(φ (μ (λ)))
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www.phimulambda.org

https://tv.dyne.org/c/phimulambda

Uncovering underlying intersections between philosophy (φ), mathematics (μ) and logic (λ).

Other embeddings include:
- Computing
- Cognitive Science
- Linguistics
- Statistics

@DivyaRanjan1905
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Forwarded from wahdat al wujūd
It is interesting to note that Category Theory has elicited exactly the same reaction within the community of pure mathematicians that system-theoretic approaches have generated in the community of experimental or empirical scientists. Initially, category theory was dismissed out of hand by many mathematicians as at best a cumbersome language for stating well-known facts about algebraic topology. Later, when it became clear that category theory could answer important open questions in a variety of areas, it was conceded to be of some limited usefulness for specific applications, but still of no significance as an independent branch of mathematics. This attitude is still prevalent; indeed, just a few years ago, I served on the Executive Committee of the Department of Mathematics at SUNY Buffalo, when that department was in the process of hiring an eminent category theorist. A substantial group of senior faculty tried to block this appointment on the grounds that category theory was not real mathematics; they were dissuaded only with difficulty from writing to other departments to collect opinions on whether category theory was mathematics or not.


Robert Rosen, Old Trends and New Trends in General System Research
The bastard child of ML, Scheme and Coq. A programming language of the ML family, but inspired by Scheme's minimalism and syntactic structure and built on top of pure λ-calculus with dependent types, similar to Coq's. Made by ex-maintainer of GNU Emacs, Stefan Monnier:

https://gitlab.com/monnier/typer/
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Over the last week I have done the following with Guix:

- Got my Guix channel managed to use it as a testing ground for patches upstream

- Added GNU Emacs with Lucid toolkit to upstream

- Added my Emacs package, binder to Guix upstream

- Updated SBCL to 2.5.0

- Added two Spline Sans fonts to Guix

- Signed up to Emacs, Rust and Haskell development teams on Guix

- And, finally, sent a series of 44 patches to package a Rust terminal application, bottom
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Also, thanks to the good work of Hilton Chain and others, the Zig programming language (v0.13.0) has been fully bootstrapped from scratch and directly available to be installed and used on Guix.

Bootstrappability should be a requirement among language designers and compiler engineers. A language that cannot be bootstrapped is a nightmare to package securely and to build fully reproducible programs. It took a long time before Haskell achieved this, and even that has certain issues.

Guix currently is among a rare breed of GNU/Linux distributions that really care about bootstrappability. And why should anyone care? Well, because how can you trust a compiler if you can't rebuild it from scratch?

There are real benefits to bootstrappable builds for users, developers and distributors, check them here.
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W. Richard Stark, Lisp, Lore and Logic: An Algebraic View of Lisp Programming, Foundations and Applications (1990)
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John McCarthy, Generality in Artificial Intelligence (Turing Award Lecture) [1971]
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Forwarded from 𝙨𝙮𝙢𝙗𝙤𝙡𝙞𝙘𝙨
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Forwarded from Books
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1844. Grassmann publishes the first full exposition of his system, his Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik dargestellt and durch Anwendungen auf die ubrigen Zweige der Mathematick, wie auch auf der Statik, Mechanik, die Lehre vom Magnetismus und die Krystallonomie erläutert. Whereas on the title page of Hamilton’s Lectures on Quaternions, Hamilton was identified by a large array of titles and memberships, Grassmann’s title page identified him only as “Lehrer an der Friedrich Wilhelms Schule zu Stettin.” The book attracts almost no attention and about 600 copies of it were in 1864 used for waste paper.

Grassmann’s Die lineale Ausdehnungslehre (Linear Extension Theory) demonstrated deep mathematical insights. It also in one sense contained much of the modern system of vector analysis. This, however, was embedded within a far broader system, which included n-dimensional spaces and as many as sixteen different products of his base entities (including his inner and outer products, which are respectively somewhat close to the our modern dot and cross products). Moreover, Grassmann justifies his system by philosophical discussions that may have put off many of his readers. The abstractness of his presentation and the originality of his insights also contributed to the difficulties readers had in comprehending Grassmann’s message, as is evident from comments made by various mathematicians who had struggled with the book. Möbius, for example, labeled it unreadable, Baltzer reported that reading the book made him feel “dizzy and to see sky blue before my eyes,” and Hamilton wrote De Morgan that to read the Ausdehnungslehre he would have to learn to smoke.

1845. After Grassmann’s unsuccessful efforts to persuade Möbius to write a review of his book, Grassmann, at Möbius’s urging, writes a review of his own book—the only review his book received! He also publishes a paper containing a new discovery in electrical theory that he had derived using his new methods. The result: more neglect, until the 1870s when Clausius made the same electrical discovery and published it, only then realizing that Grassmann had preceded him.


Michael Crowe, A History of Vector Analysis (1969)
(φ (μ (λ)))
1844. Grassmann publishes the first full exposition of his system, his Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik dargestellt and durch Anwendungen auf die ubrigen Zweige der Mathematick, wie auch auf der Statik, Mechanik, die Lehre vom Magnetismus…
Apart from Abel (dying at age 24 out of dire poverty) and Galois (dying at 23 due to stupid politics), Grassmann suffered an unnecessarily cruel fate with regards to his mathematics. Goes on to say how a lack of being amongst the "chosen ones" can hamper your credibility.

Grassmann was prolific and too ahead of his time, he was able to foresee a vector space in its fullest manner, opening a whole new branch of mathematics. Without Grassmannians and exterior products you can do nothing in differential geometry.

No wonder that even though Grassmann didn't receive credit during a big part of his life, he receives only lip service today. Due to the lack of historical engagement among students and worse teachers of mathematics, nobody actually ever read a page of Grassmann's brilliant work, it's outrageous how they could put it to using as 'waste paper'.

He did not give up though, he went on to use his mathematics in physics, he studied linguistics for much of his later half, publishing one of the most comprehensive texts in Sanskrit and its relationship to Greek. His work on the Rig Veda is an often cited reference. Yet, no one today even in linguistics hears about Grassmann but only in passing, let alone compare his math and linguistics.

Just as Galois opened several branches of mathematics without living through any of them, Grassmann envisioned more things than what could be within the mathematical intuition of his time.
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The death of Pascal as described by E.T Bell in Men of Mathematics (1937)
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Forwarded from Programming Deadlock
11-ghuloum.pdf
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An Incremental Approach to Compiler Construction
Images created solely using mathematical equations by mathematical artist Hamid Naderi Yaganeh.
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