"Mathematics must subdue the flights of our reason; they are the staff of the blind; no one can take a step without them; and to them and experience is due all that is certain in physics." – Voltaire (1694-1778) #quote#mathematics#math#maths
Mathematician James Harris Simons, known for the classification of holonomy of 3D manifolds and his famous Chern-Simons form, passed away on May 10, 2024, in New York City, at age 86.
Despite his later cooperation with NSA to help US to invade Vietnam and entering financial business (which is notorious for redistributing wealth to enlarge economic inequality), his legacy in #mathematics and #physics still benefits our exploration in secrets of the universe.
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).
@RossGayler@Heterokromia@cogsci to me it seems you need to be more clear on your requirements. Are your non-negative and multidimensional requirements independent, as far as you can tell?
If so, a multidimensional (do you know how many dimensions/animals you have?) modulo space sounds a viable solution. That'd be something denoted as https://www.HostMath.com/Show.aspx?Code=%5Cmathbb%7BZ%7D_k%5En , with k being the cardinality of one dimension (would they need to have different cardinalities?), and n being the number of dimensions.
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.
@JeremyMallin But that would imply the First Directive was non-prime (also non-composite), which is a paradox. Which is probably how Kirk skated through all those court martials over the years.
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.