiking obeys to an “all” or “nothing” threshold principle, which essentially is a binary process; therefore it can be incorporated into the Mathematical Theory of Information. In this manner, we see Information as a whole process.  

The detected events from a system are transformed into data. At this point it is interesting to make clear that a data can be potentially anything emerging from the system, either work and heat (“free energy” is negative) or “forced” data (data obtained through a measurement device). However, a system can also absorb data from the environment in cases that the events inside a system require energy from the surroundings (in these cases “free energy” turns positive). Data are produced by a measurement device (biological or non-biological). Data are consequence of the interaction event-device, which can be seen as a symmetry breaking, gradient, and/or change of Entropy. Actually, the concept of what energy is maybe rooted to this change of Entropy. Anthropomorphic noise may arise by ignoring this fact, consequently not considering the limitations of the measuring device. Likely, the mental process (mind) is also based on gradients or entropy changes, and also susceptible to anthropomorphic noise. Ultimately, the anthropomorphic noise can be cancelled (at least partially) if its source is noticeable. From a cybernetics analysis, knowledge can be conceptualized as an evolutionary process. Knowledge is similar to control, therefore cybernetics principles such as Ashby´s Law of Requisite Variety [15], and Conant-Ashby’s principle “every good regulator (controller) of a system must be a model of that system” [16] are suitable to understand what knowledge is. This means that the regulator can be a subsystem that recreates the varieties of a higher-level system (or environment) to successfully compensate distortions (varieties) imposed by the environment. Interestingly in this context, Heylighen has elaborated a similar association with Entropy [17].      The interpretation of data, as a neuronal binary process, may be physically performed in the context of Entropy (to say
Shannon’s Entropy). Evidentialism claims that interpretation (judgment) of data equals so-called “evidence”; then this “evidence” magically is projected as an external fact (“proof”). Information, as a process, is basically external, and must be clearly distinguish from interpretation of data, which is an internal process influenced by personal circumstances. Moreover, in evidentialism the observer is at an unconscious internal position, but he erroneously believes is an external observer, because his “evidence” has been also erroneously projected as being an external event. Knowledge and science depend on observation. The key point is that observation is physically never a passive phenomenon. Merely looking at something implies certain degree of merging or correlation between the observer and what is observed. At the quantum level this interaction is even more accentuated, more generalized and almost instantaneous, to the point that materialization itself likely depends on it. This physical phenomenon is usually called decoherence, and it has its roots in multiple entanglement between EPR pairs. Exactly how things are brought to our physical reality is still debatable, and this topic is beyond the scope of this article. The interested reader may consult these references: [18 - 22]. 

