16 years ago, I wrote:

A guy at a cactus store once told me how it's cause for celebration when a saguaro adds another rib. As if to remind me of the inevitable pitfalls of desire, he was quick to point out that a saguaro could discontinue a rib as well, and how that was cause for discouragement.

Last month, I wrote about progress I made on the Snake-in-the-Box problem. The satisfaction I got from beating what Wikipedia said was the best result in 10 dimensions was deflated a couple weeks later when I learned that Wikipedia's results were out of date. In 2023, a team in France reached the same result that I had. Wikipedia's Snake-in-the Box page now reflects their results.

I've kept working on the problem and I now seem to be ahead in 11, 12, and 13 dimensions. I'm acutely aware that someone else may have beaten me to these records or even done much better. You can never know for sure. Someone could be working on the problem alone and keeping results private for who knows what reason.

I'm having fun either way. I'm rewriting my code to run on Nvidia hardware and I'm interested to see how that goes.

I see more people walking around in the open space across the street now that some houses in my neighborhood are rented via Airbnb. It's not out of control and most visitors are well‑behaved but those of who've lived here for a while miss how quiet it used to be.

Speaking of quiet, there were no trick-or-treaters yesterday as has been the case every Halloween since I've been living here. A friend who lives in the SF bay area gets over 1000, yikes.

From a professor of American history at the University of Edinburgh:

I learned about the Snake-in-the-Box problem when it was featured in xkcd #3125 a couple months ago. It's about finding the longest possible path along the edges of a hypercube that doesn't visit a vertex adjacent to where it's already been.

The longest-known snakes in various dimensions, per Wikipedia:

d	1	2	3	4	5	6	7	8	9	10	11	12	13
length	1	2	4	7	13	26	50	98	190	370	712	1373	2687

In dimensions 8 and below, it's been proven that the longest snakes known are the longest possible. In higher dimensions there's currently a gap between the longest-known snake and the best-known theoretical upper bound. It's like looking for needles in very big haystacks: the number of possible snakes grows more than exponentially with respect to the number of dimensions.

There seems to have been more research into Snake-in-the-Box a decade or two ago than there is today. The University of Georgia had a group of grad students working on it; an appreciation for the subtlety of the problem comes across in their writing.

I liked the problem immediately and started writing code. It consumed much of my attention for eight weeks. I started getting good results this month and I've published a paper about a length‑373 snake in 10 dimensions.

Wikipedia policy doesn't allow citations to self-published papers, not even for results as easy to verify as this. I'm working on getting my work acknowledged in a trusted publication before I change the 370 in Wikipedia to 373.

The Snake-in-the-Box problem arose in 1958 in the context of coding theory. The 2012 paper that demonstrated a length‑370 snake in 10‑d listed practical applications:

Longest snakes and coils identify longest sequences of n‑words whose properties make them useful in applications including error-detecting codes, analog-to-digital encoders and converters, fault diagnosis in multiprocessor networks, modulation schemes in multi-level flash memories, and, somewhat remarkably, identifying gene regulation networks in embryonic development.

That's all true but it's unlikely that my little contribution to this problem will find practical use. I doubt anyone has an application that needs a single-bit-error-detecting 10‑bit Gray code with a little more than 370 code points. But you never know.

I'm writing a paper describing research I did on my own. I'm facing a quandary at the point where a team would say "We demonstrate...". I have no good options:

• the royal "we" is pompous
• "I demonstrate" is rare in this context and emphasizes the author
• passive voice is weak
• "This paper demonstrates" is insipid

What would you do? My current draft:

Abstract. The Snake-in-the-Box problem is the challenge of finding the longest possible induced path in the edge graph of an n‑dimensional hypercube and proving its maximality. The problem has been solved for hypercubes of up to 8 dimensions. In dimensions 9 and above, research has placed lower and upper bounds on the maximum possible path length. This paper demonstrates a new lower bound of 371 in the 10‑dimensional case and describes the heuristics used for its discovery.

In seeking advice on the web, I learned about the case of American physicist and mathematician Jack H. Hetherington who'd used "we" in a paper he wrote by himself, only to learn that the journal he intended to submit it to would reject it on those grounds. Rather than reword his paper, he added his cat as a co‑author.

The little hospital in my town is on the verge of bankruptcy. It's the only hospital for over 50 miles in any direction and it would be a big deal to lose it.

My district's State Senator, Marie Alvarado‑Gil, was in Lone Pine last week to discuss the hospital. She said she'd ask the mayor of Los Angeles to send us money. From the Mammoth Times:

"Los Angeles owns so much of Inyo County," said Alvarado‑Gil, who represents Mono and Inyo counties in the State Legislature. "We need to try to get L.A. to invest in an area with lots of (L.A. Department of Water and Power) employees and families."

Among Angelenos, there is a lack of awareness of the needs of the Owens Valley, which is basically an extension of L.A., she said.

District 4 covers a lot of area. Ms. Alvarado‑Gil does represent my county but she lives about five hours away, on the other side of the Sierra Nevada. If she spent more time in the Owens Valley, maybe she'd notice that no one living here thinks we're basically an extension of L.A.

Or maybe not. Marie Alvarado‑Gil was elected as a Democrat but joined the Republican Party since she's been in office, evidence of some kind of mental defect.