Beyond causality
In order to bridge the yawning gulf between the humanities and the sciences we must turn to an unexpected field: mathematics
By Gordon Gillespie
https://aeon.co/essays/to-better-understand-the-world-follow-the-paths-of-mathematics
mathematics
Katherine Johnson died #OTD in 2020.
Her work included calculating trajectories, launch windows, and emergency return paths for Project Mercury spaceflights, including those for astronauts Alan Shepard and John Glenn, and rendezvous paths for the Apollo Lunar Module and command module on flights to the Moon. Her calculations were also essential to the beginning of the Space Shuttle program, and she worked on plans for a mission to Mars.
Dutch-Swiss mathematician and physicist Daniel Bernoulli was born #OTD in 1700.
He is particularly remembered for his applications of mathematics to mechanics, especially fluid mechanics, and for his pioneering work in probability and statistics. His name is commemorated in the Bernoulli's principle, a particular example of the conservation of energy.
https://en.wikipedia.org/wiki/Daniel_Bernoulli
Books by Daniel Bernoulli at PG:
https://www.gutenberg.org/ebooks/author/41345
Charles Lutwidge Dodgson (aka Lewis Carroll) was born #OTD in 1832.
An interesting comment from one proofreader at @DProofreaders : "It is said that Queen Victoria enjoyed the Alice books so much that she sent for all the author's works, and was then appalled to find herself confronted by mathematics."
"Curiosa mathematica, Part I: A new theory of parallels" by Dodgson, Charles L. coming soon at PG.
Lewis Carroll at PG:
https://www.gutenberg.org/ebooks/author/7
"My methods are really methods of working and thinking; this is why they have crept in everywhere anonymously."
Happy Birthday Emmy Noether!!
She made many important contributions to abstract algebra. She proved Noether's 1st and 2nd theorems, which are fundamental in mathematical physics. She developed theories of rings, fields, & algebras. In physics, Noether's theorem explains the connection between symmetry & conservation laws.
![Portrait of Emmy Noether, around 1900.
Unknown author Publisher: Mathematical Association of America [3], Brooklyn Museum [4], Agnes Scott College [5], [6] - Emmy Noether (1882-1935), Archived
The photograph shows Noether as a poised young woman, reflecting the academic environment of the era. Dressed in period attire typical of the late 19th to early 20th century, she appears composed and introspective, a visual contrast to the intellectual revolution she would later ignite in mathematics.](/proxy/post_attachment/656703/c37623fa20.jpg "Portrait of Emmy Noether, around 1900.
Unknown author Publisher: Mathematical Association of America [3], Brooklyn Museum [4], Agnes Scott College [5], [6] - Emmy Noether (1882-1935), Archived
The photograph shows Noether as a poised young woman, reflecting the academic environment of the era. Dressed in period attire typical of the late 19th to early 20th century, she appears composed and introspective, a visual contrast to the intellectual revolution she would later ignite in mathematics.")
Years After the Early Death of a Math Genius, Her Ideas Gain New Life
A new proof extends the work of the late Maryam Mirzakhani, cementing her legacy as a pioneer of alien mathematical realms.
By Kristina Armitage
French mathematician and philosopher René Descartes died #OTD in 1650.
He is known for his influential arguments for substance dualism, where mind and body are considered to have distinct essences, one being characterized by thought, the other by spatial extension. He has been dubbed the "Father of Modern Philosophy" and the "Father of Modern Mathematics."
https://en.wikipedia.org/wiki/Ren%C3%A9_Descartes
Books by René Descartes at PG:
https://www.gutenberg.org/ebooks/author/44
Why nothing matters
It took centuries for people to embrace the zero. Now it’s helping neuroscientists understand how the brain perceives absences
By Benjy Barnett. Edited by Richard Fisher.
Edited 350d ago
I'm tinkering with an argument based on algorithmic complexity that if it were possible to make something like an "automated mathematician" or "automated scientist", then these would be expected to eventually produce outputs that we humans would be unable to distinguish from random noise.
Getting the whole argument just right is fiddly, but the basic idea is this. You feed some kind of theory into the AM/AS, which is a black box. It churns on this and spits out a result, which is added to the theory (I'm neglecting the case that the result is inconsistent with the theory). It can now churn on theory + result 1. For any given and potentially very large N, after doing this long enough, it's churning on theory + result 1 + result 2 + ... + result N. Whatever it spits out will be dependent in particular on results 1 - N. When N is large enough, unless you know these results you will not be able to understand what it outputs because the output will almost surely depend critically on one or more of results 1 - N. In other words, the output will look like noise to you. If the AM/AS is appreciably faster at producing results than people are at understanding them, there will be an N beyond which no one can understand the output up to that point. It'll become indistinguishable (unable to be distinguished) from random noise.