A nerve impulse is essentially a binary code. The transmission of nerves is in the order of 103 bits/sec, and this can be considered as an operational capacity. Just comparing with the thermodynamic operational capacity of matter at 1020 bits/sec, it means that our nervous system is naturally handicapped to recognize most of the physical reality.  Therefore, whatever we see if just a much reduced average of matter’s inner computation. Perhaps, this human natural lack of capacity for observation makes us very vulnerable for misinterpretation of the information [23]. Besides, when observing at a continuum of variables the human vision has a limited power of discrimination (resolution). The maximal visual resolution is approximately 2.807 bits (= log2 1/7), which means that humans can ascertain up to one interval position out of seven inside a continuum. However, the amount of information transmission is less than 2.807 bits because some amount is lost at the boundaries among intervals; therefore this generates interobserver disagreements [10]. Naturally, the human brain is very susceptible to confuse the messages (data) with the background noise. The so-called background noise arises as a mismatch between the allowable degrees of freedom of the measurement device and degrees of freedom of the event. This discordance is likely the source of the anthropomorphic noise. If and “explanation” of this noise is pushed, this may result in a “misinterpretation”.  Therefore, people frequently claim to see “signs” referring to paranormal phenomena. Our eyes and our brain may fool us. “What we have here is a signal-to-noise problem. Consider a few cases of false pattern recognition: the face of the Virgin Mary on a grilled cheese sandwich; the face of Jesus on an oyster shell (resembles Charles Manson, I think). We evolve as a social primate species whose language ability facilitated the exchange of such association anecdotes. The problem is that although true pattern recognition helps us survive, false pattern recognition does not necessarily get us killed, and so the overall phenomenon has endured the winnowing process of natural selection. The Darwin Awards (honoring those who remove themselves from the gene pool), like this column, will never want for examples. Anecdotal thinking comes naturally; science requires training” [24]. Our limited observation capacity restricts our extension of knowledge. Ontologically, a complete knowledge is utopia. A totally external observer of any system, strictly speaking, is impossible for the simple reason that the universe is apparently the only close system, at least from our own physical reality perspective. Ultimately, all systems dwelling inside the universe are not stringently isolated from the rest of the universe, therefore they are subsystems or, better say, elements of the universe.  The universe may be the only system with pure unconditional entropy. Biological systems, including humans, and inert systems are elements of this big system called universe. Therefore, an element inside of a system cannot be neutral in relation to the system it belongs to. However, this fact should not be an excuse for denial of our own limitations. The sense of individuality and “free will” that we perceived can be explained through physics; in fact Entropy is not only a measurement of probabilities, but also is a measurement when choosing among probabilities.  A detail analysis of philosophy of knowledge is beyond the scope of this article. Maybe knowledge itself is a provisional term, as a complete knowledge of anything is utopia. Philosophically, the theory of knowledge is usually centered in Plato’s definition of knowledge as a “true justified belief” (TJB). Here, we have disregarded such definition because of its deep anthropomorphic connotation. The three words, “true”, “justified” and “belief” require an intelligent being, i.e. a mind, to do an interpretation of the observations. In this setting the role of the observer is not well established, as it is not clear if the observer is acting as an internal or external one. Philosophical theories of knowledge have to deal with these controversial issues. Indeed, Edmund L. Gettier in 1963 set a milestone when he demonstrated that the TJB was not enough to establish knowledge [25]. In his seminal article Gettier gives two examples fulfilling Plato´s definition of knowledge; however, cannot be considered as knowledge. Thereafter, many philosophical attempts of modifications of TJB has been performed to explain what knowledge is, but none so far has been totally satisfactory, since they could not completely resolved the Gettier Problem [12, 26, 27].  

Essentially, Gettier’s contradiction of definition of knowledge based on TJB is similar to Popper’s falsifiabilism, as both states that in science it is more important to find contradictions than confirmations. Confirmatory observations are commonplace, because such observations are usually skewed to fit a theory. Much more difficult is to find defects or contradictions, which require an external observer position for a comprehensive assessment of phenomena. Ironically, much more insight effort is required to place oneself as an external observer than as an internal one. Nonetheless, a complete external observer is impossible, as we are also constituents of the system universe. A merge between the observer, the observed phenomenon and the process of observation itself is inevitable. This assertion is a great contribution of the second order Cybernetics [28]. Contrarily, for confirmations the observer assumes a rather comfortable internal position, if such position is taken to an extreme, then all data may appear valid, and consequently an impartial position is impossible. Therefore, an internal observer is either unable to falsified or “degettierized” a theory or a statement.  Anthropomorphism and the anthropic principle are by-products of an internal position of the human mind. The more internal is the observer, the more misinterpretations are produced (associated to anthropomorphic noise). In such circumstances, humans groups become closer and progressively more ritualistic. Knowledge, as a provisional term, should be placed into different scenarios, which means that the observer must realize his own dimensional space-time. In this manner, the observer himself may acquire a putative external position in relation to the system being observed. Moreover, the observer must also realize the fitness of his measurement device, which must be appropriate for the allowed degrees of freedom for a determined dimensional space-time grainity. Observations, and subsequently knowledge, can be spanned from quantum through cosmological levels. The so-called background noise might be just detection of events by the measurement device, and, then transformed into “data” that is not understood or misinterpreted. The measurement device must fit the dimensional space-time otherwise interpretations would be deviant. At the extremes of dimensional space-time, either near the Planck level and the boundary of the universe, uncertainty may be maximal, and observers and measurement devices may be turn into black holes (because of the extreme concentration of energy/matter). In fact the measurement of the space-time framework is a measurement of uncertainty, and no measurement device can surpass this uncertainty before being transformed into a black hole [29, 30]. This may be the basis of skepticism, in the sense that no knowledge can be accomplished. Knowledge, paradoxically, is potentially greater when approaching maximal uncertainty. Meanwhile, the uncertainty constantly increases, because the universe is constantly expanding. By stretching the Uncertainty Principle, we can say that no system is equal to another system, neither to itself at any moment.  

