inImaginative Bayes of Understanding

People don’t understand what understanding is. I came to this conclusion after following closely the debate about the future of AI and reading tons of literature afterwards.

There are plenty of concepts which approach this issue from different perspectives: anthropological, computational, mathematical, pedagogical, physiological, psychological, even, quantum physical. One can try to draft a vague sketch of the unified theory of understanding by superposing at least most interesting of them.

Here comes my attempt.

My understanding of Bayes’s theorem is more than naive. It’s primitive.Yet I take the liberty to share it as a starting point in the topological (or metaphorical) outline of the idea of understanding.

Take P (A) — this is the probability that A is true. And — this is our belief before we make an observation. This is our initial level of knowledge. This is the input signal.

Then P (B) is the probability that B is true. B is data that we obtain from an observation. This is an update of our knowledge. This is a filter.

P (B | A) is the probability that our observation B is true, provided that our belief A is true. This is the probability of the observational result matching the knowledge that we have. It shows how much the input knowledge and filter data differ.

Now we need to calculate the value for P (A | B) — the probability that our belief A is true if our observation B is true. This will be our new level of knowledge after taking into account observational data.

So we came to the formula:

P (A | B) = P (B | A) * P (A) / P (B)

We take the probability of observational results being true given the probability of our old knowledge is true, multiply by the probability that our old knowledge is true and divide by the probability that the observation is true. We get the probability that our old knowledge is true given the probability of observational results is true. This is the probability of our new knowledge being true.

This is the direct Bayesian inference. It does not say anything about where the value of P (A) comes from if we know nothing in advance. It is believed that it is equal to 50/50, if we do not know anything.

But we can’t have zero knowledge. Rather, we may have zero knowledge in a specific domain, but we certainly know something outside it.

This is where the question of understanding arises. Understanding is not about knowing a specific solution to a particular problem. Understanding is the creation of an algorithm for solving all problems of a certain class, and not one specific problem.

Understanding is not built on our direct interaction with the environment, but on the relationships between the various environmental phenomena that we recognize by association with what we already know about the environment. The input for understanding comes from observation, not from belief (old knowledge). In understanding we invert Bayesian inference in the following way:

P (B | A) = P (A | B) * P (B) / P (A)

The probability that our observation is true, provided that the probability of our belief is true is obtained by multiplying the probability that our belief is true, provided that the probability of our observation is true, multiplied by the probability that our observation is true and divided by the probability that our belief is true.

In this case, we obtain the value of P (A) (the probability that our prior belief is true) by analogy between what we know from unrelated but metaphorically linked areas with what we observe. The reliability of our knowledge ceases to be equally probable (that is, complete ignorance) and gains real weight.

Thus, we begin to create an understanding of what we did not understand. And we can continue to test this understanding until the probability of the reliability of the observation, subject to our understanding, is high enough so that we can begin to use the new understanding as an algorithm to achieve the desired observation in similar conditions.

In this logic, we observe something that makes us curious. We come to the understanding by trying to satisfy our curiosity — we search mentally by analogy for the cause of the phenomena we are curious about. We imagine what we don’t understand by mapping it against things which we do understand.

Metaphorical mapping of understanding is topological by nature. We superpose domains of known concepts to map the topologically invariant contours of a domain of the unknown that we can only vaguely imagine. Our mind plays with images, spaces and shapes rather than with symbols or statistical distributions in order to invent the understanding.

Once the images settle in a metastable order of winnerless competition we probe how firmly they stand. Only after getting satisfied with the result can we translate it into words, numbers or other symbols.

This is the algorithm of actions of living (fluid, imaginative, prior, scientific, associative) intelligence, which generates (creates, invents, imagines) new understanding on the basis of observation, imagination and mental topography, but not by discriminating the results of observation on the basis of old knowledge.

I am researching and writing all this stuff because I am badly in need of a self-motivated, truly autonomous artificial agent to power a virtual environment that will help human beings to retain humanness, that is the ability to understand other humans. I’m also very curious to know what understanding is.