Think Anyway.
Author's Note: This essay was originally handwritten in Chinese as a late-night reflection before going to bed. The English version was translated with the assistance of AI.
Throughout history, different governments have designed different institutions. Through wave after wave of historical change and the collapse of countless dynasties, humanity's understanding of institutions and human society has reached new heights. Today, the societies we face consist not of hundreds, thousands, or millions of people, but billions. In response, humanity has developed various organizations and institutions to govern society and the individuals within it.
We have never abandoned our pursuit of a perfect system. Even though we have never achieved one, we have always tried to move closer to it. Ever since Plato attempted to construct an ideal city-state from scratch in The Republic, humanity has spent more than two thousand years imagining what the best possible system might look like. To me, our pursuit of institutional perfection resembles the concept of a limit in calculus: we can continuously reduce the distance between ourselves and an ideal value without necessarily ever reaching it. And so, within our finite terms of office and lifespans, we revise laws, add provisions, and rewrite institutions almost "infinitely."
But can humanity really revise its way to a perfect system?
For the following discussion, I will temporarily adopt a somewhat Platonist perspective, distinguishing "mathematics itself" from "the language humans use to describe mathematics." This philosophical assumption is not a necessary condition for Gödel's incompleteness theorems to hold; it simply makes the following discussion more intuitive. (For more on this, see physicist Eugene Wigner's famous 1960 paper, "The Unreasonable Effectiveness of Mathematics in the Natural Sciences." Although the paper does not attempt to prove Platonism, after reading it, you might begin to find the relationship between mathematics and the real world a little terrifying.)
But first, let me explain why I want to begin with mathematics in a series primarily about human systems. Mathematics is something most people consider precise (although I certainly don't, especially when I can't solve a problem). Yet mathematics as a discipline is not nearly as simple or complete as we might imagine. This seems rather counterintuitive, or perhaps even contradictory. Compared with human society—a system we all know to be deeply flawed and unstable—mathematics itself is extraordinarily precise. Yet even when dealing with such a precise subject, humanity has still been unable to design a formal system for it that is both sufficiently powerful and capable of resolving every question within its own framework.
Someone might ask, "Why should using human language to describe mathematics create problems?" Or, "Why can't we design a perfect system specifically for mathematics?" At this point, we can consider two things. The first is whether, from the perspective of mathematics itself, the formal languages we use can fully describe everything we want to describe. The second is whether, from the human perspective, using these languages to understand mathematics introduces limitations of its own.
As for the first question, since I am not "mathematics" myself, I cannot exactly tell you how it feels. But several decades ago, a mathematician became deeply fascinated by this issue. In 1931, Kurt Gödel published On Formally Undecidable Propositions of Principia Mathematica and Related Systems I (Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme I), establishing the results later known as Gödel's incompleteness theorems. Very roughly speaking, for any sufficiently powerful, effectively axiomatizable, and consistent mathematical system capable of expressing sufficiently rich arithmetic, there will necessarily be statements that the system cannot resolve from within itself: propositions that can neither be proved nor disproved under its rules.
There is, however, one very important condition here: the system must be "sufficiently powerful." Some weaker mathematical systems can indeed be complete. For example, when dealing with certain very limited arithmetic structures, we can have perfectly useful, even complete formal systems. The problem arises precisely when we want a language to express more, handle more, and become more powerful. That expressive power itself brings new limitations. In other words, a mathematical language can be extraordinarily precise within its expressive scope while still being unable to guarantee that it can completely and uniquely resolve everything we wish to address.
Of course, I am not trying to argue that Gödel has "proved" social institutions must be imperfect. Society is not a formal system, and laws are not mathematical axioms. What truly interests me is a more general tension that his work brings to light: we are constantly trying to use a finite set of rules to deal with something far richer than the rules themselves.
Now, let us turn to the second problem with mathematical language. There is another, much simpler, almost mundane point: learning and understanding mathematical language takes time. When I was three, I remember a classmate asking me on my first day of school, "What is one plus one?" I did not answer, but not because I couldn't understand that one apple plus another apple makes two apples. I simply had no idea what "plus" and "equals" meant. Think back to your first year of elementary school. Unless you had secretly been studying mathematics ahead of time, you probably didn't know what "x" meant either.
This is actually quite interesting. If we turn our attention back to human society, we can find many similarities. When people talk about governance, they may instinctively assume that smaller societies are easier to govern, but this is not necessarily the most fundamental reason. In my view, just as with mathematical systems, what makes society difficult is not simply the number of people, but the increasing complexity of the information that needs to be processed. The more complex a society becomes, the harder it generally is to govern, and vice versa. This might sound like stating the obvious, but it can actually help us understand some of the more fundamental logic behind society, law, and institutions.
When we are in a group of just six people, information usually travels easily, and the range of personalities, occupations, values, ideas, relationships, and combinations of interests is relatively limited. But when that number becomes six hundred, sixty thousand, or six hundred million, things begin to look entirely different. Suppose a government introduces a law: whenever someone encounters situation X, they must do Y. In a small society, perhaps X only takes a dozen or so common forms. But in a large society, X might take hundreds or thousands of different forms, or even so many that they cannot possibly be exhausted.
