Introduction: chance as a method of knowledge, not as a renunciation of explanation#
The I Ching, or Book of Changes, is perhaps the oldest and most sophisticated oracle of humanity. Its procedure - casting stalks or coins to generate a hexagram - strikes many people as a simple game of chance, a superstitious practice whose answers would be relevant only by chance. Those who consult it, however, usually marvel at the uncanny pertinence of its answers: how does an apparently random mechanism offer advice so well-adjusted to the present situation?
This paradox - that chance can be a vehicle for meaning - is the starting point of our journey. Far from being an anomaly, this intuition resonates with the most advanced developments of contemporary science. The twentieth century has taught us that the sharp separation between an “ideal order” (knowable by pure reason) and a “sensible disorder” (mere imperfection) is unsustainable. In fields as diverse as mathematical logic, quantum physics, chaos theory, or computational statistics, chance ceases to be an obstacle to knowledge and reveals itself as a constitutive dimension of reality and as a powerful epistemological tool.
This article does not intend to “validate” the I Ching with science -an operation that does not hold epistemologically, because science does not validate hypotheses, it can only falsify them (Popper, 2002). Rather, it aims to show that a deep convergence exists between the vision of change embodied by the oracle and the most advanced ways of understanding reality that science offers us today. Both traditions, the ancient Chinese and the contemporary Western, coincide in the same gesture: learning to read the order in the apparent contingency.
Genesis of Western rationalism: Parmenides against Heraclitus#
To understand why chance was for centuries marginalized as a source of knowledge, it is necessary to go back to the foundational opposition between Parmenides and Heraclitus.
Heraclitus of Ephesus (c. 535-475 a.C.) maintained that change is the essence of reality: “everything flows” (panta rhei). The world is a perpetual becoming, a game of opposites that transform into one another. For Heraclitus, tension and strife are the mother of all things, and order (logos) is not a static structure, but the immanent law that governs change itself. The vision of Heraclitus in fact is very similar to that of the I Ching, a text aptly named the Book of Changes for precisely that reason.
Parmenides of Elea (c. 515-450 a.C.) postulated exactly the opposite: change is an illusion of the senses; the true being is one, immutable, eternal, and indivisible. Only what is can be thought; the non-being (change, multiplicity) is unthinkable. His poem On Nature established the bases of Western ontology: being is, non-being is not.
Although both positions had followers, it was Parmenides who imposed himself on the main stream of Greek thought. Perhaps this silent victory explains why the West has struggled to understand the I Ching: a culture that learned to distrust change cannot easily come to terms with an oracle that, from its title, proclaims itself as the Book of Changes. Plato, Aristotle, and the whole rationalist tradition inherited his contempt for change and his search for an immutable order. Plato transferred that immutable being to the world of Ideas; Aristotle, although more attentive to physical reality, maintained the primacy of substance over change and established the logical principles that governed Western science for two millennia.
One of those principles is the principle of the excluded middle, formulated explicitly by Aristotle: “of two contradictory propositions, one is true and the other false, there is no middle ground”. A thing is or is not; it cannot be both things at the same time. This principle is the pillar of classical logic and, by extension, of the scientific method that seeks univocal causal explanations.
However, the twentieth century has put this principle to the test. Quantum mechanics, with its Heisenberg uncertainty principle and the superposition of states, shows that a system can simultaneously be in apparently contradictory states until a measurement is performed. The famous Schrödinger’s cat is alive and dead at the same time before opening the box, and quantum reality does not respect the excluded middle. This erosion of classical logical principles is one of the clearest signs that the Parmenidean vision of a perfectly separable and univocal order does not fully explain the nature of the real.
The weight of words: chance, probability, coincidence, stochastic#
Before continuing, it is convenient to stop at the words with which we name uncertainty. Their etymology reveals a shared intellectual history.
- The Spanish word for chance - Azar - comes from the Arabic al-zahr (“die”). The die symbolizes the unpredictable, that which escapes a necessary order.
- Probability derives from the Latin probabilitas, from probare (“to prove, to demonstrate”). In classical rhetoric and philosophy, the probable was that which deserved assent but did not reach absolute certainty. It operated in the intermediate terrain of doxa (opinion), not of episteme (true knowledge).