If you're into software development, this would be analogous to a software system that generates syntactically-correct code and then adds that code as a new call in a growing software library. If you were to run this long enough, virtually all the programs it generated that were short enough for human beings to have any hope of reading and understanding would consist almost entirely of library calls to code generated by the system. You'd have no idea what any of this code did unless you studied the library calls, which you wouldn't be able to do beyond a certain scale. If the system were expanding the library faster than you could read and understand it, there'd be no hope at all.
I'll leave it as an exercise to the reader whether this is a desirable thing to do and whether it's happened yet. I would offer, though, a question to ponder: what reason is there to believe that a random number generator hooked up to an inscrutable interpreter produces human flourishing, for any given meaning of "human flourishing" you care to use?
#tech #dev #mathematics #AutomatedMathematician #AutomatedScientist #AI #GenAI #GenerativeAI #ThoughtExperiment
Getting the whole argument just right is fiddly, but the basic idea is this. You feed some kind of theory into the AM/AS, which is a black box. It churns on this and spits out a result, which is added to the theory (I'm neglecting the case that the result is inconsistent with the theory). It can now churn on theory + result 1. For any given and potentially very large N, after doing this long enough, it's churning on theory + result 1 + result 2 + ... + result N. Whatever it spits out will be dependent in particular on results 1 - N. When N is large enough, unless you know these results you will not be able to understand what it outputs because the output will almost surely depend critically on one or more of results 1 - N. In other words, the output will look like noise to you. If the AM/AS is appreciably faster at producing results than people are at understanding them, there will be an N beyond which no one can understand the output up to that point. It'll become indistinguishable (unable to be distinguished) from random noise.
If you're into software development, this would be analogous to a software system that generates syntactically-correct code and then adds that code as a new call in a growing software library. If you were to run this long enough, virtually all the programs it generated that were short enough for human beings to have any hope of reading and understanding would consist almost entirely of library calls to code generated by the system. You'd have no idea what any of this code did unless you studied the library calls, which you wouldn't be able to do beyond a certain scale. If the system were expanding the library faster than you could read and understand it, there'd be no hope at all.
I'll leave it as an exercise to the reader whether this is a desirable thing to do and whether it's happened yet. I would offer, though, a question to ponder: what reason is there to believe that a random number generator hooked up to an inscrutable interpreter produces human flourishing, for any given meaning of "human flourishing" you care to use?
#tech #dev #mathematics #AutomatedMathematician #AutomatedScientist #AI #GenAI #GenerativeAI #ThoughtExperiment
Edited 15d ago
"A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature. "
~Henri Poincaré (29 April 1854 – 17 July 1912)
Poincaré at PG:
https://www.gutenberg.org/ebooks/author/5958
Algebra is more than alphabet soup – it’s the language of algorithms and relationships
By Courtney Gibbons
![The word algebra comes from the title of al-Khwarizmi's book Al-Jabr.[13]
Al-Khwarizmi - Esposito, John L. , ed. (1999) The Oxford History of Islam, Oxford University Press ISBN: 0195107993. ; April 2006 (upload date) by Spm
https://en.wikipedia.org/wiki/Algebra#/media/File:Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg](/proxy/post_attachment/714514/2871b612b3.jpg "The word algebra comes from the title of al-Khwarizmi's book Al-Jabr.[13]
Al-Khwarizmi - Esposito, John L. , ed. (1999) The Oxford History of Islam, Oxford University Press ISBN: 0195107993. ; April 2006 (upload date) by Spm
https://en.wikipedia.org/wiki/Algebra#/media/File:Image-Al-Kit%C4%81b_al-mu%E1%B8%ABta%E1%B9%A3ar_f%C4%AB_%E1%B8%A5is%C4%81b_al-%C4%9Fabr_wa-l-muq%C4%81bala.jpg")
Alan Turing’s Lost Work Could Reveal How Tigers Got Their Stripes
The world-famous mathematician Alan Turing found a possible mechanism for iconic animal patterns thanks to differential equations
By Manon Bischoff
English mathematician Henry Briggs died #OTD in 1630.
