“To say that algebra means anything else than just its own forms is to mistake an application of algebra for the meaning of it”…
— Charles Sanders Peirce
“If Computation is a Science of Abstracting [1][1a] [1b] [1c] our Material World – and – Mathematics is the Science of uncovering Patterns [2] and Relationships in our Material World – and – Linguistics is the Science of Language [3] – and – “The limits of my language mean the limits of my world” – Ludwig Wittgenstein [4] – then – Is Computation, Mathematics and Language – Human Sensemaking [5] [5a] tools [6] for the Semantic [7] Abstraction [8] of an emergent Material World?”…
Computation — a Semiotics Perspective — https://blogs.commons.georgetown.edu/cctp-748-spring2018/2018/05/05/the-meaning-behind-computer-systems-a-semiotics-perspective/
“Logic and mathematics are nothing [9] but specialised linguistic structures”…
- Jean Piaget
Footnotes:
[1] Foundations of Computer Science – http://infolab.stanford.edu/~ullman/focs.html – Computer Science: The Mechanisation of Abstraction – http://infolab.stanford.edu/~ullman/focs/ch01.pdf
[1a] How Aristotle Created the Computer – by Chris Dixon – https://a16z.com/2017/08/01/how-aristotle-created-the-computer-atlantic/
[1b] Geometrical Thinking Offers a Window Into Computation – https://www.simonsfoundation.org/2021/04/07/geometrical-thinking-offers-a-window-into-computation/
[1c] Abel Prize celebrates union of mathematics and computer science – The work of winners László Lovász and Avi Wigderson underpins applications from Internet security to the study of networks – https://www.nature.com/articles/d41586-021-00694-9
[2] Mathematics as the Science of Patterns – Mathematics as the Science of Patterns – https://www.maa.org/book/export/html/116188
[3] The Science of Linguistics – https://www.linguisticsociety.org/resource/science-linguistics
[4] Ludwig Wittgenstein – https://plato.stanford.edu/entries/wittgenstein/
[5] Sensemaking, the core skill for the 21st Century… – https://link.medium.com/ePUU5TriOdb
[5a] – Richard Feynman sharing his perspective on the nature of Computer Science at the 6 minute mark – “you are doing it for a human purpose” … -https://m.youtube.com/watch?v=9miKIWIYi4w&feature=youtu.be
[6] New Semantic Computational Tools for Human Sensemaking – Deep Learning Algorithms – https://twitter.com/vincentgoualher/status/1321352369850982401?s=20 – and – Sensing with tools extends somatosensory processing beyond the body – https://www.nature.com/articles/s41586-018-0460-0 – The Mind-Expanding Ideas of Andy Clark – The tools we use to help us think – from language to smartphones – may be part of thought itself – https://www.newyorker.com/magazine/2018/04/02/the-mind-expanding-ideas-of-andy-clark
[7] The Semantic Mind – https://link.medium.com/bDYfYkDiOdb
[8] Sloppy Models, Differential Geometry, and Why Science Works – https://m.facebook.com/santafeinstitute/videos/sloppy-models-differential-geometry-and-why-science-works/775975239729485/ – and – Making sense of raw input -https://www.sciencedirect.com/science/article/pii/S0004370221000722
[9] – What Data Can’t Do – When it comes to people – and policy – numbers are both powerful and perilous – https://www-newyorker-com.cdn.ampproject.org/c/s/www.newyorker.com/magazine/2021/03/29/what-data-cant-do/amp
Mathematics is a semantic language of abstraction for a discrete digital classical Material World
Computation is a semantic language of abstraction for a continuous analog quantum Material World
Both are illustrations of emergence — the evolution of Mental World abstraction in response to the increasing dimensionality of an emergent complex Material World
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