- chris dixon, 2017

aristotle → euclid → descartes → leibniz → boole → shannon → frege → hilbert → turing

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**Aristotle**'s logic, found in the six-part book the Organon, had been a central part in philosophy for more than 2,000 years. Trying to improve on it was considered almost impossible.- Immanuel Kant once commented that since Aristotle, logic has been
*"unable to take a single step forward, and therefore seems to all appearance to be finished and complete."*- All men are mortal.
- Socrates is a man.
- Therefore, Socrates is mortal.

- The example above, "Socrates" can be replaced by any name and the argument remains valid. The logical structure and validity are ∴ determined by "all", "are", "is" and "therefore".
- Aristotle's logic namely inspired Euclid's Elements (-300s), which described geometry as visual diagrams and became the default system until René
**Descartes**showed how to represent geometry as formulas (1630s).- Around 30 years later, the shift from diagrams to formulas lead to the development of calculus, by Newton and Leibniz, independently.

George **Boole** (1815-1864) is often considered a mathematician but he saw himself as a philosopher. He wanted to represent Aristotle's logic with formulas, like Descartes had done with Euclides's ideas.

- His goal was to create a symbolical ideographic universal language representing all possible mathematical and scientific knowledge. He proposed his system in The Laws of Thought (1854), which eventually created the field of mathematical logic.
- Claude
**Shannon**realized that Boole's system of logic could be physically encoded in electrical circuits. He described the process in a 1937 electrical-engineering paper, which was inspired by Boole's 90-year-old philosophical ideas. - His work inspired vast amount of progress in combining electrical circuits, which eventually led to the invention of the transistor in 1947. Phones in 2016 had about 3.3bn transistors.

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Gottlob **Frege** (1848-1925)

**Frege**developed a much more advanced logical system in Bergriffsschrift (1879), the logic system taught in philosophy and computer science classes today.- Ferge's language of meaningless symbols manipulated by defined rules, concept-script, separated objects from predicates and used quantifies ( ∀, ∃ ) to develop some of computer science's fundamental concepts like recursive functions and variables.
- Philosophy after Frege was about questions of language, not knowledge. Two of his disciples were Russell and
**Wittgenstein**→ linguistic turn - Unexpectedly, Ferge's work also exposed many logical mistakes in Euclid's Elements, which had been the standard in logical rigor (math bible) for ≈2000 years, and sparked a crisis in the foundation of mathematics: what about physics which is built
*on top*of math?- The restructuring of mathematics' foundations was mostly led by David Hilbert, who specified a program to formalize all of mathematics' logic.
- Until the 1930s, this program was the focus of a core group of logicians, notably Russell, Gödel, Von Neumann, Church and obvio, Turing.

**Turing**'s 1936 paper *"On Computable Numbers, with an application to the Entscheidungsproblem"* was a response to Hilbert's *decision problem*, which asked if there's an algorithm capable of determining if any arbitrary mathematical statement is true or false.

- His insight came from creating a mathematical model of a computer to find that the computation could still be done correctly even if the computer is limited to few simple actions, but since the only was to find the result is to do the computations, ∄ an algorithm that fulfills Hilbert's
*decision problem*.

The significance of Turing's paper lies not in its answer but in the blueprint for computer design Turing provided along the way.

*Shannon showed how to map logic onto the physical world, Turing showed how to design the computer in the language of mathematical logic.*

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this is a collection of notes that i've written over time, mostly for myself. in the spirit of working with garage doors open, i've published them and open sourced this website. works under

*writing*are original, my notes a mix of thoughts with quotes from the artwork subject of the note.⠀

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### writing

- oct 2023 · on numbers
- aug 2023 · after cinema
- oct 2022 · on cinema
- ongoing · on ai

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#### notes

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**books**- beginning of infinity, david deutsch
- desierto sonoro, valeria luiselli
- llano en llamas, juan rulfo
- recuerdos del porvenir, elena garro
- laberinto de la soledad, octavio paz
- hitchhicker's guide to the galaxy, douglas adams
- amor en los tiempos del colera, gabriel garcía márquez
- homo deus, yuval noah harari
- salvar el fuego, guillermo arriaga
- a moveable feast, ernest hemingway
- ride of a lifetime, bob iger
- sin querer queriendo, roberto gómez bolaños

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**articles**- paragraphs on conceptual art, sol lewitt
- discrete image, bernard stielger
- how to do philosophy, paul graham
- taste and design, paul graham
- aristotle invented the computer, chris dixon
- to firmly drive common prosperity, xi jinping
- how the enlightment ends, henry kissinger
- the question concerning technology, martin heidegger
- people aren't meant to talk this much, ian bogost
- after babel, jonathan haidt

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**film**- century of the self, adam curtis
- hitchcock vs hitchcock, andré bazin
- why marvel movies aren't cinema, martin scorsese
- succession, jesse armstrong

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*symbols*- ∴ (therefore)
- → (if then)
- ↔ (if and only if)
*⤷*(consequence of)- ≔ (definition)
- ⫫ (independent from)
- ∵ (because)
- ∃, ∄ (there exists/does not exist)
- ∈, ∉ (belongs to/does not belong to)

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writing keeps ideas in space

speech lets them travel in time

we use paintings to decorate space

and music to decorate time

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find the way by moonlight

see the dawn before

the rest of the world

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unconscious time, no peace of mind,

falling in space but still alive.

sketching the future in a single line,

everything's spinning, cannot sit down.

moments in space, places in time,

thoughts penciled in, now come to life.

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*As of today, no one knows how to translate paintings, flowers or music into language. Their beauty is implicit and exclusive to their form, which is why it's so hard to explain how a particular piece of art makes us feel.*⠀ ⠀

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#### Eduardo Gonzalez

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### notes

- aristotle invented the computer, chris dixon