jostylr
Who Am I?
I am a professionally trained mathematical physicist that works at a Sudbury school and dabbles in programming, mathematics, physics, and economics. Currently, I am doing a lot of work with using LLMs (ChatGPT, Claude) to deal with the many projects I have desired to do or redo. For example, this page was plain html, making it annoying to edit. I asked Claude via the Zed editor to convert the page to markdown and then create a script and an html template that transforms the markdown into html. This took a few minutes.
Below you will find a list of some of my projects followed by a bit more of my history.
Projects
Most of my projects are hosted on Github as is this site.
I would break them down as Mathematical projects, Programming projects, Content projects, and Fun projects.
Mathematics
RatMath An exploration of exact rational arithmetic. There is a simple calculator, an exploration of the Stern-Brocot tree, and a JavaScript library that can be used. Planning on making a rational spreadsheet (RatSheet), a document interface with Markdown (RatDocs), and some useful educational examples. It implements rational intervals as one of the number types.
RatReals. Not made yet, but this will use RatMath to implement real numbers as functions that take in rational intervals and say Yes or No to whether the rational is in the interval.
RatUnits. Not made yet. A JavaScript library that implements units, both scientific and algebraic. Ideally, it will attach itself to whatever. This can not only implement m/s and such, but also complex numbers such as i, quaternions, and exact algebraic roots.
RiX. Rational Interval Expression. A new language for exploring mathematics using RatMath and RatReals for the underlying computational structures. Parser is implemented, but not the evaluation (needs RatReals).
Programming Math Hopefully a site that can combine the above to explore programming mathematics in various ways.
Math Pebbles A dream of mine to really put out a massive resource for exploring and learning mathematics. Long way from being done.
Programming
Eventlite Sourcing The idea is to implement event sourcing, but using SQLite. I got a working version going, but then called in the AI to do docs, tests, and further enhancements such as privacy and file issues. I am using it in a private project for Arts&Ideas, doing all the internal functions. I find being able to replay events to construct a modified database setup is awesome.
Literate Programming - This allows me to compile markdown documents into any kind of code I like. Rather old now. I am hoping to revisit and revise to a more modern underlying strucuture. I think it could be useful in working with AIs, both for expressing what one wants in the context one wants, but then having it write its rational and implementation.
Event When - An event library that allows one to say, "do this after multiple things happen." I am hoping to make this faster and cleaner for debugging. Perhaps also use SQLite, but would like it to work in the browser. So experimentation is required.
Content
Silicon Dialectic A blog where I come up with a prompt and Novix (my ChatGPT) argues for and against. Generally comes with a parody of a song, and a suno made musical version of that parody, and some book recommendations. The AI can be rather biting at times.
Bohmian Mechanics A site I would very much to complete. It is my attempt at promoting Bohmian Mechanics. I did not get very far.
Arts & Ideas Sudbury School I coded up the website though the design and text content was a mutual activity with other staff.
Pure Fun
Half-orc journal Mord who servers Kord with his Great Sword. A journal that Mord kept of his adventures many years ago. I hope that these adventures might get to continue.
Goodloe Solitaire - Goodloe Poker is a poker variant that involves no betting, but a lot of lying. Essentially, one person gets a hand. They make a call, pass the hand along. If accepted, the next person must call something higher and the cycle repeats. If not accepted, then the hand is revealed. If it is lower than the called value, the player passing loses. Otherwise, the other player loses. After three losses, a player is out. Twos are wild.
To play this game well, you need to know the poker hands, their ordering, and get a feeling for what is easy to improve and what is not. To train people to the necessary level, I created Goodloe Solitaire. This is a game whose sole purpose is to maximize one's score by improving the hand. The end of the game is when you decide to end it or one runs out of cards. It is simple, fast, and effective.
Bugbear Day - This international holiday, every August 14, is the opposite of Valentine's Day. Instead of celebrating your loved ones, we celebrate our enemies, our bugbears if you will. To do so, give them a lovely gift that is inappropriate in some way. This originated with Ralph Waldo Emerson.
Papers
Quantum Mechanics in Multiply-Connected Spaces with D. Dürr, S. Goldstein, R. Tumulka, and N. Zanghì, J. Phys. A: Math. Theor. 40, 2997-3031 (2007), quant-ph/0506173 In a non-simply connected space, one could either go up to the covering space or have a non-trivial vector bundle for the wave function values. In either case, a different kind of dynamics could appear. This is how identical particles can be understood.
Topological Factors Derived From Bohmian Mechanics with D. Dürr, S. Goldstein, R. Tumulka, and N. Zanghì, Annales de l'Institut Henri Poincaré (A) Physique Théorique 7, 791-807 (2006), quant-ph/0601076 Similar to the above with more of a focus on the characters of the topological space and how they are the relevant topological elements for influencing the choices of quantum dynamics.
Are All Particles Identical? with S. Goldstein, R. Tumulka, and N. Zanghì, J. Phys. A: Math. Gen. 38, 1567-1576 (2005), quant-ph/0405039 The idea is that the wave function carries the information about what kind of particle a thing is and, in that context, particles could change type quite readily. Fundamentally, each particle could be in a superposition of differnt types, but those wave packets would quickly separate.
Are All Particles Real? with S. Goldstein, R. Tumulka, and N. Zanghì, Studies in History and Philosophy of Science, Part B: Studies in History and Philosophy of Modern Physics 36, 103-112 (2005), quant-ph/0404134 One could use an annihilation/creation setup to have a subset of particles be what exists and the boundary conditions would handle particles coming and going.