The issue of Evidentialism

Evidentialism is based on internal justification; as such a subject’s evidence depends on his mental status, which is directly recognized by the subject himself. Therefore, evidentialism progressively drives the observer to a deeper internal position that is suboptimal for an impartial observation. The “infinite regress argument” [31] arises in the context of evidentialism because a belief must be successively and endlessly supported by other beliefs to hold its possibility of truth. This argument may be the consequence of the inconvenience of observations based on so-called evidences. Evidentialism, ultimately, depends on individual’s interpretation of data (internalism). In evidentialism, the brain digests the data, but the data itself is incorporated or assimilated by the “system brain” resulting in a “new” system namely “brain-data”, which in turn is observed by the “system brain” (or, now better “brain-data”) itself. Then the “system brain” is an observer of itself; therefore becomes an internal observer. As established before, an internal observer is far from being in the best position to analyze a system. In the case of brain’s self-observation, the internal observer position is remarkably disadvantageous, as the brain is affected by the individual’s history (social, cultural, religious and other factors) and present status (stress level, mood, etc), as well as by the physiological neuronal redundant activity. The so-called “evidence” is, therefore, still a belief without proper justification. In fact, paradoxically, “evidence” is a belief trying to be justified by it itself (a vicious circle). Consequently, individual’s “evidences” must be confirmed (or search for confirmation) through others individuals’ “evidences” to be validated, falling into the “infinite regress argument”. Usually, this process of evidences validations requires a group. Rumination of “evidences” inside a group inevitably will drive to the fallacy of accepting such “evidences” (which are just no more than merely beliefs) as “proofs”. In this deceived manner “evidences”, just internal beliefs without substantial justification, acquire a false external projection (some sort of fake physical consistency). A group of such “evidences” are usually transformed into “absolute” or “basic” beliefs, which according to the close group there is no need to be proved (basis of fundamentalism). In case of conventional medicine this “validation” process is through peer-reviewers or experts. However, there are no means, by the group own rules or standards, to discount the amount of biases, since the past history and current status may be influencing each individual and group observation. Besides, the peer group is no usually familiar with the total amount of information being managed neither with the graining of the scale.  

The issue of Antropomorphisms


Corning’s concept of Information has anthropomorphic connotation, as it is focused in the macroscopic level. Moreover, we consider that this author assumes an internal observer position when he says that Information “can only be measured in terms of the results it achieves for specific living systems.” [32]. Strictly speaking, this can be just called interpretation of data, not Information itself. Again, here we confront a conceptual problem, which is confusing Information with interpretation of data. The same author, in another publication, claims a new theory so-called “Control Information” [33]. However, we consider that such line of conjecture is heavily contaminated with anthropomorphic noise, as it is initiated with the misleading notion that Information depends on the observer. In fact, for instance this authors says, “A further objection is that information itself cannot do anything; it cannot control a thermodynamic process without the presence of a user that can do purposeful work.” Firstly, Information as per
Shannon’s is a process not intended to do work. Secondly, this author do not take into account the observers’ position, however, from his anthropomorphic predisposition, we assume that he endorses internalism. This is in fact contrary to
Shannon’s Theory, which is basically external. For
Shannon’s Theory the bits come from the system, no more and no less, and whatever the observer does or not with the bits (message or data) are out of the question, and by no means this is any type of “control”.  Consequently, in conclusion his model do not clearly establishes what Information really encompasses.  

