Reason: Bounded Variability and the Incoherence of Uncaused Events
A Study of Dice and Systems of Chance or Why Apparent Randomness and Bounded Outcomes Cannot Coexist Without Implied Causality
Preface
This essay advances a central argument: that systems displaying bounded variability cannot coherently be described as "uncaused." Bounded outcomes, by their very nature, imply governing constraints. These constraints, whether or not we fully understand them, are the hallmark of causality. Using dice as both physical objects and conceptual models, this analysis will explore the impossibility of uncaused yet bounded events. It will trace the development of dice, the human manipulation of chance, and the philosophical treatment of randomness and determinism, showing how bounded variability fundamentally presupposes causal structure.
Is my argument correct, or it just the case that the word is not only queerer than we imagine, but queerer than we can imagine? That is to say, are uncaused yet bounded events a feature of the world? Maybe the world is a hologram, but I’m not buying that one either.
Introduction
Dice have long been a symbol of randomness and chance. Whether in games, gambling, or probability theory, they seem to embody unpredictability. Yet, dice also exemplify an important physical truth: despite apparent randomness, their outcomes are bounded and limited. No throw of the dice results in an infinite range of outcomes; they fall within strict physical constraints. This essay will argue that this bounded variability is incompatible with the notion of uncaused events. By examining dice in historical, physical, and philosophical contexts, the essay will show that causality underpins the very structure of variability that dice (and by extension, many natural phenomena) exhibit.
I. Dice as Microcosm of Bounded Systems
The conceptual distinction between fair and unfair dice sets the stage. A fair die, in theory, assigns equal probability to each face. Yet no physical die achieves this ideal. Manufacturing imperfections, wear, environmental influences, and human handling all introduce variability.
However, crucially, even imperfect dice operate within bounds. A six-sided die lands on one of its six faces, not on an undefined or infinite range of outcomes. Whether weighted, worn, or thrown poorly, the outcome space is constrained. This bounded variability points directly to causal structure: the shape, mass distribution, and surface of the die, combined with the thrower's action and environmental conditions, determine the range of possible outcomes.
Thus, dice illustrate a broader principle: variability exists, but it is never limitless. Boundaries suggest forces and constraints at work. They imply a system of causes, however complex.
II. Historical Pattern: Manipulating the Boundaries of Chance
The human relationship with randomness is ancient. Early humans used natural objects like knucklebones and pebbles as randomizers. By at least 3000 BCE, crafted dice appear in Mesopotamia and the Indus Valley. Of course, with 300,000 years or so of human history for the development of mechanisms of chance, this story almost certainly just scratches the surface.
Humans quickly recognized bias in outcomes. Whether accidental (from irregular shapes) or deliberate (through weighting or carving), dice have long been manipulated to favor certain results. Roman texts document concerns about loaded dice, and archaeological evidence supports this with finds of asymmetrical and tampered dice.
Yet, even manipulated, dice remain bounded. Loaded dice do not generate arbitrary results; they shift probabilities within a constrained outcome space. This manipulation presupposes causality: physical adjustments affect outcomes in predictable ways. The exploitation of bias would be impossible in a truly uncaused or unbounded system.
III. Systems Thinking: Dice Within Causal Networks
The outcome of a dice throw arises from a network of causal factors:
Die properties: geometry, weight distribution, material texture.
Human action: force, angle, spin imparted during the throw.
External apparatus: the dice cup, table surface, and elasticity.
Environmental factors: air currents, temperature, and surface vibrations.
No component alone determines the result, but together they form a causal web. The dice's bounded variability emerges from these interactions. Hypothetically, even remote influences like airflows exert some effect, though they are practically negligible.
This causal system refutes the notion of uncaused outcomes. Boundedness results from the structured interaction of system components. Without such a network, variability would be unbounded and chaotic. The constraints observed in dice outcomes are the signature of causality at work.
IV. Philosophy of Randomness and Causality
Polysemy of Randomness
Randomness is a polysemous term. It is used to describe:
Epistemic randomness: unpredictability due to observer ignorance.
