acomar

it's experimenting with a feature that was added to Haskell but just never caught on. it's theoretically very powerful but it's far enough from idiomatic Haskell that it sees basically zero usage in the wild as the cost for using it is that very few people can understand what you've done.

there is actually something rather special about the questions mathematicians focus on but the jargon and technical detail get in the way. ultimately, the reason prime numbers are so fascinating is because they turn up in weird places, with strange properties, and connect wildly different branches of mathematics together.

the Riemann Hypothesis is an example of this. it starts from a pair of observations: 1. the sum of the logarithms of the prime numbers less than n approximates the graph of y = x to absurd precision. there's no obvious reason why this should be true but the result just kind of falls out if you attempt to estimate the sum, even in really crude ways. 2. the sum of the reciprocals of the squares was calculated by Euler centuries ago. the way he solved the problem was to connect two different ways of calculating sin(x) -- the Taylor series and a new idea he developed which you may have tried in a calculus class. namely, he wrote down sin(x) as a infinite product of its roots. one result that happens to fall out of this comparison between the infinite sum and the infinite product is that you can factor equations like sum(1/n^2) over all the integers into a product of the reciprocals of the primes.

this second fact leads very directly to a proof of the first through some clever algebra but it's far more general. in fact, we not only get exact values for sum(1/n^2), but exact values for all expressions of the form sum(1/n^s) where s is a positive even integer -- odd powers remain an unsolved problem to this very day. in fact, these sums are hiding in the Taylor expansion of sin(x). so somehow, we've connected a seemingly arbitrary question about how to take a certain kind of sum of the integers, connected it to a product of primes, and tied both to an analytical function -- sin(x). already bizarre.

but it gets even stranger. if you let s vary as a complex number and not just as a positive number > 1, this very same approach lets you calculate the sums for negative even powers as well. remember, we're calculating sum(1/n^s) -- how can we get any result but infinity for sum(1/n^-2) -- i.e. sum(n^2)? more perplexing is that the value you can calculate from algebra and calculus over the complex numbers, following Euler's method, and Riemann's extension of it, is 0 for every negative even power. this is also where the notion that the sum of the integers is -1/12 comes from. this is the Riemann Zeta function.

so now, we've connected a seemingly arbitrary sum of the integers to an analytic function over the complex numbers via prime numbers. and worse still, if we connect this back to the first point, we discover that this Zeta function tells us the order of the error term on the estimate for sum(log p, p < x). remember, this function looks like the graph of y = x. if the Zeta function has a zero at s = 1/2, we have an exact formula for that sum and the error term is precisely O(x^1/2). we can even calculate the constant factors. this fixes all the prime numbers. it in fact gives you an exact formula to calculate them, not as a recursive function, but directly. all because some asshole in the 1700s posed a problem no one could answer until Euler: what's sum(1/n^2)?

so this is why prime numbers fascinate mathematicians. nothing we understand about them is obvious. but being able to answer seemingly arbitrary questions about them unlocks whole fields of mathematics. and new techniques in completely unrelated fields of mathematics suddenly answer deep questions about the structure of the natural numbers.

if this topic interests you, I highly recommend this series of videos from zetamath: https://www.youtube.com/watch?v=oVaSA_b938U&list=PLbaA3qJlbE... -- he walks you through the basic algebra and calculus that lead to all of these conclusions. I can't recommend this channel enough.

I've found the opposite. every time I attempt to subvert the borrow checker, I eventually discover that I'm attempting to write a bug.

most of the optimizations discussed are actually kind of obvious if you know how chess notation works in the first place. like the reason the starting move "Nf3" makes any sense is because only 1 knight of all 4 on the board can possibly move to f3 on the first move. what the OP is doing is trying to take that kind of information density and trying to represent it, first by assigning bits to each part of a possible move and then by paring it down where the space of legal moves excludes entire categories of possibilities. there's another article that goes much further into how much optimization is possible here: https://lichess.org/@/lichess/blog/developer-update-275-impr...

you've misunderstood my point -- I'm saying manufacturer claims need to be verified. 10x doesn't mean all that much to begin with and, moreover, fan static pressure claims from manufacturers get verified by virtually no one. a shady manufacturer could straight up make up these numbers and no one would be the wiser because of that lack of independent verification. it's like if a CPU GHz figure was taken at face value, without testing.

he was extremely insightful and developed new math so effortlessly. if he'd survived, a lot of math would have advanced more quickly than it did.

it also doesn't help that the fix for the increased difficulty in implementing AsyncIterator for devs (assuming the approach advocated for in the OP winds up being the one selected by the language team) relies on the as yet (?) unstabilized generators/async generators feature. I'm not really why it's not available yet as the necessary compiler features are already in place and have been for years but because it's not, this is kind of a hard pill to swallow.

such claims without tests to validate are kind of useless. they're just taking the company at their word.

> Further analysis with mass spectrometry also found serotonin, a much more strictly controlled substance, in 26 percent of the tested supplements. According to the authors, the presence of unlabeled but significant quantities of serotonin could lead to serious side effects.

wait, you can buy OTC seratonin? that seems wild given the seratonin syndrome risks.

edit: it looks like it's indirectly via 5-HTP [1].

