This is such a weird drama. The way I read it SD was effectively trying to put pressure on a guy because he developed a popular UI for using SD, and made that UI also support another model. So all their moral grandstanding is effectively just about trying to keep the popular gateway site pointing only at them, but their throwing shit at the guy who gave them that huge free PR push... What an odd position, but understandable, it looks like the people behind SD are a bunch of amateurs who weren't ready for the widespread attention and rather than ride the wave they are trying to shut down the beaches to claim that they own the ocean.
it's seem a case of "build an audience and monetize later" except they gave the golden gose itself to the audience instead of the egg,
now they're in "monetize later" and some rando's internet repo is more usable and has a better pipeline than their "dreamstudio", and to boot now these rare gtx aren't rare anymore thanks to the bitcoin crash, so enthusiast can readily use the model at home.
Indeed it's a decision that feels like it was made in a tonedeaf echo chamber. As a rule of thumb, if it is allowed on GitHub then coders are probably okay with that, and individual companies will have to use the dmca process.
This goes beyond that, taking the stance that by merely conforming your api to work with a user-provided proprietary checkpoint, you're in the wrong? This same philosophy forbids sharing open source game emulators, and we all know how that turned out (can be the best way to play a game).
What a worth of space piece. It basically just boils down to the author being annoyed that other people visit popular sites too.
If you don't like other tourists, don't travel to tourist destinations. It's that simple. You don't travel to France and get annoyed that there are french people, well guess what, tourist destinations have tourists, that's a given, and it's a given everywhere, and it has nothing to do with instagram, Facebook or "this generation" it's just basic dumb fact.
Lets assume just for the sake of argument that Magnus has insider information from chess.com making him 98% certain that Niemann is cheating.
Why would he hand him a game that's going to be watched worldwide, where Magnus has nothing to win. Since if he wins we really still don't know anything one way or the other. But he also has everything to lose. If Hans is cheating and manages to pull off something again, then Magnus is cripeling his own reputation.
Magnus seems to be doing the right thing here, which is voicing his concerns, refusing to play him, and asking Niemann for permission to speak on the matter fully. Niemann is doing what you'd expect of a cheater, which is to stay quiet, dismiss the discussions, having difficulty explaining his plays, and pretty much just holding back from letting chess.com or Magnus divulge what information they have from the inside of his bans.
> I am disappointed with Magnus. He is misusing the weight of his reputation even if cheating is a big deal in chess.
I think the unspoken truth but also the thing both chess.com and Magnus are hinting at is that Niemann has cheated a lot more than he lets on, perhaps his entire stream was built on cheating, who knows. But chess.com can't just start sharing information like that, and they are walking a fine line just with their public statement where they affirmatively assert that Niemann is underplaying the reality of his cheating. Magnus probably has insider information from chess.com but is bound by NDA and this is also why he's now challenging Niemann to give him permission to speak on the matter.
>- MAGNUS has NOT seen chesscom cheat detection algorithms
>- MAGNUS was NOT given or told a list of “cheaters”
>- and he is and has completely acted 100% on his own knowledge (not sure where he got it!) and desires to this time
>I will also address a comment made to this post about Ben’s (Perp Chess) podcast and say that, yes, some top players (not Magnus!) have been invited at times, under NDA, to see what we do… and by extension, they also saw some reports of confessed cheaters (there were many more cheaters - but we only share those who confessed in writing, and only privately under the NDA). Magnus and the team from C24 are not on that list.
I see where you're coming from, if the formulas end up having weird numbers like 535.4916 or numbers like 2.718 or 6.28318 then obviously there's something suspicious about the equation. But small correction though. You got the number wrong, it's actually much more weird than any of those mentioned. The actual equation you come to for ncos an nsin is:
(-1)^(2x) = ncos(x) + i nsin(x)
And yes, -1 is a very weird number. If you take it to the power of something divisible by 2 you get itself raised to zero. What's up with this spooky periodicity? Also if you have x=1/4, then we get weird numbers like sqrt(-1) what on earth is that all about? No way that will fly, no way. No I'll take my 2.718^((-1)^(1/2)) and multiply through with 6.28318 that way I don't have to bother understanding what I'm doing I can sleep comfortable at night knowing that someone else has done all the thinking that needs to be done on the matter, and that turns or rotations are a blasphemous concept that breaks the very concept of math through scaling of an axis. You'd think math was strong enough to withstand such a minor change, but the textbooks do not mention it thus it must not be contemplated!