Statistical randomness: observed distribution of outcomes.
Algorithmic randomness: incompressibility of information.
Ontological randomness: events without cause.
Of these, only the last claims uncaused events. The others describe human limitations or outcome patterns, not metaphysical claims about causality.
Boundedness Implies Causality
Bounded variability is incompatible with ontological randomness. Boundaries in outcomes imply structure and constraint, which in turn imply causative factors. Systems like atomic decay, though unpredictable at the individual level, follow strict statistical laws. The presence of half-lives and predictable transmutation patterns indicates underlying causative regularity.
Even quantum phenomena like entanglement operate within mathematical constraints. Though they challenge classical causality, they do not represent unbounded behavior. Instead, they display structured, lawful outcomes.
Fallacy of Category Confusion
Equating statistical description with ontological randomness commits a category error. Statistics describe frequencies of outcomes but remain silent on causality. The presence of a statistical pattern neither proves nor disproves causality.
V. Epistemic Limits vs. Ontological Claims
Human inability to trace every causal chain does not imply the absence of causality. Complexity, not causelessness, accounts for unpredictability.
Pragmatic boundaries are necessary for analysis. Infinite regress of causes is a theoretical concern, but practical investigation focuses on dominant, proximate factors. This bounded scope aligns with the observable structure of systems.
In dice throws, as in natural systems, proximate causes dominate outcomes. Human action, surface conditions, and die properties outweigh distant, theoretical influences. The consistent boundedness of results underscores the operation of causal structures.
Summary and Conclusion
Bounded variability serves as empirical evidence of underlying causality. Dice, whether fair, loaded, or poorly thrown, consistently yield outcomes within defined limits. These limits arise from the structured interaction of system components, not from uncaused events.
The polysemous nature of "randomness" fosters confusion between unpredictability, statistical description, and ontological claims of causelessness. Careful analysis reveals that bounded variability is fundamentally incompatible with the notion of uncaused events. Boundedness implies structure, structure implies constraints, and constraints imply causes.
Dice, as microcosms of this principle, demonstrate that apparent randomness emerges from complexity and human epistemic limits, not from an absence of causality. Extending this understanding to broader natural phenomena supports the view that uncaused, yet bounded events are conceptually incoherent. Observed systems, from dice rolls to atomic decay, operate within bounds that reveal their causal underpinnings.
The empirical world, when examined carefully, offers no clear example of truly unbounded, causeless events. Systems with bounded variability are systems with structure — and structure implies cause.
Reading List
De Baets, A. (2017). Responsible history: Essays on historical methodology. Berghahn Books. https://www.berghahnbooks.com/title/deBaetsResponsible
Hacking, I. (2006). The emergence of probability: A philosophical study of early ideas about probability, induction and statistical inference. Cambridge University Press. https://www.cambridge.org/core/books/emergence-of-probability/9852017A380C63DA30886D25B80336A7
Haigh, T. (2018). The cult of statistical significance: How the standard error costs us jobs, justice, and lives. MIT Press. https://www.fulcrum.org/concern/monographs/cr56n193q
Ladyman, J., Ross, D., Spurrett, D., & Collier, J. (2007). Every thing must go: Metaphysics naturalized. Oxford University Press. https://philpapers.org/rec/LADETM-5
Mlodinow, L. (2008). The drunkard's walk: How randomness rules our lives. Pantheon. https://www.amazon.ca/Drunkards-Walk-Randomness-Rules-Lives/dp/0307275175
O’Connor, T., & Franklin, C. (2018). Free will and determinism. Stanford Encyclopedia of Philosophy. Retrieved from https://plato.stanford.edu/entries/freewill-determinism/ https://philpapers.org/rec/OCOFW
Petersen, A. M. (2015). The physics of foraging: An introduction to random searches and biological encounters. Princeton University Press. https://www.amazon.ca/Physics-Foraging-Introduction-Biological-Encounters/dp/1107006791
Taleb, N. N. (2007). The black swan: The impact of the highly improbable. Random House. https://www.stat.berkeley.edu/~aldous/157/Books/Black_Swan-sub.pdf