The Innodative Disruptor

Information Flow from First Principles

Information reduces uncertainty about the future.

That single idea, taken seriously, is the whole program.1 Build probability from the ground up; put stochastic processes and real market data on that footing; derive the measures—entropy, mutual information, transfer entropy—that make “reduces uncertainty” a number; then follow the numbers outward into directed, higher-order networks of information flow between markets.

now t futures of Y alone given X’s past T X→Y = how much the fan narrows

How this is written

The style aims at the Feynman Lectures by way of Tufte: mathematics shown rather than hidden, one evolving toy model as the backbone, and figures that carry real weight.2 The reader these notes are written for is curious, wants to learn, and is not put off by mathematics—none of which is assumed beyond a willingness to follow an argument from the beginning.

Units publish here as they are written. Everything is a draft until the book says otherwise.

The units

Part I—Probability, processes, and the data

0 Data and measurement in draft
1 What probability is, and getting a feel for it planned
2 Bayes as the engine planned
3 Distributions, expectation, and dependence planned
4 Stochastic processes planned
5 Market data, and why we transform it planned
6 Predictive causality, and the spine model planned

Part II—Information theory

7 The core measures planned
8 Transfer entropy, derived and placed planned
9 Estimating information from finite samples planned
10 Why pairwise is not enough planned

Part III—Higher-order and networks

11 Symmetric higher-order information planned
12 Directed higher-order flow planned
13 Graphs, graphical models, and information networks planned
14 Learning the graph: machine learning and PGMs planned
15 Uncertainty in information networks planned

Part IV—Synthesis

16 Higher-order, multilayer information networks, and synthesis planned

Off the spine, and skippable: a pricing sidebar (binomial pricing to Black–Scholes–Merton, taken for its own sake), a fenced data-shelf practicum, and a workshop appendix. None of them gates the main path.


  1. The epistemic posture is Kepler’s: instrument-grade regularities, honestly measured, without a mechanism owed for each one. 

  2. The no-orphan-figures rule: every figure is regenerated by a named, seeded notebook, and one build script re-executes them all. Sources live in the repository