Semiotics points that Mathematical Theory of Information and Cybernetics is unable to carry semantics. However, we consider that the whole semiotics is based on anthropomorphism. In fact, for Peirce’s there is triadic philosophy: “Firstness” are the signs (“representament” or feelings), “Secondness” are the objects (an aspect of “reality” or “qualia”), and “Thirdness” are the interpretations (“interpretant” or a “more developed sing in the mind of the perceiver/obsever/communicator” or “habit formation and signification”) [34]. This theory does not establish the origin of signs. We consider that signs, either physical or linguistics should have emerged through an evolution process. On the other hand, semiotics again confuses Information with interpretation of information, besides, for semiotics without “purpose” there is no such a thing as Information [35]. Evidently, this is an anthropomorphic bias, and it reflects the present inability of semiotics to elaborate a higher theory. Human interpretations of reality, and variations of interpretations among humans, are likely restricted by the limited capacity of the brain to assess the physical domain (or “true reality”). In this context, semantics and, therefore, semiotics themselves may arise as fallacies. Perhaps semantics can be considered as a gross subjective estimation of the reality. Attempts have been made trying to correlate semiotics with Information Theory; however from the semiotics viewpoint some sort of process gathering or collecting data is inevitably required [36], which is otherwise biased, and therefore it is incompatible with a hardcore Information Theory. Maybe semiotics is a by-product of the current lack of technology to assess the functioning of the human brain. Ultimately, we think is possible that computers would recreate the system called human brain (mind). Once this gap is resolved, semiotics may be absorbed and vanished into the Information Theory realm.  We agree that Cybernetics can achieve the construction of higher domains, which may carry semantics aspects [37, 38]. Most, if not all, principles of systems and cybernetics [39] can ultimately be the expressions of universal principles. Heisenberg’s Uncertainty Principle points out that systems are dynamical entities, and as such they are always changing. Ashby’s Law of Requisite Variety most likely is an aspect of this inherent characteristic of systems, as the macroscopic world is an expression of the quantum domain. Other cybernetics principles can be placed into this context. Conant and Ashby’s principle that “every good regulator (controller) of a system must be a model of that system” is likely a consequence of Ashby’s Law placed into a hierarchical context. For instance, the secretion of insulin by the beta cells of the pancreas predominantly regulates the serum glucose level in the system human body. These cells are the main regulator of the levels of glucose; therefore, inside these cells there must be a mechanism, which mimics the external fluctuations of the glucose concentration. Regulatory loops, either negative or positive, are commonplace inside biological systems. Despite these regulatory mechanisms are highly efficient (in terms of metabolic cost and time), they are not perfect, as they execute their corrective actions after the determinate distortion or fluctuation has been occurred. They accumulate “errors” because the Entropy of all systems always increases, as established in the Second Law of Thermodynamics. The Principle of Incomplete Knowledge (“The model embodied in a control system is necessarily incomplete”) is most likely a consequence of the unavoidable raising of Entropy into systems. Mathematically, the Gödel’s Incomplete Theorem (complex systems always generate statements that are not supported by the system’s theorems) may also be a similar consequence. From a cybernetics point of view, according to
Campbell’s main thesis, knowledge is the product of variation and natural selection [40]. For instance, we can say that the beta cells of pancreas know (or have the knowledge) to secrete insulin when the level of glucose increases, and this knowledge may have been learnt through historical steps of trials and errors (i.e. Evolution). In diabetics this “knowledge” of the beta cells has been lost, or not learnt at all.         Next we will analyze the so-called Principle of David Lewis [41]. This philosopher called himself a subjectivist; therefore, we might assume that his theory is based on his individual conception of reality. In its initial version he uses a formula, difficult to understand, C(A/XE)=x, and he says “Let C be any reasonable initial credence function. Let t be any time. Let x be any real number in the unit interval. Let X be the proposition that chance, at time t, of A’s holding equals x. Let E be any proposition compatible with X that is admissible at time t”. Overall, the idea of Lewis is to establish certain degree of probability that something may occur based ongoing data concerning such event. For instance, if I know that the bus usually arrives at a station at 8 am, then I believe that the bus would arrive at 8 am, which is essentially the “credence”. The number x could be from a fraction to 1, it is a probability for A to happens; however, Lewis introduce the term “chance” as a probability of a belief. If Cr(XE) = 1 then Cr(A) = x.  The proposition X, according to Lewis is “chance”. Chance as such is difficult to understand even for the same author. In fact, his own conceptualization of “chance” is very semantic, and he concludes: “it is a function of three arguments. To a proposition, a time, and a world it assigns a real number. Fixing the proposition A, the time t, and the number x, we have our proposition X; it is the proposition that holds at all and only those worlds w such this function assigns to A, t, and w the value x. This is the proposition that the chance at t, of A’s holding is x.” E is the “admissible” proposition, which according to Lewis, “Admissible propositions are the sort of information whose impact on credence about outcomes comes entirely by the way of credence about the chances of those outcomes…The power of the Principal Principle depends entirely on how much is admissible. If nothing is admissible it is vacuous. If everything is admissible it is inconsistent…I have no definition of admissibility to offer, but must be content to suggest sufficient (or almost sufficient) conditions for admissibility.” Then the author outlines that there are two types of generally admissible information, to say historical information and hypothetical information. In this context we understand for “admissible” something that is possible or feasible. As such, this “Principal Principle” is itself intricate and difficult to understand, and therefore very difficult to criticize. Lewis uses two factors not included in his formula, which are the time t and the world w. Both are very important for him to sustain his theory, since the “credence” has to happen in a certain period of time, and concomitantly inside a physical scenario that holds the “chances”. The chances are possibilities but with certain probability to happen, therefore the summation of his “credence” function at the end must be 1. However, his formula reveals a weakness, as the “admissible proposition E” begs for being a probability. In the “credence” that the bus arrives at 8 am at determined station, the time t is set, as well the physical scenario (to say the station and all the surrounding elements) or “world w”. For instance, If I go to the station at 7:45 am, there is a “chance” (“proposition X”) that the bus in fact would arrive at 8 am.  From 7:45 to 8 am events might happen that could affect the “chance” that the bus would arrive at 8 am. These events may be significant or insignificant for this to happen, which we think depend if they are physically closer or distant to a space-time reference, respectively. For instance, if the bus station is in New York, and I hear at 7:46 that there has been a military coup in Burma, it is extremely very unlikely that this incident would have the “chance” to change the bus schedule, as Burma is geographically sufficiently distant from
New York. However, it is still possible that the driver would be a native of
Burma, and he has been distracted listening to the news, and the bus would be delayed. Conversely, if the news at 7:46 announce that there has been a serious accident few minutes ago in the same route use by the bus, then the “chance” the bus arrives at the station at 8 am is less likely. A causality factor is, therefore, inherent to “chance”, which makes explicit the weakness of this “principle”. For instance, we can extremely say that the “credence” that the bus would arrive at 8 am at this station depends on the “chance” (or possibility) that the Big Bang actually happened; otherwise this universe and this planet, and the bus, the station, etc might not even exist! This principle therefore, biased by local causality, is a local (macroscopic) gauge conjecture. How can it be applied to other physical scenarios? Can it be thinkable at quantum scale, black holes, and relativistic frames? We doubt, since subjectivity is likely impossible out of our “macroscopic” realm. We might be being paradoxically anthropic; however this type of argument may be valid to unveil the anthropomorphism of the “principal principle”.  In fact, Lewis says, “In general, C is to be reasonable in the sense that if you started out with it as your initial credence function, and if you always learn from experience by conditionalizing on your total evidence, then no matter what course of experience you might undergo your beliefs would be reasonable for one who had undergone that course of experience”.  

