These are the conclusions—or maybe a sort of capstone—for what you might call the Plankton Valhalla Purpose Series of essays, which you can find here:

1. Boundaries Are in the Eye of the Beholder
2. Recursion, Tidy Stars, and Water Lilies
3. Purpose from First Principles
4. This essay

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We delved quite deep for just three essays. In this fourth and final piece, let me briefly retrace the path of our rabbit-hole exploration.

It all began with an observation: the “boundaries” we see in reality—the distinction between discrete “things” in the world around us, concrete or abstract—are figments of our imagination. The fundamental laws of physics do not account for any of them: boundaries shouldn’t exist!

This is how we left the surface for our downward exploration. How can discernible patterns even exist? How can anything be stable and coherent in a universe that started as a giant explosion of randomness and unrelenting forces?

The second essay took us deeper. We found that recursion, the simple situation of something affecting its own future state, is all you need to turn randomness into patterns. The details of the exact processes don’t matter here: if there is recursion, the differences concerned—however random, however small initially—can reinforce, erase, and clone themselves, creating repeating or otherwise predictable structures.

But patterns are not just the product of recursion: they can support still more recursion, with the same probability-amplifying effects. Thus patterns can form out of nothingness and build on top of themselves and each other, even mass-producing effects that would otherwise be almost impossible in a soup of erratic non-recursive interactions.

I call these unlikely-made-likely results of recursion Water Lilies. They constitute almost everything remotely stable and predictable in our Universe. But a fundamental problem still remained unsolved at this stage: where do boundaries come from? Why do Water Lilies feel not only distinct from each other, but also inevitable to us?

In the third essay, we reached the deepest point by partially answering that question:

• human beings use imagined Water Lilies, called “goals”, to design action plans in order to make useful things happen in reality, and
• we’re not very good at distinguishing between these Intentional Water Lilies and the more numerous Wild Water Lilies that happen by chance.

We constantly downplay how many non-intentional feedback loops there are, and how stupendously complex their outcomes can be. This bias towards seeing purpose in everything is understandable but, like all biases, it often leads to spectacular failures. It is often useful, but not always justified.

It’s now time to return to the surface: how do all those boundaries come about, really? On the way back out of the depths and towards the answer, I will briefly touch on two major concepts: information and meaning. They might sound daunting, but with the thinking toolkit of recursion and Water Lilies they’ll be a picnic for you.

What Information Really Is


(Photo by Ilse Orsel, Unsplash)

In this series (as in several other Plankton Valhalla essays) you’ve seen me throw the word “difference” around a lot. This term is not commonly used in the sciences, at least not in the technical connotation I use here. That’s a pity, because it is a fantastic tool to understand the world. It’s intuitive, because everyone knows what a difference is. There’s no trick or mystery: a difference is simply something that distinguishes two things.

Yet, easy as it is, “difference” is a universal idea, perhaps the most universal possible, because nothing can exist without differences—no people, no planets or stars, no atoms or elementary particles, no time, no space. Everything exists as differences.

This concept is particularly useful because it affords us a straightforward, no-nonsense way to define information:

Information is those differences which make a difference.

This is a direct quote from Gregory Bateson, a renowned 20th-century anthropologist-cyberneticist and, as far as I know, the first to use the idea of differences as something more fundamental than information itself: there must be differences that don’t make a difference, too, and those differences are not information.

To understand Bateson’s reasoning behind his terse (and a little cryptic) definition, let us see how he applied it.

Consider a man felling a tree with an axe. Each stroke of the axe is modified or corrected, according to the shape of the cut face of the tree left by the previous stroke. This self-corrective … process is brought about by a total system, tree-eyes-brain-muscles-axe-stroke-tree …

More correctly, we should spell the matter out as: (differences in tree) - (differences in retina) - (differences in brain) - (differences in muscles) - (differences in movement of axe) - (differences in tree), etc. What is transmitted around the circuit is transforms of differences. And, as noted above, a difference which makes a difference is an idea or unit of information.

— Gregory Bateson, Steps to an Ecology of Mind (emphasis mine)

See all the familiar elements? He’s talking about a recursive process—a self-correcting feedback loop—and the things going around this loop are differences. Not energy, not matter, just differences.

Each difference depends on the differences in the previous step: brain to muscles, muscles to axe, etc.

, “Differences in Retina” (eye receiving light), “Differences in Brain” (brain cross-section), “Differences in Muscles” (arm anatomy), and “Differences in Movement of Axe” (hand swinging axe)“)

(Image by Nano Banana Pro—don’t use it as an anatomy reference!)

