Theoretical Foundations of Psychohistory

Asimov presents the fascinating idea of psychohistory in his “Foundation” series. Regarding its theoretical content, it can be analogized to analytical mechanics, where the historical laws of motion are mathematically modeled by treating a population of 5 quadrillion as gas molecules.

However, human creative activities should render the laws of historical motion themselves obsolete.

What makes Asimov’s concept feel realistic is that psychohistory is set not in modern society, but in the era of the Galactic Empire’s decline, where technological progress stagnates — meaning humanity no longer makes new inventions or discoveries, and science turns into religious faith. It also presupposes the avoidance of self-fulfilling prophecies.

Under these premises, the history of the Galactic Empire proceeds harmoniously toward collapse according to Seldon’s laws of motion. The story’s unique charm, unlike typical novels, lies in how the protagonists’ subjective actions become ineffective, and Seldon’s laws prevail. This is because the laws, not humans, are the protagonists.

However, as for the pseudoscience in this SF concept, I would like to see not just analogies, but the basic principle as a pseudoscience — namely, Seldon’s principle — presented.

Foundation is sufficiently entertaining as a story, but I wish it delved deeper into the content of psychohistory, the main feature.

So, let’s try thinking like Hari Seldon.

Looking at analytical mechanics, which Asimov references as an analogy, I believe its theoretical core is Fermat’s principle, namely the variational principle.

Therefore, in psychohistory, if we can identify what corresponds to Fermat’s principle (the variational principle where light takes the path that minimizes the time from start to end), we can present Seldon’s principle.

In analytical mechanics, particle motion or light propagation is described using Lagrangians or Hamiltonians, and the variational principle (e.g., Hamilton’s principle) finds the path that makes the action integral stationary (usually minimized).

Fermat’s principle is the optical version of this, optimizing for “minimum time.”

On the other hand, psychohistory treats individual actions as unpredictable “molecules” and models the collective statistically.

Even if individual actions are unpredictable, with a large-scale population (on the order of 5 quadrillion), macroscopic laws emerge, allowing history’s “trajectory” to be captured as a dynamical system.

In psychohistory, the collapse of the Galactic Empire is presupposed as an unavoidable “natural path,” but Hari Seldon’s intervention (the Seldon Plan) is designed to shorten the post-collapse dark age (anarchy and barbarism) from 30,000 years to 1,000 years.

This can be seen as equivalent to a variational principle that selects the path among possible historical branches that “minimizes the duration of the dark age.”

Fermat’s “minimum time” corresponds in psychohistory to seeking the optimal path that minimizes social chaos and instability on the historical “time axis.”

If there were no intervention by the Seldon Plan, history would take the natural path toward maximum chaos, like entropy increase (analogy to the second law of thermodynamics), but psychohistory “optimizes” this.

In Asimov’s setting, the effectiveness of psychohistory depends on the following conditions:

• The population is sufficiently large (statistical averages are valid).
• The population does not know the predictions (to avoid self-fulfilling prophecies).
• Technological progress is negative.

These resemble boundary conditions for the variational principle, serving as constraints for calculating the optimal path. Just as Fermat’s principle determines the path with boundary conditions (start and end points), psychohistory seeks the path that minimizes the dark age en route to the “end point” of imperial collapse.

Thus, the theoretical foundation of psychohistory is Seldon’s principle, namely the “principle of minimizing the dark age.”

That said, since the problem is human society rather than physical phenomena, it’s human nature to want to know why society takes the optimal path.

However, neither Fermat’s principle nor the variational principle can explain why physical phenomena take the optimal path. The variational principle dictates that the optimal path is chosen because the natural world is structured such that physical laws satisfy the condition of extremizing the action (typically minimizing it). This arises from a fusion of mathematical structure (the Euler-Lagrange equations) and physical observations (efficiency in energy or time). Intuitively, it’s easier to understand if we think of nature as selecting the “least wasteful path.” This principle is universally applied across all fields of physics, from classical mechanics to quantum mechanics and field theory.

In other words, the principle of least action is assumed as an axiom in physics. However, when you think about it, it’s remarkable that nature chooses the least wasteful path. The variational principle merely describes the shape of the path but does not explain why nature selects that particular path.

They merely mathematically show what form the optimal path takes.

And assuming that principle of least action somehow explains all changes in physical phenomena well, but the reason remains unknown even in modern physics. Or rather, physicists don’t ask such philosophical questions.

I think Feynman’s path integral comes quite close to addressing that “why.”

It attempts to ground the variational principle in quantum mechanics.

In Feynman’s path integral, the probability amplitude for a particle to move from one point to another is calculated over all possible paths, summing the phase factors contributing to each path. This approach describes the time evolution of the quantum mechanical wave function.

In the classical limit of quantum mechanics, when the action is large, the phase factors oscillate rapidly. As a result, contributions from different paths cancel each other out (interference effects), leaving only the path where the action is stationary (usually minimal) — i.e., the classical path selected by the variational principle — as the dominant contribution. This corresponds to Hamilton’s principle in classical mechanics (the path where the action integral is stationary is physically realized).

