00. Models of Reality

The models of reality

We describe reality with basic structural models. Much of data science happens at the points where they meet.

Nowadays, Data Science stands on four fundamental pillars. They sustain the field and provide it with the tools to solve the problems we face.

These models are:

• Language: signs, text, syntax, meaning...
• Code: symbol, instruction, process, memory, calculation...
• Maths: vectors, algebra, proof, statistics, logic...
• Systems: signals, causality, transformations, circuits, experiments...

On the shoulders of giants

Every scientist is part of a beautiful search for knowledge and insight. We want to understand things, make them better, fix them. Others came before us and opened the gates of an immense library of scientific knowledge, and kept the sturdy walls of this shining beacon of knowledge.

We want to acknowledge here some authors that informed and inspired these texts. They are worth your time if you want to read them yourself:

• Saussure showed that language is a system of signs.
• Chomsky found the rules of generative grammars.
• Kolmogorov gave possibility its mathematics: a space, its events, their measure.
• Turing reduced calculation to symbols moved by rules.
• Von Neumann built the machine that moves them.
• Oppenheim taught us to read the signals.
• Shannon stood between them all. He counted the symbols, weighed them by probability, and found the hidden meaning in surprise.

Reading list:

• Ferdinand de Saussure. Course in General Linguistics (1916).
• Noam Chomsky. Syntactic Structures (1957). It's short and readable. The more technical original is "Three Models for the Description of Language" (1956).
• Andrey Kolmogorov. Foundations of the Theory of Probability (1933, English edition 1950). It's slim but dense.
• Alan Turing. "On Computable Numbers, with an Application to the Entscheidungsproblem" (1936). Charles Petzold's The Annotated Turing walks through it line by line.
• John von Neumann. First Draft of a Report on the EDVAC (1945). For something more readable, try his short book The Computer and the Brain (1958).
• Alan V. Oppenheim. Signals and Systems, with Alan S. Willsky (2nd ed., 1997).
• Claude Shannon. "A Mathematical Theory of Communication" (1948). The book version, The Mathematical Theory of Communication with Warren Weaver (1949), adds Weaver's essay for non-specialists, which is a perfect entry point.

We stand on their shoulders, and on those of many more. But Shannon is, in my opinion, the first true Data Scientist. The founder of a field that is not statistics, not computation, not systems, not language, but something that needs all four, and that transcends them in application and technology.

No one should call themselves a Data Scientist until they read the essay A Mathematical Theory of Communication.

But what is Data?

It is not obvious why, but we need to simplify this question. You may not know that Data is the plural form of the singular "Datum", from Latin dare, to give. A thing given. So what is a "Datum"?

We established the four pilars as the basis of Data Science, so we should be able to answer in all four of them. The LCMS models (Language, Code, Math, Systems) produce four different starting points.

• Language: A Datum is a statement of fact, or by extension the answer to one question.
• Code: A value stored in memory that a program can read and act on.
• Math: One Datum is a function mapping an entity to a value.
• System: A Datum is each of the values a Signal measures.

We can see a pattern emerging. A datum is something given. Something individual. Something linked to source. A mark.

A datum is a recorded difference.