Maths/CogSci/MathPsych lazyweb: Are there any algebras in which you have subtraction but don't have negative values? Pointers appreciated. I am hoping that the abstract maths might shed some light on a problem in cognitive modelling.
The context is that I am interested in formal models of cognitive representations and I want to represent things (e.g. cats), don't believe that we should be able to represent negated things (i.e. I don't think it should be able to represent anti-cats), but it makes sense to subtract representations (e.g. remove the representation of a cat from the representation of a cat and a dog, leaving only the representation of the dog).
Why are algorithms called algorithms? A brief history of the Persian polymath you’ve likely never heard of.
Over 1,000 years before the internet and smartphone apps, Persian scientist and polymath Muhammad ibn Mūsā al-Khwārizmī invented the concept of algorithms.
I bet that a lot of people in the Fediverse already know this very pretty pencil-based 3D art. But in case you haven’t, be prepared to marvel.
This sculpture is known as the hexastix and a variant series created by artist George Hart is titled 72 Pencils.
If you can get 72 unsharpened hexagonal pencils, and some flat rubber bands, you can attempt to create this. Search for a video by @standupmaths for a pseudo-tutorial.
"Numbers are free creations of the human mind, they serve as a means of apprehending more easily and more sharply the diversity of things." – Richard Dedekind (1831-1916) #quote#mathematics#math#maths#numbers
American mathematician Anna Johnson Pell Wheeler was born #OTD in 1883.
She received her Ph.D. in 1909 with a dissertation on "Biorthogonal Systems of Functions with Applications to the Theory of Integral Equations," a topic in functional analysis that was innovative at the time. Wheeler was instrumental in bringing German mathematician Emmy Noether to Bryn Mawr in 1933, after the latter's expulsion from the University of Göttingen by the Nazi government.
Italian mathematician and physicist Vito Volterra was born #OTD in 1860.
One of Volterra's most famous contributions came in the field of mathematical biology with his work on population dynamics. He formulated the The Lotka–Volterra equations which are frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.
French mathematician and physicist Henri Poincaré was born #OTD in 1854.
He is considered one of the founders of the field of topology. He was among the first to present the Lorentz transformations, part of the groundwork for Albert Einstein’s theory of special relativity. Poincaré also studied the behavior of planetary orbits and contributed to the three-body problem in celestial mechanics, exploring the stability and motion of celestial bodies.
Okay, it's time. Time to change servers. Time to have local & federated timelines that don't make my eyes bleed. Time to support an indie effort.
Does anyone want to share about their server? My main interests are #Music - I play #Eurorack#Synth, #Guitar, #ChapmanStick, and software, with varying degrees of skill - and #Mathematics - I'm attempting to get into grad school for #Math to facilitate a career change. I'm also liberal af, if that matters one way or the other on your server.
"Mathematics may be defined as the subject in which we never know what we are talking about, nor whether what we are saying is true." – Bertrand Russell (1872–1970) #quote#mathematics#maths#math
German mathematician and mathematics educator Felix Klein was born #OTD in 1849.
He is best known for his substantial contributions to group theory, complex analysis, non-Euclidean geometry, and for connecting mathematics with other disciplines, notably physics. His notable achievements are the Erlangen Program, Complex Analysis and Algebraic Geometry, Klein Bottle, and Klein's Quartic Curve.
"The proof that π is a transcental number will forerver mark an epoch in mathematical science. It gives the final answer to the problem of squaring the circle and settles this vexed question once for all. This problem requires to derive the number π by a finite number of elementary geometrical processes, i.e. with the use of the ruler and compasses alone."
Lectures on Mathematics delivered from Aug. 28 to Sept. 9, 1893 at Northwestern University, p. 52.
French mathematician and physicist Siméon-Denis Poisson died #OTD in 1840.
He is known for his significant contributions to mathematical physics, particularly in the fields of mechanics, probability theory, and electricity. He made crucial advancements in understanding the behavior of fluids & the mathematical treatment of physical phenomena. Some of his most notable contributions include: Poisson distribution, potential theory, fluid mechanics, electromagnetism.
Holy crap. Someone won the Texas Lotto -- to the tune of $95 million -- by buying every combination of number available. They apparently invested approximately $25.8M to accomplish that. (Paywall busted below) https://archive.is/etkX9
Proof they bought every number is they ALSO cashed in every combination of five-out-of-six wins possible, per that article. #math#lotto#mathematics#odds