I came up with a pretty neat family of functions related to different bases. They've got some nice pathological behavior if you ask me
#MathSky #Maths #Mathematics
sunjestermusings.blogspot.com
An interesting family of functions
You probably already know that we represent numbers using base 10 (or decimal) notation. You may also know that this choice is, ultimately...
![Abstract
We provide a clearer presentation of the Chair44 monotile, a new strongly aperiodic
monotile in three-dimensional Euclidean space E3
.
With LLM tools (ChatGPT Astra), Ioannis Tsiokos recently reported the first
known strongly aperiodic monotile in three-dimensional Euclidean space E
3
, the Chair44
monotile (see Figure 3, taken from Tsiokos’ preprint [11]). Hats off to Tsiokos for this
discovery, the framework he developed, and the human inquiry that led to the Chair44
monotile.
However, the paper itself and the formalization that it claims for support are not
in a form that is readily usable to anyone who wants to understand or check it. This is
not just because of the needless length or complexity of the argument (which is indeed
overwhelming as presented), or because the formal repository is not in normal form, or
because much of the text is misleading or poorly organized, but mainly because there
is so much irrelevant puff to push through. These are hallmarks of an LLM-driven
research paper.
We must, absolutely, insist on a higher standard for scientific discourse. The aim
must be to communicate, clearly, with people in the community — certainly this is an
historical requirement for publication.1](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:ysaiuavm2f7d4th42c4valhw/bafkreiaosjugf6tpo6hjqor3cxkfxhrhmmtv6qkvup2luprwbry2oia2pi)