This quote also demonstrates the relativity of boundaries, showing that we’re actually talking about a single thing, the “total system, tree-eyes-brain-muscles-axe-stroke-tree”. Bateson continues immediately after the above quote with a complaint about our tendency to consider our boundaries as absolute and fixed:

But this is not how the average Occidental sees the event sequence of tree felling. He says, “I cut down the tree” and he even believes that there is a delimited agent, the “self,” which performed a delimited “purposive” action upon a delimited object.

— ibid.

Seeing things through the lens of recursion helps you break out of this ossification of mental boundaries, and it makes it clear how information flows: always in loops.

All that is left to clarify is this difference-making business. What for, and how?

Difference for What?

The raison d’être of all information’s difference-making is, of course, purpose. Remove all goals and purposes, and randomness would reign supreme. Differences would still form loops (mindless recursion), but none of them would “make a difference”.

Without purpose, you wouldn’t bother learning new things and investing in your future, because why would you (the what-for kind of “why”)? You would have no reason to obtain tools or stock food, nor to pay attention to anything beyond your immediate surroundings. Instinctive impulses may keep you alive for a while, but you’re bound to ruin and starve yourself very soon—you wouldn’t be aiming to stay alive, after all.

As soon as purpose comes into play, though, it automatically implies the existence of a plan. Suddenly every difference can be classified: is this difference important for the success of the plan or not? Does it further your sub-goals and increase the probability of realizing your final goal? Does it hinder, alter, or disrupt the plan? Or does it remain completely neutral with respect to that specific purpose?

The lumberjack felling the tree is a purposeful process—ready-to-burn lumber is not likely to arise unless the man’s brain initiates the loop with that specific outcome in mind. He is undoubtedly the starting point of the feedback loop, but, as soon as it gets started, the boundary of what is significant expands to include all involved elements, his brain only a member among many. The “transforms of differences” that Bateson described—(differences in tree) - (differences in retina) - (differences in brain)…—count as information as long as they contribute to the execution of the lumberjack’s plan.

To put it another way, the differences that don’t make a difference for his plan are not information: the subtle creases in the bark of the tree, the unlucky worm that finds itself on the axe’s path, the soft breeze caressing the man’s brawny arms, the image of nearby birds impressing themselves on his retinas, and so on. None of this is relevant to the tree-felling plan.

The technical term for differences that don’t make a difference is “noise”. Noise is what we want to ignore in order to focus on the things that do matter.

To recap: no purpose → no plan; no plan → no difference-making; no difference-making → no information.

Aside: “Information” in Physics ⚛️

You’ll often hear physicists talk about “information” in contexts where there clearly isn’t an intrinsic purpose, like black holes and quantum interactions. This is a case of tolerated King-Midas effect.

Although they know that those systems have nothing to do with purposes and intentions, they find it convenient to imbue them with their own “observer goal”. Since their purpose is to understand a certain physical phenomenon, automatically all differences that affect that phenomenon “make a difference”, hence their use of “information”.

I think this custom is ill-advised, because it introduces subjectivity, after the fact, into impersonal phenomena. Use “differences” instead!

Anyway, until my proposed terminology spreads to the whole field (it’s just a matter of time now, I know it), remember that some scientists use the term in a confusing and misleading way. They really mean “differences”.

What Does It Mean to “Make” a Difference?

The “difference made” by a piece of information is what we call meaning.

If information is about making some—any—difference, meaning is the specific difference being made in a given case. (A fancier way to say it is that meaning is the correlation of a piece of information with the successful execution of a plan.)

When you say that something is meaningful, you mean that it has a bearing on the achievement of one or more of your goals.

The position of the dent in the tree is meaningful to the lumberjack, because he uses that information to direct his next swing of the axe, pushing the world closer to his desired state of “tree is felled”. The meaning of the dent, then, is the set of changes in brain patterns following its observation, as well as all the fine muscular adjustments in the man’s arms as he swings the axe the next time, but also the new shape of the dent as a consequence of that new stroke… and so on, encompassing the whole cascade of consequences up to the final achievement of the goal.

The fact that the dent, at that particular time, is just so, and not otherwise, has an impact—however small—on the mode and timing with which the tree is felled and the purpose fulfilled. This impact is meaning.

(Photo by Jan Meeus, Unsplash)

On the other hand, the chirp of a bird perched on a branch nearby is meaningless to the lumberjack in the context of his tree-felling plan. Of course, that same dent is meaningless to the bird (if it is not too close), who instead finds meaning in the calls of other birds. It may be hard to state exactly what that meaning is, but you can sum it up as “the differences in the bird’s behavior compared to the case in which it had not heard those calls.”

The implication is that it makes no sense to talk about the meaning of something if you don’t know what purpose is involved.

