#squiggy

A unit circle (blue curve) satisfies the equation \[ x^2 + y^2 = 1\] but if instead of the Euclidean norm you use the p-norm, you have the equation \[ {|x|}^p + {|y|}^p = 1.\]

When p=1 you get what's called the "Manhattan" metric, and the "circles" are diamond-shaped (red curve); as p goes to infinity the "circles" become more and more nearly square, and are called "squircles" (green and purple curves).

Today I learned that if one generalizes trigonometry to squircles, it's called "squigonometry" and the x and y coordinates of points on the squircle are given by the squine and cosquine functions.

https://en.wikipedia.org/wiki/Squigonometry

What on earth could "in the same ratio" mean here?

I wish the terminology around intelligence / sentience / consciousness / self-awareness / moral patienthood was better-settled. I want to be able to say that Claude is intelligent without other people inferring that I meant any of the others.

For example, it is uncontroversial for me to say that my cat is intelligent. Certainly it is generally agreed that some cats are more intelligent than others, and this a fortiori means that some cats are intelligent. Believing this doesn't commit anyone to a position on whether cats are "conscious", whatever that might mean.

Claude produces seemingly coherent, seemingly relevant responses to my natural-language utterances, and, when I express a request, its response is often satisfactory. I would like to have a word to communicate this that will not provoke an argument about whether Claude "really understands".

Back in 2019 I wrote a proposal for my employer that was not adopted but might be useful for someone else. I am working it over as a log article. But all I have to work from is a PDF I had saved.

I groaned as I realized that before I got to the fun writing part, I was going to was going to have to begin by converting it to markdown-plus-HTML, and at some point I would need to redo the diagrams in Inkscape, all very tedious…

No, I just gave it to Claude and told Claude to do those things. Which it immediately did, and I got on with the writing part.

Baum did not have a good track record of foreseeing which trends would last and which were only silly fads. He mocked automobiles and ragtime music, but went all-in on radium therapy.

RE: https://wandering.shop/@cstross/117382330824033578

“That's radium,” answered the Chief. “We Horners spend all our time digging radium from the mines under this mountain, and we use it to decorate our homes and make them pretty and cosy. It is a medicine, too, and no one can ever be sick who lives near radium.”

(L. Frank Baum, _The Patchwork Girl of Oz_, 1913)

From one of the answers:

“Incidentally, the value of α and β is

\[2\arcsin\left(\sqrt{\frac{79-23\sqrt{5}-\sqrt{2190-906\sqrt{5}}}{496}}\right)\frac{180^\circ}{\pi}\]

\[\approx19.86662296^\circ\]

Best geometric diagram I've seen lately. Prove α = β.

https://math.stackexchange.com/q/5150895/25554

I gather there are some people who really enjoy actually writing the code. And I think I did too at one point. But after 50 years of writing code, I feel like I've done it enough and it no longer has anything to teach me.

I still want to design the program structure and its processes, and get everything just right. But having done that, I feel like actually writing the code is a chore that I'm glad I no longer have to do.

I'm not claiming that has any moral valence, not that this is good, or bad, or the result of greater maturity, or anything like that. It's just where I am now, personally.

I think it explains some of the difference between my response to Claude and many other people's. For them a joyful activity is being taken away. To me, it feels like the slow tedious part is being handled by my assistant.

You have the choice to not be this person.

I'm looking for work, please boost!

I'm a software engineer with 35 years of experience. I've worked across an unusually wide range of domains: mobile game backends, privacy-preserving data platforms, high-throughput COVID testing infrastructure, email and account systems, e-payment processing, job marketplace systems, and bioinformatics. I pick up new domains quickly and have a history of doing it repeatedly. I understand how to turn business needs into engineering requirements.

I prefer to work remotely but I am open to an in-office job in the Philadelphia area or especially in Philadelphia itself. I've often worked remotely since the 1990s and can operate with minimal supervision. Several of my favorite projects were self-directed: I identified the need, built the thing, and shipped it. My preferred time zone is America/New_York, but I'm flexible.

Some of the many, many technologies I've used are: Python, Perl, TypeScript/JavaScript, Haskell, Go, C, Java. Postgres, MySQL, SQLite. Flask, SQLAlchemy. AWS (Lambda, S3, RDS, SQS, EC2). Docker, Git. Github and Gitlab.

I've also repeatedly picked up new languages and stacks as needed: Haskell for differential privacy research, TypeScript for a 24/7 AWS Lambda system, Flask for my most recent employer. I've become productive with new systems over and over, and I can do it quickly.

I'm a published author (Higher-Order Perl, Morgan Kaufmann), longtime blogger, and conference speaker with a reputation for making complex ideas clear.

I am a U.S. citizen.

My résumé is at https://
plover.com/~mjd/cv/Mark%20Jason%20Dominus.pdf

mjd@pobox.com

Thanks!

#OpenToWork #remoteWork #softwareEngineering #Python #backend #hiring
#fediHire
#getFediHired

@two_star This seems up your alley. OP wants a covering of an 8×8 array with a monomino and 21 trominoes of three colors, such that no trominoes of the same color share any edge, and only one pair of the same color shares a vertex.

https://math.stackexchange.com/q/2746678/25554

#tilingTuesday

Oh, this is easy, it's just the Stern-Brocot tree.

Another random thought because I can't sleep: Let Q* be the set of rationals in [0,1] and let D be the subset whose denominator is a power of 2.

There ought to be an order-preserving bijection between Q* and D, but can one be exhibited explicitly?

#orderTheory

#squarePacking

https://erich-friedman.github.io/papers/squares/squares.html

Context for interested non-answerers: 한글 is the name of the Korean alphabet. The _standard_ romanization, officially adopted in year 2000, is “hangeul”. However, the form “hangul” is better established and still in wide use outside of Korea.

(Also, probably easier for anglophones to intuit.)

In English text, how should I romanize “한글”?

(Informed opinions only please.)

Today I learned about the figure-8 immersion of the Klein bottle. Instead of starting with a tube and then sticking the tube through the wall of the tube to get it to join up in the opposite direction, you start with a double tube whose cross-section has the shape of a figure 8. Then you bend the double-tube around into a circle like a hula hoop and join the ends, but you give the double-tube a half-twist as you bend it, so that it turns into a single tube with a half twist.

The self-intersection is still a circle, but instead of being the place where the tube punches through the wall of the bottle, it's the set of crossing points of the figure-8s.

https://en.wikipedia.org/wiki/Klein_bottle#The_figure_8_immersion8

#textureTuesday