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How likely is it that Putnam answers were in DeepSeek's training data?

The solutions weren't published anywhere. There is also no good automatic way to generate solutions as far as I know, even expensive ones (previous sota was 10 solutions and one before was 8 using pass@3200 for 7b model). Potentially the developers could've paid some people who are good in putnam-level math problems and lean to write solutions for LLMs. It is hard to estimate likelihood of that but it sounds like waste of money given relatively marginal problem/benchmark.

AoPS seems to have a forum dedicated to Putnam (including 2024): https://artofproblemsolving.com/community/c3249_putnam and here is a pdf with solutions to Putnam 2023: https://kskedlaya.org/putnam-archive/2023s.pdf

These are still need to be formalized in Lean which can be harder than solving the problem sometimes

How much does it costs to manufacture? Are there any other benefits from using isotopically pure Si-28? Are there any other isotopes used in common thermal conductive material that are more conductive?


I understand isotopically pure Si-28 may be preferred for quantum computing devices. The Si-28 has no spin or magnetic moment, reducing the rate of decoherence of certain implementations of qubits.

https://spectrum.ieee.org/silicon-quantum-computing-purified...


The point of improving the thermal conductivity of silicon is that silicon is what chips are made of instead of, say, diamond.

Of course cost would have to be acceptable.


I was thinking more about isotopes of copper than carbon but I can't find data about thermal conductivity of isotopically enriched copper.


I don't think there would be much difference because much of the conductivity of copper is from the conduction electrons, not phonons. Isotopic purification increases thermal conductivity in silicon because it decreases phonon scattering.

Isotopically pure diamond, now there's something to look at.

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

"The 12C isotopically pure, (or in practice 15-fold enrichment of isotopic number, 12 over 13 for carbon) diamond gives a 50% higher thermal conductivity than the already high value of 900-2000 W/(m·K) for a normal diamond, which contains the natural isotopic mixture of 98.9% 12C and 1.1% 13C. This is useful for heat sinks for the semiconductor industry."


> The burden of the proof should lie with the Israelis that they were not involved in committing war crimes.

This is the opposite of innocent until proven guilty, it is up to the accuser to present evidence not the other way around.


> This is the opposite of innocent until proven guilty

No one is stating they are guilty, but serving in the IDF gives reasonable grounds to suspect someone could be involved in violations of human rights. This military's main task is to maintain an illegal occupation over millions of people. When you apply for a UK visa, for example, you do have to answer questions whether you were involved in war crimes, so it's pretty standard.

> it is up to the accuser to present evidence not the other way around.

I think you are confused, the context of this conversation is hiring for companies, not a court hearing. This principle does not apply here. If they cannot reasonably convince they didn't abuse Palestinians, they just don't get considered, that's it.


What country are you from? It is entirely possible they are still terrorists you just decided as society to ignore it.


The ICC has never issued any arrest warrants for our elected/appointed government officials if that's what you are asking.


They've also not targeted your country either like they did Israel. Even Hungary has recognized their strange obsession with Israel recently. The ICC is part of the U.N. and have passed more resolutions against Israel, then the rest of the world combined. It's pure insanity. Especially when comparing a democracy in the Middle East, a place where every other country is either authoritarian, totalitarian, run by terrorists, or dictators. Bashar-Al-Assad has killed over 700,000 people, yet somehow Israel is worse. It's pure insanity.


[flagged]


It's best we stop here, this conversation will go nowhere.


ICC don't have retroactive jurisdiction from quick google so your point still doesn't make sense.


One of the most difficult things you can do in a discussion like this.

But also, one of the most important.


> a two state solution was never acceptable to Israel

Wrong, they accepted the 1947 partition plan and agreed to the Oslo accords


The Oslo accords were intended - in the words of Rabin - to give the Palestinians 'less than a state', and arguably the division of the West Bank into Areas A, B and C have allowed for the expansion of settlements in the latter.

Whether the 1947 partition was accepted as a final state depends on who you ask, it's fairly clear that prominent figures viewed it as a stop along the way to a more comprehensive settlement. Take Ben Gurion ("After the formation of a large army in the wake of the establishment of the state, we will abolish partition and expand to the whole of Palestine.") or Chaim Weizmann ("partition might be only a temporary arrangement for the next twenty to twenty-five years"). Menachem Begin's Herut continued to use the slogan 'Both banks of the Jordan River", and this language is reflected in Likud's founding charter.


Not just 1947, Jews have been been in the area continuously and have bought land many times. 27 million dunams, which is equivalent to about 7-8 million acres if I'm not wrong, but were attacked since Jews are somehow an exception for owning land. During the same time period Israel was created, Lebanon, Syria, Iraq, and I believe 2-3 other Arab Muslim countries were created, yet those countries were not attacked.


Mm, regurgitated human prose-slop sounds delicious to me


It's not the most enticing thing. If the prompt is nicely crafted, you get more intentional results, and maybe that's interesting. Seems a tough sell. I suppose there are authors like Simenon and Pratchett who would churn out books at the rate of at least one a year, and fans might wish for increased output, so maybe there's a niche for a slop-assisted author.


> Why should I be bothered to read what nobody could be bothered to write?

There are some long abandoned fanfiction that nobody would bother to continue and which I would have liked to see a continuation of a sufficient quality.


Flexible glass exists, if used in a non-sphere container, the container flexing will allow more volume with same surface area. Using flexible glass as a very thin coating around paper, a container could be kept lightweight and the shipping cheap.


A thin coat of flexible glass around lightweight biodegradable material (like paper) might work - it is lightweight, nonreactive, not brittle or dangerous but might be somewhat more expensive to manufacture.


That would be amazing. I'm not sure how that would be possible though. Soda lime glass, our most commonly used glass, has a melting point that begins at 700C (~1300F) and doesn't become very workable until much higher temperatures than that! This is far too hot to be anywhere near most ordinary kinds of paper.

Other glasses have much higher melting points than that, with fused silica melting at 2200C!


I found his blog to be candid and well thought out usually


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