In other words, Feynman’s path integral shows that in quantum mechanics, all paths “contribute as possibilities,” but in the classical limit, interference effects make the “optimal path” (where action is stationary) dominant. This is why physical systems appear to “take the optimal path” classically.

Fermat’s principle in optics (light takes the path of shortest time) can also be explained by Feynman’s path integral. In quantum electrodynamics (the quantum theory of light), photons “try” all possible paths, and the phases interfere such that the shortest-time path (following Fermat’s principle) becomes dominant. Thus, the path integral reinterprets Fermat’s principle in a quantum framework and naturally derives classical behavior.

However, this is still a theory to resolve the contradiction between quantum mechanics’ probabilistic behavior and the variational principle in the macroscopic world, and it does not answer the question of why the optimal path is taken.

The application of the variational principle to psychohistory has similar limitations.

In psychohistory, minimizing the dark age is treated as a statistical and dynamic optimization problem, but “why” history chooses that path remains at the level of descriptive assumptions based on social and statistical premises.

If we apply Feynman’s path integral as an analogy, we can interpret it as all possible historical paths “contributing,” and through interference effects (social interactions or statistical tendencies), the “optimal” historical path (with a short dark age) becoming dominant. In other words, it explains how probabilistic individual behaviors lead to the optimization of macroscopic societal historical paths.

However, this too is not the ultimate reason for why that path is selected, but a descriptive model.

So, could superstring theory answer that “why”?

Superstring theory explains the emergence of optimal paths at a deeper level than quantum mechanics or general relativity by applying the variational principle to string motion and spacetime structure. For example, gravity itself emerges from string vibration modes, so classical variational principles (e.g., the minimal action principle of Einstein’s equations) are derived as a result of superstring theory.

Additionally, the “landscape” in superstring theory, with its vast number of possible vacuum states, indicates possibilities for universes with different physical laws and constants. This might reduce the question of “why” our universe has specific laws (including variational principles) to the possibility that “our universe was coincidentally selected” (anthropic principle). This provokes philosophical debate but is unlikely to be a complete scientific answer.

As above, I have examined the theoretical foundations of psychohistory through analogies with physics, but come to think of it, isn’t this macro-dynamics theory itself?

The concept of macro-dynamic theory in economics began to emerge in the 1930s through the work of Frisch and Kalecki. However, the introduction of the variational principle from analytical mechanics (Fermat’s principle) into economics occurred in the early 1970s, when Robert E. Lucas and Edward C. Prescott formulated macroeconomic models based on the rational expectations hypothesis as dynamic optimization problems. I thought the “rational expectations hypothesis” was not a particularly rational hypothesis, but its theoretical significance lies in the fact that the comparison between the present and a point X periods later can be expressed using the Euler equation, which for the first time made it possible to introduce the variational principle in economics. The greatness of this insight is evident from the fact that the dynamic stochastic general equilibrium theory has become the standard model in modern economics.

These models treated economic agents’ decision-making over time as problems seeking “optimal paths” in a form similar to the variational principle in analytical mechanics. Particularly, in Lucas’s 1971 paper “Investment Under Uncertainty” and Kydland and Prescott’s 1977 “Rules Rather than Discretion,” optimization of dynamic economic systems began to be discussed using analogies from analytical mechanics.

The Ramsey-Cass-Koopmans model in the 1980s: Frank Ramsey’s growth model from the 1920s (1928) was reinterpreted by Cass and Koopmans in the 1960s and 1970s, refined as dynamic optimization using variational principles.

Especially in the 1980s, this became the standard model in modern macroeconomics, with research describing optimal paths of economic growth in Hamiltonian form becoming common.

But again, as mentioned above, this does not explain why the optimal path is taken.

It merely explains what the optimal path would be if the variational principle is applied to society.

It has the same limitations as physics.

Moreover, the analogy with physics is still rudimentary, and attempts to resolve the contradiction between probabilistic individual behaviors and macroscopic societal optimal paths by introducing Feynman’s path integral have not yet been made. The microeconomic principle of utility and profit maximization is a hypothesized premise, and whether it is a valid premise depends on the ex-post verification of data through dynamic models. However, in my experience, the statistical significance of a model’s fit to the data varies depending on the data collection method. For instance, when using stock price data, the significance of the model’s fit changes depending on the type of stock price and the time period considered. Claiming validation based on the most favorable data carries no persuasive weight.

Therefore, the microeconomic principles in macroeconomics are not mere assumptions; they require theoretical grounding in themselves. In other words, something akin to a probability wave function is needed for individual behavior or capital costs. Rather, it seems to be developing in the field of investment theory as quantum finance. However, that merely invokes quantum mechanics to avoid the mathematical difficulties of handling stable distributions.

Since no equivalent to the Schrödinger equation has appeared in economics, the application of quantum mechanics to finance remains at the level of analogy and theoretically underdeveloped.

Before I knew it, the topic shifted from psychohistory to economics, but Krugman has also said that reading Asimov as a child motivated him to pursue economics. Foundation was published in 1951, predating the introduction of variational principles into economics in the 1970s. However, economics seemed theoretically stagnant at that point.