- Coincidence is related to Casualness, which comes from casus (“fall, fortuitous event”). The casual is what happens by accident, without purpose or necessity.
- Stochastic derives from the Greek stokhastikós, from stókhosthai (“to aim, to conjecture”). It is related to stókhos (“target, objective”). The stochastic is the art of aiming at a target - a perfect image of the tension between a fixed objective and the shots that deviate due to random factors.
A common idea underlies all these words: an ideal order (certain, perfect) and an imperfect realization that deviates from it. For the classical Greeks, that ideal order was the logos or the Platonic Ideas; chance was what stained the sensible copy. This way of thinking would deeply mark Western science and statistics for centuries.
Platonic idealism: episteme fronting doxa#
Plato radicalized the opposition between the intelligible world (of Ideas) and the sensible world (Plato, s.f.). From Ideas it is possible to reach episteme: true, necessary, universal knowledge. The sensible world only fits doxa: opinion, probable belief but never certain. In this framework, the “probable” - to eikos - is precisely that which belongs to the scope of doxa. It is useful for practical life, but radically insufficient for true knowledge.
This legacy has permeated, in a way often unconscious, the way in which science and statistics conceive the relation between model and data. A linear regression model, for example, postulates an underlying structure:
$$Y = \beta_{0} + \beta_{1}X_{1} + \cdots + \beta_{k}X_{k} + \epsilon$$Here, the independent variables $\beta_{0} + \beta_{1}X_{1} + \cdots$ represent the ideal order (the “true” relationship between variables), while the error term $\epsilon$ collects everything that deviates from that order: imperfections of measurement, omitted variables, pure randomness. The classical objective is to reduce noise to approach as close as possible to the true structure -a direct echo of the Platonic project of ascending from sensible copies to the contemplation of Ideas.
Tyche and the Greek paradox: chance as a practical tool#
However, the relationship of the Greeks with chance was highly ambivalent. Along with the philosophical disdain for doxa and the probable, a practical recognition existed that chance -tyche- governed inescapable aspects of life. Tyche was the goddess of fortune, represented with a cornucopia, rudder, and wheel, symbolizing the instability of human assets. Her cult spread especially in the Hellenistic period, and cities adopted her as patroness to try to “domesticate” her whims.
But there is an even more revealing example of how the Greeks, despite their theory, used chance as a mechanism of justice: the kleroterion. It was a lottery machine, a stone slab with slots where the tokens of citizens were inserted. By turning a mechanism, those who would occupy public office or form part of the popular tribunals in the Athenian democracy were randomly selected (Hansen, 1991).
Why did the Athenians, so zealous of the logos and so distrustful of doxa, trust the selection of their rulers and judges to chance? Because they understood that election by vote or by influence was easily corruptible: money, fame, and oratory could twist the decision. Instead, the draw -klerosis- guaranteed that no particular interest could corrupt the process. Chance became thus a filter of subjectivity, a mechanism to prevent the ego, ambition, or power from tilting the scale.
This paradox is fundamental: the Greeks theoretically relegated chance to the world of imperfection, but adopted it pragmatically as the only means to reach just decisions in the public sphere. The Athenian democracy was not based on the “popular will” expressed in votes (that was seen as manipulable), but on the draw, which embodied equality and incorruptibility.
The I Ching: chance as a filter of the ego#
The parallelism with the I Ching is here remarkable. In the consultation of the oracle, the procedure of the draw (with yarrow stalks or coins) fulfills exactly the same function as the kleroterion: it neutralizes the interference of the conscious will, the desires, and the fears of the consultant. If the answer depended on direct interpretation without a random mediator, it would be impossible to distinguish between what the oracle “says” and what the consultant wants to hear.
The I Ching starts from the premise that change (yi) has a dynamic structure, but that to access it we need a procedure that temporarily suspends our subjectivity. The draw is not a recourse to “blind chance”, but a technology of de-centering that allows the configuration of the moment to manifest without being corrupted by the ego. Just as the Athenians trusted the kleroterion for the selection of magistrates because chance could not be bribed, the I Ching trusts random sampling for the generation of the hexagram because contingency does not obey our preferences.