All too often, people leave the purpose implicit when they communicate, assuming that other people will share the same goals as they do, only to be surprised when they find that those people see very different meanings in the same things. For example, the difference “it is raining” is “information” for both the bride on her wedding day and the farmer worried about the recent drought, but the meaning is very different for each of them. Since they have dissimilar goals, “it is raining” affects their respective plans in completely different ways.

Carving Nature at Your Joints

Something interesting is beginning to emerge. The presence of purpose creates this rather clean distinction between information and noise, between meaningful and meaningless. This distinction is a little blurry in practice, because information can have different “degrees of meaning”, from “barely impactful” to “revolutionary” for your plans. But it is still clear in principle: if it has a detectable influence on the feedback loops of a purposeful process, it is meaningful, otherwise it isn’t.

The late and great philosopher Daniel Dennett gave a good example of how this affects thought:

The anteater, unlike the insectivorous bird, does not devote its cognitive energies to tracking individual insects, sampling their trajectories, and making a fine-grained prediction of their future locations; it just averages over the ant-infested area, and lets its tongue take up the slack. A philosopher might say that “ant” is a mass noun in the anteater’s language of thought; some regions have more ant in them than others.

— Daniel Dennett, Elbow Room

The Great Anteater, Joseph Wolf

A mass noun is a noun of which you can have amounts, but not individual units. “Jam” and “heat” are mass nouns because you can ask how much there is, but not how many. The opposite is true for count nouns like “fork” and “country”. What Dennett is saying is that, for a bird, “ant” is a count noun, because it needs to hunt them one by one. The anteater, however, doesn’t even have to look at the ants to eat them: it pours its incredibly long and sticky tongue into a hole in the ground, and collects a large amount of “ant” in a matter of seconds. The insects stick to the tongue in clusters, and are promptly sucked out of their nest and swallowed. When the beast finds that a place has little “ant” left, all it needs to do is to move on to another place where there’s more of it.

For the anteater, the number of ants has no meaning. The difference between “this ant” and “that ant” plays essentially no role in achieving its caloric needs. Thus, no boundaries need exist in its mind between individual ants.

The “mental boundaries” of an animal like an anteater are probably hard-coded by evolution, dictated by their particular anatomy and pre-established foraging “plans”. Humans make up for the shortness of their tongues with the nimble flexibility of their minds, but the effect is the same. We juggle multiple goals at once, accomplish some, give up on others, and adopt new ones all the time. The dense hierarchical web of our plans creates a legion of criteria for determining what is meaningful and what isn’t—what warrants the drawing of a boundary and what doesn’t. (Stalin might have had an anteater-like mindset when he allegedly said “one death is a tragedy; a million deaths is a statistic”.)

Back to the Surface

The original, strange question that kicked off this series was this: if boundaries are in the eye of the beholder, why do you keep seeing them everywhere, and tend to believe them necessary, objective truths?

I can finally answer that question for you in one sentence: we see boundaries because we have goals; we have goals in order to stay alive.

To survive in a mutable world, we need to predict the future as well as possible. We need to make mental simulations of what would happen in hypothetical scenarios ahead of time. We set up goals and craft intricate webs of plans to make certain favorable states of the world much more probable than they would be otherwise. For any input of our senses, we feel the irresistible urge to assess its relevance to our goals—to know what difference, if any, it makes for our plans.

The search for meaning is built into how we work as organisms. Processing information is living.

But—guess what—our brains are smaller than the Universe. We need to use a few tricks to enormously simplify our inner simulations while retaining a modicum of useful foresight. We do that by only focusing on the few differences that make a significant difference for a given purpose, and ignoring all the rest. That is to say, in our minds we sever the countless ties and interactions that exist between things, retaining only the handful that we care most about.

Severing those ties has the effect of turning what is really a seamless network of connections into a set of discrete “things”: the delimited agent called “lumberjack” acting on the delimited object called “tree”; the thing called “anteater” acting on the mass noun “ant”.

In this manner—in the gaps left by this rough and subjective severing of links—boundaries arise in our perception of the world.

This is a dangerous gamble. It means that, if you make the mistake of hallucinating non-existent purposes, or of dismissing some feedback loops as meaningless “side effects”, this mistake won’t just lead to poor outcomes but warp your whole understanding and perception of reality at its very roots. Failing to assign purpose its proper, modest, role means erecting mental walls where none exist and walking right into pits you just can’t perceive. It means venturing into a world that fights against you from inside your own head.

But the same trick is also why you’re able to say fancy things like “pass me the ketchup” and “the projections for our year-close budget ain’t pretty, folks.” This method of simplifying our simulations provides nothing less than the basis for all thought and communication. 💠

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Notes

• Cover picture: Buste De Jeune Fille Avec Un Couronne De Laurier, Henri Martin