I define Bayesian Brain Theory to be a field of research that is based on the belief that the central function of the brain is inference/prediction. An overview can be found on Wikipedia. I see my theory of the brain as being part of BBT. However, my views on the physical basis of inference are an extreme outlier. It seems everyone else in the field adheres to The Irrational Brain Hypothesis and equates “being rational” with “performing math.”

A great virtue of BBT is that it is entirely devoted to treating the brain as an observer (or multiple observers), as in my effort to take The Neuron’s Point of View. This stands in sharp contrast to conventional applications of Information Theory to the brain, as summarized in The Unreasonable Ineffectiveness of Information Theory.

Bayesian Brain Theory Explains Perception

BBT has provided beautiful accounts of mental phenomena, particularly illusions. For example, the moving image below illustrates “the barberpole illusion.” There is no way to know the actual direction or speed of motion in the image. All the motion could be caused by one thing moving with one velocity. However, we perceive the direction to be the slowest that is consistent with our local sensory data. This is in part because the “laws of physics” insure that velocities tend to be near zero, and we have learned this “prior” through experience. Our perception depends on the combination of this prior evidence with the current sensory evidence (Weiss et al., 2002). The result in this case is that the perceived direction of motion varies depending on the aperture through which we view it (note that our entire visual field is technically an “aperture”).

Similarly, there is no way to be certain of the color of light reflecting from the dress above. The color we see depends on our inference of at least two unknowns, the reflective properties of the fabric and the color of the illuminating light.

Sane people see this dress as gold and white. But I am told that delusional people see it as black and blue. This is presumably because delusional people misjudge the color of the illuminating light. That is forgivable. But these poor souls must be pretty far gone to think that anyone with the slightest sense of aesthetics, or desire to make money, would design and fabricate a dress in the colors of a bruise.

It is a shame to let the truth get in the way of humor. The fact is that there is no way for anyone to be certain of the color of this dress, or any external object (for the same reason that we cannot observe real cats). We can only make rational inferences given the evidence we have.

At the moment we see something, we cannot choose our evidence. It is what it is, and we perceive what we perceive. Given time and effort we could further investigate this dress by observing it with different colors of illuminating light (particularly white, an equal mixture of all colors, since it is most common and therefore our brains have learned to see in the presence of white light). In this way we could gain more evidence, so that our judgement would be better informed.

All percepts and beliefs and opinions are rational and based on evidence. But they are not all based on equal amounts of evidence.

How does the brain infer/predict?

BBT has been highly successful in explaining mental phenomena as rational inference. My own views are well aligned with the field in regard to mental phenomena. But my views are radically outside the mainstream with respect to the physical basis of reason and inference.

So far as I know, BBT has never predicted any biophysical property of the brain that was not already predicted as well or better by another theory. The only exception I know is my own theory (for example, see Kim and Fiorillo, 2017, which I summarize on the page General Theory of the Brain). However, the only aspect of my theory that I used to predict biophysical observations, and which was not a conventional feature of Information Theory, was The Neuron’s Point of View.

I attribute BBT’s lack of success in dealing with physical phenomena to the general challenge of taking the perspective of a physical thing. This challenge is made much more difficult by widespread adherence to the philosophy of functionalism, and to a misunderstanding of what it means, physically, to be rational.

Bayesian Brain Theory Assumes that Nature is Irrational

I argue that all of nature is rational, so that there is no need for the brain to solve math problems. It seems that nearly everyone else who subscribes to Bayesian Brain Theory implicitly subscribes as well to the Irrational Brain Hypothesis. They think that the brain is designed to solve math problems, and particularly to calculate probabilities, in an attempt to “approximate rationality.” This presumably makes a healthy adult human brain less irrational than other physical systems.

Karl Friston is the most famous advocate of this view, as expressed in his “Free Energy Principle” (FEP). It says that to infer/predict requires an approximate calculation of probabilities, and that this occurs by minimizing “free energy” (which is a mathematical term, not physical energy). The entire proposal that the brain needs to do this is based on the assumption that nature is irrational.

To “Approximate Rationality” Means to “Perform Math”

If nature is inherently irrational, then to predict/infer, the brain must solve two distinct problems. First it must acquire information. Then, to be less irrational, it must perform math through a sequence of steps to calculate probabilities conditional on that information. This calculation is what it means to “approximate rationality” according to the FEP and related accounts. Since nature is assumed to be inherently irrational, the brain cannot do the math properly, and it can only calculate approximate probabilities.

A summary of Friston’s FEP is provided in Friston (2010a). My critique, and his response to my critique, was published shortly afterwards in the same journal (Fiorillo, 2010; Friston, 2010b). I further commented on the FEP and BBT in the following years (Fiorillo, 2010; Fiorillo, 2012, Fiorillo, 2017). However, my criticism now is substantially more thorough than it was in any of these publications. I hope to soon present a more detailed critique of Bayesian Brain Theory, focused in particular on The Irrational Brain Hypothesis and the Free Energy Principle.

Note that Friston’s use of the term “FEP” appears to have substantially evolved since 2010 (Friston et al., 2022). My discussion here concerns “FEP” as he defined it in 2010. However, I do not think that his definition has changed in a way that is relevant to the issues discussed here.

The Brain Does not Perform Math

If nature is rational, as it is in Rational Observer Theory, then probabilities rationally and objectively and correctly quantify evidence, without any need for nature to perform the math and calculate the probabilities. By “perform” and “calculate” I am referring to a physically implemented temporal sequence of steps. If rationality is inherent to nature, nature has no need to perform math. Math is reason/logic, and all rational relations are inherent to nature.

My view of numbers, unlike that of followers of the IBH and FEP, is consistent with the standard understanding of numbers in physics. When we say a particle has a location and velocity and trajectory that can be represented by numbers, we believe this to be true even if no physicist observes the particle, and even if nature itself has no ability and no need to perform any calculations. A rational universe does not need calculators or mathematicians to find probabilities any more than it needs them to evolve over time.

I explain in General Theory of the Brain that mathematics and probabilities are only descriptive of the brain, not prescriptive. I emphasized this in part because, according to Friston and other advocates of BBT and The Irrational Brain Hypothesis, reason and mathematics and probabilities are prescriptive of the function of a healthy and intelligent brain. I am convinced that this is wrong. Since nature is rational, rationality is not a goal. It is just the way all things must be.