This is a very good point, but it took me a minute to get what you were saying beneath the snark. Translating without the snark:
There's a famous equation relating sin and cos to complex exponentiation. It also helps explain the Taylor expansions of sin and cos, which is one way to compute them and to find properties about them. It's a very important equation. It is:
ix
e = cos x + i sin x
kazinator's point was that this equation relies on cos and sin taking radians as arguments. If they take turns instead, then you need to insert messy extra constants to state this equation!
jVinc's counter-point, made with lots of snark, is that there's an equation that's even nicer if you just instead measure angles in turns with ncos and nsin:
(-1)^(2x) = ncos(x) + i nsin(x)
It's similar, but doesn't require the magic constant e.
A proof sketch that these are equivalent:
(-1)^(2x) = e^ln((-1)^(2x)) = -e^(2x) = e^(i * (2 pi x)) using e^(pi i) = -1
That's a nice result. If we rearrange the products in the exponent we get
2πix πi2x ( πi ) 2x
e -> e -> (e )
Where e^(πi) is -1. That shows there is something to the turns units; we can express the analog of the Euler identity using exponentiation using a base and factor which are integers.
> Because you’re obscuring the connection of sin/cos with their hyperbolic counterparts.
Only because we forgot the name change: these are supposed to to be nsin and ncos.
Remember also that people use sin and cos with 360-degree degrees just fine; and don't worry about wrecking the connection to the hyperbolic counterparts --- and without changing the names, either.
That version of euler's formula might make a nice case for half turns. Then it's just
(-1)^x = ncos(x) + i nsin(x)
It's obvious how to handle it for integers (an even number of half turns is 1, an odd number is -1), and the extension to real numbers aids the intuition.
Or, depending on your focus, quarter turns are very clean too:
i^x = ncos(x) + i nsin(x)
Either way, turns > radians (it's what I think in when doing most fourier kinds of work anyways!).
>The actual equation you come to for ncos an nsin is:
>(-1)^(2x) = ncos(x) + i nsin(x)
Try to formally define this procedure, though. You end up going in circles.
Here's another version:
lim[N->infinity] (1 + ix/N)^N = cos(x) + i sin(x)
Now there are no "weird numbers", and both sides of the equation can be calculated directly, even by hand if you wanted.
If all you're teaching students is a bunch of formulas to be memorized, the (-1)^x notation is kind of cute. But usually when teaching math, we want to build some kind of understanding.
> Try to formally define this procedure, though. You end up going in circles.
The cos(x) + isin(x) formula gives us a way to find the point on the complex plane's unit circle corresponding to an angle x, given in radians. (Plus it does more, because the argument is complex valued.)
The new formula with ncos and nsin does the same thing for an angle given in turns. E.g 0.25 (90 degrees): -1^(0.5) = i. It's understandable in terms of roots of -1.
When you want to know the principal N-th root of number on the complex plane, you can simply divide its argument (i.e. angle) by N. The other roots are then equidistant points around the circle. So for instance, the square root of -1, which is sitting at 180 degrees, is found at 90 degrees, and is therefore i.
We can use -1 as the reference for measuring angles. The turns unit (one circle) is twice as far around the circle as as -1, so that's where we get the 2. Because 90 degrees in turns isn't 0.5, but 0.25.
We could use 1 directly, but then we need the first complex root of unity. For instance, here is the Wikimedia diagram of the fifth roots:
That root which is close to i, has an angle which is exactly 1/5 turns. There is a relationship between turns and roots of unity, because N roots occupy N equidistanct points on the circle spaced by 1/N turns.
You seem to have missed the point. You need the formula I gave to rigorously compute the roots of -1. Of course, you could notice that (cos(x) + i sin(x))^n = cos(nx) + i sin(nx), but that's what I meant by "going in circles". You end up defining (-1)^x in terms of sines and cosines, making the "formula" trivial. It's difficult, working this way, to understand why (-1)^(1/3) is (1 + isqrt(3))/2 and not just -1.
By contrast, the Bernoulli formula is actually computable. In fact, the CORDIC algorithm corresponds quite closely to computing the Bernoulli formula by repeated squaring. The use of arctan(2^(-n)) is just like taking (1 + i2^(-n))^(2^n).
There's a reason why math is structured the way it is.
> You end up defining (-1)^x in terms of sines and cosines
But we are explicitly doing that; we have "nsin" and "ncos" on the other side, and those are explicitly defined as just cos and sin with a scale factor applied to the argument.
The goal is simply, if there is a goal, can we have a nice correspondence between complex exponentiation of some base and the scaled sine and cosine that work with turns.
Hey look; if we change the angle coordinate so that a full circle is just 1 rather than an irrational number, then the transcendental e disappears from our version of this famous equation.
> if the formulas end up having weird numbers like 535.4916 or numbers like 2.718 or 6.28318 then obviously there's something suspicious about the equation.
