You often see this I think, in "pretty" proofs compared with the more direct approach. A clever early step or some bit of startling insight.
214 karma · joined June 22, 2020
You often see this I think, in "pretty" proofs compared with the more direct approach. A clever early step or some bit of startling insight.
I've only watched the movie version, but all these feel like they were words spoken by a character in CATS the musical.
A website was soon set up: "HarMannenFalt.no"[2] (Has the Man fallen?), displaying no more than the word "NEI" (No). The sentiment of the joke was felt by all, as many had grown tired of all this attention being directed at what was essentially, on its surface, just a mountain, standing there, doing nothing.
I was a student at the time, and remember many idle screens around campus set to this page, reeking of that sarcastic mock-worry only a student body could put on. But I suspect a lot of us were secretly waiting for the moment when the text would change into "JA".
And soon enough, something did in fact happen. A neighbouring mountain, Veslemannen (The Little Man), saw a considerable increase in daily movement in 2018, before finally there was a minor landslide in 2019. But this was not the landslide we had been promised and waited for, as The Man himself was still standing tall as ever. A "JA" was not really in order, but then perhaps neither was really a "NEI".
Instead, the website was updated to show "TJA", a Norwegian word somewhere between yes and no, with meaning closer to "Well, perhaps".
As an aside: A second website with identical design was also created: "HarDovreFalt.no"[3]. A play on the concept with allusion to the vow of our founding fathers: "Enige og tro inntil Dovre faller" (Agreeing and true until Dovre falls)[4]. The "NO" on this second site, I think, is far less likely to change any time soon.
[1] https://en.wikipedia.org/wiki/Mannen
[4] https://no.wikipedia.org/wiki/Enige_og_tro_inntil_Dovre_fall...
As for my BMI, I'm 183cm at 85kg, which I understand nudges me just inside of "overweight".
As an aside, I have said for a long time that I wish it was socially uncontroversial for a guy to wear a loose skirt or dress in public, and that if I found one I liked I would wear it all the time.
One of the silliest battles I have found myself fighting against society has been my search for comfortable yet attractive men's pants. I deeply dislike the restricting fit of modern pants, especially tighter fitting jeans, but also the semi-current fashion in suits and pants in general.
It may be that a catalyst for this conflict has been my anatomy. My thighs and butt are huge, compared to other guys of similar proportions, and so apparently they cannot be contained by modern fashions. Every time I try to put on a pair, they're either too loose in the waist, or too tight in the thighs, and always sit too low for my liking, digging into my groin if I force the belt to sit at my waist. And should i find a pair that feels acceptable at first, my optimism only lasts until I have to sit down and feel the edge of these clothes digging uncomfortably into my flesh, rekindling my hatred for these trends and their designers.
The current resolution to my woes has been Darcy Clothing's line of suspender pants[1], which I have had tailored after purchase to taper and fit my height. However, this look is quite jarring in a modern environment, so I tend to wear a sweater over the suspenders. Still, I sometimes need to take it off, and wearing something like this day in and out puts quite a label on you.
Still to this day I keep my eyes open, hoping that the pants of my desires will appear in a shop somewhere, or that trends will change, and we get style in service of comfort, instead of discomfort in service of style.
It's like a positive feedback-loop (though I guess morally negative) between manufacturers, developers, and users, all three dragging/pushing on the other to roll down the hill of faster hardware and heavier apps, none of them really in control or able to stop, and therefore also not directly to blame. The upgrade-train to Waste City has no breaks. Still, it seems to me at least that the manufacturers are the only ones strictly happy about the situation.
It's funny, but dancing in particular has been my greatest fear for as long as I can remember, so I've always done my best to avoid situations where I'd be forced to do it. Not only did I not see the point or appeal, but I deeply dreaded the prospect of going on the dance floor.
As fears go, however, this one is quite innocent, and also fairly simple to face. And how empowering wouldn't it be, to overcome ones biggest obstacle? So not too long ago, when I was invited to a dance class by a group of friends, I decided I'd go, just the one time, as some sort of exposure therapy.
The dance was tango. As I had expected, I was anxious, stressed, and scared through the entire class (although it was very helpful having the excuse that it was my first day). What I did not expect was how fascinating the dance would turn out to be. How beautiful and elegant, yet also technical and structured. I saw our instructors dancing some dead simple improvised steps, and somehow, despite not being planned out at all, they were totally synchronized. There had to be some brain-to-brain communication going on, a sort of body language that I could not yet perceive or understand, but that I knew I wanted to learn.
