What began as a five-line Python script to flip a coin 100 times turns into an exploration of what randomness actually is. Starting from the law of large numbers and the design of pseudo-random generators (the Mersenne Twister, rejection sampling), the essay asks whether quantum randomness could instead be a deterministic pattern sampled at coarse time intervals — an "odometer universe" that counts rather than rolls. It shows why a purely periodic or low-discrepancy source would leave a measurable statistical fingerprint (a bounded deviation instead of the √n growth that real quantum random number generators exhibit), and connects the idea to Boltzmann's ergodic hypothesis, Gerard 't Hooft's cellular-automaton interpretation of quantum mechanics, and the Hossenfelder–Palmer superdeterminism proposal. It closes on the block universe and Wolfram's computational irreducibility. All code and tables in the piece are real output. Originally published at recepcinet.com.
What began as a five-line Python script to flip a coin 100 times turns into an exploration of what randomness actually is. Starting from the law of large numbers and the design of pseudo-random generators (the Mersenne Twister, rejection sampling), the essay asks whether quantum randomness could instead be a deterministic pattern sampled at coarse time intervals — an "odometer universe" that counts rather than rolls. It shows why a purely periodic or low-discrepancy source would leave a measurable statistical fingerprint (a bounded deviation instead of the √n growth that real quantum random number generators exhibit), and connects the idea to Boltzmann's ergodic hypothesis, Gerard 't Hooft's cellular-automaton interpretation of quantum mechanics, and the Hossenfelder–Palmer superdeterminism proposal. It closes on the block universe and Wolfram's computational irreducibility. All code and tables in the piece are real output. Originally published at recepcinet.com.
Standard Quantum Mechanics posits that randomness is ontological, a fundamental feature of reality where outcomes (such as radioactive decay or wave function collapse) are governed by irreducible probabilities (the Born rule). In this paper, we challenge this paradigm through the lens of Computational Finitism. We demonstrate that "quantum randomness" is an emergent property of Computational Irreducibility within a strictly deterministic, finite-alphabet substrate. Using a 1D Modulo-9 Cellular Automaton with non-linear update rules, we generate sequences that pass rigorous statistical tests for randomness (Shannon Entropy > 99.4%, flat autocorrelation) without a single random number generator. Furthermore, we apply this framework to particle physics, modeling gamma emission not as a probabilistic event, but as a deterministic "sawtooth" clock ticking until it hits the Topological Resonance Boundary (TRB = 9), triggering a state reset and photon emission. We conclude that the universe does not roll dice; it computes them.
Randomness is a scarce and precious resource: cryptography, scientific simulation, gambling regulation, and even foundational physics all depend on being able to produce numbers that no one — not even the generator itself — could have predicted in advance. Classical computers cannot create such numbers on their own, because they are deterministic machines; every pseudorandom number generator (PRNG) is, in principle, a fixed algorithm whose entire output is fixed the moment a seed is chosen. Quantum random number generators (QRNGs) promise something categorically different: unpredictability guaranteed by the indeterminism of quantum measurement itself. This paper examines whether “true” randomness is achievable at all, surveys the physical arguments (rooted in Bell's theorem) that quantum measurement outcomes are not merely unknown but undetermined, and then asks a narrower, more computational question: can a machine-learning model tell the difference between the output of a well-designed PRNG and genuine entropy? We built and tested a small experimental pipeline comparing a deliberately flawed linear-congruential generator, a mildly weak variant, two industry-standard PRNGs (Mersenne Twister and PCG64), and operating-system entropy (as an accessible proxy for physically-sourced randomness). Gradient-boosted and logistic-regression classifiers detected the flawed generator with 100% accuracy but could not beat chance (49–51%) against modern PRNGs, mirroring published results in the cryptographic and quantum-optics literature. We conclude that while true randomness is very plausibly achievable through quantum processes certified by Bell-inequality violation, no black-box statistical or machine-learning test — however sophisticated — can, on principle, certify the difference between a good PRNG and true randomness from output alone; the distinction is one of provenance and physical mechanism, not detectable pattern.
In role-playing games (RPGs), players are called upon to assume the role of a character moving in an imaginary environment and facing several challenges. Their success or failure often depends on randomizers like cards or dice. Regarding the latter, the most commonly used in RPGs are the Platonic solids with the addition of the ten-sided die. They are commonly simulated through classical computers, however, since true randomness is not in their nature, they can only generate pseudorandom numbers. On the contrary, quantum computers exploit the nondeterministic nature of quantum mechanics, so they are perfect candidates for truly random simulations in games of chance. For this reason, this paper proposes and tests various quantum circuits for sampling uniformly distributed discrete values within a fixed range, corresponding to the number of faces of the dice. The simulations reveal the pure randomness of the output of the implemented circuits. They were then used to generate random numbers within a three-dimensional dice-rolling game.
How much of quantum mechanics can a machine with no dice fake? This deposit accompanies the article "The Universe with No Dice" (Quest for Entropy #1), which builds a fully deterministic, classical toy universe and shows that a bounded observer inside it counts Born-rule statistics and double-slit interference to within about one percent of the quantum prediction, with the model's exact failure mode published as a falsifiable limit rather than hidden in error bars. Article: https://questforentropy.substack.com/p/the-universe-with-no-dice Code and reproduction instructions: https://github.com/masteris777/quest-for-entropy-the-universe-with-no-dice
This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a (Wittgensteinian) philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics (like Bohmian mechanics or 't Hooft's Cellular Automaton interpretation) are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low (or even zero) probability, their very existence implies that the no-signaling principle used in proofs of randomness of outcomes of quantum-mechanical measurements (and of the safety of quantum cryptography) should be reinterpreted statistically, like the second law of thermodynamics. In appendices I discuss the Born rule and its status in both single and repeated experiments, and review the notion of 1-randomness \nintroduced by Kolmogorov, Chaitin, Martin-Lo"f, Schnorr, and others.
Abstract This is a review of the issue of randomness in quantum mechanics, with special emphasis on its ambiguity; for example, randomness has different antipodal relationships to determinism, computability, and compressibility. Following a (Wittgensteinian) philosophical discussion of randomness in general, I argue that deterministic interpretations of quantum mechanics (like Bohmian mechanics or ’t Hooft’s Cellular Automaton interpretation) are strictly speaking incompatible with the Born rule. I also stress the role of outliers, i.e. measurement outcomes that are not 1-random. Although these occur with low (or even zero) probability, their very existence implies that the no-signaling principle used in proofs of randomness of outcomes of quantum-mechanical measurements (and of the safety of quantum cryptography) should be reinterpreted statistically, like the second law of thermodynamics. In three appendices I discuss the Born rule and its status in both single and repeated experiments, review the notion of 1-randomness (or algorithmic randomness) that in various guises was investigated by Kolmogorov and others and treat Bell’s (Physics 1:195–200, 1964) Theorem and the Free Will Theorem with their implications for randomness.