OT. No Repeat Tiles

Breitbart isn't the most reliable source. They do provide a link to the paper

but it has four authors - David Smith, Joseph Samuel Myers, Craig S. Kaplan, Chaim Goodman-Strauss.

New Scientist reports the story a little differently

David Smith may have found the shape, but it took expert help to prove that it was non-repeating.

The maths behind Penrose Tiles has been known for decades. How is this different?

This wasn't any age-old conjectural quandary. Penrose came up with an aperiodic tiling in the 1960's, and this a one-tile solution to the same problem. Computers are handy tools for doing big exhaustive searches, but they don't obliterate anything.

There's no suggestion that "the establishment" thought that it was "impossible", and aperiodic tiling isn't the kind of problem that you can solve with plain old common sense.

It is a decidedly exotic problem, and you need appreciable mathematical sophistication to realise that the problem actually exists.

I can't see how.

Which you can't cite. English language science journalists can be pretty unreliable. New Scientist does better than most of them.

What this case proves is that there is one example of a single shape that can offer aperiodic tiling. Neither article says how David Smith came up with the shape. so the "hunch" is your invention.

Not that you can list any of the "broad mathematically generalised charasteristics". You are just blowing smoke.

"Graduate level abstract algebra"? All algebra is abstract,. How do you split out "graduate level algebra"? You are pontficating again.

Abstract knowledge wouldn't be abstract if it did have a practical use, and when somebody finds a practical for it it can pay off generously.

Looking at the shape I was reminded of a few of the poly-cyclic aromatic hydrocarbons I had to study in third year organic chemistry. If you start embedding nitrogen molecules in the rings you get pentagonal elements. An aperiodic flat repeating polymer with long conjugated bonds could do all kinds of interesting stuff.

might have fun with it. He was levitating frogs in a powerful magnetic field when he and I were both living in Nijmegen (not that we ever met) but now he's into single layers of graphene.

It's not an unattractive tile, or pattern. I wonder when they will be in production?

Mathematical proofs that will stand up to scrutiny require experts but it still required the intuition of a human to find the right shape.

It is an interesting one and breaks a widely held belief about what is actually possible in tiling a 2D plane - not unlike Penrose tiling.

You are over optimistic about the timescales but in some domains where a combination of brute force and deep learnable heuristics can triumph I suspect several of the famous outstandingly difficult mathematical challenges may fall to AI within the next decade (perhaps sooner).

Machines don't get bored or make trivial typo mistakes like we do.

I never expected to see a computer that could master Go and yet now there are several that can bootstrap ab initio from the basic rules and surpass the best human players in under a month.

Draughts turned out to be misleadingly simple. Chess was a tougher nut to crack requiring initially dedicated parallel hardware (but now it is hard to find a serious chess program that can't beat a human GM).

Go seemed to be intractable with so many possible moves and game states.

Automated circuit design has been tried. It will be interesting to see if A"I" can do any.

I've seen a human do exactly that, when my neighbour, aircraft designer Henry Millicer, solved the problem of minimising wing root turbulence - a seriously difficult 3D problem. Books had been written and lives spent on this, when he pointed out that any solution to the problem can be reduced to an iterated 2D problem, solvable by an undergraduate using only 2nd order ODE's. That invention is responsible for the characteristic shape of the wing-fuselage junction you see in modern airliners.

Most CPU's these days already contain chunks of stuff designed exclusively by AI. It makes a lot fewer mistakes than a human - especially on boring repetitive stuff and awkward edge cases.

Intel is working on its own neuromorphic designs to challenge Nvidia in that market. It isn't clear which of them will gain most market share. What is certain is that current CPUs are now way more complex than any individual human can fully understand. The next generation will have substantial parts designed by an AI to use fewer gates and less power to implement the same functionality.

and

Probably not. John Larkin's design skills aren't great.

Doing the same thing much faster isn't "completely different", though it may look that way to the customer. The way that essentially identical ideas get patented by different people on different continents at much the same time does suggest that the human brain is a pretty efficient search engine. It isn't always clear what it is searching through, though I can name one case where it was a particular issue of the journal of cystallography - one paper suggested a patentable invention to me in November 1987 and and few months later the guy who had edited the article showed up with provisional patent from the previous May (when he'd been editing it).

It's kind of boutique and the shape may be hard to manufacture or prove less durable due to stress concentration in the interior angles. also getting the pattern right is essential. Some sort of pattern assistant is probably warranted.

What does "AI" mean as regards CPU design? I don't think I can go online to an AI machine and say "design me a CPU."

Well, read the data sheet. People do lay out boards and write compilers.

I doubt that any individual human fully understands my dishwasher.

AI sounds like a fad to me. People have been writing papers about "neural networks" for decades. NN's are cargo-cult caricatures of a biological brain.

I think not. Besides, you have no idea how I, or anyone else, designs stuff. I have no idea myself, beyond noting that certain attitudes seem to work.

Do you design stuff?

All that CPU power can't tell me if it will rain tomorrow.

John Larkin's favourite put-down. It would have more force if he ever posted anything that implied that he designed stuff - as opposed to slinging it together and seeing if it worked.

Because you won't listen.

Weather is pretty predictable over periods up to about ten days. The "butterfly effect" takes a while to build up.

You've read enough to know that chaotic systems aren't predictable, but not enough to realise that it takes a while for them to diverge enough to matter. With the weather it's about a fortnight. With the solar system it's about a million years.

We keep telling you this, but it never sinks in.

That you choose to remain wilfully ignorant and parade that ignorance here is your problem not mine.

You can ask AI to do well posed things like design me a faster multiply algorithm using less power and/or less silicon and it will do it.

Deep mind already has the first new matrix multiplication algorithm under its belt - the first new breakthrough in that field for 50 years!

NS article is paywalled. This one isn't:

It is around 10-20% better than what the very best human minds have ever been able to come up with since computers were invented. It has made the inventive step by extrapolating from the training examples it was shown and then finding new insights that have eluded human minds.

Same happened with Go where it found a host of novel positions and whilst Alpha Go was essentially taught to play Go by humans the next generation more generally AI Alphazero was able to bootstrap itself from the rules to stronger than the best human in about a month.

AI is getting close now to being able to layout boards or silicon better than most humans. The best combination is invariably a human to do the rough placement and machine assist to do the tedious parts like getting all the tolerances and connectivity exactly right.

Right now humans assisted by AI/computer tools can leverage the strengths of each. AI doesn't get bored or make fencepost errors.

You choose not to understand things and then snipe at straw men of your own invention to bolster your argument from a position of ignorance.

Neural networks are good enough to emulate the characteristics of a brain - the only thing lacking is sufficient numbers of them with high enough connectivity to emulate higher cognitive functions.

What we think of as consciousness and self awareness is an emergent behaviour in a sufficiently complicated network of neurons. Artificial machine based ones haven't become that big yet but they will eventually.