[1]: https://www.webmd.com/vitamins/ai/ingredientmono-794/5-htp

I mean, lots of animals use tools, including chimps. those tools aren't nearly as sophisticated, so it depends on how you define tool use, but the point still stands. this is all besides the point.

thanks, I appreciate this

> "We haven't yet found a specific neural structure for recognizing faces" is far from evidence that no such structure exists.

proving a negative is, famously, quite hard. an unsolved problem, even. facial recognition has a plethora of evidence beyond an argument from evolution. the notion that we humanize tools is one that, as yet, lacks that evidence. I urge people to be more skeptical of arguments from evolution. we understand very little about our evolution and it's easy to insert our own worldviews and beliefs into such arguments, allowing them to state virtually anything we like in a plausible envelope with the shape of a scientific argument. I'm not just calling the argument about humanizing tools pseudoscience -- I'm applying it equally to every other argument from evolution that lacks other motivating evidence.

except no such neural structure has ever been found. humans have been using tools for longer than we've been human -- without solid evidence that this tool is interpreted as a social actor, based on real neuroscience, this kind of claim rooted in an evolutionary argument is psuedoscience. people have been making arguments from evolution to say all kinds of nonsense things since Darwin (like justifying racial hierachies). which neural structure is posited to cause us to humanize our tools?

if anything, the historical evidence points in the opposite direction -- that people objectify far more than they humanize, even when the cost is measured in hundreds, thousands, or millions of lives. that's merely an observation, not a hypothesis or a claim about what people will do or about what they are capable of doing. we ought to humanize more often.

metaphors, you see, are always literal

> How do we know it's automatic without knowing the quality of each request?

what purpose does the filter serve if it allows virtually all requests through? your response amounts to "trust the FBI, they don't need oversight".

> I think the FBI understands the process and doesn't send flimsy requests in the first place.

I would love to see your evidence for this.

> If it's a rubber stamp, why are any rejected?

because those requests were egregiously bad?

warrant approval is bad across the board, even when the requests are public[1]. what reason do we have to assume they're better when they're sealed? "the FBI is self-regulating" doesn't pass muster when we can see the warrant requests they put forward and get approved when the details are public.

[1]: https://www.popehat.com/2014/07/15/warrants-bulwark-of-liber...

this was exactly what the free software advocates have been saying would happen (has happened) without protections to make sure modifications got contributed back to free software projects.

might be FODMAP sensitivity.

this worked for me for a while but in the last year, I've started getting episodes even though I've taught myself to sleep on my side, breathe through my mouth, keep my airway open by tilting my chin away from my chest, etc.. these kinds of techniques only work so well.

from what I've read, they're a standard practice in traditional finance/risk management circles? it's what makes the whole situation with SVB so much more mind-bending. this isn't some new technology that's never existed before. why were VCs insisting that money had to be held at SVB, knowing that by doing so, they'd put their funded companies above FDIC insurance thresholds?

was it incompetence or greed?

the bank was already experiencing a slow run as startup funding dried up. SVB got hit by interest rates twice - once because the value of their assets fell and a second time because the money spigot into tech turned off and a huge influx of deposits turned into steady net-withdrawals. they managed their risk awfully.

you're aware that barrels of oil are sold in USD and this status is what maintains the American position as the world's reserve currency, right? you're also aware of the wars, coups, and sanctions that have been used over the past 60 years to maintain that position? Venezuela and Iran are the only two countries to have left that standard and we've ratcheted up sanctions on both in response.

I mean if you set the bar beneath the floor, yeah, sure. but my bar is "not a scam" so hell no. why the hell would I touch tether or any other stable coin following six whole years of reporting on how much of a scam stable coins are? am I supposed to trust their reserve "audits", which amount to a "trust us bro" letter sent to the auditor? are you aware that these verifications of reserves were done by depositing the requisite amount of money into a bank account that was set up for the auditors to have access, with no indication of where the money came from or whether it even belongs to tether? are you aware of their incestuous relationship with bitfinex, a fact that should raise a hell of a lot of questions, especially after the collapse of Alameda and FTX?

you can't sell me USDC because I'm not buying. "X scam is more of a scam than Y scam" is not a sales pitch for Y. it's a statement that should lead you to reconsider why you have any money with any of these people. or, you know, you can be another notch on the belt of the grifters, scammers, and vultures that dominate crypto. I guess the second is a more exciting way to live.

a lot of the African nations moving closer to China come to mind

those have very low limits - 10k per tax identifier

in CA, unpaid wages pierce the corporate veil and damages are owed. so there will definitely be lawsuits, including class action.

no but expect the US to start invading weaker countries that depeg from the dollar. the US is, at present, the world's reserve currency. that status is what creates the petrodollar. as countries move towards Russia or China, that hegemony is threatened.

if you think tether is well run, I have a bridge to sell you

the economists at the fed think the only possible cause for inflation is demand pressure, forgetting the historical supply crunches that have led to inflation. wages are up and unemployment is down because production is still reeling from covid, especially as the largest generation in history retires. so amusingly, in their failed ploy to crush labor power, the feds have fucked the banks.

(this is not to excuse the greed of the bankers - this crisis is the purest essence of capitalism, it's inherent contradictions on full and gory display.)

if profits don't go up, shareholders get mad and the stock price tumbles. this is just capitalism.

people make grammatical mistakes often enough when typing that you kind of need to parse sentences in the way that makes the most sense. this sometimes means parsing correct grammar as a mistake because the fixed version makes perfect sense. then you read the article and laugh at yourself because yep, both kinds of proton are quite complicated.