Bayesian Methods and Universal Darwinism. Karl Friston explains the 'Bayesian Brain' theory. Universal Darwinism is the collection of scientific theories which explain design found in the universe as the creation of Darwinian processes. In spite of devoting many years to this pursuit she eventually abandoned it, having come to understand the low probability of any confirming evidence showing up that could be considered scientific. Since then her research has been roughly split between consciousness studies and Memetics.
Her efforts on Consciousness, what the philosophers refer to as 'the hard problem", has been informed by her research into Memetics. Memetics is the study of cultural evolution by means of replicating memes and is a theory within the umbrella of Universal Darwinism. Richard Dawkins, who first introduced Memetics in his book The Selfish Gene , which is considered one of the great works of 20th century biology, called Blackmore's book The Meme Machine the best shot Memetics could have in establishing itself as a scientific discipline.
John Campbell That would be me! This site is a result of my lifelong fascination with Darwinian processes and their potential for providing a unified understanding of Science. Although I cannot claim original research in a particular subject matter I have attempted to provide synthesis and context for the many exciting theories under the tent of Universal Darwinism. As one who reveres Einstein, I follow his injunction that the purpose of science is to ' awaken this feeling the cosmic religious experience and to keep it alive in those who are receptive to it.
Richard Dawkins Richard Dawkins recently retired as Simonyi Professor of the Public Understanding of Science at the University of Oxford after an illustrious career combining eminence in research and the furthering of pubic understanding of science.
He is one of the foremost theorists of the past century within the field of biological evolution, and can be credited with introducing the first scientific theory of cultural evolution: Dawkins is an outspoken defender of science. This means the genotype corresponds to the sufficient statistics of the prior beliefs a phenotype is equipped with on entering the world. Keeping in mind that organisms may sense their environments through both chemical and neural means, we may associate sensory exchanges with the environment s with adaptive states.
In other words, the phenotype embodies probabilistic beliefs about states of its external milieu.
This formulation tells us several fundamental things:. Here, the only things that can change are the sufficient statistics; namely, the genotype and phenotype. This means there are two optimizations in play: In other words, a good genotype will enable the minimization of free energy by equipping the phenotype with prior beliefs that are sufficient to maintain accuracy or a higher probability of adaptive states. Thus, the phenotype may be thought of as a type of experiment, which gathers evidence to test prior beliefs; i.
This simply means selecting models or genotypes that have a low free energy or high Bayesian model evidence. Because the Bayesian model evidence is the probability of an adaptive state given a model or genotype p s m , natural selection's negative variational free energy becomes free fitness. At this level of free energy minimization, evolution is in the game of orchestrating multiple phenotypic experiments to optimize models of the local environment.
Another specific example of the general ability of the free energy minimization principle to describe evolutionary change is in neuroscience where it is fairly easy to demonstrate the centrality of this principle in explaining evolutionary, developmental and perceptual processes in a wide range of mental functions Friston, The brain produces mental models which combine sensory information concerning the state of the environment, with possible actions with which the organism may intervene.
The initiation of an action is a kind of experiment in the outside world testing the current beliefs about its hidden states. The overall drive of the free energy principle is to reduce the model complexity, while maximizing its accuracy in achieving the predicted outcome. Crucially, the ensuing self-organization can be seen at multiple levels of organization; from dendritic processes that form part of the single neuron—to entire brains. The principles are exactly the same, the only thing that changes is the way that the model is encoded e. This sort of formulation has also been applied to self-organization and pattern formation when multiple systems jointly minimize their free energy for example, in multi-agent games and morphogenesis at the cellular level.
Clearly, the application of variational Bayesian principles to ecological and cellular systems means we have to abandon the notion that only humans can make inferences. We will take up this theme below and see how freeing oneself from the tyranny of anthropomorphism leads us back to a universal Darwinism.
The free energy minimization principle may also be applied to processes of cultural evolution. A compelling example here is the evolution of scientific understanding itself. Science develops hypotheses or theoretical models of natural phenomena. These models are used to design experiments in the real world and the results of the experiment are used to update the probability of each hypothesis composing the model according to Bayes' theorem.
In the process free energy is minimized through a balance which reduces the model's complexity Occam's razor while increasing the model's predictive accuracy and explanatory scope. The evolutionary interaction between models and the systems they model, as described by the free energy minimization principle, may be applicable to additional natural phenomena beyond the examples above.
Several attempts have been made to describe universal Darwinism in such terms. We have previously noted the wide range of scientific subject matter that has been identified within the literature as Darwinian processes—and have offered an interpretation in terms of inferential systems Campbell, ; an interpretation closely related to that of the free energy minimization principle. Richard Dawkins offered a description of biological evolution in terms of replicators and vehicles Dawkins, , a description which Blackmore and Dennett have generalized to interpret universal Darwinism Dennett, ; Blackmore, The Price equation describing evolutionary change may be cast in a form which distinguishes between change due to selection and transmission.
Changes due to selection tend to decrease model variation whereas changes due to transmission or copying of the model serve to increase variation. The transmission changes of biological models are often in the form of genetic mutations Frank, From the perspective of universal Darwinism, we might expect a mechanism capable of increasing model variation within non-biological evolutionary processes that is analogous to biological mutation.
As an example we might consider the process of evolutionary change in scientific models during transmission. These may appear less clear; there is less consensus on how new and sometimes improved scientific models are generated. It may seem this process has little in common with the somewhat random and undirected process of biological mutation. In some instances, these evolutionary approaches have inferred successful models for systems which have long eluded researchers Lobo and Levin, The reluctance of many researchers to endorse a Bayesian interpretation of evolutionary change may be somewhat puzzling.