We think that the “principal principle” is a reformulated Plato’s TJB, and rhetoric evidentialism mixed with semiotics. Thereafter, Lewis has presented revisions of his principle between 1999 and 2001. For Menzies this is a counterfactual theory of causation [42]. He says, “However, intense discussion over twenty years has cast doubt on the adequacy of any simple analysis of singular causation in terms of conterfactuals.”  Menzies explains that Lewis’s theory has the following problems: 1) context-sensitivity, as it considers that “any event but for which an effect would not have occurred is one’s of the effect’s cause. It is almost impossible to determine which previous event is not related to the outcome of a later event. Just see above that a bus in New York could be delayed because of a military coup in
Burma. On the other hand would be easier to link a previous event with any other later event, if we use the Big Bang argument.  2) It uses the controversial concept of temporal asymmetry. We think that the concept of time, and similarly energy, are formalisms derived from the function Entropy, since the latter is always increasing (inside the system universe as a whole). Any theory strictly submissive or dependable on previous events is deemed to failure, as the past cannot be comprehensively analyzed, therefore outcomes remain essentially unpredictable. 3) Transitivity, which conceptualizes a chain of effects and reactions that produce an effect; but, “a number of counter-examples have been presented which cast doubt on transitivity…The strategy Lewis adopts in his (2000) is to defend transitivity by diagnosing the sources of our inclination to accept them”.  We agree that transitivity is not absolute and moreover it cannot be forecast, because the past cannot be recreated. This weakness of this theory may be rooted in the fact that it is an internalism, and as such relies only in Newtonian physics where reversibility, even of time, is commonplace. 4) Preemption, can be seem as expectation of a final result or effect. Therefore, it is considered as predetermination, and again this is rooted in Newtonian internalism. In Chaos Theory systems are highly dependable in initial conditions; however, it is impossible to know the previous conditions.  From a Popper’s point of view this “principle” could be itself an empty statement, and when extended to particular situations would generate other empty statements. This “principle” begs for confirmations and not for contradictions. Indeed, this “principle” does not account the issue of observer’s position, and therefore it is not compatible with Information Theory because it is ultimately an internalism. 

