That turns out to be the key to the whole of my idea of locative calculus; Loculus for short.
I finally have the outline of the 5 part series of research papers.
Loculus I โ Foundations and Arithmetic of State-Bearing Variables Loculus II โ Algebra, Functions, and Domains in State-Bearing Mathematics Loculus III โ Geometry, Trigonometry, and Vector Analysis in State-Bearing Mathematics Loculus IV โ Differential and Integral Calculus of State-Bearing Variables Loculus V โ Ordinary Differential Equations and Dynamical Systems in State-Bearing Mathematics
Anyway, writing continues on my PhD – I need something to do after work and on weekends.
Welcome to the 232nd Carnival and my fourth time hosting the event.
To see past entries in the Carnival Of Mathematics and future scheduled hosts, please visit The Aperiodical.
I am honored to again host the Carnival of Mathematics! I learn so much from hosting; things I usually wouldnโt be exposed to are jam packed into every Carnival Of Mathematics post. Be sure to dig into the archive!
Here are the entries. Enjoy!
From Alice To The Mad Hatter: The Road To A PhD
By Storm Bear Williams
Everyone’s path to a PhD is different. Mine is more madcap than others.
This post is about the bottom center panel, โGame Theory final examโ.
I don’t know much about game theory and I haven’t seen any other discussion of this question. But I have a strategy I think is plausible and I’m somewhat pleased with.
(I assume that answers to the exam question must be real numbers โ not โโ โ and that โaverageโ here is short for ‘arithmetic mean’.)
First, I believe the other players and I must find a way to agree on what the average will be, or else we are all doomed. We can’t communicate, so we should choose a Schelling point and hope that everyone else chooses the same one. Fortunately, there is only one distinguished choice: zero. So I will try to make the average zero and I will hope that others are trying to do the same.
Iโve just uploaded to the arXiv my paper โPlanar point sets with forbidden 4- point patterns and few distinct distanceโ. This (very) short paper was a byproduct of my recent explorations of the Erdรถs problem website in recent months, with a vague emerging plan to locate a suitable problem that might be suitable for some combination of a crowdsourced โPolymathโ style project and/or a test case for emerging AI tools. The question below was one potential candidate; however, upon reviewing the literature on the problem, I noticed that the existing techniques only needed one additional tweak to fully resolve the problem. So I ended up writing this note instead to close off the problem.
Editor’s Note: Terance’s website if loaded with his work in mathematics.
Mathematics With Friends
by Ioanna Georgiou and illustrated by Asuka Young
“Mathematics with Friends” is a blog that takes a maths-related dialogue from the Friends TV series every month and explores the maths mentioned further. It comes with its own characters and amazing illustrations.
Books That Are About Maths, But Not About Teaching It
By Tom Briggs
In the spirit of getting straight to the point without providing my entire life history, please click below for a list of books that are about maths, but not about teaching it. Read beyond the link if you’d like a bit of context.
The list has been put together at The StoryGraph[2]: it can be browsed without creating an account and it can be searched, sorted and filtered, which I thought would be helpful as there are over 160 books.
A respectful story about the passing of a colleague. These things are never easy. Also an interesting correlation with Paul Halmos, the Hungarian-American mathematician. The full story is in the link below.
Math teacher Ben Orlin writes and draws the (aptly named) blog Math With Drawings and is the author of a new book, Math for English Majors: A Human Take on the Universal Language. To mark its publication, he devised this entertaining accompanying quiz. You can read the Ars interview with Orlin here.
Math, we like to say, is math. It often seems that mathematics is something beyond our controlโsomething unyielding, universal, inhuman.
But is it really?
Yes and no. Math may be the language of the cosmos, but itโs also a human language, with its own quirky etymologies, classic literature, and hilarious regional accents. In fact, you could say that math has as many stylesโas many idiolectsโas it has speakers.
Viterboโs conjecture was refuted by Pazit Haim-Kislev and Yaron Ostrover
by Gil Kalai
Claude Viterboโs 2000 volume-capacity conjecture asserts that the Euclidean (even dimensional) ball maximizes (every) symplectic capacity among convex bodies of the same volume. In the recent paper A Counterexample to Viterboโs Conjecture, Pazit Haim-Kislev and Yaron Ostrover disproved the conjecture.
In a dimly-lit tavern on the South Bank of the Thames, Philip Henslowe โ builder and owner of the Rose Theatre โ is celebrating the success of Shakespeareโs latest blockbuster, Henry VI Part I, among the cutthroats, actors and other lowlife of London. He spreads thirteen playing cards on a table in a circle. โPick a card,โ he grins. โAny card.โ
And this article is complete with cryptic, vintage explanations!
Editor’s Note: Now I want to visit the Dulwich College Archive!
Book Review: The Best Writing on Mathematics 2021
by Ioanna Georgiou
Mircea Pitici (Editor) PRINCETON UNIVERSITY PRESS 2022, 320 PAGES PRICE (PAPERBACK) ยฃ20.00 ISBN 978-0-691-22570-8
This book contains articles written in 2020. The editor speaks of the difficulties accessing libraries and resources, something we are all a bit too familiar with. Here I will comment on each of the twenty-six articles selected as the โbestโ and draw an overall conclusion at the end.
Editor’s Note: We have to start doing a better job in archiving and making available the collective of human knowledge to everyone. The defunding of libraries has to stop. The abusive research publication industry has to stop.
Welcome to the 206th Carnival and my third time hosting the event.
To see past entries in the Carnival Of Mathematics and future scheduled hosts, please visit The Aperiodical.
