The Meaning of Being Digital

1
The Meaning of Being Digital

• Harry Halpin
• University of Edinburgh
• http//www.ibiblio.org/hhalpin

2
What is Digitality?

• The field of computing is rife with the
  presumption of a shared definition of digitality.
• Yet defining what suffices for being digital is
  not clear.

3
Being Digital Informal Definition

• Need a definition that covers both digital
  phenoumena like digital computers and DC
  Power
• Being digital is simply having a difference that
  does not make a difference.

4
Goodman on Marks and Difference

• Goodman defined finitely differentiable Given
  some physically distinguishable marks, it is
  possible to determine for any given mark whether
  it is identical to another mark or marks.
  (Languages of Art, 1968).
• Despite the variation in handwriting, we
  recognize hand-written letters from a finite
  alphabet.

5
Equivalence and Digitality

• So, equivalence classes of marks are types.
• Given a finite number of types in a system, a
  system is digital if any token falls into one of
  the types.
• Therefore, in between any two types there can not
  be an infinite number of other types.

6
Towards a Definition of Analog

• This is not to say there are characteristics of a
  token which do not reflect its assignment in a
  type.
• In an analog system, every difference makes a
  difference, since between any two types there is
  another type that subsumes a unique
  characteristic of the token.
• An number analogy
• integers digital
• continuous analog
• But not reducible to mappings on number lines!
  These are exemplars, not definitions, numbers
  work at a level of abstraction removed from flex
  and slop

7
Digitality and the World

• Lewis (1971) took aim at Goodman's interpretation
  of digitality in terms of determinism by arguing
  that digitality was actually a way to represent
  continuous systems using discrete combinatorics.
• Example discrete mathematics can represent
  continuous subject matters.
• So, analog analogue of world.

8
Engineering Digitality

• Haugeland agrees that digital systems are always
  abstractions built on top of analog systems
  (1981).
• Digitality allows perfect reliability and
  flawless copying.
• Since once a system is in a digital state
  (type), it does not change unless it is
  explicitly made to change (1985)
• So digitality is a mundane engineering notion,
  root and branch. It only makes sense as a a
  practical means to cope with the vagarities and
  vicissitudes, the noise and drift, of earthy
  existence(1981).

9
Defining Digitality

• Digitality is a convergence between a subjective
  abstract mode of thought and an objective system
  that physically implements the very same
  abstraction.
• Contra Mueller (2007), physical systems are
  digital objectively.
• Yet there are multiple ways one can legitimately
  state a system is digital, since it is dependent
  on a mode of thought.

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Abstract Modes of Thought

• When reading letters in a book, we concentrate on
  the letters, not any minor variations in the
  quality of the paper.
• It is a convergence between a discrete mode of
  thought, our alphabet (and language in general),
  and a medium, the book.
• Different modes of abstract thought can
  interpret the same physical system as digital in
  different manners. The marks 11 can mean eleven
  in decimal and three in binary notation.

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Physical Implementations

• If we attempt to use an analog system as if it
  were digital and it does not have the proper
  physical characteristics, such as writing letters
  in water, then digitality seems to elude us.
• Why can some differences dont make a
  difference? How can one define the boundaries of
  digital states?
• How can this be physical so that it can
  convergence with a mode of thought (form of
  life, i.e. an activity and way of use that is
  also physical)?

12
Fuzzy Boundaries

• Take the phenomenon of being late or early to a
  meeting, and even on time.
• One cannot be 12.3936 percent late, or 39.56
  percent on time.
• Fundamentally, there are three discrete states,
  so these states are not analog-as-continuous, for
  it seems they resist measurement on a continuous
  scale.
• With being on time and being late there is
  often no difference that makes a difference, so
  these states could be considered a digital mode
  of thought.
• Think also out of/in the desert or night/day
  time
• But what is the physical substrata that interacts
  with this?

13
Converging Boundaries

• To physically implement digitality, there must
  be a small chance that a system can be considered
  to be in a state that is not part of the discrete
  states given by the abstract mode of thought.
• The fuzzy physical boundary allows within a
  margin of error a discrete boundary decision to
  be made.
• So a system is digital if that buffer created by
  the margin of error minimizes the chance the
  system is not part of a discrete state in the
  mode of thought.

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How To Be Digital

• The hands on a clock can be on the precise
  boundary between markings on the clock, just not
  for very long.
• It does requires a continuous amount of time to
  go from one digital state to another, but this
  time must be so infinitesimal that it can be
  ignored by the mode of thought.
• This is why digital systems always have a
  temporal component, such as the double clock in
  digital circuits that Smith notes.
• While there are differences that make differences
  in physics, on the level of the digital those
  differences don't make a difference its noise

15
Higher and Lower Order Digitality

• In a given level of a digital system, the margin
  of error does not propagate upwards to other
  levels of abstraction.
• This former level of abstraction is first-order
  digital, and other latter levels can be
  higher-order digital.
• First-order digital is created from analog
  (analogue of world) physics ala Lewis.

16
Higher-Order Analog?

• Higher-order analog on top of lower-order
  digital states.
• In order to capture analog music stored in a
  digital format, one should sample the wavelength
  twice as often as the highest frequency of the
  waveform, and this leads the human to have an
  analog experience of the music. Is this really
  analog?
• Digital and Analog are based is modes of thought,
  as our phenomenology of them is constrained
  cognitively. These constraints can be objectively
  studied and world can be thought of as
  metaphysically analog, contra Wheelers digital
  ontology.

17
Sampling and Digitality

• To create physical systems through engineering,
  we build on physical substrata that have low
  probabilities of being in states that do not map
  to the discrete states of the level of
  abstraction in our mode of thought.
• Mueller a transistor can be in a voltage state
  that is clearly of type on or off, but it can
  also be on the borderline between the two - it
  just so happens that our computing machines are
  made with systems that do not usually get stuck
  in intermediate states (2007).

18
Parting Thoughts

• Digitality is not only a physical process, but a
  mode of thought.
• The vast proliferation of digital technologies is
  possible because there are physical substrata,
  some moreso than other, which support the
  implementation of the digital and give us its
  advantages, flawless copying and perfect
  reliability in a flawed and imperfect world.

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Cited Works

• Goodman, Nelson (1968). Languages of Art An
  Approach to a Theory of Symbols. Indianapolis
  Bobbs-Merrill.
• Haugeland, John. (1981). Analog and Analog,
  Philosophical Topics 12 213-226.
• Haugeland, John. (1985). Artificial Intelligence
  The Very Idea. Cambridge, Mass. MIT Press.
• Lewis, David. (1971). Analog and Digital, Nous
  5 321-327.
• Mueller, Vincent (2007). Representation in
  Digital Systems In Proceedings of Adapation and
  Representation. Paris, France. http//www.interdis
  ciplines.org/adaptation/papers/7
• Smith, Brian Cantwell (1996). On the Origin of
  Objects. Cambridge, Mass. MIT Press.
• John Archibald Wheeler. (1990) Information,
  Physics, Quantum The Search for links. In W.H.
  Zurek (ed.) Complexity, Entropy, and the Physics
  of Information. Redwood Addison-Wesley.

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Any Questions?

• Merci!