Mathematicians can say whatever they want
A legacy mathematician would use the word "proof" only to describe [("Refl is a value of type 0 + 0 = 0")]
(emphasis added)
So it seems like you're walking back the claim you made about what a (legacy) mathematician would say. Again, a legacy mathematician or any mathematician wouldn't describe that as a "proof."
The native vocabulary is "3 is a value of type Nat" or "Refl is a value of type 0 + 0 = 0". A legacy mathematician would use the word "proof" only to describe the latter, and think it odd to use the word for the former.
Neither of these would be considered a "proof" by a mathematician. Those are just statements of fact. A mathematical proof is a logical argument of deduction that shows that some statement must be true if some set of premises are true. Statements of fact are used in proofs, but a single statement of fact wouldn't actually constitute a proof.
As long as every $250 bill is coated with peanut residue. Let's put some eugenics into the mix.
Claude plays safari is when the real fun* begins.
*human extinction
They should make that one again, but put Al Gore on it.
Quarters are low-value enough (approximately 0.25 USD, if my math is correct) that fraud detection by humans is probably a very low priority. A counterfeiter would have to make a truly large mass of them to make it worth the production costs, and laundering all that without arousing suspicion has got to be some back-breaking labor, which defeats the purpose of counterfeiting. So given the low chance of loss and the low amount of loss from letting a counterfeit quarter through, most people don't find it worth the effort to try to detect it, unless some other alarms get raised.
Combine that with livestreaming, and it seems like there's some major opportunity for growth here.
Hm, perhaps the trophy hunting business could be improved with a sort of minimum caliber/destructiveness requirement on all weapons used for the hunting.
Independence Day was 1996, not 1986. For a really good underrated McTiernan film closet to that, I recommend Last Action Hero from 93, starring Arnold Schwarzenegger with middle-aged Charles Dance (Tywin Lannister in Game of Thrones) as the villain. It was overshadowed by the Jurassic Park juggernaut, but it's a fantastic meta comedy action film parody. Feels a decade or two ahead of its time, as this kind of self-referential satires became far more common in this century than the last.
I remember 2014 being the year of Gamergate and Ferguson, but I don't recall anything about ants.
(Emphasis added) Evidently, you do.
According to the Wikipedia article, it seems that there was a "Cecil Effect" in Zimbabwe after the affair, where westerners hunting lions there became less common than otherwise would have been expected, resulting in less pleasant lives for the locals due to more lions and less money. I don't know much about the trophy hunting business, but what little I know about it from podcasts and radio shows makes me not surprised; it always seemed to me that westerners paying huge sums of money to hunt exotic animals in Africa was almost an unalloyed good, with the only significant downsides being for the individual animals themselves and other westerners who care more about optics or suffering of animals than about the suffering of other humans. The "I consent! I consent! I don't!" meme comes to mind.
Anyone remember the affair of Cecil the Lion that was also around that time (seems like about a year before the affair of Harambe)? I recalled that it caused a bunch of drama online similar to Harambe, and then suddenly no one ever talked about it again. I'm always reminded of it when I run into Jimmy Kimmel on the news or social media, because he famously shed tears on his show while talking about the affair. I think these and Kony, referenced in another comment, stick to memories for being some of the earlier examples of social media hot flashes that tore through the internets and then went away, which became very common and even the default in the past decade.
With 2014 online drama being defined by the affair of reproductively viable worker ants, I wonder if future historians will think we just had a really strange animal-loving phase in the mid-2010s.
usual unsavory types that caused the original high denomination bills to go out of circulation, I don't imagine the average American would have much use for these.
I feel like this might be part of the point. Because the USD is so popular and the 100 dollar bill is the highest value denomination, it has become one of the de facto standards for criminal financial transactions and thus featured heavily in films and TV shows and music. As a result, Benjamin Franklin has become even more immortalized, to the point that his first name is used interchangeably with $100 in some contexts. The $250 bill would likely supplant that, and thus Donald Trump's face would be featured heavily in future films and shows about crime, and perhaps there would even be a song called "All About the Donalds." All of which would probably make Trump's ego very happy.
Fair point on the chuddiness and the lack of requirement of instantiation. That's a level of postmodernism than even I thought possible.
But for the other point, there's arbitrarily often and there's arbitrarily often. Given the limits of biology, I don't think it's possible for a human to change genders in a literally infinitely small amount of time, and, as such, however often a human were to change their/xir/zir/etc gender in their/xir/zir/etc finite lifespan, it would only sum up to a finite number. As such, all that does is to have another finite number to be multiplied by, which means the result is still finite.
