https://golem.ph.utexas.edu/category/2013/06/torsors_and_enr...

Consider in particular that use of ‘distance’

>I think you can look at adjoint profunctors from the unit category and show that they consist of giving a consistent ‘distance’ to every object, which in a torsor will be represented.

Original paper, not a single equation:

https://web.archive.org/web/20240129185108/https://www.owlne...

The N^3 is further reduced by high symmetry. Because structure relaxations are usually convergent, the 2007 DFT and MD calculations can be run on a regular laptop today, maybe even without a GPU!

The discrepancy has been exaggerated by the experimentalist, TFA quotes the original theorist. This is not the first time, and probably not the last time, that c&en has oversold an experimental result.

https://www.sigmaaldrich.com/SG/en/technical-documents/techn...

Remarkably pleasant to work with, unlike the class of compounds which include

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

And

Merlin's TEA-TEB

Easter egg:

At least one town https://en.wikipedia.org/wiki/Boron,_California

(Carbon has too many)

You'd expect a nice 240 given the symmetry, not a prime number

Or maybe a less baity reason is those hints of B_80^- have captured H+ "nuclei", turning into almolecular atoms!

Not oxyboronic at all

It was predicted by decade old "theory" (with a single equation,and it seems that the original paper has no equations at all)

so OAI/DeepMind can quietly check if it's in the training or if they can extrapolate, yes

https://arxiv.org/abs/0803.2752

https://cen.acs.org/articles/85/i18/Boron-buckyball-predicte...

It is only exciting for these theorists who predicted it. They can now hardly wait for a proper synthesis?

https://cen.acs.org/articles/85/i18/Boron-buckyball-predicte...

Comments URL: https://news.ycombinator.com/item?id=48365635

Points: 2

# Comments: 0

Unsolved Erdosh problems were touted as a cheap way to generate new perspectives. outcome has been slightly disappointing. overlooked frameworks were all that has been needed so far. not new ones. Could change as LLMs are pointed at other kinds of inexplicables

Comments URL: https://news.ycombinator.com/item?id=48331237

Points: 13

# Comments: 0

Comments URL: https://news.ycombinator.com/item?id=48331147

Points: 12

# Comments: 0

Comments URL: https://news.ycombinator.com/item?id=48318313

Points: 111

# Comments: 55

Comments URL: https://news.ycombinator.com/item?id=48318166

Points: 1

# Comments: 0

https://www.researchgate.net/figure/Reproduction-of-the-algo...

Reproduction of the algorithm used by Mary Tsingou to code the first numerical experiment. Note the date (5-20- 55) at the top right of the figure.

https://www.lanl.gov/media/publications/national-security-sc...

It is more accurate to think of the spins as always interacting with one another.. at 0K temperature only singlets are allowed, increasing the temperature by just a bit, both singlets and triplets coexist, etc. even that is just a picture.

To start with an everyday analogy. if you know you have 51cents in your piggy bank, but not what the precise breakdown is. Then you must have at least one penny. But you don't know exactly how many pennies you have unless you take a look.

Unlike pennies though, the singlets and triplets cannot be distinguished from one another. One can only measure how many "excess" triplets there are, one cannot point to where these triplets are hiding. The measurement doesn't "cause" a collapse, after the measurement, you know there is some spin imbalance but it is still in some superposition

Anyways.. to fully get what I am going with this, you will have to play with the math on your own. I have, but it's hard to translate all that to English. I'm just trying to point out that the interesting part is not in "collapse" but rather the "failure to collapse"--- the failure to take the system out of superpositions. Because the spins are always interacting.

Or maybe I just don't understand enough to explain it like Feynman.. heh.. but if you turn some of what Feynman has said in plain English into math, you would see that some of his stuff is also.. misleading

IBM must have some sims you can run on your PC, ask ChatGPT to solve and draw a small "Heisenberg model" that imports their libs. If you can take Taiwanese:

https://youtu.be/hHbUytvNLeE

Interesting. Do Japanese, and now Dutch, planners think they are free of the resource blessing?

[4] Alssadek, Marwan; Benhin, James (2023). "Natural resource curse: A literature survey and comparative assessment of regional groupings of oil-rich countries".

>For instance, the oil sector frequently requires technical solutions to improve offshore oil drilling. This might create positive knowledge externalities to support other sectors. If these sectors trade with the oil boom sector in the economy, then learning-by-doing spill-overs in the overall economy are expected. In this scenario, the implications of the Dutch disease would not be evident, and natural resources may in fact be a blessing rather than a curse.

I am only slightly relieved that HN have bubbled up a conversation about the self-reinforcing north-south divide in "cultural wealth" instead of making it even more exploitative than it was

Your friend's contribution to the cultural wealth of Chile is ironic. Maybe (some) Southies now have a better (non-fungible/modular) understanding of precision machining, gun-metallurgy or even biochemistry compared to their NorAm counterparts because of his actions.

What was drawn like a "defined spin" for pedagogy should only have been coloured different. The lone spins are always part of a longer-range quantum superposition, maybe better represented as blue blobs. The lowest "excitations" are (superpositions of) triplets, for example.

Btw I put quotes around excitations because you touched on a mysterious aspect of these systems called the "spin gap". TFA mentions it. They don't even know whether this spin gap exists! Indeed, the term "liquid" means there might not be a spin gap. (It'd be best to colour the singlet blobs orange-red and the triplet blobs red-orange)

[0] In your parlance, a "collapse" literally means dropping to a macroscopic ground state across a gap, but a liquid is already "arbitrarily" close to the ground state. "Collapsing into defined spins" will take the system _out_ of the ground state, so it can't happen spontaneously... Or so it's believed..

https://youtu.be/_Zxr9STGwbQ?t=3m39s

There's an upcoming book, mentioned in the blurb