eka-mark

I teach people math.

[eka-mark]

“Despite being one of the most familiar and widely recognized natural phenomena, lightning remains relatively poorly understood. Even the most basic questions of how lightning is initiated inside thunderclouds and how it then propagates for many tens of kilometers have only begun to be addressed.”

— Joseph Dwyer & Martin Uman, The physics of lightning (2014)

[eka-mark]

I'd like to reiterate this because of the recent Quanta article on this subject.

[tpwrtrmnky]

Like. Look. Listen. I have taught introductory quantum physics at a university level, and I need you all to incorporate this into your trans advocacy: There are situations where you need to make a decision to prioritize being comprehensible to your target audience above being The Most Unassailably Correct.

[eka-mark]

I also teach quantum physics sometimes. I'd love to hear about the compromises of this nature that you've found useful, if you'd like to expand on this! Do you have in mind things like ignoring the subtleties of the spectral theory of unbounded operators on Hilbert space, in favor of a more "everything is just linear algebra" approach, for example?

[eka-mark]

My former students keep recommending me to their friends by saying I'm a better math tutor than any LLM. :)

[eka-mark]

How cool is it that a category object in the category of groups is the same thing as a group object in the category of categories (or even in category of groupoids)? There's just no obvious reason why swapping the words "groups" and "categories" should lead to equivalent definitions. I guess this is one of those cases in which category theory validating all the things you would want to be true.

I've been reading this short expository article, which explains the relationships between these and crossed modules, all of which are apparently incarnations of (strict?) 2-groups. I don't understand crossed modules at all yet, but I'm looking forward to working out for myself what the smallest finite strict 2-groups are, concretely. Maybe later this year I'll be able to read Baez & Lauda's notes on 2-groups.

It's crazy that category theorists use the term "2-group", though, since that has long meant something totally different in group theory: a 2-group in the original sense is a group whose elements all have order a power of 2, which is a completely unrelated concept.

[eka-mark]

Happy Euler Day to all who celebrate!

[eka-mark]

In honor of the equinox, here's a simple derivation of an accurate formula for the position of the Sun in the sky (at a given date and latitude): https://arxiv.org/abs/1208.1043. It makes for a nice supplement to a classical mechanics course.

[eka-mark]

Accurate reckoning. The entrance into the knowledge of all existing things and all obscure secrets.

opening lines of the Rhind Mathematical Papyrus, c. 1550 BC

(source for this translation)

[eka-mark]

I'm glad we call it the "harmonic oscillator", and not the "Euler oscillator". It's more descriptive, and Euler has enough stuff named after him. But he was the first to work out its equation of motion! Nobody before Euler had so much as taken a derivative of a trig function.

[eka-mark]

One of the easiest ways to impress people with your mathematical acumen is to get really good at trigonometry. For high schoolers, undergrads, and people with little mathematical training, I recommend Trigonometry by Gelfand & Saul.

[eka-mark]

I taught people math for a total of 421.75 hours in 2025, which is a new record for me!

[twocubes]

pretty good peel

[eka-mark]

Beautiful! Those who want to know more about this shape (an approximation to the Euler spiral) and how it arises can read this exposition about orange peels.

[eka-mark]

I’ve been rereading Terry Tao’s intro to differential forms and integration roughly every year or so, since I discovered it in high school. It doesn’t disappoint.

[transgenderer]

how do i teach myself actual mathematics as a moron in chungus life sciences who is currently being cut off from pursuing further chemistry because i don’t understand even something as basic as matrices

hmm. i think you might have to hire a tutor unfortunately. i hear @eka-mark on here is pretty good! uh. i mean yeah you could definitely try to self-study. khan academy....? sorry i wish i had more for you. i dont think theres much of a "trick" here. learning math is just hard

[eka-mark]

It's true! I'm pretty good. You can book a free consultation to chat about your goals and background via my site.

[twocubes]

Permutation City Planning by Leona's Games

An urban planner meets an algebraic miracle

i am told that exceptional outer automorphism of S₆

[eka-mark]

This is a great puzzle! If you know some group theory, there's enough information on Wikipedia to solve it, with a little work.

[eka-mark]

One mother for two species via obligate cross-species cloning in ants - Nature

In a case of obligate cross-species cloning, female ants of Messor ibericus need to clone males of Messor structor to obtain sperm for produ

Living organisms are assumed to produce same-species offspring. Here, we report a shift from this norm in Messor ibericus, an ant that lays individuals from two distinct species. In this life cycle, females must clone males of another species because they require their sperm to produce the worker caste. As a result, males from the same mother exhibit distinct genomes and morphologies, as they belong to species that diverged over 5 million years ago. The evolutionary history of this system appears as sexual parasitism that evolved into a natural case of cross-species cloning, resulting in the maintenance of a male-only lineage cloned through distinct species’ ova. We term females exhibiting this reproductive mode as xenoparous, meaning they give birth to other species as part of their life cycle.

[eka-mark]

I finally figured out how to solve my 4x4x4 Rubik's cube, which got me thinking about the math of puzzles like these. So I started learning how to use GAP in order to explore some cube-related calculations. It seems to be the computer algebra system best suited to writing code involving permutations of finite sets. I'm about halfway through the official tutorial.

[cryptotheism]

Hey CT did you see we can now quantitatively detect when transmutation happens in particle accelerators? It's a shit yield and very short-lived but imagine how crazy the ghosts of alchemists are going

https://home.cern/news/news/physics/alice-detects-conversion-lead-gold-lhc

Oh yes I saw this! We've known that particle accelerators could do this for a while but it's nice to finally see firsthand confirmed evidence of it happening! Real neat!

[literallymechanical]

Transmutation yields from other processes are actually high enough for commercialization, just not for gold. One example is the moly cow, like these:

99-molybdenum is produced by transmutation of uranium in nuclear reactors under neutron bombardment, and then shipped to hospitals in in "moly cows." You don't actually use the molybdenum itself, though. A moly cow is actually a technicium generator! In the cow, 99-Mo gradually transmutes into 99m-technicium (which, notably, has a higher atomic number) through beta decay.

99m-Tc has such a short half-life that it can't be shipped on its own, but 99-Mo lasts days. So, over the course of about a week, 99m-Tc is "milked" from the moly cow and injected into patients for medical imaging, to detect tumors and soft-tissue stuff that's hard to see with other methods.

This is a very common, routine use of transmutation, 20 million 99m-Tc scans are performed per year!