Gradient of Thought

Why do certain ideas seem almost inevitable once we begin thinking about them, while others remain difficult to reach? This essay explores the possibility that thought has a landscape: a space of concepts in which some ideas are easier to reach than others. I speculate about conceptual spaces, the dynamics of thought and intellectual originality.

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I was in my early teens, and I remember spending a lot of time thinking about what, if anything, existence was ultimately supposed to mean. The more I thought about it, the less convincing the idea of some inherent purpose seemed. Why should there be one? The universe exists, we exist within it, and yet nothing about existence itself seemed to demand that it should be for something. At first, that conclusion felt almost unsettling. But cosmic insignificance did not leave me pessimistic. I could still live, care about things, make things, learn things, and give my own life whatever meaning I wanted.

Years later, I discovered that this was not a particularly new idea. I had independently arrived at something that other people had already arrived at, and different facets of it had already been given names like existentialism, absurdism, etc.

At first, I took this as evidence that a person can reach fairly sophisticated ideas without first being given the vocabulary for them. But recently I started wondering whether there is a deeper way to interpret this.

Perhaps I did not merely discover an idea.

Perhaps I was drawn toward it.

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The shape of thought

Imagine a space containing the different ways a mind could conceptualise something: a space of ideas, distinctions, relationships and abstractions.

Some ideas would be very close together. Once you understand one, another might be almost unavoidable.

Others might be extremely far apart. You might need to pass through dozens of intermediate concepts before the second one becomes thinkable.

There might also be regions that are unusually easy for human beings to reach.

A mind starts somewhere inside this space. It has a particular vocabulary, a particular way of making distinctions, a particular architecture, and a particular collection of experiences.

From there, thought does not move completely arbitrarily. It moves as a function of its current state. Some directions are easier than others. Some conclusions feel natural. Some questions almost seem to answer themselves once you have accepted certain premises.

This makes me think of a physical landscape.

Put a ball on a surface and it will tend to move in certain directions. It does not need to “know” where it is going. The shape of the landscape determines the directions that are naturally available to it. The ball may eventually settle once it reaches the bottom of a valley in this landscape.

Perhaps thought has something similar. Perhaps there are gradients in conceptual space. And perhaps some ideas behave like attractors, the valleys.

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Attractors

Consider the question:

Does life have an objective meaning?

It seems possible to start from quite different places and still end up near a surprisingly small set of positions. Someone might say that meaning comes from God. Someone else might reject that and conclude that there is no meaning at all. Another person might reject both and say that meaning is something we create locally. Someone else might arrive at a position resembling Stoicism.

These are not completely identical philosophies but there are recurring structures.

And that makes me wonder whether some philosophical ideas are not simply ideas that happen to have been proposed many times.

Perhaps they are stable regions in human conceptual space.

Maybe if enough human minds begin asking the same question, with enough of the same underlying cognitive machinery, many of them will eventually roll into approximately the same valleys.

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Originality

This leads somewhere that I find particularly interesting.

If our reasoning naturally follows the gradient of our conceptual landscape, then intelligence might make us better at travelling along the gradient without necessarily helping us escape it.

Perhaps an extremely intelligent person can explore a familiar conceptual territory much more deeply than everyone else and still never notice that there is another territory nearby.

This would mean that intelligence and originality are not identical. One can be extremely good at reasoning and still be constrained by the concepts available to reason with.

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We usually think that being more intelligent means being able to reason further. But what if the problem is not how far you can travel?

What if the problem is where the landscape allows you to go?

Suppose two people begin with the same philosophical question. One arrives at absurdism. The other arrives at Stoicism.

Perhaps one of them is wrong. But that may not be the whole story.

Maybe they have different conceptual landscapes because they make different distinctions about the world.

Maybe the first person’s way of organising reality makes absurdism the natural attractor, while the second person’s makes Stoicism more natural. And this raises a much stranger possibility. Some of the most important intellectual advances may not consist of finding a new answer inside an existing conceptual landscape. Perhaps they consist of changing the landscape itself.

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Landscape transformation

A new idea can sometimes do something peculiar. Before it exists, several things may seem unrelated. After it exists, they suddenly become close.

This is similar to how a mathematical abstraction can make several apparently unrelated problems turn out to be examples of the same structure and how a scientific theory can connect phenomena that were previously studied separately.

In these cases, the important thing is not simply that a new proposition has been added to our knowledge. A new map itself is formed between the ideas. Things that previously seemed unrelated become connected through a new structure.

Suppose there is some enormous conceptual space.

A human mind can only occupy a tiny region of it. The same idea may be close to one mind and almost impossibly distant from another. This does not necessarily mean that one mind is “smarter” in the ordinary sense. The two minds may simply have different ways of organising distinctions.

One person might naturally see mathematical structure everywhere, another may see causal structure, another social or symbolic structure. Each mind would therefore have its own routes through conceptual space. Now imagine two such minds discovering apparently unrelated ideas.

Could there be a transformation between their conceptual spaces?

Perhaps one person’s philosophy could be mapped onto another person’s in a way that preserves some deeper structure. For example, maybe absurdism and Stoicism are not just two competing answers. Perhaps there exists some transformation under which certain parts of one become recognisable as the analogue of certain parts of the other.

I do not know whether such a transformation actually exists. But I find the possibility much more interesting than simply asking which philosophy is “correct”. It would mean that comparing philosophies is sometimes like comparing coordinate systems.

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It turns out that the idea that concepts have a geometry is not entirely new. Peter Gärdenfors developed a framework called Conceptual Spaces, in which concepts can be represented geometrically using dimensions and distances. His work is concerned with the structure of concepts, similarity, concept formation and related problems in cognition.

That is very close to one part of what I am thinking about. But I am wondering about the dynamics of thought.

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I don’t know how far this idea can be taken. But it makes me wonder whether some of the limits of thought are not limits of intelligence at all, but limits of the landscape that intelligence is moving through.

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