Presbyterian priest Thomas Bayes had no idea that he would make a lasting contribution to human history. Born in England in the early 18th century, Bayes was a quiet man with an inquisitive mind. During his life, he published only two works: "The Goodness of the Lord" in 1731 in defense of God and the British monarchy, as well as an anonymous article in support of the calculations of Isaac Newton in 1736. However, one argument Bayes made before dying in 1761 set the course of history. He helped Alan Turing break the German Enigma encryptor, the US Navy track down Soviet submarines, and statisticians identify the Federalist Papers. And today, with the help of it, they solve the secrets of the mind.
It all began in 1748, when the philosopher David Hume published The Inquiry into Human Knowledge and, among other things, questioned the existence of miracles. According to Hume, the likelihood of error by people claiming to have seen the resurrection of Christ outweighs the likelihood that this event actually happened. But Reverend Bayes did not like this theory.
Encryption apparatus "Enigma"
Photo: AFP 2016, Timothy A. Clary
Determined to prove that Hume was wrong, Bayes attempted to quantify the likelihood of an event. To begin with, he came up with a simple scenario: Imagine a ball thrown on a flat table behind your back. You can make guesses about where he landed, but it’s impossible to tell without looking at how accurate you were. Then ask a colleague to throw another ball and tell you if it is on the right or left of the first. If the second ball is on the right, it is more likely that the first has landed on the left side of the table (by this assumption, there is more room to the right of the ball for the second ball). With each new ball, your guess about the location of the first ball will be updated and refined. According to Bayes, various evidences for the resurrection of Christ similarly indicate the reliability of this event,and they cannot be discounted, as Hume did.
In 1767, Bayes 'friend Richard Price published On the Significance of Christianity, its Evidence, and Possible Objections, which used Bayes' ideas to challenge Hume's arguments. According to historian and statistician Stephen Stigler, in Price's article, “the basic probabilistic idea was that Hume underestimated the number of independent witnesses to a miracle, and Bayes’s results showed how increasing the amount of evidence, even if unreliable, could be stronger than small the degree of probability of the event and thus turns it into a fact."
The statistics that grew out of the work of Price and Bayes were powerful enough to handle a wide range of uncertainties. In medicine, Bayes' theorem helps to consider the links between diseases and possible causes. In battle, it narrows the space for localizing enemy positions. In information theory, it can be used to decrypt messages. And in cognitive science, it makes it possible to understand the meaning of sensory processes.
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Bayes' theorem was applied to the brain at the end of the 19th century. German physicist Hermann von Helmholtz used Bayes' ideas to present the idea of transforming sensory data, such as awareness of space, into information through a process he called unconscious inference. Bayesian statistics became popular, and the idea that unconscious mental calculations were inherently probable no longer seemed far-fetched. According to the Bayesian Brain Hypothesis, the brain continually makes Bayesian inferences to compensate for the lack of sensory information, just as each subsequent ball thrown onto the Bayesian table fills in the gaps in the location of the first ball. The Bayesian brain forms an internal model of the world: expectations (or assumptions) abouthow different objects look, feel, sound, behave and interact. This system receives sensory signals and roughly simulates what is happening around.
For example, vision. Light reflects off objects around us and hits the surface of the retina, and the brain must somehow create a three-dimensional image from two-dimensional data. Many three-dimensional images can be obtained from them, so how does the brain decide what to show us? Probably applies Bayesian model. It seems almost unbelievable that the brain has evolved so much that it has become capable of making statistical calculations close to the ideal. Our computers cannot handle such a huge number of statistical probabilities, and we seem to do it all the time. But maybe the brain is still not capable of this. According to sampling theory, the methods of consciousness can approach Bayesian inference: instead of simultaneously issuing all the assumptions that can explain any sensory signal,the brain takes into account only a few of them, selected at random (the number of times each of the assumptions is chosen is based on the frequency of the corresponding cases in the past).
