Strength-Liquidity Tradeoffs in Beliefs

A graphical contraption for mapping beliefs

The Contraptions Book club March pick is Giordano Bruno and the Hermetic Tradition by Frances Yates. Chat thread here. We will discuss this the week of March 24th.

The 2025 Summer of Protocols call is out, with a curriculum development grant opportunity for faculty (deadline April 1), and a science fiction short story contest with prizes (deadline April 14). Check it out.

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Why do some notions evolve to a status of commodity reality, where they are an uncontroversial part of nearly everybody’s beliefs, while others gain no traction or stall out at permanent disagreement?

I came up with an interesting visualization and idea to think about such questions last week: A tradeoff curve I call the Strength-Liquidity Tradeoff (SLTO) principle of beliefs. The SLTO principle shapes how beliefs about some aspect of reality evolve — say the reality of UFOs, Christian heaven/hell, or the emergence of a particular notion of “AGI” in the future. It provides a way to analyze memes and reality data together, and think about such things as religions, crypto memecoins, and conspiracy theories within the same frame as sober, evidence-backed theories and notions on which a lot of material realities rest. This does not mean I’m equating the two kinds of notions. I’m merely analyzing them in the same frame in terms of their social dynamics.

I find the SLTO principle a useful frame for thinking about stock markets, narrative markets, culture wars, and big, trendy discourse topics.

Here is a picture:

Belief strength measures how strongly someone believes in a notion.

Belief liquidity measures how many people believe in a notion at a given strength.

A particular point on the diagram represents a particular combination of strength and liquidity. Say 1 billion people believe in ghosts, with say 50% confidence. Since there are about 8 billion people on Earth, you’d plot this condition at (1/8, 1/2). All these people might be willing to exchange tokens representing this notion, or widgets designed to try and shape reality in accordance with the notion (such as amulets that claim to ward off ghosts). They might perhaps try to use such tokens and widgets as the basis of economies, on which entire polities might be based.

In the late Middle Ages, indulgences issued by priests were used precisely in this manner — enough people believed in the Christian heaven/hell (or found it expedient to profess such belief) that it was a viable situation.

Now, without saying anything about whether a notion is true or real, we can still measure the amount of salient reality data that people might narrativize to form their beliefs. The raw amount of salient data (for instance, concerning reported miracles) determines the location of what we might call the reality frontier. The data that locates this frontier includes basically anything, though not everything contributes to the location of the frontier with equal weight. In the case of belief in Christian heaven and hell, you can include things like the existence of church buildings, amulets, copies of the Bible, and so on. Whatever you believe about the proposition that the Christian heaven and hell exist, these are salient things to consider. It is reality in the Philip K. Dick sense: Even if belief in Christianity suddenly dropped to zero, the churches and copies of the Bible wouldn’t go away.

So we are not saying anything about whether or not this data is meaningful or whether or not it validates beliefs. Merely that it is salient and exists in a real way regardless of your beliefs. It is reality data only in the sense of being drawn from material reality (for example, pieces of toast with burn patterns that look like Jesus, or AI-generated images thereof), not in the sense of being proof or disproof for anything. For any given piece, some might view it as proof of the notion, others might view it as disproof, and still others might consider it irrelevant and not salient. But so long as at least one person considers it salient to a notion, it helps shape the reality frontier for belief in that notion.

This reality frontier is represented by the current location of the SLTO curve. You can’t objectively deduce its location, since the axis variables concern beliefs about what is salient, but you can infer it simply by measuring the popularity of a belief at different strength levels. For example, by doing a survey on how confident people are that UFOs are real or unreal. I assert the responses will cluster around a tradeoff curve that will look like my idealized one in simple cases. And the location and shape will have some relationship to the mass of reality data we have in the form of UFO sighting reports, government denials, popular media, and the subculture around them (we are only asserting that the reports exist as realities, not that what they claim is true).

It is reasonable to suppose that most people will form beliefs at (strength, liquidity) coordinates that enjoy some degree of plausible support from available reality data. On this basis, they may create shared narratives, provide social proof to each other, and validate each other’s proposed arguments for why the reality data constitutes evidence for particular propositions being true or false. People in the same (strength, liquidity) zone, by definition and construction, are within persuasion-reach of each other. They may form stable societies with thriving economies, and turn their modes of mutual persuasion into legal systems backed by the force of law and violence. As the story of Giordano Bruno (which we’re reading about right now in our book club) shows, real people can be subjected to real trials by real legal systems, and really put to death over notions that to us are perhaps about as real as the Harry Potter world.

