UK hobbyist stuns math world with 'amazing' new shapes | Hacker News Reader

UK hobbyist stuns math world with 'amazing' new shapes

phys.org

140 pointsmojomark45 comments

What I like about the amateur aspect of this story is that it should encourage people to just pursue what interests them. So long as you eschew prestige you can do literally anything you want. Prestige is just a euphemism not worth it anyway - and hacking is what you do when you don't know. When combined, these attitudes together can get some pretty good stuff done.

> hacking is what you do when you don't know

this. this is where the new/good stuff comes from.

"While all agreed "the hat" was the first einstein, its mirror image was required one in seven times to ensure that a pattern never repeated."

The article has a small error here - it should say approximately 7. The ratio between the tiles and their mirrors is phi^4.

https://cp4space.hatsya.com/2023/03/21/aperiodic-monotile/

Hatfest:

https://www.maths.ox.ac.uk/node/64321

Registration is required, but free. I live in Oxford; I might rock up. I'd like to meet (or at least hear) Roger Penrose.

Previously discussed at https://news.ycombinator.com/item?id=36119920. Original paper at https://arxiv.org/abs/2305.17743.

Also just to clarify, this is a new development from the one a couple of months ago. The same authors have now described an aperiodic monotile without flips.

phys.org's coverage makes absolutely no mention of the source of the shape! https://phys.org/news/2023-06-aperiodic-tile-hat-true-chiral...

What a trash publication.

Valid point. I like to peruse the headlines on phys.org before I go to bed for the evening, ran accross this and thought it might be of interest to HN. Write up was enough for me, but agree that they are shit for references for those that want to dive deeper.

Cited suggestions on alternative, albeit but more formal, free paper/story summary app are welcome if you have one. I'm all ears for sure!

From a mathematician quoted about the non-reflective monotile:

> She said she expects the specter and its relatives "will lead to a deeper understanding of order in nature and the nature of order."

So, for a lay person, this tile seems like a cool curiosity, but it's not clear why it should tell us anything more general about something so broad as "the nature of order". Can someone with a better grasp of the relationship between tiling and other domains explain why one might expect the implications to be wider?

If I recall correctly, the existence of aperiodic tilings had ramifications e.g. for the kinds of crystal structures that can arise in nature. The fact that a single tile can do it seems like an even more fundamental statement, even if concrete implications are not yet in sight.

It's a generic throwaway statement.

My guess would be this is a call for research funding rather than a concrete expectation.

I find David Smith's former job interesting in relation to the story. I guess that as a print technician he dealt with 2D patterns a lot.

This is extremely cool and impressive.

I feel like they gloss a bit over the man... How did he approach the problem would've been interesting to see, for example.

Anyone knows if the shape is copyrighted? Like Penrose's or Escher's are.

how can a shape have a copyright

It's a sequence of coordinates for the vertices of the shape. Is that different from a sequence of words in a story or a book.

cf. the threshold of originality[1]; the answer to that question is "it depends on the shape, legal precedent, and the laws where you live"

1: https://commons.wikimedia.org/wiki/Commons:Threshold_of_orig...

There not true. Penrose tilings as a whole are generated randomly, with overall features determined only by the two simple tile shapes.

Legally, it can be different. For example, a typeface is a sequence of coordinates for the vertices of the shape, but (https://en.wikipedia.org/wiki/Intellectual_property_protecti...):

“Typefaces cannot be protected by copyright in the United States (Code of Federal Regulations, Ch 37, Sec. 202.1(e); Eltra Corp. v. Ringer), but fonts can be protected by design patent and may be protected by copyright.”

As I understand things, if the USA legal system were to choose to apply the same rules to these tiles, their exact shape would be copyrightable, but variations on it wouldn’t, even if the variations, for all intents and purposes, are identical to the original.

Corporate logos are a widespread example of copyrighted shapes, usually defined as Bézier curves these days.

You're conflating trademarks with copyrights; while there is some minor overlap, corporate logos are examples of trademarks, and applying copyright concepts will lead you to concluding that you can use an apple with a bite taken from it as your computer company's logo, as long as you don't use one derivative of that which apple uses. Which will entirely fail to hold water when apple sues you over it.

Which is kind of funny, because Apple arguably stole the Apple trademark from Apple records and then proceeded to go into the music business contrary to their agreement. They even distributed a system beep sound called “sosumi.”

Apple didn’t stole the Apple trademark from Apple Records.