That was six months ago, and since then I've gone to some sort of tango thing multiple times a week, every week I've been able to. I'm still nervous on my way to a class, and it takes a few dances to warm up and get loose each session, but I'm starting to enjoy it and feel like I'm actually dancing. In the process, I've come to understand more deeply what people mean when they say "there's more to life than X".
> Outline a proof of the snake lemma
Satisfied with the output, my friend then asked it to outline a proof of the Riemann hypothesis, and rather than being tricked into gibberish maths jargon or miraculously producing such a proof, ChatGPT accurately and briefly summarized the hypothesis, explained some limitations of current knowledge and paths such a proof might take. It did a better job at it than I would have.Because of these examples, even though they are examples of mathematics rather than computation, I don't think it's fair to be so dismissive. It's a bit of a well known fun fact that a lot of professional mathematicians are terrible at mental arithmetic.
One simple trick, I think, is to avoid extensive use of pronouns. A sentence like "Because of that, it doesn't find it there" might be clear enough when you know the context, but is meaningless if you don't. Filling in "that", "it", "it", and "there" would help tremendously. It will make sentences awkward if you avoid them completely, of course, but I think sentences that contain nothing but pronouns are a red flag.
After having spent a lot of time on learning it (before moving on to Latin for a couple of years, and later French), I've become more skeptical of some of the elements that drew me in to begin with. According to the comprehensible input hypothesis of language acquisition, studying grammar is not as important as the number of hours spent taking in messages that you understand in the language. So, a simple grammar is actually not so important. Of course, it will let you start immersing more quickly after less grammar study. But you might also have spent that time instead immersing with a "real" language in content that is more enjoyable and interesting (good entertainment in/translated to Esperanto is scarce) and come out of it with a useful skill with roots in the real world. (Sorry fellow Esperantists if that comes across as harsh...)
Esperanto also does away with a lot of redundancies, like grammatical gender, or arbitrary groups of verbs with distinct conjugation schemes. On its surface that's a good thing. It makes it easier to memorise the rules. However, it also makes the language more fragile as a medium of communication, or less noise resistant. Grammatical gender and redundancy in syntax is very useful to a fluent speaker whose brain is familiar with all the arbitrary rules, because these things provide our brains with different checksums to rely on when parsing spoken sentences. That utility is largely why such grammatically redundant features have persisted.
He could have resigned early simply because going through with the game would have left a bad taste in his mouth. I'll bet it's annoying to play someone with a history of cheating, regardless of whether they are still currently known to be breaking the rules or not. Imagine having to sit through a game that you love to play, only with a nagging thought in the back of your mind that sucks the joy out of the experience and turns it into a chore.
Recently, I posted a comment in a questions thread on /r/math asking where I could get a more thorough treatment of the philosophy of mathematics, as these lectures can get a bit arm-wavey, but the responses I got were disappointingly dismissive. One guy said all this philosophy was "not interesting" and considered the foundational stuff to be "just a construction". I get that it may not be directly useful for current research to a mathematician trying to get published, but common!
[1] https://www.youtube.com/watch?v=V49i_LM8B0E&list=PLPH7f_7Zlz...
One development that is new is the one where reviews and encyclopedia entries are written by people seemingly detached from reality. That's a sobering thought for anyone looking for factual answers.
I'm never more than an Alt-Tab away from a terminal, and have some nice and simple aliases for creating new plaintext notes, or accessing old ones. Yet I also need to keep a notebook or piece of paper closeby for handwritten sketches, notes, diagrams, etc. I studied maths and physics, where solving problems with pen and paper is simply how you do things. Come to think of it, I'm quite thankful for that part, because it is a powerful skill to have developed for managing ideas.
I have friends who are bad at handwriting, and who hate it and avoid it for that reason. Some of them claim that handwriting is a useless skill. I also have parents who are bad at typing, and who prefer handwriting for that reason. They do see the utility of touch typing, however.
I know both well, and value both very highly. I maybe won't be so strict on my kids as to force them to learn a writing style designed for pens we no longer use, but will encourage them to try it, and to at least get comfortable with writing by hand.