Readit News> This method created a new sort of infinity that mathematicians were unfamiliar with, and it was vastly larger
I understand that the construction of the reals paved the way for the later revolutionary (and possibly disturbing, for people with strongly held philosophical beliefs about infinity) discovery that one infinity could be larger than another. But in the narrative laid out by the article, that comes later, and to me it's clear (unless I misread it) that the part I quoted is about the construction of the reals, before they worked out ways to compare the cardinality of the reals to the cardinality of the integers and the rationals.
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.
> Suddenly, the monstrosity of infinity, long feared by mathematicians, could no longer be relegated to some unreachable part of the number line. It hid within its every crevice.
I'm vaguely familiar with some of the mathematics, but I have no idea what this is trying to say. The infinity of the rational numbers had been known a thousand years prior by the Greeks, including by Zeno whom the article already mentioned. The Greeks also knew that some quantities could not be expressed as rational numbers.
I would assume the density of irrational numbers was already known as well? Give x < y, it's easy to construct x + (y-x)(sqrt(2))/2.
I don't get what "suddenly" became apparent.
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’ve had fancy brands like Zyliss and OXO. I’ve had cheap store brand models and cheaper Amazon MYSSNGVWL type stuff as well. Knowing they would probably break didn’t make it feel better when they eventually broke.
Anyway the new salad spinner is large, heavy, with a steel pin into a brass bushing, has a metal handle and nylon gears in a sealed gearbox with exposed stainless screws for servicing. I opened it up and greased it on first use, mostly just to pretend to be servicing it, just to see what that felt like. It felt good!
The best part is it came with a catalogue that had order codes for spare parts. They wanted to help you maintain it. It was built to last and the manufacturer was on your side.
https://www.dynamicmixers.com/en/our-products/salad-spinner/...
I’m starting to feel silly writing all this about a salad spinner, but where is my car version of this?
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."
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.
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.
[1]: https://www.publicbooks.org/ditching-the-new-yorker-voice/
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.
It could be insider knowledge that Intel/AMD/other has made a huge step forward and has reduced Nvidia's moat (unlikely considering his public support for Nvidia's hardware, but possible).
It could be that the AI bubble is popping.
It could be that he wants to "lock in" the gains that Nvidia has made; having that much capital in one company tied to a pretty volatile sector is risky.
Maybe he thinks that the beneficiaries of AI will be B2B companies like Microsoft with connections to most major businesses.
Maybe it's a changing view on how much compute will be needed to fuel AI developments moving forward.
And this is just the list I could thing of off the top of my head. There are plenty of other reasons this move could be happening. Absent an inside line on Thiel, anything else is speculation.