The model

In this model we have centered knowledge, experience and other related terms in the context of Theory of Information. A basic algorithm is also intended. 

The axis is as follows: (SYSTEM SOURCE-EVENT)à DATA à(SYSTEM RECEPTOR-KNOWLEDGE) 

Event is a raw fact that just happens in a system, without being measured. At this point, the event has no units because it is supposedly to be unknown (“pure”). Once events are measured they immediately transform into data, which usually have units. Measuring produces a distortion on the event, which is actually the data. The next step is a proposed non-anthropomorphic concept of Diagnostic Capacity based also on non-anthropomorphic concepts of Knowledge and Experience.  Knowledgeactual + Experienceactual = Diagnostic Capacity 

Knowledgeactual is the database size accumulated in the brain of the observer. Broadly, it is the memory of the observer. This memory is in reference to the diagnostic area. Experienceactual is the functional power of interaction of the observer’s Knowledgeactual with the system under observation. At this point, we have to clarify our concept of knowledge. Plato’s definition of knowledge has not too much value because is anthropomorphic. We have redefined knowledge as a dynamical process of data transmission a-la
Shannon. The transmission of data, disregarding the number of steps, has to follow a coding/decoding development from the system source to the receptor. The ultimate receptor in the diagnosis process is the pathologist’s brain. Inside the brain also a similar development of coding/decoding happens. This chain eventually would reach a summarized conclusion, namely diagnosis. The background noise and the transmission data error must be considered. Therefore, pertinent corrections must also be effected to avoid misinterpretations. Besides, we consider that inside the brain a local process of verification/falsification occurs as well. Data can be qualified as knowledge if can be tracked to the initial event without significant distortion. In conclusion, the process of knowledge is based on informatics. It is a coding/decoding transmission that matches in both directions: forwards and backwards. For us, any statement to qualify as knowledge has to fulfill this rule; otherwise it would be just an “empty” statement. Knowledgeactual is purely based on pragmatism. This means that real knowledge is only generated through coding/decoding and validated also through coding/decoding, forwards and backwards. Strictly speaking, books and articles in medicine do not provided knowledge but author’s interpretations or just opinions.  

The above conceptualized process of knowledge is dynamical, because depends on the times this forwards/backwards process is performed and on the accumulated memory. However, the Knowledgeactual is not necessarily a strict proportional function of the number of forwards/backwards or the amount of accumulated memory. Experienceactual, on the other hand, is a function of the accuracy and velocity performing the transmission (coding/decoding – decoding/coding plus brain internal verification/falsification). Experienceactual directly depends on the Knowledgeactual, because as an accumulated size of database, Knowledgeactual implies that the database is meaningful. In fact, for a meaningful database an intrinsic condition is that the forwards/backwards verifications have been already effectively performed. Ultimately, knowledge and experience are sides of the same coin. The key resides in the coding/decoding plus the internal verification/falsification process. Similarly important are how to implement and make functionally efficient this mechanism, and how to accumulate memory from this process. In analogy with computers, the coding/decoding + internal verification/falsification is the software of the brain. On the other hand, the Knowledgeactual is the memory, and Experienceactual can be considered as the computational power. Meaningful data are those directly related with the fulfillment of constrains of the system. In other words, in the case of diagnosis, data that have direct relation with the probable diagnoses. In general, the strength of the human brain depends more on its computational power than on its memory.  

Types of data The obtained data is sorted out according to their significance. Diagnostic Capacity acting on the transmission channel produces a diagnosis. The latter, as explain above, is dynamical: coding/decoding + verification/falsification development. For better functionality of the model, we have divided the types of data as follows:  

1) Null data: is a virtual data in the observer’s database, but does not presently exist in the system source. A null data can be erroneously transformed into a meaningful data and vice versa. 2) Meaningless data: data that exist in the system source, but do not match the core message plus data overruled by another stronger data. Meaningless data do not (necessarily) account for computation.3) Meaningful data: data that exist, match the core message, and cannot be overruled by other data. Admittedly, this division is a deviation from a formal mathematical information theory, as separating Meaningless data from Meaningful data introduces an observer’s bias: what are Meaningless data and Meaningful data for the observer? How the observer can differentiate Meaningless data from Meaningful data? But, do not forget that the observer already has a Diagnostic Capacity. But again, how the Diagnostic Capacity can be measured? Maybe it can be measured in bits through rigorous neuropsychological tests. In the hypothetical event that this might be possible it would not have practical significance. When observing a histologic section, the pathologist cannot look at each pixel. According to Aperio Technologies, “A typical pathology specimen measures 15mm x 20mm. At 400X magnification (using a 40X objective lens) the required image resolution is about .25u/pixel (u = 1/millionth of a meter). That means the digital image of a typical specimen measures about 80,000 x 60,000 pixels, and contains about 14.4GB of data. That’s big”  [43]. In real practice, pathologists use less than 400X magnification. We use mostly 25 to 40X magnification; thus, the number of pixels and the amount of data received as impulses by the retina and brain is much less. This fact at human level has the advantage of reducing the time per slide.  

