Revolution Within The Mind
The goal of most humans is simple: To survive on their own terms.
Making decisions and taking action are critical to survival. In different environments, humans have to carry out different, repeated actions over and over again. Before humans take actions, we have to decide to do so. Decisions are needed to determine the precise nature of actions needed to bring us closer to our chosen goal. To make decisions and take action, we need to understand our situation — the environment we are stuck in. We must be able to form mental concepts of observed reality, and as reality appears to change our concepts must change with it.
We can think of any abstract concept as a set of connected data-points, coherently organised together. For example, the concept of the number “six” could be thought of as a collection of memories, each containing six objects. One memory could be six sheep in a field, another could be six pens in a pencil case. The concept “six” unites these disparate data points. Concepts are hierarchal: Your concepts of individual numbers like “six” and “seventeen” could be organised into a more general concept of “number”. And so on.
Concepts are useful because they simplify our thinking by allowing us to ignore lots of information. For example, after I learn what “six” is, I know it has nothing to do with the colour of the objects, only their number. Ignoring makes information processing, and hence decision making, faster.
We can think of knowledge about a particular environment as a set of experiences (data-points) organised into concepts. The formation of new concepts is driven by two main forces.
The first is induction — extracting generalities from particular cases, like extracting the number six from sheep and pencils above. Induction is an internal-looking process. Insights are generated by noticing similarities between memories already acquired, experiences you already have. It is a creative process, involving the birth of new connections between data points.
The second force is top-down deduction — checking concepts themselves for consistency, looking for anomalous data points which don’t fit the general rule. Deduction is an external-looking process. You have to work out whether newly gathered data fits within your top-down framework. When anomalous data are found, deduction is a destructive process. You tear down the conceptual framework to start anew.
This cycle of destruction and creation is repeated until our concepts are self-consistent — no concept disagrees with another — and match-up with reality as we see it. When this happens, the concept becomes a coherent pattern of ideas which can be used to describe (and simplify) observed reality. This gives a pleasing sensation, and makes one recall words like “understanding” or “mastery”.
Unfortunately, this feeling is fleeting.
Popper & Kuhn
Before we dive into why its fleeting, a digression.
Boyd’s model is similar to both the Popperian and Kuhnian views of scientific knowledge formation.
Kuhn argues that science progresses by successive, rarely occurring paradigm shifts, with long periods of stagnation in between. Paradigm shifts occur when anomalous data is found which doesn’t fit the contemporary scientific worldview. Mainstream scientists resist changes to their discipline, so the pathbreaking work is usually done by mavericks outside orthodox scientific bubbles. When this work is successful (explains observations in a more general way), most researchers “shift” their thinking in line with the new paradigm. There is an analogy between the Kuhnian “paradigm” and Boyd’s conceptual framework. Both are mental models, lenses which you use to observe reality, and so they affect the reality you observe.
In Popper’s view, knowledge is gained in an endless cycle of conjecture and refutation. We observe data, make a guess about a general rule which describes the data, and then do our best to falsify the guess. Science preserves the “good” conjectures — those that fit the data well and have survived lots of tests — and reject the failures. Over time, our models become successively better approximations of reality. While we can never know our current conjecture is correct, we know all our previous ones were false. Popper’s view of science is related to Boyd’s concept loops. Creative inductions are conjectures, while destructive deductions are falsifications.
In practice, people do not immediately look for data which disconfirms their point of view. Instead, anomalies build up until the individual is overwhelmed, and has to build up a conceptual framework from ground zero. This happened to me during the 2016 elections. In June I was so sure the world was a certain way, and a large majority broadly shared my liberal metropolitan views on freedom, equality and Europe. After Brexit, then Trump, my world-model collapsed and I spent the next few years rebuilding it almost from scratch.
It collapsed because it was incomplete.
Kurt Gödel’s theorems broke maths.
They place limits on how much you can know within any closed system, and hence placed limits on large areas of knowledge itself.
His first incompleteness theorem says any consistent system must be incomplete; this means there are true statements within the system which cannot be proved. His second theorem states that even though such a system is consistent, its consistency cannot be proved within the system itself!
Gödel showed that the consistency of the rules of arithmetic could only be proved by invoking a broader, more general, set of rules which contained the first smaller set. In order to show the consistency of the larger set of rules, an even larger set must be assumed. To prove consistency, this cycle must be continued over and over again for increasingly more elaborate systems.
The incompleteness theorems apply directly to this model of concept formation.
Concepts are necessarily incomplete, since they depend on an ever-changing set of observations. These observations are also incomplete, since what we look for depends on our current conceptual framework.The consequences for concept formation are huge. In order to determine the consistency of any new system — of any concept — we must construct another system which encompasses it.
The second law states: whenever we attempt to do work inside a system, we must anticipate an increase in entropy.
If we consider a human agent and his immediate environment as a system, then the actions of the human agent will increase entropy. This is because the individual will act in accord with her conceptual framework of his situation, which will be incomplete. Her actions will have unintended consequences, creating entropy, disorder and confusion.
This is why feelings of understanding are fleeting. Due to incompleteness of concepts and the entropy created by actions, disorder will always tend to increase, leading to confusion and overwhelm if we hold onto the same conceptual structures.
Applying incompleteness and entropy to concept formation reveals another insight: Any inward-attempt to improve the match-up of concept with observed reality will worsen the mismatch.
This is because our memories are an imperfect representation of reality, so improving models based on our experiences is a kind of overfitting. It is the problem of induction — just because all swans I have seen are white doesn’t rule out the possibility of a black swan. The only way to improve existing concepts is to falsify them and then refine them based on new data.
In order to improve overwhelm by uncertainty, you have to shatter your old conceptual framework and build a new, more general one by creative induction. Uncertainty and disorder can be diminished by creating higher and broader concepts to represent reality.
Over time, uncertainty is introduced into our new model, and we must tear it down and start again. In this way, learning is an endless cycle of creative induction and destructive deduction, a tiny Kuhnian revolution occurring within our minds.