A GPS for the mind

10 March 2022
10 Mar 2022
New York, NY
10 mins

When I get stuck on a really hard problem, whether it’s some impossible bug in my code or my sofa not fitting through my front door on moving day, I close my eyes and … think really hard. Somewhere behind my shut eyelids and confused eyeballs, things are happening. Electricity is flowing through the vat of brain-stuff and spindly wires that somehow make up my thought process, and for a few seconds, they just kind of do their thing. Until, if I’m lucky, an answer pops into my head a few moments later.

One of my favorite questions to ponder these days has been: when I’m thinking or remembering, just in that moment when my eyes are closed and I’m sending all that extra energy to my brain, what’s really happening? There are no hard drives to spin into place in my brain. What’s taking up all that time? It’s easy to wave your hands and say “it’s just computing” or whatever, the way you expect slow computers under load to be. But often when I’m heads-down thinking, I’m not crunching numbers or solving logic puzzles in my head. I’m not really sure what I’m doing, but it usually feels like just staring into the void and hoping for some idea to pop into my mind.

What’s happening up there? What is thinking?

If we want to build better thinking tools, I think it’s important to have a mental model for what thinking is, so that we can design human + tool systems that better accomplish whatever it is. Without a satisfying model, the work of designing these tools may amount to little more than assembling a patchwork of ad-hoc mechanical aids.

Pathfinding in a maze of ideas

For thinking about thinking, a good place to start seems like association. Vennevar Bush, in As We May Think, writes:

The human mind […] operates by association. With one item in its grasp, it snaps instantly to the next that is suggested by the association of thoughts, in accordance with some intricate web of trails carried by the cells of the brain. It has other characteristics, of course; trails that are not frequently followed are prone to fade, items are not fully permanent, memory is transitory. Yet the speed of action, the intricacy of trails, the detail of mental pictures, is awe-inspiring beyond all else in nature.

If we imagine the repository of ideas and memories in a mind as a kind of tangled web of ideas, “thinking” definitely involves traversing and scrambling across this web somehow, with some intent. The more obvious, trivial thoughts are the associations that are immediate and close by, and the more insightful thoughts may be jumps between ideas that are only loosely connected, or only connected by second- or third-degree leaps in association.

This model of thinking as “traversing a graph of ideas” leaves out an important element, though, because most good thinking happens with a goal. When I’m thinking deeply, I’m trying to understanding something new by internalizing an explanation, or I’m trying to find a solution to a problem in front of me. I’m not blindly jumping from idea to idea, hoping for an insight – there are far too many ideas, and many more connections between them, for random walks through idea webs to ever yield anything interesting. So clearly, there’s some directed-ness to the way our minds are navigating our internal webs of ideas – good thinking is effective navigation through the idea maze.

If thinking is navigating the idea maze, then good ideas may be interesting paths through the maze. This very essay you’re reading is a kind of a purposeful wandering hike through my own idea maze, laid out in a way that’ll hopefully plant some new seeds in your own garden of ideas. Ideas are paths through idea mazes, and writing is a way to chart those paths for others to follow.

In Reader-Generated Essays, Henrik makes the same observation:

What I am doing right now, writing this essay, is, technically, a linear walk through the network of my ideas. That is what writing is: turning a net into a line. But it is also very concretely what I do, since I have externalized my ideas in a note-taking system where the thoughts are linked with hyperlinks. My notes are a knowledge graph, a net of notes. When I sit down to write, I simply choose a thought that strikes me as interesting and use that as my starting point. Then I click my way, linearly, from one note to the next until I have reached the logical endpoint of the thought-line I want to communicate.

He goes on to imagine how we could automatically assemble essays from records of your thinking in your notes. I think that’s an exciting idea!

I’ve written previously about how we can think of intelligence as data compression. An intelligent model of the world tries to explain and predict a large breadth of observations from a few known facts. I wrote then:

To effectively compress images, a compression algorithm would be advantaged to “learn” facts about the world, like that colors are usually contiguous in images, and that the ground is often green and grassy while the sky is often white and blue. To effectively compress English text, the model might be advantaged to “learn” abstractions like common words and frequent grammatical constructs, so it can avoid inefficient, rote memorization of letters as much as possible.

Thinking often involves a similar kind of search for better explanations, and applications of those explanations. Creative, “divergent” thinking involves our minds going out and exploring our idea mazes to try to find latent explanations – associations or relationships between previously unrelated ideas that may make our worldview more robust. Solution-seeking, “convergent” thinking involves the reverse – searching for explanations and associations in our minds that fit some problem at hand, so that we can decompose new problems into patterns we recognize how to solve.

It seems to me that if we want to model our minds as “graphs of ideas”, which a lot of thinking tools do these days, we should think of “thinking” as a purposeful pathfinding process through this graph, where we wander in search of satisfying latent connections with high explanatory power or aesthetic value.

I like this framing of thinking as pathfinding a lot, because it lets us model “thinking” as a kind of well-defined end-to-end process. Every day, we take in new experiences, guided by our current model of the world. As we encounter new observations, we try to find latent associations – new explanations composed of things we already know – that can satisfyingly explain things we see in the world.

Thinking tools are navigational aids

With this model of thinking as a kind of graph-traversing hunt for explanations, we can more rigorously design and evaluate thinking tools. A good tool for thinking should make the combined human + tool system more effective at hunting for novel explanations within our idea mazes.

Whether we find ourselves exploring a real forest made of matter and mud or an idea forest made only of mind-stuff, there are a few essential components we need in a pathfinding tool.

It should tell us what’s around us. When we’re thinking of an idea, we should be able to immediately recall other, related thoughts from our past: have we thought the same before? Have I read something about this? Does anyone I know work on this stuff? Are there any traps – fallacies or obvious but disproven hypotheses – we should avoid? Tags in notes, semantic search, and hyperlink-dense notes are all about making these tools better at telling us which ideas are in the neighborhood of other ideas.

AI models that understand natural language are opening up powerful new ways for tools to help us explore neighborhoods of interesting ideas. Instead of jumping between manually-annotated links in a forest of bullet points, language model-powered thinking tools should let us grab any sentence or idea and ask large swaths of the Internet questions like “What ideas support this claim?” or “Who’s tried this experiment before?”

I often feel like our individual notes and ideas only fill out a vacuously sparse subset of the space of good ideas, like dust motes suspended in stale air. With better tools, we should be able to map out entire sections of the idea-space, instead of optimistically poking holes in the space of ideas. I think that starts with tools that can ensure we don’t miss great ideas lurking just nearby good ones, just because we didn’t save a note in the right place or know the right person with the right complement of ideas.

A good tool should also tell us where the well-travelled paths are. A map with a thousand interesting places is no use if we see no roads to get us there. Our map of the idea maze should tell us which roads have been travelled before – which passing thoughts we may have thought already, and which unexpected connections between ideas came before us in someone else’s mind.

Unlike humans, tools powered by modern datasets like Common Crawl and models like GPT-3 can hunt for the well-travelled paths in the idea maze across all of published literature – every open-access book, every paper, every blog, and every Tweet.

When we look at the various features that have gained popularity in “tools for thought” on the market, like bidirectional links between ideas, hierarchical bulleted-list notes, or the “daily notes” journaling system, they all boil down to different ways to help us find interesting new paths in our idea mazes:

With further advances in AI and interface design, we may invent tools that proactively search for interesting explanations amongst known ideas, going on a billion autonomous walks through the combined knowledge garden of humanity every second, paving new roads faster than humans can do alone. A more grounded way to imagine this world may be to think of what automated theorem provers do for the space of possible mathematical proofs, and imagine this capability expanded across every discipline.

Collaborating with this kind of autonomous thinking tool might be trippier than working with real humans. When your collaborator can propose ideas and remember precedents faster than you can process, the main design challenge may become one of interface and throughput: how does the way humans think change when our recall and creativity outpaces our understanding?

In the novel Accelerando, Charles Stross imagines a kind of future personal computing device that not only connects you to a global network and helpfully answers questions, but becomes woven into the way the wearer’s brain works at a more fundamental level. When Manfred, the main character, loses access to his device for a while, he nearly loses his sense of self, unable to remember what he was doing or perceive the world around him at nearly the same rate.

Sometimes, I feel that a part of my work studying and writing about thinking tools is convincing the rest of the world that the space of possibilities in this domain far exceeds the space of possible note-taking tools and productivity workflows. Notes and search engines are merely text buffers that we use to store information in between the times when we occupy ourselves deeply with those ideas. The real possibility space of tools that help us think – tools that guide us through the vastness of the space of all good ideas – is much broader. And the extent to which we’ve explored it pales in comparison to the trillions of great ideas that may lurk just nearby, if only we had better maps to get us there.

Navigate, don't search

On proving yourself

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