on numbers

numbers were the first writing system to exist. it started with the same symbol being used for all numbers: IIIIIIIIIIIII

  • earliest improvement: group symbols together.
  • allowed people to go from tallying "another one, another one..." to counting "forty-one, forty-two..."

a bigger improvement came along with the idea to have different symbols for different numbers.

the best example of this new kind of writing systems are Roman numerals. they used 7 symbols (I, V, X, L, C, D, M) and 3 main rules:

  • symbols must be ordered by decreasing value, from left to right.
  • having symbols side-by-side is the same as adding them together.
    • VVIII = 5+5+1+1+1
  • a symbol cannot be repeated if it can be combined.
    • VVIII → VV=X → XIII
  • these simple rules made Roman numerals faster and more accurate for mathematics than tally symbols, which is why they stayed in use for ~2400 years, from around -900 until the 1500s.

the biggest leap Roman numerals made was allowing people to manipulate numbers without needing to count each symbol individually: their design implicitly teaches people how to do math.

  • the system, however, relied on M as as the symbol with the highest value (1000).
  • this meant that performing operations on large numbers could only be done by carefully counting each instance of the same symbol (=counting tally marks).
  • simple operations on large numbers became very difficult and error-prone → new system needed

1500s, writing numbers as letters

Hindu-Arabic numerals were invented in 9th century India but only became commonly used until the 1500s.

  • they use a set of 10 symbols (0-9) and only one single rule: the value of a digit depends on its position in the number.
    • 002=2 ⠀ 020=20 ⠀ 200=200
  • this rule allows the system to be universal and work like an alphabet: every number in existence can be represented in a unique, distinct and understandable way (just as no word exists that can be said but can't be written).
  • their design also simplified complex operations and significantly reduced chances of errors: an avalanche of new mathematical progress followed shortly after their adoption (Galileo, Newton, the Enlightenment, birth of modern Physics...)

the leap in progress from Hindu-Arabic numerals is a consequence of deep insights on how math, numbers and design work.

every numeral system incorporates certain knowledge about which relationships of numbers are the most interesting to use.

  • tally symbols → Roman numerals: new knowledge about addition and rules about arbitrarily defined symbols.
  • Roman numerals → Hindu-Arabic numerals: complex mathematical ideas (commutativity, associativity, distributivity) expressed through profound design ideas (abstract representation, parsimony, spatiality).

∴ design and mathematical insights work together:

  • math and design —science and art— are entangled.

the main advantage of improving the design of a numeral system is making it useful for unpredictable innovations and progress.

Roman numerals allowed new ideas and uses of numbers like salaries, taxes and interest rates to spread, but their design also deeply limited scientific progress.

⤷ no major abstract mathematical discovery was made during the ~2400 years they were in use.

  • when thinking about how our numeral system could be limiting further unknown progress, the question becomes: how does one make the leap to a smarter way of writing numbers?

note mentions

  • ego-simple-noframe

    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.











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

    ⠀ ⠀

    ⠀ ⠀

    writing keeps ideas in space

    speech lets them travel in time

    we use paintings to decorate space

    and music to decorate time

    ⠀ ⠀

    ⠀ ⠀

    find the way by moonlight

    see the dawn before

    the rest of the world

    ⠀ ⠀

    ⠀ ⠀

    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.

    ⠀ ⠀

    ⠀ ⠀

    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.

    ⠀ ⠀

    ⠀ ⠀

    Eduardo Gonzalez





  • the discrete image

    stiegler agrees with derrida's critique of the opposition of the signifier and the signified, which proposes that language is always already writing, and in order for language to be written, it must already be a writing, a system of traces, a grammatic of discrete elements.

    image mental ∄ → image mental ≔ image object

    • ∄ image-object sans image mental,
    • ∄ image-mental sans image object.
    • image-object lasts, image-mental ephemeral.
    • ∄ image → ∄ imagination sans memoire ∴ question de l'image porte sur traces et inscriptions, ≈ écriture.


