1. Repetitio :: Between Rennaissance and Age of Reason
2. Questio :: What is a "representation" ?
3. Exercitio I:: Binary counting.
4. Presentatio I :: Baroque calculating machines
5. Lectio :: The steampunk period
   • Jacquard Loom
   • Charles Babbage
   • Ada Lovelace
   • George Boole
6. Presentatio II :: Binary adder.

• represent (v.)
  late 14c., "to bring to mind by description," also "to symbolize, serve as a sign or symbol of; serve as the type or embodiment of;" from Latin repraesentare "make present, set in view, show, exhibit, display," from re-, intensive prefix , + praesentare "to present," literally "to place before," from praesens) "present, at hand, in sight; immediate; prompt, instant; contemporary," from present participle of præesse "be before (someone or something), be at hand," fro prae- "before" (see pre-) + esse "to be" (from PIE root *es- "to be").

• The description or portrayal of someone or something in a particular way.
  1. The depiction of someone or something in a work of art.
  2. A picture, model, or other depiction of someone or something.
  3. (in some theories of perception) a mental state or concept regarded as corresponding to a thing perceived.
  Name some examples of X being a representation of Y.

• polymath, KH FRS, Victorian gentleman etc.
• mathematician, philosopher, inventor and mechanical engineer
• "father of the computer"
• author of "difference engine" (could solve polynomial equations of 7th order)
• author of "analytical engine" (a generic programmable computer)

• daughter of Lord Byron
• mother promoted Ada's interest in mathematics and logics, student od Augustus de Morgan
• associate of Charles Babbage ("Enchantress of Numbers")
• author of the first computer program (algorithm for computation of Bernoulli numbers)
• died young of uterine cancer

Note A, p. 694 :: Again, it [the Analytical Engine] might act upon other things besides number, were objects found whose mutual fundamental relations could be expressed by those of the abstract science of operations, and which should be also susceptible of adaptations to the action of the operating notation and mechanism of the engine . . . Supposing, for instance, that the fundamental relations of pitched sounds in the science of harmony and of musical composition were susceptible of such expression and adaptations, the engine might compose elaborate and scientific pieces of music of any degree of complexity or extent.

The distinctive characteristic of the Analytical Engine, and that which has rendered it possible to endow mechanism with such extensive faculties as bid fair to make this engine the executive right-hand of abstract algebra, is the introduction into it of the principle which Jacquard devised for regulating, by means of punched cards, the most complicated patterns in the fabrication of brocaded stuffs...We may say most aptly that the Analytical Engine weaves algebraical patterns just as the Jacquard-loom weaves flowers and leaves.

• another Victorian gentleman
• at 17 years of age "a thought struck him suddenly, which became the foundation of all his future discoveries"
• author of "Laws of Thought or An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities" (1854)
• Boolean algebra
• being a professional prof cost him his Life

• united algebra and logic
• replaced propositional form of Aristotle's logic to equation-like formulae and introduced "laws" which can solve them
• logical formulae could contain more than two subject-predicate propositions (i.e. no A that is B is C that is D)
• introduced logic functions and truth tables