The Diagnostic Capacity depends of patterns of recognition, and potentially it can be apply into artificial intelligence and neural-computer systems. For instance, Chinese letters known as the most intricate existing symbols have been successfully recognized using Mathematical morphology, and the derived techniques allow pattern of recognition in the setting of noise and distortions [44]. The Diagnostic Capacity among pathologists is likely extremely variable, depending on training, interests, specialization, type of practice, etc. Therefore, for simplicity we considered Diagnostic Capacity on individual basis, provisionally namely eigen-Diagnostic Capacity for each pathologist. This does not necessarily imply that is not possible to find more generic assessment of Diagnostic Capacity. Identifying patterns of recognition may help to solve this issue. In the future, the role of experts could be just establishing patterns of recognition in each entity, and produce a database that can be managed by artificial intelligence. Subsequently, diagnoses could be expressed in terms of probabilities. The Meaningful data have to satisfied or to match constrains of the system, which is in fact the accomplishment of a compressed data formalism namely diagnosis. As stated before the Meaningless data is a function of the observer’s Diagnostic Capacity (provisionally called eigen-Diagnostic Capacity). Observers with similar eigen- Diagnostic Capacity are able to pick up similar Meaningful data. Observers with different eigen-Diagnostic Capacity are not able to pick similar Meaningful data, and most likely would pick different Meaningful data, but the overlapping of Meaningful data is feasible. The observer with the least Diagnostic Capacity has more chances to misinterpret Meaningless data for Meaningful data. Just accounting Meaningful data as a function of eigen-Diagnostic Capacity, immediately disregards the Meaningless data at a determined level. Since the Meaningless data does not count, the computation process is simplified. For instance, at clinical level, a patient complains abdominal pain, and then the physician circumscribed (asking and touching) the location of the pain (Meaningful data), and disregards automatically other sources of abdominal pain not related to that location (Meaningless data). If there is another pain judged to be reflex or ancillary, the physician may considered not relevant for localizing the lesion, and it can be either irrelevant and/or null, which is Meaningless data. The levels are interrelated. Therefore, overruling can occur among data between groups, however comparing data from different levels may complicate the computation. Nevertheless, since this model is dynamical it is likely that interaction among different levels happen, thus the mathematical formulas to apply will be more complicated, but still based on
Shannon’s Entropy. For this purpose Theil’s decomposition theorem can be suitable, because through this method the events fall into sets. “In informal terms, the decomposition theorem has the following interpretation. Consider the first message that one of the set of events occurred. Its expected information content is H0. Consider the subsequent message that one of the events falling under this set occurred. Its expected information content is Hg. The total information becomes H0 + Σ PgHg” [45]. Mutual information or correlation Entropy may also be useful for this purpose [46]. The levels, for practical reasons, can be considered as the degrees of freedom in diagnosis process because they increase the capacity to obtain data. Each level has its own methodology, and each methodology has its own degrees of freedom, therefore each methodology is itself a level. To illustrate, just a simple abdominal palpation has degrees of freedom in depth, and can be set as deep, medium or superficial palpation. When a clinician uses a light to examine the throat is increasing his visual degrees of freedom. A chest x-ray increases the degrees of freedom to examine the lungs; the different incidences of the x-ray also increase the degrees of freedom. CT scan and MRI also increase the degree of freedom facilitating the diagnosis process. The same applies to laboratory tests. The physician can diagnose a septicemia based on clinical data, but a blood culture will increase the degrees of freedom for such diagnosis. The diagnostic power among different levels depends on the allowed degrees of freedom. In turn, the degrees of freedom are associated with the capacity of a measuring device in such level. For instance, cytology, in general, has less degrees of freedom compared with histopathology. Comparing diagnostic accuracy among levels is therefore just a worthless exercise, if the degrees of freedom are not taken into account.    From the Pathology point of view the levels can be separated into:1)     Pre-Pathology:            Clinical            Clinical Laboratory           Radiology.2)     Pathology:Gross      HE microscopy      Histochemistry      Immunohistochemistry      Electron microscopy, etc. 