This use of chance as a filter explains why, despite its apparent randomness, consultants experience an astonishing relevance in the answers. By surrendering to chance -instead of fleeing from it- an underlying structure is accessed that cannot be captured by the conscious mind when it is trapped in its own expectations. It is what the Chinese call wu wei: acting without forcing, letting the natural course unfold.
Carl Jung and synchronism: another form of connection#
To elucidate this experience of relevance, it is essential to speak of Carl Gustav Jung (1875-1961), the Swiss psychiatrist who wrote the foreword to the famous translation of the I Ching made by Richard Wilhelm in 1923 (Jung, 1982). Jung not only used the oracle in his investigations into the archetypes of the collective unconscious, but developed the concept of synchronicity to account for phenomena where events not connected by a causal relationship present a significant coincidence.
In his foreword, Jung contrasts the Western scientific method, based on the isolation of variables and the search for linear causes, with the Chinese approach, which attends to the total configuration of the moment. He writes:
“The actual language of the Chinese sage, however, seems to interest him more than the ideal form. The checkered tapestry of natural laws that constitute empirical reality possesses for him greater significance than a causal explanation of facts, which on the other hand must usually be separated from each other in order to treat them in an appropriate way.” (Jung, 1982)
And further on:
“The way in which the Yi Ching tends to contemplate reality seems to disapprove of our causalist procedures. The concretely observed moment presents itself to the ancient Chinese more as a fortuitous event than as the clearly defined result of concurrent and causal chain processes. The question of interest seems to be the configuration formed by casual facts at the moment of observation, and by no means the hypothetical reasons that apparently justify the coincidence. While the Western mind carefully sifts, weighs, selects, classifies, separates, the Chinese representation of the moment embraces everything, down to the smallest and most absurd detail, because all ingredients compose the observed moment.” (Jung, 1982)
For Jung, the I Ching does not operate under the principle of causality, but under that of synchronicity: an acausal but significant connection between the configuration of the draw and the situation of the consultant. Chance is not a noise that obscures an underlying causal chain, but the medium through which a totality with meaning is expressed.
This concept has a direct echo in contemporary science. Quantum mechanics, with its entanglement and its non-locality, has shown that correlations exist that cannot be explained by local causal interactions. Jungian synchronicity, while not claiming to be a physical theory, points in the same direction: reality can reveal non-causal orders that, nevertheless, are significant.
The limits of the rationalist ideal: Gödel, chaos, and quantum mechanics#
The twentieth century subjected the rationalist program inherited from Parmenides, Plato, and Aristotle to three fundamental shocks that forced a reassessment of the I Ching.
Gödel and the incompleteness of formal systems#
Kurt Gödel demonstrated in 1931 that any sufficiently powerful formal system (like arithmetic) is incomplete: true propositions exist that cannot be proven from within the system (Gödel, 1931). Furthermore, the system cannot prove its own coherence.
The philosophical consequence is immense: mathematical truth transcends any closed formalization. Even in the realm of the ideal, order does not allow itself to be captured completely in a system of finite rules. The Platonic dream of a total, closed, and demonstrative episteme vanishes (Hofstadter, 1979).
Chaos theory: determinism without predictability#
Chaos theory, developed by Edward Lorenz and others in the second half of the twentieth century, showed that non-linear deterministic systems can be unpredictable in the long term due to sensitivity to initial conditions (the “butterfly effect”) (Lorenz, 1963). Although the equations that govern the system are perfectly deterministic, a small variation in the initial state amplifies exponentially, making long-term prediction impossible.
Here the Platonic separation becomes fuzzy: order (determinism) generates its own unpredictability, which for any finite observer is indistinguishable from chance. “Noise” is not necessarily a material veil that hides a perfect Idea; it can be the expression of a non-linear dynamic with a fractal structure.
Quantum mechanics and the end of the external observer#
The experiments of Alain Aspect, John Clauser, and Anton Zeilinger (Nobel Prize in Physics 2022) with entangled photons confirmed the violation of Bell’s inequalities (Aspect et al., 1982; Aspect et al., 2022). This implies that, if locality is maintained (nothing travels faster than light), then realism must be abandoned: the properties of quantum systems are not predefined before measurement. The act of measuring does not reveal a pre-existing property, but participates in its definition.
