A History of Computation (Ron Pressler)

Finite of Sense and Infinite of Thought: A History of Computation, Logic and Algebra (Ron Pressler)

9 flashcards · Other · by lakesare

Visually imagine Leibniz.
Leibniz mansplaining monads to his friend and disciple, Queen Sophia Charlotte of Hanover, queen consort of Prussia, in front of the Charlottenburg Palace in Berlin
[Leibniz (1666)] Visually imagine stepped reckoner.
A replica of Leibniz’s stepped reckoner, the first mechanical calculator to perform all four arithmetic operations. The device was discovered in 1879 in an attic at the University of Göttingen by workers fixing a leak in the roof The "stepped reckoner" is so named because it uses a series of stepped gears or levers to perform calculations, rather than the traditional method of using a system of pulleys and gears.
But when I came to reckon up what remained to me of my capital, I found it amounted to something less than four hundred pounds!
To count, compute, or calculate, as in number or amount. to esteem or consider; regard as. Old English ( ge)recenian ‘recount, relate’, of West Germanic origin; related to Dutch rekenen and German rechnen ‘to count (up)’. Early senses included ‘give an account of items received’ and ‘mention things in order’, which gave rise to the notion of ‘calculation’ and hence of ‘being of an opinion’.
[Leibniz (1666)] Visually imagine characteristica universalis.
The universal language of all human thought. Frontispiece of Leibniz’s Dissertatio de arte combinatoria, printed in 1690 Universal language or notation that would allow one to express any mathematical or logical idea, and thus to reason and calculate with the same level of rigor and precision as with arithmetic and algebra. The concept has also been associated with the idea of a "formal language," a language that is defined by a set of precise rules and symbols, and can be manipulated using mat…
[Leibniz (1666)] What did Leibniz mean by: calculation VS meditation? Here Leibniz contrasts calculation employing a pen and paper with meditation, that can be done entirely in the mind and involves the direct manipulation of concepts rather than symbols.
calculation - syntax (pen and paper) meditation - semantics (manipulation of concepts)
Visually imagine auto-da-fé.
Public ceremony held by the Spanish Inquisition during which individuals accused of heresy were publicly tried, convicted, and punished. Luis González Obregon describes the three basic types of tunics used to distinguish those being punished by the Inquisition. These were the Samarra, Fuego revolto, and the Sambenito. The Samarra was painted with dragons, devils, and flames amongst which the image of the prisoner could be distinguished, signifying that the impenitent heretic was condemned to be…
How does auto-da-fé translate from Spanish?
Act-of-faith. Auto" is a shortened form of the Spanish word "auto sacramento" meaning "act of sacrament". "De" is a preposition meaning "of" and "Fe" stands for "faith". Together the phrase "Auto de fe" translates to "act of faith" referring to the religious ceremony and judgement held by the Spanish and Portuguese inquisition against those accused of heresy or other religious crimes.
In the Curry–Howard–Lambek correspondence, what does each of these stand for: Curry Howard Lambek?
Curry Howard - ⇒ ≡ → Lambek - category theory Another has said, “Have you heard of the Curry-Howard-Lambek isomorphism? … These three different theories … were developed separately — constructive logic, typed lambda calculus, and category theory — and the isomorphism says that these are actually identical. Why do these three completely separate theories have the same structure? Because all three of them are about composability.
What's Ron Pressler's view on Curry–Howard–Lambek correspondence?
The systems are in such harmonious correspondence because they all re-describe the same ancient description of that phenomenon. The three began to separate into different disciplines only towards the end of the nineteenth century and the beginning of the twentieth. Logic was separated from algebra by Gottlob Frege, immediately triggering the criticism that the correspondence between the two is an argument for having only one. Frege responded that there would obviously be a correspondence betwee…