And you can subvocalize (that is, think them in your mind) two different voices at once if you deliberately try to, and it's a skill that gets easier with practice. Though, no matter how much I practiced it, I was never able to get to where it would take place automatically without my forcing it.
Before birth. ...Hey, don't point that pitchfork at me, point it at Socrates. In his defense, that kind of does describe when LLMs acquired their knowledge (if we consider "birth" to be the moment when the already-trained weights are sent to the GPU) https://en.wikipedia.org/wiki/Anamnesis_(philosophy)
Long before Erdös, we had Plato and Socrates develop the theory of anamnesis, that there is no such thing as learning, but rather, whatever we supposedly learn, we actually remember (we knew it already and had forgotten it). Presumably this should be understood only of universal facts (like mathematics), not contingent facts (like who was the president of the U.S. in 1950).
Before the discovery of the fundamental theorem of calculus, enormous ingenuity and whole careers were spent doing calculations which the fundamental theorem trivialized. To be clear, I'm not just saying that the people involved were doing lots of mechanical arithmetic (though they did that, too). I'm saying they did creative, inspired, nontrivial mathematics to calculate certain things, all of which was then trivialized and made obsolete by the fundamental theorem of calculus.
Mathematics is a bridge to what Neoplatonists call the intelligible world. Currently, mathematicians navigate that world on foot. It's exciting to think that soon we might have cars and trains in that world so we don't have to painstakingly walk everywhere.
I find that I don't necessarily mind when a book repeats itself, and a good helping of anecdotes can help a point get across. Ralph Waldo Emerson famously said, "I cannot remember the books I've read any more than the meals I have eaten; even so, they have made me." Trying to distill a book down to the minimum logically equivalent length is like eating the smallest possible portion of a supplement one time and then wondering why it doesn't do anything for you.
Agree. I do a lot of travel and in 3rd-world countries it is quite common to get 2g spam, it's really unacceptable that Apple doesn't offer a way to turn off 2g short of lockdown mode.
One place where the big i and small L look almost identical, and a pretty funny/annoying place for them to do so, is when you're typing a WiFi password in OSX (if you toggle "Show password"), at least as of MacOS Monterey 12.1. I also see them as almost identical in my browser's URL bar (Firefox 148.0.2 on aforesaid version of OSX) which isn't just an annoyance but might even be a security concern!
All-uppercase distorts the shapes, making them unfamiliar to ESL readers who have less practice. You must know that famous meme about how you can read English perfectly fine if the letters (besides first and last) of each word are scrambled: "Aoccdrnig to rscheearch at Cmabrigde Uinervtisy..."
Granted, I'm not an expert in this area. I'm actually just relaying what an ESL ex of mine told me. She hated whenever she had to read things like "Calvin and Hobbes" which use all-caps, for this exact reason. Come to think of it, she was Japanese, I wonder if it has to do with growing up with a logographic writing system.
I didn't read the OP but one pet peeve of mine is the uppercase I vs. lowercase L in sans-serif. Especially in contexts like randomly-generated passwords which you have to manually copy for whatever reason. Does the article address this in any way? Or is the context limited to "real" language where that's not as much of an issue?
Smallcaps hyperlinks is even worse than it might initially sound: many ESL speakers have difficulty with text written in all-caps, and it totally makes sense why, if you think about it.
On rare occasions where the other methods don't yield anything, I have friends in academia who have access and who are happy to help out. But yeah, it's totally medieval that this knowledge isn't freely available to the world.
I'm working on arranging talks and poster presentations at various conferences/seminars to spread knowledge of my latest academic paper, "Specieslike clusters based on identical ancestor points". In the paper, among other things, I argue that (we should define species in such a way that) for any organism in any species, either the species is made up almost entirely of descendants of that organism, or else the species is made up almost entirely of non-descendants of that organism. This is a funny property because most people who hear about it fall into one of two camps, those who say it is obviously true, and those who say it is obviously false!
Sorry for not seeing your message until now. Journals, at least in mathematics, generally don't require you to have a university affiliation, so as long as the paper is good on its merits, you can get it in, though I don't know to what extent it might be more of an uphill battle due to implicit peer reviewer bias etc. Re: reference products: one generally scraps what one can together through a combination of arxiv.org, Anna's archive, or emailing the authors.
This is a common misconception. People without academic affiliation (based on their email address) require someone to vouch for them before they can submit to arxiv. And papers submitted to arxiv (with or without affiliation) are reviewed, and many are rejected.
>Peer review has never really been blind and I suspect PIs will reject papers from "outsiders" even if they are higher quality.
I'm a complete outsider (not even in academia at all) and just got a paper accepted in the top math biology journal [1]. But granted, it took literally years to write it up and get it through. I do really worry that without academic affiliation it is going to get harder and harder for outsiders as gates are necessarily kept more and more securely because of all the slop.
J.S. Mill's autobiography is a fascinating read. He spends quite a lot of it discussing his early childhood, explaining that in his opinion he was not particularly special, rather, it was his father who pushed him to all those accomplishments. His father sheltered him from other kids so he was not aware that his accomplishments were unusual!
"The main axiom we introduce [...] states that for any organism in any species, either the species contains at most finitely many descendants of that organism, or else the species contains at most finitely many non-descendants of that organism."