Information Flow from First Principles
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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.
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.
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The epistemic posture is Kepler’s: instrument-grade regularities, honestly measured, without a mechanism owed for each one. ↩
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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. ↩