A lot of people seem to have this mythical idea about "attractiveness" or "good looks" or "being pretty" or "beauty" or etc. that exists as a concept outside of human judgment, as if how "attractive" someone is isn't defined by how many and how hard other people actually are "attracted" to them. I think this sort of thinking is especially encouraged in women, which is why the idea that "all women are 10s" is so common among women. And why the idea "straight men will judge you, a straight woman, as less attractive" registers as something different from "you, a straight woman, is less attractive."
Greater Male Variability hypothesis wins again!
The twist is that Male Lead is the monster, and the climax is his grotesquely personified id rapaciously chasing Female Lead through a hellscape maze of his own creation. A surface-level analysis might fault the film for once again portraying male sexual frustration in a negative light, and yeah, that element is certainly there, but film (at least indie film) like all modern art is meant to challenge the viewer. On some level, one ought to reflect on how much of a monster one becomes on the inside when Stacy rejects you. I think the film earns it.
I'm reminded of a Spongebob meme I saw a while ago, a comic made up of screenshots where, IIRC, Spongebob is ordering from Squidward, with alternating frames, saying, "In my medieval fantasy story, it turns out that the church is actually evil," "How original," "And the demons are actually the good guys!" "Daring, are we?" It's quite possible and even likely that there's some valuable insight and even challenge there, but this is such well-trod ground that comports with the general thrust of basically all media in the mainstream that this description, in itself, makes it sound boring, if not tiresome. That said, it all comes down to the execution, of course.
I'm reminded of some sort of social justice guideline for gender inclusivity in forms that I read in the mid 2010s that said that it was a harmful bias or something to imply that there was only a finite number of genders. This, of course, is a statement of fact that there exists at least one human who has infinite genders, since there are only a finite number of humans who exist, and if each one only has a finite number of genders, then the number of genders is, at most, the sum of products of only finite numbers, which is also finite. I'm not sure if I've run into this mythical being yet, though there have been candidates.
One of each. Kettlebells are generally not used two at a time like dumbbells often are. In fact, I don't think I've ever seen a kettlebell exercise that involves using two at a time.
I would argue that it is better for all involved when abusers are punished, and someone tries to burn it all down because they didn't get thier way we'll punish them for that to.
You say "we'll punish them for that," and I'm assuming that "are punished" before that has an implicit "by us." I agree that, in a fictional world where "we" accomplished such a thing, that it would be better for all involved. Unfortunately, accomplishing such a thing is Very Hard. Doesn't mean it's impossible, but I'm too cowardly to be willing to throw myself on the barbed wire so that my comrades behind me can walk over my body in the tiny chance that we actually do accomplish this. And, as such, I can't begrudge anyone else for being so cowardly.
It could be both. The Shake-Weight was often compared to one, so why not actually go all the way? I'm sure there are advantages to a sex toy that can make 5 seconds feel like 5 minutes, or even longer.
With the caveat that there's very little empirical support for any of this, I'd say that this sort of advice is generally wrongheaded. Scott Alexander wrote on SlateStarCodex, IIRC, a very long time ago about how some cognitive behavioral therapy techniques seemed to have metaphorically "gotten into the water supply," such that using them on people actually in therapy became less effective, because they had already gotten the vast majority of the benefits that come from using them. I'd guess, for the vast majority of the populace, especially among the male and romantically unsuccessful, this basic advice is something they've heard and implemented plenty.
I'd guess I interact more with incels than most people by nature of being a nerd who interacts with anime/video game fans, and the vast majority of them simply don't lack the types of social skills that get developed from engaging in social activities all the time (some certainly do, though - though in those cases, I'd guess that they're intrinsically resistant to the technique). They dress well, are well-groomed, can hold good conversation without going into autistic ramblings, make decent money, and are usually not awful-looking (though probably somewhat below average?). They can barely even get matches, much less first dates, much even less second ones. There's something else they're missing.
Because if we don't privilege them, then they will cause us harm. At some point, the harm that would be prevented by not privileging them could outweigh the harm they would cause and, as such, be worth it, but it's hard to tell where that threshold is and if we've crossed it. In the long run, we can strip them of their ability to cause us harm, but that's one of those Very Hard Problems, and in the long run, we're all dead anyway.
My guess is that horror movies are in the sweet spot of being not too high budget while also being a significantly better experience when watched in one shot on a large screen in a dark room with a crowd compared to watching alone at home. Spectacle movies like Star Wars fit the latter but not the former, while comedies fit the former but only a little of the latter.
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This is the second most offensive opinion I've read on this website.
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