Quantum mechanics does not allow an external observer who contemplates passively an objective world. Knowledge is situated, participatory, relational. This idea, central in interpretations like that of Copenhagen or the relational one (Rovelli, 1996), breaks definitively with the Platonic ideal of a spectator who accesses an immutable truth from outside.
Statistics of change: learning from variability#
Faced with these breaks, statistics and machine learning have developed approaches that no longer treat chance as a simple hindrance.
Bootstrapping (Bradley Efron, 1979)#
Bootstrapping is a resampling method that consists of repeatedly extracting samples with replacement from the observed data, and recalculating the statistic of interest in each replica (Efron, 1979). Through bootstrapping, an empirical distribution of the estimator is constructed without the need for strong parametric assumptions (normality, etc.).
Philosophically, bootstrapping abandons the pretense of accessing an external “true population”. Instead, it takes the sample as its own universe of exploration, and through generative repetition maps the implicit possibilities. It is a perfect example of what we call auto-sampling: knowing what cannot be known from outside by learning to read, over and over again, the interior of what one already has.
Regime-switching models#
In time series, Markov switching or threshold models recognize that parameters can change over time. Markov models in general capture the idea of states, each with its particular dynamics and particular structure of transitions toward other states.
This reminds us of the hexagrams of the I Ching and their moving lines. In fact, the I Ching could be seen as a Markov chain of 64 states and, depending on the sampling method we use -coins or yarrow stalks-, we will have different transition probabilities between those states. The structure is not immutable; it mutates, as the hexagrams transform by the movement of their lines. These models incorporate variability not as noise, but as part of the system’s dynamics.
Non-parametric models and machine learning: the flexibility versus interpretability trade-off#
Machine learning methods such as decision trees, random forests, neural networks, or support vector machines (SVM) share a fundamental characteristic: they do not impose a predefined parametric functional form or strong assumptions about the error distribution. Unlike classical linear regression -which assumes a linear structure with normal, independent, and homoscedastic errors-, these models “learn” the structure from the data, allowing complex interactions, non-linearities, and local effects.
This flexibility comes at a cost: interpretability. While a linear model offers coefficients that can be read as “partial effects” of each variable, a random forest or a deep neural network acts as black boxes: their predictive capacity is high, but they do not deliver a simple description of the underlying relationships.
This difficulty for interpretation is not a mere technical deficit; it has deep philosophical implications. If the reality we try to model does not allow itself to be trapped in simple functional forms or in univocal causal relationships, then the Platonic aspiration to reach a clear, eternal, and universally valid episteme reveals itself as inadequate. Not because reality is chaotic or irrational, but because its order is situational, emergent, and often non-linear. Knowledge, then, consists not in possessing an eternal formula, but in developing tools capable of adapting to the changing configuration of each context.
In this sense, machine learning resonates with the logic of the I Ching: the rule is not unique and eternal, but adjusts to the moment. The decision tree segments the space according to local conditions; the random forest averages multiple perspectives; the SVM traces complex boundaries that separate classes without assuming a simple geometric shape. All of them abandon the pretense of a universal truth expressible in a simple equation, and instead offer a situated utility, echoing George Box’s maxim: “all models are false, but some are useful”.
George Box: all models are false, but some are useful#
The statistician George Box synthesized this epistemological attitude in a phrase that has become famous:
“Essentially, all models are wrong, but some are useful.” (Box & Draper, 1987)
Box pointed out that no mathematical model (not even the laws of physics) captures reality in its entirety. The question is not whether a model is “true” -because it never will be- but whether it is good enough for the purpose at hand. This idea frees the scientist from the obsession with finding the hidden ideal structure, and orients them toward practical utility, empirical validation, and humility before complexity.
The I Ching operates exactly under that logic: it does not offer an “eternal truth” that predicts the future with certainty, but a configuration of the moment that, well interpreted, guides action. Its utility resides not in its correspondence with a fixed external reality, but in its capacity to generate sense and guidance in situations of uncertainty.