I am honored to again host the Carnival of Mathematics! I learn so much from hosting; things I usually wouldnโt be exposed to are jam packed into every Carnival Of Mathematics post. Be sure to dig into the archive!.
Iโm on the life long journey to recover from math-phobia. Which is why I have thrown myself into the math world head first! Next to momming and mathing, writing is my favorite thing. So, Iโm trying to do the blog thing. This is my first post from September.
In mathematics, particularly matrix theory and combinatorics, a Pascal matrix is a (possibly infinite) matrix containing the binomial coefficients as its elements. It is thus an encoding of Pascal’s triangle in matrix form. There are three natural ways to achieve this: as a lower-triangular matrix, an upper-triangular matrix, or a symmetric matrix.
Here Professor Higham steps his way through an example.
How can a 240-year-old logistics problem be used in quantitative finance? Dr Ivan Guo’s research lies predominantly in the areas of stochastic control and financial mathematics. In this interview with the Sydney Mathematical Research Institute, Ivan describes how stochastic transport theory applies in financial maths and how financial models are applied. He also debunks some misunderstandings about his field.
“You may have seen DALLยทE mini posts appearing on social media for a little while now โ itโs been viral for a couple of weeks, according to Know Your Meme. Itโs an artificial intelligence model for producing images, operating as an open-source project mimicking the DALLยทE system from company OpenAI but trained on a smaller dataset.”
Peter Rowlett presents a good introduction to DALL-E and offers several awesome examples.
One of my (many) interest areas is in algorithmic music composition. But it was not until @CarnivalOfMath mentioned that content didn’t need to be blogs, that I thought to submit this.
This piece is one where I use the Golomb ruler to determine the bar position, and length, of notes in a composition. I wrote a short piece of JavaScript which creates the data, incorporate it with a MIDI library which exports a MIDI file, that in turn can be loaded into a sequencer. I then assign each note to specific sound, based on their duration and what my ear tells me is good. (Being a synth-based composer, some sounds change a lot over time and are therefore better for long notes.)
The notes are always determined by me, a human, to match a particular key signature (to they sound in tune) and varied according to previous trial runs of the algorithm. So, for example, if notes of length 10 and 11 do not appear simultaneously I can assign them the notes E and F which (normally) do not sound good together. Similarly, I try to ensure that the start and end of the composition include notes which give an element of “resolution” which is prevalent in most western music. (Just because it’s based on maths, doesn’t mean it has to _sound_ that way!)
Finally, I sprinkle additional sounds generated by a different algorithm.
Click the image within the link to see a representation of the music, and you’ll clearly see the ruler being used.
Welcome to the 195th Carnival and my second time hosting the event.
To see past entries in the Carnival Of Mathematics and future scheduled hosts, please visit The Aperiodical.
I am honored to again host the Carnival of Mathematics! I learn so much from hosting, things I usually wouldn’t be exposed to are jam packed into every Carnival Of Mathematics post. Be sure to dig in to the archive!.
This is a video by me discussing how crazy I get when I see crazy math memes on Facebook and Twitter. Most are not educational and further separate mathematics from would-be students. We as mathematicians must do everything we can do to get people to EMBRACE mathematics, not shy away from it.
Ed Pegg noticed that 2021 = 43 x 47 which are successive primes with 20 and 21 being successive integers. He asked for similar solutions and Robert Israel quickly found the next biggest solution, a number with 36 digits. I (Lewis Baxter) found more than 1500 bigger solutions, the largest having 3011 digits. This month I certified the two primes (which are 20690 apart). Unlike other “titanic” primes they are not the value of some small arithmetic expression.
Mr. Honner sent this link in, bragging about what his students came up with. “This was the coolest math my students produce this year,” Mr Honner gushed!
“Iโve taught this topic for many years and never thought of this approach. Iโm grateful to have learned something new from my students, who never fail to impress me with their creativity. And Iโm glad I gave them time and space to solve what I thought was an impossible problem! When I teach this next time, Iโll be sure to do it again. And Iโll be sure to share this ingenious integration.”
Holmer Breaks down how they can be solved using trigonometry. Geometrically, you can visualize it as an equilateral triangle centered directly above the inflection point, where its vertices coincide with the three roots.
when cubic polynomials (axยณ+bxยฒ+cx+d = 0) have three real roots – they can be solved using trigonometry
a geometrically, you can visualize it as an equilateral triangle centered directly above the inflection point, where its vertices coincide with the three roots pic.twitter.com/cmv6sGoXM0
“Exactly half a year ago I wrote the Liquid Tensor Experiment blog post, challenging the formalization of a difficult foundational theorem from my Analytic Geometry lecture notes on joint work with Dustin Clausen. While this challenge has not been completed yet, I am excited to announce that the Experiment has verified the entire part of the argument that I was unsure about. I find it absolutely insane that interactive proof assistants are now at the level that within a very reasonable time span they can formally verify difficult original research. Congratulations to everyone involved in the formalization!!
In this Q&A-style blog post, I want to reflect on my experience watching this experiment.”
#GeometrySketchbook is a hashtag that has been used for a daily maths art challenge throughout June. A huge variety of media and art styles have been used; if you’re interested in mathematical art you’re sure to find something inspiring here.
“Erik and Martin Demaine, a father-and-son team of โalgorithmic typographers,โ have confected an entire suite of mathematically inspired typefaces.”
The verb โpuzzleโ โ to perplex or confuse, bewilder or bemuse โ is of unknown origin. โThat kind of fits,โ said Martin Demaine, an artist in residence at the Massachusetts Institute of Technology. โItโs a puzzle where the word โpuzzleโ comes from.โ
Storm Bear World 
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