Projects, scientific reflection, and poetry
The most financial of the wisdom books — deuterocanonical, written around 190 BC. Ben Sira quotes his own recovery rate on a bad debt (“hardly the half”), sizes suretyship “according to thy power”, locates the point of “enough” where gold starts costing sleep, weights the deferred feast by survival, places fraud “between buying and selling” at Becker's detection threshold, and prescribes the ledger two centuries before our era.
Read the article →Three narratives, one skeleton: geometric compounding. The buried talent versus the master's bank, the Matthew effect (“unto every one that hath”), Jacob's equity contract with Laban, the replicator equation revealed by the angel, Joseph's fifth smoothing fourteen years, and the doubled dream as a Bayesian signal crossing its action threshold.
Read the article →Three books, three registers. Qoheleth's hedonic treadmill, the eight portions against ruin, the discount rate of the ungodly in Wisdom, human capital, and then Leviticus — which almost by accident states the first known discounting formula (the jubilee) and the first known actuarial table.
Read the article →The Book of Proverbs contains an implicit economic theory — not an investment manual, but a set of claims made three millennia before stochastic processes. Six verses taken seriously and translated into equations: the negative median exponent of hasty wealth (13:11), the cost that compounds against you (21:5), the ant's buffer stock (6:6), the law σ√(ρ + (1−ρ)/n) (11:14), the symmetry breaking W* = −s/r₋ (22:7) and the dynastic growth condition (13:22).
Read the article →Accumulation studies the drift of a wealth process; survival studies its absorbing barrier at zero. Seven defensive laws, each proved then simulated: the convexity of L/(1−L), the variance drag μ − σ²/2, the gambler's ruin formula, the unstable fixed point D* = M/i of a debt, the collapse ODE of a pyramid scheme, and the Cramér–Lundberg cushion theorem ψ(u) = e−Ru/(1+θ) — exponential safety bought with saving.
Read the article →Wealth as a differential equation. Six objects, one story: the master equation dW/dt = sY + rW and its linear → exponential switch; the time to freedom T(s) and its hyperbolic sensitivity to the saving rate; geometric Brownian motion with its median at μ − σ²/2; the Kelly criterion and its asymmetric parabola; the accumulator's harmonic mean; and the crossing H(t) = W(t) that dates the midpoint of a financial life.
Read the article →Discovering equations from data (SINDy), encoding PDEs into a loss function (PINNs), and taming a vortex wake with reinforcement learning: this article tours the marriage between machine learning and physics, from reduced-order models (POD, DMD, Koopman) to a flow-control case study with HydroGym — with interactive animations throughout.
Read the article →How does an agent learn to act when it is never shown the right answer? This article introduces the agent-environment loop, Markov decision processes, Bellman equations and Q-learning, before opening onto Deep RL — with Manim-style animations for value iteration and model-free learning.
Read the article →How do you find the maximum of an expensive-to-evaluate function, with no gradient and no analytic form? This article covers Bayesian optimisation end to end: Gaussian processes, SE and Matérn kernels, the three families of acquisition functions (PI/EI, UCB, entropy), and the full loop. It includes a Manim animation and two interactive demos, with applications to hyperparameter tuning and uncertainty quantification for frost alerts.
Read the article →The Kalman filter solves a fundamental problem: how to fuse noisy measurements and the known dynamics of a system to obtain the best possible estimate of its state? This article introduces the state-space model, derives the prediction and update equations, explains the Kalman gain and its geometric interpretation, and shows why this filter is the optimal linear MMSE estimator.
Read the article →When the covariance of a process depends on time and not just on lag, the classical Fourier spectrum fails. This article introduces time-varying frequency (TVF) data and builds the hierarchy of solutions — STFT, Wigner-Ville, and finally wavelets — explaining why the mother wavelet and its dilations offer adaptive resolution where Fourier cannot.
Read the article →In many time series — particularly financial returns — the variance is not constant over time. Some periods are calm, while others display intense volatility. This article introduces ARCH and GARCH models, which allow us to model conditional variance and the phenomenon known as volatility clustering.
Read the article →Many time series contain periodic components imposed by physics (seasonal temperature, ECG rhythms, communications signals). This post introduces the random-phase harmonic model, derives the autocorrelation, explains why the spectrum has "lines" at fixed frequencies, and extends to the realistic signal + noise setting with a clear link to ARMA approximations.
Read the articleBetween divine knowledge and acquired wisdom: a reflection on learning in the age of artificial intelligence. From the medieval origins of "infused knowledge" to our modern ocean of information, this text explores the tension between instant knowledge and knowledge gained through effort. Science is not beautiful because it knows everything, but because it pushes us to search, to explore, to fail certainly but to bounce back.
Read the articleThis article presents a principled construction of symmetric encryption schemes from pseudorandom generators. Starting from the analogy with the one-time pad, it explains how pseudorandomness enables indistinguishable encryptions in the presence of an eavesdropper. The discussion then extends to variable-length messages, stream ciphers, and shows why deterministic encryption and naive keystream reuse fail under multiple-message security.
Read the articleRecurrent networks introduce a key idea: a hidden state updated at every timestep. This post explains why vanilla RNNs struggle with long sequences (vanishing gradients), then shows how GRUs and LSTMs use gating mechanisms to control forgetting and memory. The focus is forecasting intuition, practical model choice, and a compact math view.
Read the articleModern cryptography relies on a subtle idea: a system can appear random without being truly random. This article introduces pseudorandomness, perfect secrecy, the limits of concrete security guarantees, and explains why the asymptotic, complexity-theoretic approach has become central to defining cryptographic security.
Read articlePerfect secrecy formalizes an extreme (and elegant) security guarantee: the ciphertext should reveal absolutely nothing about the message. This article introduces the information-theoretic definition, the indistinguishability experiment, the one-time pad, and Shannon's theorem explaining why perfect secrecy requires keys at least as large as the message space.
Read articleTime series forecasting is often presented as a specialized discipline, yet it naturally fits within the supervised learning framework. This article explains how forecasting problems are structured, how multi-step predictions are constructed, and why classical statistical models should always be compared with machine learning approaches in practice.
Read articleKerckhoffs' principle is a foundational concept in modern cryptography. It states that a cryptographic system must remain secure even if the encryption algorithm is fully known to the adversary, as long as the secret key remains unknown.
Read articleVigenère weakens simple frequency attacks but remains vulnerable. This article explains Kasiski's insight—repeated patterns reveal the key length—and connects classical cryptanalysis to the emergence of modern cryptographic definitions and security proofs.
Read articlePresentation of OpenSpot (FindSpot), a computer vision project for detecting and classifying parking spaces from images. The article compares several CNN architectures (MobileNetV3, EfficientNet, ResNet) with respect to accuracy, inference speed, and real-world deployment constraints.
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