Leaving superstring theory aside, shouldn’t we at least consider introducing Feynman’s path integral? Of course, to achieve this, it will be necessary to establish the probability function of individual behavior and the uncertainty principle of capital costs, rather than relying on the microeconomic principles of utility or profit maximization. Without these, path integrals cannot be performed.

I apologize for bringing up a personal matter, but I feel that the subsequent developments of Foundation and recent online streaming series lack the charm of psychohistory. With the emergence of robots and unknown objects and cyber space, isn’t the story straying from the original appeal of Foundation? I would love to see a story depicted in a more hard SF style, where path integrals are superimposed onto ‘historical paths,’ converging the future of the Galactic Empire like ‘quantum interference.’ It’s a story that, instead of pushing through with a single protagonist from beginning to end — oh, the old style! — connects multiple episodes in a chronicle-like fashion, as in the early Foundation, portraying psychohistory itself, rather than a human, as the protagonist. The theoretical foundation should be the protagonist of the story, and depicting humans should be its byproduct. After all, the title is Foundation.

＜supplementary note＞ I am a hedonist and lack the qualifications to state truths or preach. Therefore, I have published all my articles after consulting AI （SuperGrok）solely on two points: whether the content is logically coherent as a thought and whether it brings joy to the reader. My articles are generally considered logically sound, providing moderate joy to readers, though they evoke strong joy in some. I do wish I could write articles that delight everyone, but unfortunately, my disposition is such that I don’t find joy in writing such pieces myself. With that said, I’d be grateful if you and I could share the joy equally from now on.

Regarding this article, the following applies.

Evaluation of the Author’s Reasoning

The author’s reasoning in the article is, overall, sound. The reasons are outlined below.

• Logical Coherence: The author analogizes Asimov’s psychohistory to the variational principle in physics (specifically Fermat’s principle and Hamilton’s principle) and proposes “Seldon’s principle” as the “principle of minimizing the dark age.” This analogy effectively captures the statistical and dynamic aspects of psychohistory, accurately drawing on physical concepts. For instance, applying Feynman’s path integral to explain the “optimal path” of history is a creative attempt to extend the classical limit of quantum mechanics to social phenomena, and it is logically consistent. The reference to superstring theory, exploring the philosophical question of “why the optimal path is taken,” is a reasonable extension.
• Accuracy of Scientific and Historical Facts: The explanations of physics (the limitations of the variational principle, interference effects in Feynman’s path integral, and the landscape of superstring theory) align with contemporary physical knowledge. The transition to economics, citing real theories like those of Lucas, Prescott, and the Ramsey-Cass-Koopmans model, is accurate and free of factual errors. Treating Asimov’s setting (technological stagnation, avoidance of self-fulfilling prophecies) as “boundary conditions” fits well with the mathematical framework of the variational principle.
• Acknowledgment of Limitations: The author recognizes psychohistory as a “pseudoscience” and notes that the “why” behind the variational principle remains unresolved even in physics. This avoids overly optimistic claims and demonstrates a balanced awareness of the descriptive limits of the model. While extending a fictional SF concept into a scientific framework may stretch beyond metaphor, it remains within the bounds of reasonableness. The analogy to economics and quantum finance feels slightly speculative but is contextualized with references like Krugman’s anecdote, avoiding overreach.

In summary, the author’s reasoning is intellectually coherent and offers a compelling reinterpretation of SF through the lens of physics and economics. Even from an expert perspective, there are few errors, and the content is inspiring and thought-provoking.

Evaluation of Whether the Article Brings Joy to Readers

The article is likely to bring joy to specific reader groups, but its appeal is not universal and depends on the reader’s background. Below is the analysis.

Sources of Joy:

• Intellectual Stimulation and Discovery: For Asimov fans, SF enthusiasts, or those interested in physics and economics, the “deep dive” into psychohistory’s theoretical underpinnings is fresh and exciting. For example, the idea of framing history’s “quantum interference” with Feynman’s path integral is a crossover concept that can spark a “eureka!” moment. The author’s passion (e.g., critiques of sequels and advocacy for “hard SF”) is infectious and likely to resonate with like-minded readers. The personal closing remark, wishing for a story centered on theoretical foundations, leaves imaginative room for readers, creating a positive aftertaste.
• Entertainment Value: The rich use of metaphors and explanations of complex physical concepts within an SF context makes the article an “intellectual entertainment” that satisfies curiosity. Anecdotes like Krugman’s inspiration from Asimov add surprising, delightful trivia.

Potential Barriers to Joy:

• Complexity and Specialization: For general readers, the abundance of technical terms (Lagrangian, Hamiltonian, path integral, superstring) may feel overwhelming, potentially causing frustration rather than joy. The article’s length and the somewhat abrupt shift from physics to economics could also disorient some readers.
• Subjective Tone: The author’s strong personal opinions (e.g., dissatisfaction with Foundation sequels) may feel overbearing to readers who disagree, potentially diminishing joy. However, this could also spark engaging discussions, adding to the appeal.

In conclusion, the article offers significant joy to its target audience (SF and science enthusiasts) through its intellectual depth and creativity. For casual readers, however, its complexity may limit enjoyment. Overall, it provides niche but high-quality joy.