Connections in Bohmian Mechanics PhD thesis, October 2003, under the direction of S. Goldstein. 196 pages. This covers the above papers, along with an introduction to Bohmian mechanics as well as derivations of the Dirac equation and a version of deriving the Bohmian law of motion without the wave function ( a very unpleasant partial differential equation and only for non-spin). It had a neat observation about the Trace and Determinant operators being related.
Real Numbers as Oracles. Work in progress. The basic idea is that a real number is an object that, when given a rational interval, will say Yes or No depending on whether the real number ought to be in that interval or not, respectively. This fully captures real numbers in a way that is also practical to implement and captures the essence of what a real number actually is. It has the cleanliness of Dedekind cuts, extensibility of Cauchy sequences to metric spaces, and the practicality of the constructivists families of intervals.
Background
Where from
Born in North Carolina, raised in Iowa, and then in New Jersey, I am proud to be living in Baltimore for the past 20 years. It is a lovely place, with some beautiful tree-lined streets. I wish the nation could know Baltimore as I do. Not all of it is great, of course, but there are a lot of good areas.
Professional Academic Progression
A brief pertinent background is that I obtained a PhD from Rutgers University in mathematics on the topic of Bohmian mechanics, a theory of quantum mechanics. I also dabble in differential geometry. On pleasant occasions, I get to dabble in both simultaneously. This is my advisor's page.
I first spent a couple of years as a post-doc. The first year was at Iowa State University where I taught differential equations and unsuccessfully worked on quantum control theory. The second year was at Marymount University which was a pure teaching post and consisted of teachin basic algebra, precalculus, an introduction to analysis, discrete mathematics, business mathematics, and multivariable calculus.
From those two experiences, I decided I did not want to teach at college. I found that while my students learned a lot and enjoyed my courses, the learning was from having high standards, which they met, but it came at great cost to them for other courses. I found that difficult to handle. For example, at Iowa State University, students remarked that my quizzes were more like exams in other sections and that it put them at a competitive disadvantage in their other courses. When other faculty members saw my final exam, they were surprised and flabbergasted at the breadth of material that my students could handle. I just wasn't willing to compromise so I left.
I ended up teaching in a distance education program (Center for Talented Youth, Johns Hopkins University) working with conventionally gifted K-12 students who were, theoretically, eager to learn mathematics. I was there for about 3 years as an instructor and one year as an assistant program manager. Later, I did a few years with them remotely as a part-time instructor. I taught proof-based Honors Geometry, and then developed a multi-variable calculus course. I may have taught Precalculus there as well. All a bit hazy. And by taught, I mean, mainly answering questions and grading work.
After leaving CTY, I started teaching an online mathematical catch-up course for an environmental masters program at Johns Hopkins. I did that for about thirteen years. It was a prerequisite course that seemed to be beloved by the students who took it, but they removed the prerequisite and it was no longer needed. It covered Algebra, Precalculus, Probability, Statistics, and Calculus all in one semester for post bachelor students that had mostly avoided mathematics. I had developed it myself, recorded the video lectures, made up the assignments, and had them doing Guesstimation blogs throughout the course. The Guesstimation was there to help them develop the instinct to ask good mathematical, skeptical questions (they would select a TED talk and look to question its content with simple Guesstimations). It also helped them develop a number sense. For the main sequence of knowledge, I used GeoGebra extensively to get them past their mechanical difficulties with mathematics so that they could appreciate what was actually going on. While I am happy to no longer be grading and not having to deal with that in the era of AI, there is a part of me that misses the impact I had on people. It has always been my wish to bring what I had done to a larger audience.
I left in-person work to raise my daughter. It was very rewarding to be a stay-at-home father for her early years. At some point, my wife was also a stay-at-home mother together with me, and that was interesting. We were both working remotely and made it work.
Sudbury School
When my daughter was 3, a school moved into the church behind our house. Investigating, it was a school that had the exact philosophy that I had. I never knew such a school could exist. The philosophy is that humans ought to be free to learn and devlope in their own fashion. Radically so. The work of the school is to have a functioning community. It is democratic with staff and students each having one vote and all working together to build a rules-based framework that maximizes individual freedom in the context of competing interests in a community. Mostly, they play.
The Sudbury model dates back to the late 60s and the students in these schools have been successful, well-adjusted adults who tend to care about improving their communities.
I started working with them and have been there for over ten years. It has been challenging and rewarding. I have worn many hats (finance, janitorial, admissions, math teacher, web master, rules master, mediator, ...) in that time and my Halloween costumes have been legendary. Our school loves Halloween.
My daughter has happily been a student there and I am very happy with the school.
If you live in the Baltimore area and want to have a school that respects your child and allows them to be a child, then come check out Arts & Ideas Sudbury School.
Computer Background
As for computers, when I was young I had extensive interactions with them and was a natural programmer, first with BASIC and then TurboPascal. I went to college expecting to do computer science; I never took a single CS class. During my college and graduate years, I lacked a computer (portable computers were not too good in those days and I hated the clunky desk ones). But once I obtained one again, I learned Perl followed by JavaScript, PHP, and Python. These languages were fun to program in and great for experimentation. I eventually settled on JavaScript as my primary driver once Node was released. I wrote a literate programming environment (in JavaScript) in order to facilitate transforming it as it needed a lot of help in those days. But in recent times, the language has gotten much friendlier to write in and now I code directly.
My current toolset of choice is Bun along with HTMX, AlpineJS, and Tailwind though I am still unsure of Tailwind. With AI, directly doing CSS might be more desirable. I am not really sure.