He is notable for changing the original logarithms invented by John Napier into common (base 10) logarithms, which are sometimes known as Briggsian logarithms in his honour. The specific algorithm for long division in modern use was introduced by Briggs c. 1600 AD. Historically', the "common logarithm" was known by its Latin name logarithmus decimalis or logarithmus decadis.
Prime numbers, the building blocks of mathematics, have fascinated for centuries − now technology is revolutionizing the search for them
By Jeremiah Bartz
Prime numbers at PG:
https://www.gutenberg.org/ebooks/search/?query=prime+numbers
“I Reunite Architecture and Perspective”: Hirschvogel’s *Geometria* (1543)
One theory about wormholes — those speculative cosmological structures that tunnel between distant points in the universe — holds that spacetime can be folded like a piece of paper, bringing the near and far into proximity.
https://publicdomainreview.org/collection/hirschvogel-s-geometria-1543/
Online version:
https://digital.slub-dresden.de/werkansicht/dlf/8077/1?tx_dlf%5Bpagegrid%5D=1&cHash=b4db56391c1bb332830d76c2e3d08615
John Nash, The Mathematical Genius Whose Battle With Schizophrenia Inspired 'A Beautiful Mind'
Although John Nash's career in mathematics was hampered by a paranoid schizophrenia diagnosis in 1959, he went on to win a Nobel Prize in economics in 1994 for his work on game theory.
By Austin Harvey
https://allthatsinteresting.com/john-nash
More information:
https://en.wikipedia.org/wiki/John_Forbes_Nash_Jr.
Epic Effort to Ground Physics in Math Opens Up the Secrets of Time
By mathematically proving how individual molecules create the complex motion of fluids, three mathematicians have illuminated why time can’t flow in reverse.
By Leila Sloman
Mathematical physics at PG:
https://www.gutenberg.org/ebooks/subject/7053
Spiral into the ‘golden ratio’ – and separate the myths from the maths
Named for the Italian mathematician Leonardo Bonacci (c1170-1240), the Fibonacci sequence refers to a numerical set that, usually starting with zero and one, adds the previous two integers together to arrive at the next (0,1, 1, 2, 3, 5, 8, 13, 21, etc).
https://aeon.co/videos/spiral-into-the-golden-ratio-and-separate-the-myths-from-the-maths
More information about the Fibonacci sequence:
https://en.wikipedia.org/wiki/Fibonacci_sequence
Imaginary numbers are real
These odd values were long dismissed as bookkeeping. Now physicists are proving that they describe the hidden shape of nature
Karmela Padavic-Callaghan
Mathematics - Philosophy at PG:
https://www.gutenberg.org/ebooks/subject/17657
Mathstodon.xyz is a Mastodon server for people who love maths, and includes LaTeX rendering in the web interface. Maths chat is especially welcome, but any topic of conversation following the code of conduct is OK.
This server has a post size of up to 1729 characters.
You can find out more at https://mathstodon.xyz/about or contact the admin account @christianp
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《大學入門微積分》筆記
Introduction to University Calculus Notes吾習單維彰教授《大學入門微積分》之課，謹將筆記照片上傳於網路。感謝單教授與國立中央大學之辛勤教誨與付出！
I have studied Professor Shann Wei-chang’s course Introduction to University Calculus and hereby upload photos of my notes to the internet. I sincerely thank Professor Shann and National Central University for their dedicated teaching and efforts!
如欲下載原圖，請訪問吾之網誌：《大學入門微積分》筆記
If you want to download the original image, please visit my weblog: Introduction to University Calculus Notes
原影片課程：YouTube原版 bilibili搬運
#筆記 #數學 #基礎 #微積分 #入門 #單維彰 #大學 #大學入門微積分 #中央大學 #笔记 #数学 #基础 #微积分 #入门级r #单维彰 #大学 #大学入门微积分 #中央大学 #note #math #mathematics #basic #calculus #introduction #Shann_Wei-chang #university #college #NCU
This month's Distributed Proofreaders blog delves into the newly uploaded "Newton's Principia."
"In it, Newton expounds, with mathematical proof, what is now the bedrock of modern physics: his groundbreaking laws of motion and universal gravitation, and his explanations of the motion of planets, moons, comets, tides, fluids, and other physical phenomena."
https://blog.pgdp.net/2025/08/01/newtons-principia/
Newton's Principia at PG:
