An account of sense-making


David Spivak

James Dama




When you say “oh, that makes sense” or “no, that doesn’t make sense”, you’re talking about whether or not the story fits together or adds up right. But you may also say “I have a sense of when people are feeling awkward” or “I seem to use my sense of smell more than other people do”. Could it be that all these notions of sense are actually the same in some deeper way? Could it be that when we “make sense” of things, we’re actually doing the very activity that has “made” all of our senses to date? In this post, we’ll give you a sense of why that might be right!

Summary: When you say “oh, that makes sense” or “no, that doesn’t make sense”, you’re talking about whether or not the story fits together or adds up right. But you may also say “I have a sense of when people are feeling awkward” or “I seem to use my sense of smell more than other people do”. Could it be that all these notions of sense are actually the same in some deeper way? Could it be that when we “make sense” of things, we’re actually doing the very activity that has “made” all of our senses to date? In this post, we’ll give you a sense of why that might be right!

Background: UCLA’s Institute for Pure and Applied Mathematics (IPAM) ran a workshop called Mathematics of Collective Intelligence this winter, where I (David) gave a talk called Sense-making: Accounting for Intelligibility. Some of the ideas in the talk were mathematical, but the story arc was philosophical, and basically speculative. Recently, I was talking with my colleague James Dama, and he was able to give a much firmer scientific story, one which goes a long way toward justifying the speculations from the talk. So here we jointly write this post—David on the story arc, and James on the science—attempting to make the idea more widely known, so it can be refined, disputed, affirmed, etc.

Motivating story: Imagine two kids in math class, both of whom are trying hard to get an A, but in markedly different ways. The first one copies whatever the teacher writes on the board, making sure to have a faithful copy in their notebook. The second one does what we’ll call sense-making; let’s suppose we listen in to the second kid talking; we hear the following exchange:

“Wait, what?! Why would that be 2xy!? Shouldn’t it be x+y? I mean, why would… I mean, if x was 4 and y was, I don’t know, 2, or wait… if x was 2 and y was -2… Oh, but then….. Oh!!!!! I seeeee… right, because of the distrib-whatever rule you just said! Ok that makes sense now; phew.”

How do we account for all that activity?? What is the student doing, and why does it have that frustrated, searching flavor? And what does it mean when the student says that it “makes sense now”?

Imagine that the next day, when the teacher asks a question, the first student looks through their notes to find a similar example, but before they finish, the second student raises their hand excitedly and knows the answer when called on. Later, the teacher is explaining something and makes a typo; the second student shouts out “that should be 3x, right?” and the teacher says “right”. The first student must erase the “2x” in their notes, while the second student is thinking about what this whole thing is about; why are we learning this? When it comes time to take an exam, the second student does much better.

Point of the story: The second student—the one who did the thing we call “making sense”—actually developed a new ability to track the relevant aspects of the mathematical situation, as judged by their newfound ease in vibing with the math, their success on a test, etc; in other words they developed a sense of the math. Moreover, the sense-making activity had the character of trying to account for what they saw. The frustration at the beginning was coming from the fact that things weren’t fitting together, the accounts weren’t settling. The relief arrived when the “accounts settled”, when everything fit into a simpler synthesis.

Question 1: The work we call “sense-making” in math class seemed to make a new sense for how to work successfully with the math. Is it plausible that all of our senses—our sense of danger, our sense of eyesight—were created through a process that is structurally analogous to what the math student did to get their sense of the math?

Question 2: The way the good math student made sense was by trying to account for what was present, namely the symbolic statements the teacher was making. Is it plausible that all sense-making—the way all of our senses were made—took place using a similar sort of accounting process, i.e. by working to structure the present situation according to a more broadly-applicable system?

I’ll return to narrating this blog post in the last section, but up next James will show, using scientifically-grounded stories, that both of the above questions can be answered affirmatively, i.e. “yes: it’s plausible that all of our senses were made by a process analogous to the good math student’s sense-making work, and yes: it’s plausible that this work involves accounting for present variety within a uniform system. To explain what it is that is turning into sense, James adds a notion that he calls sensitivity, which comes before sense is formed. Anyway, here’s James.

David had asked about our sense of sight and the development of the eye as a case of sense-making, and so I (James) told a plausible scientific just-so story about how the development of visual senses in biology might look like the same sense-making the students were doing. Here is how it went:

First, David’s stories both start with a sensitivity without sense. Both the students cared about their grades though they didn’t know how exactly to earn the grades. Analogously, life is made out of biomolecules, especially DNA and RNA, that are sensitive to light from the very beginning. Light can damage those molecules and cause mutations, but this fact is originally not well dealt-with by early life.

Second, the stories describe a phase of adapting to the sensitivity, but still without real sense. The students learn particular answers to particular questions, but one is not attempting to understand their connections and the other is trying but not yet understanding. In pre-visual biology, there are many examples of local adaptations to react to light exposure without coordinating the reactions together into a single sense. Organisms developed with simple light detectors in their cells—allowing the cells to react to light—before they developed the coordinating intercellular communication to organize all the separate detections into organism-level responses.

Third, the stories describe a phase of synthesizing the adaptations into a sense that accounts for the sensitivity. The student who learns the principles of the math problems finds a way to coordinate all the mathematical ideas into a coherent whole, and also better understands mathematical meaning itself as the sense behind the grades. In biology, visual sense seems to arise from the coordination of local cellular responses to light into coherent organism-level patterns. Each of the local detectors evolves to couple to intercellular communication networks, such as the nerves and their precursors, and the nerves evolve to coordinate whole-organism responses to the light fields falling on the whole organism.

Finally, the sense separates from and supersedes the original sensitivity. Once a student has learned the principles of mathematics, it’s normal for them to stop trying to memorize each of the problems that they’ve seen before (and to stop prioritizing grades when deciding which math to learn next). Once the organism has evolved to respond to light-like stimuli as a whole organism, specialized new light-sensitive organs like eyes can evolve to take over the responsibility for triggering those behaviors. At that point it’s unambiguous that the organisms have evolved to make sense of light. The old distributed light detectors might become vestigial and disappear, and the behaviors that the new eyes govern, like collision avoidance or target seeking, often have very little to do with the early DNA and RNA sensitivity to light.

All put together, the story goes like this:

  1. An agent has passive sensitivities.
  2. The agent adapts to act sensitively but incoherently.
  3. The agent adapts to coordinate its sensitive activity into coherent actions.
  4. The agent’s coordination of its sensitive actions constitutes a sense.

The new sense begins as a system for coordinating coherent actions to respond to the original sensitivities, but it can then become much more.

That answers Question 1 directly, but where is Question 2? Well, “accounting” is exactly the name for one of the key communication processes that economic actors use to coordinate their economic behaviors coherently! Without accounting, complex economic activity becomes incoherent and senseless.

Accounting is therefore one of the rare cases of sense-making where we do the relevant coordination consciously and deliberately at a nuts-and-bolts level, and that makes it a great analogy for thinking about the nuts and bolts of the other cases that are more unconscious or automatic. We don’t yet know all the nuts and bolts of neural signaling in the biological vision case, and we don’t yet know the nuts and bolts of mathematical intuition for the students’ case. Accounting makes an unusually common, firm, and clear comparison case for building up understandings of these other, less transparent cases of sense-making.

Conclusion: Hopefully the above gives a reasonable enough account of how “sense-making” as working to understand and “sense-making” as the making/creation of our senses have deep structures in common. If this idea clicked for you, the reader, then you can probably track a commonly-missed aspect of how important the sense-making activity is: by making sense of things together, we are in fact improving humanity’s collective ability to sense the world—i.e. to track the relevant aspects—even as things get more and more complex.

Post script: In my (David’s) IPAM “Sense-making” talk, I had also discussed the common intuition that when someone makes sense of previously-scattered information, it feels like something “clicks”. James and I discussed this as well, and he connected the “click” to the concept of hysteresis—a sudden phase change, where a significant but small amount of energy can push a system into a new equilibrium—and to his academic work on coarse-graining and adaptive sampling. I was fascinated to learn that his pursuit of these ideas is rooted in an attempt to understand the causal structures of societal change. This is roughly the root of my interest as well, as I explained a few years ago on John Baez’s blog.

Hopefully we (either James and David, or the “we” that includes any interested reader) can one day take some of these ideas and lift them out from statistical physics and philosophy and into a category theoretic formalism. Indeed, category theory is a principled language for creating accounting systems in general—including self-referencing ones such as the category of categories—and hence it appears suitable for articulating a principled account of the life-enabling activity we call sense-making.