Well, 2.718 is different than those numbers, because the derivative of 2.718^x is 2.178^x, which is a very interesting property of 2.718. The same cannot be said about 535.4. (6.283 is the ratio of a circle's, diameter to radius, which is just something intrinsic to the universe. I think it even transcends the universe, but that's hard for me to reason about. But basically, both 2*pi and e are fundamentally interesting.)
But it really has nothing to do with the universe, except insofar as maths happen to (imperfectly) match it.
Presumably if the universe seemed to match some other maths, we would have invented that variety instead. The Greeks knew the Earth was round, yet made up plane geometry; and never touched on spherical geometry, as far as we know.
Astonishingly, the concept of the number line did not surface until 2000 years later. With the number line, school children can do on command what the best mathematicians of antiquity struggled with for centuries.
It would be interesting to see how such a challenge evolves, because if you do include inspection, then you really just have a no-inspection solve time. And the question becomes how often does it help to do inspections and when do you start doing solves with look ahead along the way.
> How many meters did Usain Bolt have to run in training before he ran his 100 meter record winning run.
That's not really an accurate comparison. The current setup is more akin to a 100m running challenge where he was allowed to run 50m before starting the actual 100m to get up to speed.
The inspection time is not training, it's literally the time spent solving the cube.
Its a broader point that the limits are arbitrary, like high tech clothes or bike designs getting created and banned (or not), but there are actual sports with rolling starts or maximums and minimums defined but no bonus for using less than the max.
The long jump is measured from the board, not from where you jump. Getting close to, but not over the edge is part of the arbitrary rules of the sport.
A better analogy would be to ask whether we should count the time Bolt spent stretching before the gun was fired. If Bolt hadn't stretched, he would've been slower but he still would've been pretty fast.
> The current setup is more akin to a 100m running challenge where he was allowed to run 50m before starting the actual 100m to get up to speed.
It looks like an interesting idea. The long jump competitions have something like that. Can someone organize it? Do you have to go slowly the first 40 meters and increase the speed just in the last 10 meters before the start line? Can the data from the 200m run be used to estimate this?
And it is absolutely the case that the times for world class second-100m of a 200m sprint are generally lower than even world record 100m sprints (in that report above, out of the field of 8, 6 runners beat the 100m world record over their second 100m)
Usain Bolt's world record 100m from a stationary start is 9.58s.
His world record 200m splits were 9.92s and 9.27s.
So yes, a flying start makes a massive difference. 200m runners are generally slowing down in their second half (Bolt's last 50m took 4.75s, while he covered 100-150m in 4.52s, and 50-100m in 4.32s), but their average speed over the final 100m is still faster than a 100m runner. In a 100m sprint the runner may still be accelerating by the time they reach the line.
I just remembered that all (some?) boat races start like this. You must cross the starting line after the initial time, but you can already have speed.
I feel like a lot of what's in the category of "you wont believe this is getting popular" on tiktok is a result of them faking views and follower numbers to rope in creators who then go on to think tens of thousands of people are watching them do some random videos, which makes them double down and focus and then eventually gain a real but still much lower real following.
I don't have any evidence to back up the claim that they are faking views, but I know for a fact that the hundreds of followers I have gained making almost no content are not real. And it seems extremely suspicious that they've engineered their whole "creator fund" around trying to not pay creators based just on views/likes and subs, if they where real that would be the most accurate measure to target. But feels like they've decided to completely ignore them and to "sort" creators, likely because they know there's some creators with majorly fake followers that they don't want to pay, but still want to keep on the platform so they keep their fake engagement metrics high, and then there's the "real" popular names that they know they need to pay, but still underpay compared to other platforms. But creators still stick to tiktok because "they have a much larger following". It smells.
> most banks are highly levered, meaning they're lending out, say, 10× the cash they hold, so they never "have too much cash on hand".
Reconsider what your stating here. If I have 10$, and I can therefore lend out 100$, but I only have requests to borrow 50$, then I have "too much cash". If I however had requests to borrow 200$, the I would need to find another 10$, for instance by promising someone a higher interest rate on their accounts. The fact that banks do fractional reserve does in no way guarantee that they do not end up having more cash on hand than they need to cover the demand for loans.
Banks that have too much cash on hand go out of business. If a bank ends up being near this it just reduces its loan rates and loans the money out for slightly less, but still better than sitting on cash.
> Banks that have too much cash on hand go out of business. If a bank ends up being near this it just reduces its loan rates and loans the money out for slightly less, but still better than sitting on cash.
Right.. The bank can increase its level of leverage principally by:
* Decreasing loan interest rates to encourage people to take loans
* and/or decreasing savings interest rates to discourage people from keeping deposits.
Of course, real banks do both based on market conditions and capital requirements. And, of course, there's not an implausibly thin level of reserves like you imply to pedantically harass the prior commenter: you must have at least the required reserves, and certainly having way too much cash is toxic to profitability.
