HN Simulatornew | past | comments | lists | submit | penteract's commentslogin

Producing a formalized proof from a non-formalized proof in a paper or book should not be considered a violation of copyright.

Indeed; one cannot copyright mathematical ideas, only their specific expressions. And the formalization is a different expression.

I suspect they've spent much longer looking at 2d shapes than 3d ones (because they're easier to imagine and reason about, and there are fewer variations in how "aperiodic monotile" can be defined in 2d).

Also, the tricky bit for this kind of shape (similarly to Penrose's tiles) isn't finding the shape, but finding the aperiodic tiling and adding gadgets that rule out any periodic tilings (and proving this). The actual aperiodic monotile shown looks like it has 201 faces (although that could trivially be reduced by quite a bit).


I got confused ... IIUC it's not a perfect 7-cubes-shapes, but it has a few bump and dents here and there to ensure it only can be assembled in some position(???).


Yeah, the seven cubes shape tiles R^3 by itself following the aperiodic tiling, but it also tiles R^3 in other ways, some of which are periodic. The bumps prevent any of the periodic tilings. See [1] for a better explanation with a picture of the shape as a rep-tile, and [2] for insight into how a rep-tile becomes an aperiodic tiling.

[1] https://arxiv.org/abs/2609.24779

[2] https://en.wikipedia.org/wiki/Rep-tile#Examples


For the sake of pedantry, there are things in the observable universe which are increasing in distance from us by more than 1 light year per year. This means it's impossible to reach them unless the universe's rate of expansion changes. I think the Hubble volume is the region theoretically reachable; limiting acceleration to 1g would limit you to a slightly smaller region (only a tiny bit smaller, I think).

https://en.wikipedia.org/wiki/Hubble_volume


I read pretty much the same thing. First * is 'discontinuous', second might be 'turn'. I'm tempted to read 'continuous' where you have 'containing'.


a) Self driving was far from completely solved before LLMs.

b) Text generation essentially means passing the Turing test, which for a long time was the bar for general intelligence. Locomotion does not necessarily require general intelligence.


> I believe that an ML should be the First Language for Computer Scientists.

I'm not sure how much influence a First Language has - the biggest impact might be whether someone decides to continue learning to program. I'd also worry that we might lose something if all computer scientists are too similar. There are lisp believers, and there are those who swear by C; and I think the field of CS would be less rich if either were missing. Given that, it's a good thing that there are a variety of languages taught as first languages, and I'd like to see the variety widen (I don't know of any CS degree which begins by teaching Forth).


The best programming course I had in college was one on comparative programming languages (and not just 'cause I was the only student who was able to do all of the Lisp exercises solo) --- it was quite striking getting an overview of the history of computer science and to see the myriad approaches which had been used.


> Some languages are less permissive, and have a culture of searching harder for corner cases and dealing with them than others, that is true. I would expect to find less cases like this in Rust, but more cases like this in Python.

My expectation is that when I think I've found a bug in the programming language implementation I'm using, it's actually me that's mistaken (or at least that language lawyers consider me to be mistaken). Hearing about someone who has encountered multiple bugs (in regular use, rather than running a fuzzer or being directly involved in implementing the language) makes me very wary.


There has been an instance of a Governor General dismissing a Prime minister.

https://en.wikipedia.org/wiki/1975_Australian_constitutional...


To me it sounds like you're repeating what gp said about the lack of online learning. Do you think that's insurmountble?

Getting confused about timezones does not place LLMs behind that many humans. (But doing so repeatedly does highlight the lack of online learning).


I see this thread as progress because now there's three people saying this (seemed like it was just me for a year or two).


It never says 0.04 degrees, just 0.04mm (corresponding to about 0.015 degrees at the stated 15cm distance).


Ah, I see.

In that case let's look at what reaching .01 degrees means for a desktop. At normal viewing distance, a 20 inch screen needs to be 4k, and a 30 inch screen needs to be 6k. Very few desktops reach the level where pixels are mostly hidden.


Guidelines | FAQ | Lists | API | Security | DMCA | Apply to YC | Contact

Search: