Learnt that Alan Turing intended to build a machine to calculate Riemann Zeta Function. This is how the blueprint looks like. Source: http://www.turingarchive.org/viewer/?id=118&title=1 …pic.twitter.com/CF3P1X7tMu
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Using this as a tapestry, weaving in the stories of Gleick, Strachey, and Landin's collaboration into this becomes easy: https://twitter.com/prathyvsh/status/1197525794245009408 … I now perceive what is happening as a meaningful unfolding story of humans collectively building up the idea of computation.
Its only half a page of this paper on History of Lambda Calculus by Barkley Rosser and he has already made me examine the way functions work inside a computer closer. He puts forth the idea that all functions are operationally unary even when defined as multi-arity.pic.twitter.com/qjKUI0dhpy
As the research deepens what I'm bumping against now is the opposition of Aristotelianism vs. Augustinism in Middle Age philosophical thought: https://twitter.com/prathyvsh/status/1207313250733314050 … Augustinian thought emphasized non-mechanizable intuition over Aristotelian mechanizable empiricism.
The characteristic number idea introduced by Leibniz here feels like a hidden link between logical transitivity and arithmetic/algebraic commutativity of multiplication on numbers: https://pron.github.io/posts/computation-logic-algebra-pt1 …pic.twitter.com/ThcfPFQ1XV
In terms of conceptual leaps, Gottfried Leibniz single handedly made significant contributions to the field of computation: Characteristica Universalis + idea of logical computation + built a mechanical computer + formalized binary arithmetic. And all these ~350 years ago!pic.twitter.com/WX6PU2AiV9
TIL in early days, algebra used to be known as “Universal Arithmetic”. Source: A Treatise on Algebra by George Peacock (1830) — one of the early treatise on symbolic approach to algebra https://archive.org/details/atreatiseonalge02peacgoog … /via https://pron.github.io/posts/computation-logic-algebra-pt2 …pic.twitter.com/D55eXLLegj
Interesting to note that in 1840s Babbage's algebra was speculated to turn powerful enough to express the structure and function of human body — its “muscles, integuments, membranes &c.” and “functions of respiration, digestion, and assimilation”. Source: https://pron.github.io/posts/computation-logic-algebra-pt2 …pic.twitter.com/iTpP2it2df
A recurrent idea I bump on in this research is that some of the well-known mathematical systems emerged out of religious beliefs. George Boole, inventor of Boolean Algebra, as an ecumenist who rebelled against the Trinity worship of his time. Source: https://pron.github.io/posts/computation-logic-algebra-pt2#the-monist …pic.twitter.com/MslWr6hcJi
This take on mathematical systems emerging out from faith based thought is outlined in the history of Victorian era Mathematics by Daniel J. Cohen: https://amzn.to/2NeEDKD pic.twitter.com/gbgLY5YxzW
Boole’s original algebra had a notion of time which seems to be curiously missing in modern treatments. Unearthing these sort of subtle details that are brushed under the rug for fitting the cast of modern treatises is a good reason to go prospecting the history of a field.pic.twitter.com/2SBLc0SHta
TIL about Automated Mathematician: https://en.wikipedia.org/wiki/Automated_Mathematician …, a discovery system written in Lisp by Douglas Lenat (of Cyc fame) via Douglas Hofstadter's foreword to Gödel’s Proof:pic.twitter.com/uyLI0eiKrS
Dana Scott’s recollection of how Lambda Calculus gets recycled every decade is well worth a watch for the personal anecdotes he shares. There’s also this instance of absurdity where he shares why the symbol ”Lambda” in Lambda Calculus was chosen :https://twitter.com/prathyvsh/status/1026069704090107906 …
If you follow the threads of evolution of technology closely in different domains, say linguistics and logic in this case, one can’t help but find a sort of consilience among disparate seeming domains. Here is Frege replacing subject/predicate by argument/function dichotomy:pic.twitter.com/EX6yfGNiWm
This ties together with the idea that there are links among disparate ideas appearing throughout the computational universe: https://twitter.com/prathyvsh/status/1152945019071766528 … Cf. Montague quantification (linguistics) has connections to continuations (functional programming): https://en.wikipedia.org/wiki/Montague_grammar …
I’d be compiling and serializing this stories of computation into a browsable website up next. Collecting materials for research, feel free to suggest any articles/books you think would enrich the narrative this way:https://twitter.com/prathyvsh/status/1198085261281779712?s=20 …
Robin Gandy, student of Turing, on ”the uncluttered mind”. If you are an entrant to the field of logic/scientific inquiry, it could be tempting to see this as an encouragement to forego learning about literature of a field to go at it with a “fresh mind”, but this could be naïve.pic.twitter.com/ge8y7v2lJw
Alan Turing was a generalist and read widely on very different topics. He was fluent in German and up-to-date in the mathematical advances of his time as can be seen in the references of his paper:https://twitter.com/prathyvsh/status/1168766689460150278 …
Gödel who produced a proof for God’s existence: https://en.wikipedia.org/wiki/G%C3%B6del%27s_ontological_proof … claimed Turing’s notion of computation as philosophically erroneous to model human cognition. Kleene rejected it as a “pie in the sky”. Source: https://pron.github.io/posts/computation-logic-algebra-pt3 …pic.twitter.com/2g5BjWDCdu
Finished this erudite three part essay on the history of intersection between computation, logic, and algebra by @pressron. I highly recommend this series to those interested in the history of computation:https://pron.github.io/posts/computation-logic-algebra-pt1 …
Conjecture: Alan Turing knew a thing or two about Poincare’s embezzlement at the three body problem of late 19th century: https://en.wikipedia.org/wiki/Three-body_problem#Special-case_solutions … (or one of the related threads) which inspired him to answer the Entscheidungsproblem in the negative: https://en.wikipedia.org/wiki/Entscheidungsproblem#Negative_answer …pic.twitter.com/e6BGOZ221o
Pretty interesting essay on type theory by @mrkgrnao here: https://colimit.net/posts/normalisation-by-evaluation/ … Breaks down the more complex concepts to their composites and gives interesting metaphors to ground them.pic.twitter.com/dACEPD1b7r
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