This could explain the origin of visual illusions: the brain chooses the “best guess” according to the rules of Bayesian inference, and it turns out to be false, since the visualization system fills information gaps with a selection from an inappropriate internal model. For example, it seems that two squares on a checkerboard have different shades of color, or the circle looks concave at first and becomes convex after 180 degrees rotation. In such cases, the brain initially makes the wrong assumption about something as simple as lighting.
It also helps explain why the earlier information is received, the stronger its impact on the person with his memories, impressions, decisions, explains Alan Sanborn (Adam Sanborn), who studies problems of behavior at the University of Warwick. Potentially, people prefer to buy from the first seller they meet. Slots are more likely to continue the game if it started with a win. The first impression is often difficult to refute, even if it is fundamentally wrong. “Once you get the initial information, you’ll make assumptions that agree with it,” Sanborn clarifies.
This variability goes all the way at the neutron level. “The idea is that neutron activity is a random variable that you are trying to derive,” says Máté Lengyel, a neuroscientist based in Cambridge. In other words, the variability of neural activity is an indicator of the likelihood of an event. Let's consider a simplified example - a neuron responsible for the concept of "tiger". The neuron will oscillate between two levels of activity, high when there is a signal for the presence of a tiger and low, which means that there is no tiger. The number of times the neuron is highly active increases the likelihood of a tiger being present. “In essence, in this case, we can say that the activity of a neuron is a sample from a probability distribution,” says the scientist. - It turns out if you develop this idea in a more realistic and less simplified way,then it includes many things we know about neurons and the variability of their responses."
One of Sanborn's colleagues, Thomas Hills, explains that the way we choose among mental images is somewhat similar to how we search for physical objects in space. If you usually pick up milk from the back of the supermarket, the first thing you do is go there when you go to a new store for milk. This is no different from looking for internal images in the brain. “One can imagine memory as a kind of record of the rational frequency of events in the world. Memories are encoded into mental images in proportion to past experiences. So if I ask you about your relationship with your mom, you can start thinking: here is a memory of a positive interaction, here is another memory of a positive interaction, and here is a negative one. But on average, the memories of your relationship with your mom are good, so you say “good,” - says Thomas Hills. The brain is a kind of search engine that selects memories, creating what Hills calls “structures of belief,” the idea of bonding with parents, definitions of “dog,” “friend,” “love,” and everything else.
If the search process goes wrong, that is, the brain makes a selection from information that is not representative of the human experience, if there is a mismatch between expectations and the real sensory signal, then depression, obsessive-compulsive syndrome, post-traumatic disorders and a number of other diseases arise.
This is not to say that the Bayesian brain hypothesis has no opponents. “I think the Bayesian framework, as a kind of mathematical language, is a powerful and useful means of expressing psychological theories. But it’s important to analyze which pieces of theory actually provide an explanation,”says Matt Jones of the University of Colorado at Boulder. In his opinion, supporters of the "Bayesian brain" rely too much on the part of the theory that speaks of statistical analysis. “By itself, it does not explain the diversity of behavior. It makes sense only in combination with what actually turns out to be a free assumption about the nature of knowledge representation: how we organize concepts, look for information in memory, use knowledge for argumentation and problem solving”.
In other words, our claims about the psychological processing of information that cognitive science has traditionally done show how Bayesian statistics are applied to brain function. The model translates these theories into the language of mathematics, but this interpretation is based on conservative psychology. Ultimately, it may be that other Bayesian or non-Bayesian models fit better into the variety of mental processes that underlie our sensory perception and higher thinking.
Sanborn may disagree with Jones' views on the Bayesian brain hypothesis, but he understands that the next step is to narrow down the variety of models in action. “We could say that sampling itself is useful for understanding brain activity. But there are many choices. How much they agree with Bayesian theory remains to be seen. However, we can already say that the defense of Christianity in the 18th century helped scientists achieve great success in the 21st.