Let me give a more concrete example: "Anyone whose income falls below a certain threshold is eligible for financial assistance." But there may be many different combinations of circumstances that satisfy or come close to satisfying this condition. Some people have low incomes but substantial savings. Others appear to earn a reasonable amount but have many children to support. Some have just lost their jobs, causing their annual income to drop suddenly. Others have unstable incomes: employed today, unemployed next month. Some live in cities with extremely high costs of living. Others have low incomes but live with their parents. Still others earn money through cash-based work that is difficult to document.
Or, to take a more extreme example, suppose the government declares, "Anyone earning less than 100 dollars can receive financial assistance." Someone earning 99 dollars and someone earning 101 dollars may have almost identical living conditions. In some cases, because of differences in where they live, local prices, or family responsibilities, the latter may actually be worse off. Faced with these situations, the government begins adding rules: different household sizes require different thresholds; exceptional medical expenses may be deducted; certain assets must be counted; others are exempt; temporary unemployment receives special treatment. (Actually, I have just realized this sounds a lot like university financial aid policies. They are all ridiculously complicated anyway.)
Reality is continuous, complex, and full of subtle differences; institutions, however, must divide reality into clearly defined categories and boundaries. So, returning to the beginning, humanity's response to complexity is often to build even more complex systems. Sounds a little lame, doesn't it? What makes it even funnier is that more complex systems, in turn, increase the costs of understanding, implementing, and supervising them. Of course, reality is not a simple vicious cycle. Laws do not literally receive infinite patches, with a separate rule written for every possible situation. Often, new laws replace old ones, or more judgment is delegated to those responsible for enforcing them.
But this is exactly where another problem emerges. If we don't want to make the rules so rigid, why not simply let people judge each situation on its own merits?
Of course we can. But this merely exchanges one kind of flaw for another. The more a system relies on explicit rules, the more consistent and predictable it generally becomes, but the more likely it is to overlook exceptional circumstances. The more a system relies on human discretion, the better it can accommodate individual differences, but the greater the possibility that different people will receive different outcomes, along with bias, arbitrariness, or even abuses of power. Suddenly, the question changes. We no longer seem to be choosing between "flawed" and "flawless," but between different kinds of flaws.
Meanwhile, institutions and laws are, to borrow a mathematical term, discrete. And precisely because of this, institutions can compress information. In society, we have hundreds of millions of distinct individuals and an almost infinite variety of specific circumstances, yet the law can compress them into a manageable model consisting of a few thousand pages of rules. But compression necessarily involves choices. The law must decide which differences matter, which can be ignored, which people should be placed in the same category, and which circumstances deserve separate treatment.
Just as a high-resolution photograph loses some detail when compressed, institutions lose information when they simplify reality. The problem is that these details do not disappear merely because lawmakers are careless. To some extent, an institution must discard information in order to operate at scale. If a system had to know every individual's complete life history, family relationships, health conditions, assets, cost of living, future risks, personal abilities, and every exceptional circumstance before making a single decision, it might be more "comprehensive," but it would be almost impossible to operate. Institutions function not because they fully understand reality, but precisely because they refuse to understand it completely.
What makes things even more complicated is that human society differs from mathematics in one very important respect: institutions are not quietly describing an object that cannot respond to them. Once institutions are established, the people governed by them begin to understand them and change their behavior around them. For example, if earning 99 dollars qualifies someone for financial assistance while earning 101 dollars gets them nothing, then "100 dollars" is no longer just a line the government has drawn for administrative convenience. It begins to become part of reality itself. People calculate around it, avoid crossing it, and make decisions based on it. In other words, institutions attempt to compress reality, while reality, in turn, adapts to institutions.
So, returning to the question of whether smaller countries are easier to govern, a more accurate answer might be that population size itself is not the most fundamental variable. What truly matters may be the effective complexity that institutions must identify and coordinate. Population certainly affects complexity, but complexity can also arise from differences between groups, conflicts of interest, networks of relationships, the costs of obtaining information, external powers, and interactions between different institutional levels.
Take Lebanon, for example. It is a country with a relatively small population, yet the relationships between religious sects, political factions, external powers, and economic interests are extraordinarily complex. Its population may be small, but that does not necessarily mean its political system is simple.
For a simpler, and rather more ridiculous, example, consider certain friend groups. There might be only six people in the entire circle, yet they somehow manage to turn everything into a spy thriller. Suppose we construct an extremely simplified toy model: among six people, there are 15 possible pairs. If each relationship has only two possible states—allied or not allied—then these 15 relationships are like 15 switches, each with two possible positions. That gives us a total of 2¹⁵, or 32,768, different possible configurations of relationships. Real interpersonal relationships are, of course, vastly more complicated than this, but the example illustrates at least one thing: a small number of people does not necessarily imply a small number of possible relationship structures.
So the complexity of governing a society may depend not simply on its population, but on the complexity of its information, the complexity of its relationships, and the number of potential situations that can arise. This is why I said the whole thing reminded me of mathematics.
In the end, even when dealing with mathematics—something humans regard as extraordinarily precise—the formal systems we use to describe and process it encounter limitations involving expressive power, completeness, and practical usability. So what happens when, instead of numbers and symbols, we are dealing with billions of people who can think, change, cooperate, lie, understand rules, and then turn around and exploit those very rules?
Perhaps the real question facing institutional design has never been "How do we create a system without flaws?" but rather "How do we create a system whose flaws we can accept?"
Institutions cannot eliminate flaws. They can only choose which flaws to live with.
