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Practical Paracosms is a meditation on the imaginary worlds of abstract mathematics and computers through an adventurous, intuitive lens, without compromising on the technical details and correctness.
We’re aiming to be a light read to lift up your spirits and breathe life back into the bleakness of a technological future with meaningless work, shepherding the readers through the process of inventing something perspective-changing.
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Inspiration
Growing up, I rarely imagined being a magician, although fantastical stories involving magic and time travel were always my favorite. I didn’t need to muster up worlds where magic existed because every time I ran after a frog in the meadows, or picked up a paintbrush, or read a book, that made me feel as if I was floating, even though I was safely caressed by sunrays peeking through the leaves over the hammock — magic was there. I’ve managed to nurture this feeling well into my adulthood.
Although we understand the clockwork of mathematical proofs and computer programs, what are they if not magical in their existence? Sequences of logical statements and utterances of spells share their differences, but in the end, both have the power to conjure imaginary universes.
The closest real-life equivalent to magic is a virtual world that lives on sheet music of binary voltage signals. Doesn't matter if it's a game, simulations of galaxies, or a simple script; it's always a personal portal into another space. The programmer is the conductor arranging the notes. The hardware engineer and the factories pressing and printing chips and pathways on boards inside our computers assemble the orchestra, ready for symphonies.
Programming and mathematics go hand in hand. Math conceptualizes the very domains and approaches for something fundamental and creates computational frameworks for them. Programming and hardware engineering are tools for transforming ideas into palpable objects and experiences. They can also inspire new mathematical theories, and I’m on a mission to bridge the gap.
I would like to inspire software engineers toward a new era of open scientific inquiry, where pure mathematics, computer science, and real-world programming practice meet.
Motivation
I’m a research consultant at the Compositional Methods and Systems Lab studying mathematics at the Open University. I’ve been a professional software engineer with the most experience in systems software, such as embedded systems, game engines, and graphics. I’ve worked on Idu, a plant simulation game, and wrote some devlogs about the process.
I used to think I enjoyed algebra more than analysis, but the further I got in my studies, the more apparent the blurred lines were. I see the distinctions as arbitrary borders between different calculi of relations and operations, and I’m determined to pass on this intuition in a comprehensible, applicable manner.
Instead of being motivated by the inherent beauty of mathematics or some kind of objectivity of answers, I find myself seeking out the rhythms and fundamental fabrics of mathematical disciplines purely for play and a change of perspective.
Number theory is rhythmical; topology is expanding, popping, rounding, dissecting: geometry is traveling, concretizing; category theory is webbed. That’s why in my mind’s eye, most of mathematics is “visual and spatial” and incredibly palpable in my paracosms.
As an added seasoning for formalization, I think logic, philosophy of mathematics, sociology of mathematics, history of mathematics, proof theory, and type theories are indispensable.
It might be particularly surprising that studies about or the nature of mathematical practice are in a feedback loop with continuous mathematical progress. But unless mathematicians in various fields know how to communicate their work to one another, we’ll keep reinventing the bicycle.
Upcoming series
Software is mathematics:
the intuition behind category theory, type theory, abstract algebra, and how it relates to and complements programming
Building mathematical intuition for software engineers by inventing mathematical theories; illustrating how software is mathematical in its whole process, and introducing intuition behind abstract mathematics with illustrated examples, all while making the case for a symbiosis between ignored mathematics and programming
You can read the introduction to this series here:Proofs and programs:
geometric proofs in computer graphics, computer programs as proofs, baby steps in formal verification, and reasoning in programming languages
What constitutes proof in mathematics, and where do they occur in programs?
Why is it relevant to software engineering, programming language design, computer games, and more?
Illustrated by procedural plant generation algorithms, lots of fun visual stuff, and runnable code!
Potentially, future paid content…
Explorations of the feedback loop of sociology, philosophy, history, and semiotics of mathematics with new developments and paradigms in mathematics
Long-form literature reviews and associational explorations into the connections between these topicsEcology of technology: exploring the symbiotic relationship with technology, including reimagining what artificial life/intelligence means, and their mathematical underpinnings
Fantasy mathematics: what could be alternative mathematics in other worlds?
..and much more!
Currently, it takes me a long time to write a single post that conveys enough detail and intuition. Alongside work and university, my time is quite limited.
I’m currently aiming for bi-monthly writeups, some of which will be status updates on my writing and reviews of what I’m currently reading.
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