I wish I could buy ceramic Penrose P3 tiles to put on my floor or wall. They 2 different tiles instead of 1, but they're simple diamond shapes, and they tile aperiodically.
A chiral aperiodic monotile
51–60 of 83 posts
Re: A chiral aperiodic monotile
#52There was a rumour that if they found a chiral aperiodic monotile then they might call it a Vampire Tile, because it doesn't have a reflection. Seems like they didn't go with that. I also see that the old discussion has come up: "But what can it be used for?" These sorts of things are pursued because they are fun, and there's a community of people who find it interesting. Is Rachmaninoff's second piano concerto usefu…
You've reminded me of an older Quora post about: What do grad students in math do all day? Do they just sit at their desk and think? [1] Here are excerpts: """ The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you're only al…
>> What do grad students in math do all day?
> ... by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet.
A friend of mine[0] once said that the act of doing research in math is the act of inventing a language in which you can talk about the problem. Once you have that, the solution tends to come. But inventing the right language is really, really hard.
This might explain why so many research mathematicians end up married to (or in long term relationships with) linguists. His wife is a PhD in Spanish and linguistics, my wife's first degree is in French and linguistics, and I know perhaps three or four others in my immediate circle.
Anecdata, of course.
[0] Andrew Lipson: https://www.andrewlipson.com/
Re: A chiral aperiodic monotile
#53This excites me much more than the original result, which I considered to use two tiles[1]. The fact that it’s a such tiny modification of the original result is crazy. Even if you don’t intend to read the paper, look at the illustrations of the hierarchical substitution algorithm at the top of pages 6 and 7, those are just beautiful. [1] The authors discuss various historic definitions of tilings and whether reflect…
And yet again, it's only available as PDF (rather than the standard HTML), which is super annoying when you have no desire to print it out, especially to view on a small screen. Nor that is seems like this document benefits in any way to be pre-separated into discrete pages (unlike for say, slides).
HTLM may be the standard for many things, but it is not the standard for academic papers. PDF is the standard.
PDF is the optimal format for this use-case, mostly because of existing tooling which makes it very easy to make academic papers as PDFs. As far as I know no tools exist to make something comparable to an academic paper which would improve view-ability on a small screen.
Re: A chiral aperiodic monotile
#54Earlier quoted context omitted.
You've reminded me of an older Quora post about: What do grad students in math do all day? Do they just sit at their desk and think? [1] Here are excerpts: """ The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you're only al…
Hm, challenge accepted: It uses a fan and a hose to suck up dust. You use it to get rid of dirt in your home. The dirt ends up in a bag. Now and then you must get a new bag, when the old one is full. If you have some tiny item or two that lies in the way of the dust, you will want to put that away, or else it can get lost in the bag.
But can I use it to rub the fleeb? [1]
Re: A chiral aperiodic monotile
#55I wish I could buy ceramic Penrose P3 tiles to put on my floor or wall. They 2 different tiles instead of 1, but they're simple diamond shapes, and they tile aperiodically.
This feels like a niche market someone needs to go after. I would love to have a bathroom floor or a kitchen backsplash tiled in 'hat' in 4 colours (ensuring no two same-colour tiles touched of course).
Re: A chiral aperiodic monotile
#56If I was a billionaire I'd have such custom-made tiling installed in my home's hallways and terrace.
I wouldn't see it being prohibitively expensive https://news.ycombinator.com/item?id=36121506
Re: A chiral aperiodic monotile
#57I wish I could buy ceramic Penrose P3 tiles to put on my floor or wall. They 2 different tiles instead of 1, but they're simple diamond shapes, and they tile aperiodically.
Someone needs to start a Kickstarter for this. I'd contribute.
Re: A chiral aperiodic monotile
#58Earlier quoted context omitted.
You've reminded me of an older Quora post about: What do grad students in math do all day? Do they just sit at their desk and think? [1] Here are excerpts: """ The main issue is that, by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet. Communicating these ideas is a bit like trying to explain a vacuum cleaner to someone who has never seen one, except you're only al…
>> What do grad students in math do all day? > ... by the time you get to the frontiers of math, the words to describe the concepts don't really exist yet. A friend of mine[0] once said that the act of doing research in math is the act of inventing a language in which you can talk about the problem. Once you have that, the solution tends to come. But inventing the right language is really, really hard. This might exp…
That makes sense as math is a fascinating exploration of the human mind and its ability to handle abstractions; and what is happening is one's mind even when not mathematical can be difficult to explain. A linguist's rigorous approach to language and understanding of language seems to pair well with a need to explain one's thoughts.
Thank you for sharing Andrew Lipson's site, digging his LEGO sculptures, for example: https://www.andrewlipson.com/mathlego.htm
Re: A chiral aperiodic monotile
#59Earlier quoted context omitted.
You need pretty strict tolerances on the dimensions of this Spectre tile, I think. Normal Penrose tiles might be easier. That said I have no idea in the first place how you'd get your hands on bespoke tiles...
The grout when tiling allows for a fair amount of fudging things, though from experience exactly dimensioned tiles are MUCH easier to work with.
With periodic tilings you can uniformly scale them to make room for grout of any thickness. Intuitively, it seems like aperiodic tiles would have to be manufactured slightly too small to leave room for grout, and the tiling would only work if the grout was exactly the right thickness. I wouldn't want to lay them.
Re: A chiral aperiodic monotile
#60Earlier quoted context omitted.
And yet again, it's only available as PDF (rather than the standard HTML), which is super annoying when you have no desire to print it out, especially to view on a small screen. Nor that is seems like this document benefits in any way to be pre-separated into discrete pages (unlike for say, slides).
HTLM may be the standard for many things, but it is not the standard for academic papers. PDF is the standard. PDF is the optimal format for this use-case, mostly because of existing tooling which makes it very easy to make academic papers as PDFs. As far as I know no tools exist to make something comparable to an academic paper which would improve view-ability on a small screen.
What about GNU TeXmacs ?
http://www.texmacs.org/tmweb/home/welcome.en.html
(No direct relation to TeX or GNU Emacs.)
Though sadly this is not sufficient, we also have issues for HTML standardization for standalone documents, unlike, for say, PDF-A.
https://www.russellbeattie.com/notes/posts/the-decades-long-...