Until Apple entered the music industry (iTunes) there was no conflict. Apple (the computer company) used Apple trademark in the computer business. However when Apple did iTunes it had to settle the conflict with Apple Records. It was about 500 mil. USD [1].

[1] Steve Jobs by Walter Isaacson

Solid point. The logo design files themselves are also under copyright though.

Trademarks and copyright have entirely different purposes. Corporate logos are often both.

A trademark is a brand, it identifies your work. Apple puts its logo on its computers to show that they made them. Because it is a registered trademark, you can't put the Apple logo on your own computers because it will mislead people into thinking they are Apple products. However, it doesn't prevent you from using the Apple logo in any other way. You can make artwork featuring the Apple logo if it is clear that Apple have nothing to do with it. If you keep your trademark registered and actually use it, it will never expire.

Copyright is about protecting the work of the artist or the company that commissioned it. For example, making a nice logo is hard work and you want to be compensated for it, so you may want people who use it to pay you, that's what copyright is for. The Apple logo precise shape, colors, etc... are covered by copyright. It means that you can't reuse the art for any reason without permissions, so in that way, it is a stronger protection than a trademark. The idea of a bitten off apple is not covered by copyright however, copyright doesn't cover ideas, only actual work, so if it wasn't also a trademark, you could have put your own drawing of a bitten off apple on a computer you made. Copyright doesn't need to be registered and expires after about 100 years.

The third category, also different, are patents. Patents protect inventions, I don't think it makes sense to patent a logo, but I can imagine a tiling shape being patented. Or more precisely, the practical application of such a shape. Patents need to be registered and meet certain criteria, they expire after 20 years.

It isn't perfect, but we haven't found an alternative system that doesn't punish the first mover who takes on the risk.

Because nothing was invented before copyright was.

People existed before we had proper sewage. Clearly sewage systems are not needed.

The Penrose tiling is (or was) patented.

And Penrose sued Kleenex for violation, and won. They had used the tiling to make a better tissue.

Please take this as genuine friendly curiosity and not an attack - why do you care? Why is there so often a highly upvoted comment about copyright on HN posts, whether or not they have anything to do with intellectual property? Every Launch HN, every Show HN, and a huge number of random posts like this one have a comment like this one. Why is this topic so interesting for what seems to be a majority of HN users?

For me it feels like going to a car forum and seeing a post in every thread asking how the car is insured. There's nothing wrong with being into insurance, but it's not the type of thing you expect to be discussed at length on a car site, you know?

Well I could sell the first infinite piece puzzle if the shape isn’t copyrighted

Person ignorant here of copyright when it comes to mathematics. What do you need to do to copyright something? It doesn’t work the way art like music and writing does? Which is that copyright is automatic just by recording or writing something down in some way.

The idea that a shape, even a very complex one, could be copyrightable is pretty wild to me.

Not a copyright but Apple patented "rectangle with rounded corners"[0].

[0] https://www.theverge.com/2012/11/7/3614506/apple-patents-rec...

for use on electronic devices designed for portable use over communication networks.

even in 2012 sometimes articles wrote clickbait

I care very much, and I'll explain why. Whether or not a particular invention is under copyright or patent, vs in the public domain, has huge implications on whether others are free to use and play with that invention in creations of their own.

This is, after all, "Hacker" News. I would expect a lot of us would be interested in how freely we could hack on something without our creations subsequently being legally encumbered.

It's "Hacker News", not "Consumer News". Lots of people come here looking for interesting projects to contribute to, modify, incorporate into hobby projects, or even use for commercial purposes. Some of those uses may be disallowed by copyright and licensing issues. It seems like an obvious question that needs to be asked before getting excited and wasting hours writing code that can't be used.

Just from my own experience, I have gotten burned a couple of times, where a five minute check on copyright/licensing would have saved hours of wasted effort.

I wish they used a different color for each orientation to see what pattern the angles form.

Somewhat related. Just listened to this podcast about brainstorming and ideas, mentions Einstein and gave me some good tips about idea generation in general

https://podcruncher.co/play/4MXd

I can see a board game coming of this.

The hat/turtle/specter aperiodic monotiles are slightly disappointing for me. They seem much less aesthetically pleasing than Penrose tiles. Specifically, the “kite and dart” tileset is by far the most aesthetically pleasing to me. I don’t know why.

It’s quite a big discovery! but it’s also not a true ein stein as the article claims since it uses the shape and its transpose mirror image for the pattern. So 2 shapes, rather than 1.

his second shape doesn't require the mirror. "The Spectre"

Good to read the full article before criticizing.

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