One reason for this is a peculiarity, and I would suggest a flaw, in the usual Bayesian interpretation of inference that renders it unfit as a description of generalized evolutionary change. The consensus Bayesian position is that probability theory only describes inferences made by humans. As Jaynes put it Jaynes, Epistemology is the branch of philosophy that studies the nature and scope of knowledge. Thus, knowledge is the probability, based on the evidence, that a given belief or model is true. A perhaps interesting interpretation of this definition is that knowledge occurs within the confines of entropy or ignorance.
Let's say some evidence becomes available and the model's entropy or ignorance is reduced to three bits. The effect which evidence has on the model is to increase its knowledge by reducing the scope of its ignorance. It is unfortunate that both Bayesian and Frequentist interpretations deny the existence of knowledge outside of the human realm because it forbids the application of Bayesian inference to phenomena other than models conceived by humans, it denies that knowledge may be accumulated in natural processes unconnected to human agency and it acts as a barrier in realizing our close relationship to the rest of nature.
Thus, even though natural selection is clearly described in terms of the mathematics of Bayesian inference, neither Bayesians such as Jaynes nor frequentists such as Frank can acknowledge this fact due to another hard fact: In both their views this may rule out a Bayesian interpretation. I believe that the correct way out of this conundrum is to simply acknowledge that in many cases inference is performed by non-human agents as in the case of natural selection and that inference is an algorithm which we share with much of nature.https://bloglepmondfeedbde.ga/ergodic-theory/double-sting-cafe-stories-singles.pdf
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The genome may for instance be understood as an example of a non-human conceived model involving families of competing hypotheses in the form of competing alleles within the population. Such models are capable of accumulating evidence-based knowledge in a Bayesian manner.
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The evidence involved is simply the proportion of traits in ancestral generations which make it into succeeding generations. In other words, we just need to broaden Jaynes' definition of probability to include non-human agency in order to view natural selection in terms of Bayesian inference. In this view the accumulation of knowledge is a preoccupation we share with the rest of nature.
It allows us to view nature as possessing some characteristics, such as surprise and expectations, previously thought by many as unique to humans or at least to animals.
Bayesian probability, epistemology and science in general tend to draw a false distinction between the human and non-human realms of nature. In this view the human realm is replete with knowledge and thus, infused with meaning, purpose and goals, and Bayesian inference may be used to describe its knowledge-accumulating attributes.
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On the other hand, the non-human realm is viewed as devoid of these attributes and thus Bayesian inference is considered inapplicable. However, if we recognize expanded instances, such as natural selection, in which nature accumulates knowledge then we may also recognize that Bayesian inference, as well as equivalent mathematical forms, provides a suitable mathematical description in both realms.
Evolutionary processes, as described by the mathematics of Bayesian inference, are those which accumulate knowledge for a specific purpose, knowledge required for increased fitness, for increased chances of continued existence. Thus, the mathematics implies purpose, meaning and goals, and provides legitimacy for Daniel Dennett's interpretation of natural selection in those terms Dennett, If we allow an expanded scope for Bayesian inference, we may view Dennett's poetic interpretation of Darwinian processes as having support from its most powerful mathematical formulations.
An important aspect of these mathematics is that they apply not only to natural selection but also to any generalized evolutionary processes where inherited traits change in frequencies between generations. As noted in a cosmological context by Gardner and Conlon Specifically, Price's equation of evolutionary genetics has generalized the concept of selection acting upon any substrate and, in principle, can be used to formalize the selection of universes as readily as the selection of biological organisms. At the core of Bayesian inference, underlying both the Price equation and the principle of free energy minimization we find an extremely simple mathematical expression: Simply put this equality says that the probabilities assigned to the hypotheses of a probabilistic model are updated by new data or experience according to a ratio, that of the probability of having the experience given that the specific hypothesis is correct to the average probability assigned by the model to having that experience.
Those hypotheses supported by the data, those that assign greater than average probability to having the actual experience, will be updated to greater values and those hypotheses not supported by the data will be updated to lesser values. This simple equation describes the accumulation of evidence-based knowledge concerning fitness.
When Bayes' theorem is used to describe an evolutionary process the ratio involved is one of relative fitness, the ratio of the fitness of a specific form of a trait to the average fitness of all forms of that trait. It is thus extremely general in describing any entity able to increase its chances of survival or to increase its adaptiveness. When cast in terms of the principle of free energy minimization some further implications of this simple equation are revealed see above. In a biological evolutionary context, the Price equation is traditionally understood as the mathematics of evolutionary change.
However, the Price equation may be derived from a form of Bayes' theorem Gardner, ; Shalizi, ; Frank, b which means it describes a process of Bayesian inference, a very general form of Bayesian inference which according to Gardner Gardner, applies to any group of entities that undergo transformations in terms of a change in probabilities between generations or iterations. Even with this great generality it provides a useful model as it partitions evolutionary change in terms of selection and transmission Frank, a. There are numerous examples of these equivalent mathematical forms used in the literature to describe evolutionary change across a wide scope of scientific subject matter, specifically evolutionary change in biology Gardner, ; Frank, b , neuroscience Friston, ; Fernando et al.
It is interesting to speculate on the similarity of these mathematical forms to those which may be used to describe quantum physics. Quantum physics is also based upon probabilistic models which are updated by information received through interactions with other entities in the world. Wojciech Zurek, the founder of the theory of quantum Darwinism Zurek, , notes that the update of quantum states may be understood in terms of ratios acting to update probabilistic models Zurek, A conceptual shift acknowledging that inference is a natural algorithm which may be performed in processes outside of the human brain may go some way to allowing quantum Darwinism to be understood as a process of Bayesian inference conducted at the quantum level Campbell, A vast array of phenomena is subject to evolutionary change and describable by the equivalent mathematical forms discussed here.
These forms interpret evolutionary change as based on the accumulation of evidence-based knowledge.
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