    • barthes proposes that photography is ēpokhē to time, memory and death.
    • manipulation is the rule of the digital photo, contrary to the essence
    • one cannot confirm if what I see in a digital photo exists or not ∴ analogico-digital breaks with bazin's objectivité de l'objectif, l'intentionalité (phenomenology)
    • distinguish true and falls is harder, exploited and generalized w/mass media, dangerous panic decomposing social bond.
    • digital technology allows us to manipulate and transform information unlike analog technology.
    • infinitively manipulable but still a photo, it keeps something from the this was.
      • This was but there is something that isn't quite right. this is because analog photo is a technical synthesis.

    3 main types of reproducibility have constituted and overdetermined great epochs of memory and the relations to time in the west. (letter, analog, digital)

    • reproducibility of the letter (written → printed)
    • analog reproducibility (cine, photo → walter benjamin)
    • digital reproducibility
    • analogico-digital image combines 2 reproducibilities (digital, analog) ∴ shows they are not opposed and need to be overcome.
    • the analog image is ∴ always discrete since its reality effects are determined by the photographic (framing, dof) and literal context in which it is inserted. seems continuous but is discrete.

    director/editor's job is to hide the discontinuity by playing with it (analysis), continuity then comes from spectatorial synthesis (done by good artists)

    • animated image ≔ plurality of discontinuous images sequentially connected
    • spectatorial synthesis: the belief that this was is. made by audience (retinal) persistance and expectations of sequential connections
    • discontinuity dissolves all the more effectively the more cleverly it is orchestrated
    • production/realization.

    discretization opens new artistic, theoretical and scientific knowledges of the image.

    • digitization allows the this was to be decomposed analytically by discretizatizing the continuous.
    • barthes's photographic reality effect has now been integrated into all techniques of digital treatment simulation.
    • spectator's relation to the image is ∴ an analytic relation as well.
      • ⤷ the question is the relation between synthesis and analysis.

    3 kinds of images (analog, digital, analogico-digital) → 3 kinds of intuitive technical knowledges (conditions of image production) → 3 different kinds of belief.

    • the visual image is synthetic in 2 ways: synthesis as belief, the this was effect, is a combination of 2 syntheses (spectator and camera). spectator is affected in the way he synthesizes the image.
      • This requires an image-object ∴ technology.
      • synthesis from the subject comes from its knowledge of the technical conditions of an image-object's production.
    • each image, either analog or digital, contains both knowledge and gaps in knowledge. This new awareness leads to a different form of understanding and knowledge.
      • analogico-digital technology of images opens an epoch of analytic apprehension of the image-object.
        • since synthesis is double, new analytic capacities → new synthetic capacities.
        • this discretization breaks up a continuity ∴ changes the way the observer's viewing. (discretization concernant regard est transformé)
    • since greece we live in an era of the relation to language, shaped by the generalization of alphabetic writing on numbers that gave rise to logic, philosophy and science. the analogico-digital is of the same order.
    • the adoption of alphabetic writing made analysis and synthesis of language much easier. generalization → discretization.
    • relation to the analog image is going to be very discretized as digitazion techniques of animated images become widespread. this will open a critical access to the image and a chance to develop a culture of reception.

    now there's two syntheses (spectator + camera): evolution of technical synthesis → evolution of spectatorial synthesis.

    • new image-objects will create new mental images and another intelligence of movement (not knowledge of the image but a new techno-intuitive knowledge). this will be influenced by other knowledges which opens up "la chance"
    • technology gives us the chance to look at cinema in a different way. analysis (production) and synthesis (consumption) are more connected, making cinema similar to literature.
      • alphabetic writing reveals the discrete characters of language
      • reading and writing (can't do one without the other)
      • implies the rethink of hollywood's schema of analysis/production - synthesis/consumption.
    • technology will make it possible to watch a movie analytically, making text and tv closer than now.
      • we will be able to navigate though the flow of images in a nonlinear way, with toc and indexes (like books), true hypermedia?
    • technological synthesis is not a replica nor double, like writing is not a replication of speech.
    • life (anima, mental image) is always already cinema (animation, image object).

    discrete image

    • since greece we live in an era of the relation to language, shaped by the generalization of alphabetic writing on numbers that gave rise to logic, philosophy and science. the analogico-digital is of the same order.