If you plotted everybody on earth in relation to a particular notion. Most would simply not be aware of all the salient reality data, so they would be in the interior of the tradeoff curve, say at position E. The interesting people are the ones who are aware of all the reality data, and have beliefs shaped by it.

The person with the strongest belief in a notion (position C) has, by definition, the least liquid belief structure. In the green part of the diagram, where the ends of the tradeoff curve ride the axes, the (0,1) point represents pure solipsism: A completely illiquid belief held by an expert in the salient data, who is unable to convince even a single other person.

Here, by expert, I simply mean someone who has cashed out the strongest possible beliefs from available reality data, which means they have a high degree of constructivist expertise in working with the data. I am happy to acknowledge someone as an expert on the Bible and the theological traditions surrounding it without sharing in the strength of their beliefs. Perhaps as a complete unbeliever (0 on the y-axis) I’d still be willing to go into business producing things to sell to them. My definition does not distinguish theologians, UFO experts, and medical doctors, or use expert as either a compliment or an insult. That is the point. Experts on the SLTO diagram are experts in the sense of having mastered a particular sort of construction material, which I take as a proxy for maximal and sincere strength in certain beliefs. It is possible to be a cynical expert of course, where you master construction material merely to sell something to others, by professing beliefs stronger than you hold.

At the other extreme, (position D), we have the pure degen in the sense of a crypto-trader trading in memecoins. They too have beliefs shaped by all available reality data, and are on the frontier, but have no strength of belief in the underlying data. For them it is a pure meme. Counterintuitively, this is a maximal liquidity location. The people with the least belief in a notion enjoy the most liquidity because they can sell to anyone with even slightly more belief (which may or may not require practicing some cynicism).

Most well-informed, on-the-curve people are at positions like A, B. If their beliefs are stronger than the liquidity they experience, they are on the believer —> expert side of the turnpike (the arrow). Otherwise, they are on the skeptic —> degen side.

To round out the positions, position F represents being out on a limb. Strength of belief and liquidity being out beyond the reality frontier. This is an untenable position and must crash eventually (perhaps it is better to think of the liquidity level of position F as a false estimate of liquidity rather than actual liquidity — if you don’t intend to sell, it kinda doesn’t matter what you believe about liquidity).

A hypothesis I have is that position F is untenable unless a number of people are practicing cynical expertise on others. If I’m at (1,0) but professing (0.3, 0.9) very persuasively, I might be able to convince a lot of people to think there is far more liquidity than there actually is at their belief level, moving them out on a limb (and vulnerable to rug-pulls and such).

Could clueless people go out on a limb all by themselves? I think so, but for it to happen at any significant scale, some cynical operators have to be in the picture.

The green part of the diagram represents divergence, because people can grow farther apart with more reality data. The red part represents convergence, which is possible when there is in fact a there there. More data makes people converge more, until at the very limit, you get commodity reality, where the SLTO curve collapses to a point (1,1). The unfounded notion has become a completely well-founded notion. Unless you can undermine the belief in some way, through some doubt-merchanting, the market is closed for business.

Convergence to commodity reality need not happen. Salient reality data may simply stop coming in at some point, with the reality frontier stalling. It may never get to convergence, and remain an unsettled tension indefinitely, with people occupying points on the SLTO frontier where they cannot persuade each other at all, or form societies to coerce each other to different positions. This is a condition of polarization.

The other extreme, the (0,0) point of completely unfounded notions (“there is a planet around Alpha Centauri that has an intelligent purple, four-eyed quadruped species calling themselves Ploos”) is where entirely fantastical notions begin. Beliefs with no liquidity, and no strength. Such notions may stay hovering around (0,0) if there is no meaningful way to generate reality data. Simply adding more science fiction stories about Ploos won’t help because each will only move the frontier by a vanishingly small amount.

Santa Claus is an interesting notion to plot on this graph. Children raised in the Christian tradition, up to a particular age, do sincerely and strongly believe in him. There is enough real liquidity to sustain a huge economy around the notion. But it is self limiting because the core believers keep aging out of it. So the reality frontier can never get too far out.

By contrast, something like vaccine denialism is threatening to turn into the anti-Santa Claus belief, where disbelief reaches near commodity status and turns into a stable social reality, making weird heretics of a minority who remain believers even as the vaccine economy and herd immunity collapse.

Is it still reality if it goes away because enough people stopped believing in it, memeing it out of existence, because it takes a critical mass of constructive effort based on sufficiently strong belief to keep in existence at all, as a reality?