The first part likely is just an artifact of an unwritten common assumption. That is, it's probably 96% of women, who lived to adulthood, who were ever married.
Maybe, but I doubt it. The vast majority of the sources, including the two listed for this claim, are listed as "attributed", meaning "A model (Opus or Fable) claims that this is what the cited source says. In my spot checks, I've found these claims to be accurate; still, since it's just a model claiming that author x says y, there's a nonzero chance that it's a hallucination."[1]
I couldn't track down the first source, but the second source goes over something completely different. Maybe Claude accurately remembered the first source when it was stolen during the training process, but forgive me if I'm skeptical. Feel free to track it down yourself and let me know. Otherwise, I will assume it is an LLM hallucination.
(Also, given my background knowledge of the Tang dynasty, I would be surprised if the average marriage age was as high as 18!)
I don't follow what your point is here. If you're not aware, Anthropic pirated many books via libgen and similar tools for use during the training process[1]. Maybe you are not aware of this, or do not consider it theft?
Key distinction though: Anthropic can be said to have "stolen" or pirated those books when they downloaded them illegally, but not when they trained Claude, because that same lawsuit found that training is fair use.
Anthropomorphizing makes for poor analogies, but it's kinda the same way your acquisition of background knowledge of the Tang dynasty from whatever source material you used is not considered stealing or pirating either.
Did the original owners of the books no longer have them in their possession afterwards?
Theft involves removing from the source, Copyright violation is distributing copies without a legal right to do so. Training is fair use.
The judge found that it constituted copyright violation. Purchasing the books would cover their responsibilities with regards to training. The claim that they are destroying books to hold copyright is incorrect. The judge cited precedent that said instances of not destroying the originals were also fair use, his claim about destruction was to say even if this precedent were not considered fair use, the destruction that was already occurring (because it is easier to scan loose pages), invalidated one of the arguments against it.
The ruling was on training took the form
If A is ok then B is ok, but even if A were not ok, B might still be ok.
Excellent. I will thus take a copy of the latest Disney movie and train myself on it while claiming fair use as a defence to the accusation of copyright infringement.
You can do that legally as long as you do not confuse people that what you create might be an actual Disney product, or that you try to represent it as actually created by Disney.
Both of those are protected by law. Learning from a Disney movie and creating your own thing is not, and should not be, disallowed.
It's not processor op-codes, but sure it's part of the software. You wouldn't say that a set of precomputed weights in a numerical integrator aren't part of the software, would you? Or say that the graphics in a game aren't part of the software?
I'm a mathematician. It's kind of a strange statement since, if we are talking about a matrix, it has two indices not one. Even if we do flatten the matrix to a vector, rows then columns are an almost universal ordering of those two indices and the natural lexicographic ordering would stride down the rows.
I assume they're talking about how when multiplying by a matrix by a vector, it's more natural to think of the matrix as a collection of columns than as a collection of rows, and to think of the vector as a column vector.
That layout is a nearly universal convention in applied practice such as statistics. Readers would be very very confused if you flipped it the other way.
The irony is that "programmers" are much more divided on this than statisticians are.
It depends which side you are doing the multiplication on? Most linear algebra textbooks work matrix-vector, where the vector is a column vector. In that arrangement, the resulting vector is formed by dot products of the rows of the matrix with the vector.
On the other hand, you see vector-matrix multiplication a lot in other places, for example, the Markov chain literature. There, the vector is a row vector and the resulting vector is formed by dot products of the columns of the matrix with the original vector.
"Yet the average indirect cost rate reported by NIH has averaged between 27% and 28% over time."
and a lot of that is simply because nobody wants to do the detailed accounting for things like: lab electricity usage, janitorial services, misc supplies.
> The result? 90%+ of academic science is fraud.
This is dramatic nonsense; a simple made up number.
> Not even the Trump admin is alleging levels of indirect costs that high.
The 70% "indirect cost" number had latched into my brain. I was willing to concede this point, but it looks like 50, 60, 70% are accurate as of 2025 [0].
While there exist institutions with only 30% indirect cost, every single not-especially-prestigious university in my region are retaining 60% or more.
> As of May 2025, indirect cost reimbursements for [institutions of higher education (IHE)] are typically determined by an indirect cost rate that is pre-negotiated with the federal government and varies by IHE—ranging from 30% to 70%.
You could definitely replace "Tuesday" with something like that and part of the pedagogical purpose of the problem is for people to question this. The actual effect comes from not distinguishing the boys. That increases the likelihood that at least one of them will be born on any particular day, upweighing the likelihood that there are larger numbers of boys. i.e. You just get, on average, better coverage of boys-born-on-Tuesday when there are more boys.
Well, "born on a day" would not convey any information unless it means "during daytime". If that has probability 1/2, the answer would be 3/7. With Tuesday (or, indeed, any other weekday, with probability 1/7), it is 13/27.
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