Convergence: chance, filter of the ego, and participatory epistemology#
The thread that connects all these points is the following: both the I Ching and certain Greek practices (the kleroterion) and contemporary scientific developments share an understanding that chance is not an obstacle to knowledge, but a mechanism that, well used, can neutralize the observer’s biases and reveal orders that otherwise would remain hidden.
- In the kleroterion, chance filters corruption and favoritism, making a more just democracy possible.
- In the I Ching, the draw filters the interferences of the ego, allowing the configuration of change to emerge without distortion.
- In bootstrapping, resampling filters parametric assumptions, letting the variability of the data speak for itself.
- In quantum mechanics, radical indetermination forces us to accept that the observer is not external, but part of the reality they describe.
In all these cases, the sharp separation between an “ideal order” (knowable by pure reason) and a “sensible disorder” (mere imperfection) collapses. Order manifests in dynamic processes, sensitive to the context and co-determined by the observer’s intervention.
Conclusion: learning to read inside oneself#
The skepticism that labels the I Ching as mere superstition starts from an idea deeply rooted in the Western tradition: that chance is an obstacle to knowledge, and that true knowledge consists of clearing it away to reveal an immutable structure. Twentieth-century science deeply eroded that idea. It has shown that determinism can generate unpredictability, that formal truth is incomplete, that measurement participates in the measured reality, and that the most useful models are those that, instead of eliminating variability, learn from it.
In this new landscape, the I Ching ceases to be a pre-scientific residue and reveals itself as a navigation technology that, with its own means, embodies a participatory and dynamic epistemology. The random draw is not a recourse to empty casualty, but an act of symbolic auto-sampling that allows reading the configuration of the moment, filtering the interferences of the ego in a way analogous to how the Athenian kleroterion filtered corruption in democracy.
As I wrote elsewhere: "to know what cannot be known from the outside, one must learn to read, over and over again, the interior of what one already has". The I Ching does it with stalks and hexagrams; contemporary science does it with resamplings, simulations, and flexible models. Both practices invite us to abandon the dream of an absolute truth, to embrace a knowledge that is situated, recursive, and always open to change.
How to Cite This Article (APA 7th Edition)#
If you wish to use or cite this work in your research or academic publications, please use the following reference:
Romero, D. (2026, March 25). Chance, Science, and the I Ching: A Convergence in Understanding Order and Uncertainty. El IChingón. https://elichingon.com/en/articles/chance-science-i-ching/
References#
- Aspect, A., Clauser, J. F., & Zeilinger, A. (2022). Experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science. Nobel Prize in Physics 2022. https://www.nobelprize.org/
- Aspect, A., Grangier, P., & Roger, G. (1982). Experimental realization of Einstein-Podolsky-Rosen-Bohm Gedankenexperiment: A new violation of Bell’s inequalities. Physical Review Letters, 49(2), 91–94. https://doi.org/10.1103/PhysRevLett.49.91
- Box, G. E. P., & Draper, N. R. (1987). Empirical model-building and response surfaces. John Wiley & Sons.
- Capra, F. (1975). The Tao of physics. Shambhala Publications.
- Efron, B. (1979). Bootstrap methods: Another look at the jackknife. The Annals of Statistics, 7(1), 1–26. https://www.jstor.org/stable/2958830
- Gödel, K. (1931). Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme [Sobre proposiciones formalmente indecidibles de Principia Mathematica y sistemas relacionados]. Monatshefte für Mathematik und Physik, 38, 173–198. https://doi.org/10.1007/BF01700692
- Hansen, M. H. (1991). The Athenian democracy in the age of Demosthenes. Blackwell.
- Hofstadter, D. R. (1979). Gödel, Escher, Bach: An eternal golden braid. Basic Books.
- Jung, C. G. (1982). Prólogo. En R. Wilhelm (Trad.), El libro de los cambios (5a ed., p. 23). EDHASA. (Obra original publicada en 1923).
- Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmospheric Sciences, 20(2), 130–141. https://doi.org/10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2
- Platón. (s.f.). República (Libros VI-VII).
- Popper, K. (2002). The logic of scientific discovery. Routledge. (Obra original publicada en 1935).
- Rovelli, C. (1996). Relational quantum mechanics. International Journal of Theoretical Physics, 35, 1637–1678. https://doi.org/10.1007/BF02302261