Admittedly, this division is arbitrary, and we have to emphasize that it is strictly from a Pathology point of view. Each level from its own perspective can do the same division. For instance the Clinical level can assume a division like 1) Clinical and 2) Post-Clinical. Clinical Laboratory can divide as 1) Pre-Lab and Post-Lab. Radiology, as well, can divide as 1) Pre-Radiology and 2) Post-Radiology. Inside each level, each methodology may assume an arbitrary division. For instance, relatively to MRI it can be divided as 1) Pre-MRI, and 2) Post-MRI.  Of course many cases do not required Pathology diagnosis. However, when a sample is submitted to Pathology it is assumed that Pathology diagnosis is “necessary”. Although, this is not totally true, since many samples already have diagnosis. For instance, in an appendectomy visualizing a purulent appendix makes the diagnosis of acute appendicitis. So what is the purpose of sending the removed appendix to Pathology? The reason, if any, is that Pathology has more degrees of freedom for observation, and can pick something else that the naked eye may miss. In this sense Pathology can be considered as a terminal event in diagnosis process, but not for all diagnoses. 

Interim calculation 

The logical sequence proceeds as follows. Any data can supersede another data, or can be superseded by another data, usually at the same level (but superseding can happens among data of different levels). Data already considered Meaningful data could be superseded. Data already considered Meaningless data could eventually in re-analysis convert into Meaningful data. Data can be uncertain, neither Meaningful data nor Meaningless data, if such data do not have any apparent relation with constrains or diagnoses. However, uncertain data may require further analysis or investigation to find if ultimately have any relevance. The Meaningless data do not enter in computation process, but it can be saved because it may have some posterior relevance. This type of sequential logic applies for every level, including the sub-levels. A negative data (absence of positivity of an examination or test) in a pertinent context can have significant value; therefore is considered as Meaningful data, entering into computation.Next we will present an overtly simplified and preliminary analysis of two cases. The cases are very rare, but here this is irrelevant. Contrarily, we want to emphasize that it is possible to sum the amount of information in an ongoing diagnosis process. However, since we have already made the diagnosis in both cases, the amount of information (in bits) has been simplistically calculated as the log2 of the number of Meaningful data events. Then the total bits have been divided by the number of Meaningful data events to roughly calculate the bits corresponding to a single Meaningful data event. We are aware that this type of calculation is, so far, just preliminary because each data has different probability.  Case 1. Granulocytic sarcoma of gallbladderPre-PathologyClinical level:Abdominal pain RUQ                       1                        0.191                   
US thick GB without stone               1                        0.191Myelodysplastic syndrome               1                        0.191                                                         3                        0.573Pathology level:HE                                                    5                         0.955IHC                                                  16                        3.056 

TOTAL:                                           24                       4.585 bits                                      Each event: 4.585/24 = 0.191 bits 

Case 2. Multiple diffuse fibrosarcoma of bone.Pre-Pathology level:Clinical level:End-stage renal disease                          1                       0.2236 

Radiology level:Osteolytic lesions                                     1                       0.2236Scan non-uptake                                      1                       0.2236                                                                 3                       0.6708             Pathology level:HE                                                            5                       1.1180                    IHC                                                          11                      2.4596 TOTAL:                                                    19                      4.248 bits                                       

Each event: 4.248/19 = 0.2236 bits RUQ, right upper quadrant; US, ultrasound; GB, gallbladder; HE, hematoxylin-eosin stained sections; IHC, immunohistochemistry. 

It may be possible to combine the above model with Comaniciu’s image-guided decision support, which is essentially based on probabilistic (Entropy) analysis of images and comparison with a database [47]. Software algorithms would be fastidious, but once already developed the overall pathological diagnosis would be more objective. Possibly, in a near future artificial intelligence and robotics will replace pathologists.     Currently, diagnoses in medicine, including in Pathology, do not have too much epistemological significance. Indeed, many of them may be essentially empty statements. Eventually, with a model based on Information Theory, Cybernetics and Entropy, the diagnosis process would render more objective results. 

AcknowledgementsTo Mrs. María Olinda Tello-Rodriguez for her always invaluable secretarial support.  

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