I know what I'm trying to say, so I can sanity check the output. You can't, unless you listen to the monologue.
That's why I disagree with people that say "just give me whatever you gave the LLM." That's only useful if you, the writer of the prompt, have no intention of looking at the LLM output before sending it.
"Knowing" something and proving it mathematically are two different beasts.
Zeno couldn't prove that there were no gaps; he showed that infinity was different from how we understood finite things, bit that's not the same as proving there are no gaps.
Later, mathematicians proved the existence of irrational numbers. These were "gaps" in the rational numbers, but they weren't all the "same" of that makes sense? The square root of 2 and Euler's number are both irrational, but it's not immediately clear how you'd make a set that includes all the numbers like that.
Take something like the integers (1,2,3,etc.). They are infinite; given an integer, you can always add 1 and get a new integer.
However, there are "gaps" in that number line. Between 1 and 2, there are values that aren't integers. So the integers make a number line that is infinite, but that has gaps.
Then we have something like the rational numbers. That's any number that can be expressed as a ratio of 2 integers (so 1/2, 123/620, etc.). Those ar3 different, because if you take any two rational numbers (say 1/2 and 1/3), we can always find a number in between them (in this case 5/12). So that's an improvement over the integers.
However, this still has "gaps." There is no fraction that can express the square root of 2; that number is not included in the set of rational numbers. So the rational numbers by definition have some gaps.
The problem for mathematicians was that for every infinite set of numbers they were defining, they could always find "gaps." So mathematicians, even though they had plenty of examples of infinite sets, kind of assumed that every set had these sorts of gaps. They couldn't define a set without them.
Cantor (and it seems Dedekind) were the first to be able to formally prove that there are sets without gaps.
I just don't understand why this was disturbing. Prior to the construction of the reals, the existence of irrational and transcendental numbers was disturbing, because they showed that previous constructions (rational numbers and algebraic numbers) were incomplete. If those gaps were disturbing, a construction without gaps should have been satisfying, reassuring, a resolution of tension. Was there some philosophical or theological theory that required the existence of gaps, that claimed that a complete construction of the number line was mathematically impossible, because of some attribute of God or the cosmos?
I think the issue was that most irrational/transcendental numbers aren’t finitely representable. This means that they are mathematical objects which, each of them individually, somehow consist of an infinity (e.g. an infinite decimal expansion). They are the result or end point of infinitely many steps (e.g. a converging sequence) that you can’t actually reach the end of in practice, and for most of them can’t even write down a finite description on what steps to perform, and which therefore arguably doesn’t “really” exist.
Another point of contention was the notion that the continuous number line would be formed out of dimensionless points. Numbers were thought of as residing on the line, but it was hard to grasp how a line could consist solely of a collection of points, since given any pair of points, there would always be a gap between them. “Clearly” they can’t be forming a contiguous line.
Right, but that's the opposite of what the Quanta article says. The article says that Cantor and Dedekind discovered infinity in bounded intervals. What they discovered (really, what they concocted) was uncountable infinity.
I think this really depends on your role. I don't get enough emails in a day to require 3 hours of replies.
More generally, though, the response can be as simple as "We have received this email; the request will take some time, here's roughly when you can expect an update."
I like this as an optional "this will be read and considered by a human" guarantee added to a job posting. That way, you can still get the reach of digital submissions but the benefits of this approach.
No different from applying to jobs. Much like companies, there are a variety of journals with varying levels of prestige or that fit your paper better/worse. You don't know in advance which journals will respond to your paper, which ones just received submissions similar to yours, etc.
Plus, the t in me from submission to acceptance/rejection can be long. For cutting edge science, you can't really afford to wait to hear back before applying to another journal.
All this to say that spamming 1,000 journals with a submission is bad, but submitting to the journals in your field that are at least decent fits for your paper is good practice.
I don't have a "problem" with AI being used in this fashion. That being said, this article (and others on the blog) sound quite generic. They're characterized by the staccato, "I wanted this. Then this. Also this" sentence structure and headings like "The Problem" and "What it Does" etc.
The thing about an editor is that if you're not careful, your voice is lost. That's fine if the publication you're writing for has a distinctive voice or you have a specific style in mind; this article [1] describes the "New Yorker" voice as an example:
>The New Yorker sort of voice—or rather, the New Yorker voice I was using—is one that sounds on top, or ahead, of the material under discussion. It is a voice of intelligent curiosity; it implies that the writer has synthesized a great deal of information; it confidently takes readers by the hand, introduces them to surprising characters, recounts dramatic scenes, and leads them through key ideas and issues. The voice narrates the material in the first-person and describes the researcher conducting the research, encountering people, reacting to situations, thinking thoughts. The voice is smart-sounding. It is an effective voice for a lot of long-form journalism...
The "default" LLM voice isn't one that I find particularly appealing. For lack of a better term, it has these "zingers" every third or fourth sentence that, if you were writing a spammy piece, would be bolded/italicized. It also reads like the LLM has no faith in the reader's intelligence, or that it's trying too hard to make you feel smart.
This article has that feel to it. I'm not saying it was written by an LLM; I trust that the author isn't lying about only using it for editing. But it has that same style and voice that spammy LinkedIn/Facebook posts have.
Just wanted to shout out the ability to copy, paste, and transpose the data using your mouse and keyboard. The ability to combine and reorganize data without needing to program is huge. It means you can grab data from an online source, paste your results into a report you're writing, quickly flip some data, etc.
Other commenters have covered the major reasons Excel is so popular. But Excel really shines because it's designed for business. I use R and RStudio for a lot of my work, and while it's great, there are little things that it can't do that Excel can.
That's why I disagree with people that say "just give me whatever you gave the LLM." That's only useful if you, the writer of the prompt, have no intention of looking at the LLM output before sending it.
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