What god formula?
What god formula?
No, I just understand math. So yes.
Well, 13 microarcseconds is the resolution they claim to be shooting for. The nearest star is 4.2 light-years away. 13 microarcseconds at 4.2 light-years is 2500km, the earth is about 12742 km in diameter. So we can theoretically take an approximately 5x5 pixel image of Proxima Centauri b.
If you are taking requests, I am curious how ridiculous The Longest Journey would be.
Good effort. But I don’t know if it will be particularly effective considering Project 2025 has playbook stuff specifically about doing end runs around staffers.
The article is stupid as hell though.
Iirc, some SMR designs also have this property designed, though this is the very first I’ve heard of it actually being tested at scale.
Please don’t tell me you, unironically, actually use the Carmack rsqrt function in the year of our Linux Desktop 2024.
Also if you like, you can write unsafe Rust in safe Rust instead.
std::mem::transmute
Orb mommy 🔮🔮🔮🔮
deleted by creator
(please attend to primaries next time…)
So… should I have voted for Marianne Williamson or Dean Phillips, keeping in mind Dean Phillips formally withdrew from the race before my state’s primary, and Marianne Williamson couldn’t have won if she had sweeped every state after and including mine?
I think the problem is mostly that the US system of elections is turbo mega fucked.
Armorosus Diligentia
I think.
Solar attached to homes is not really a scalable solution on its own. For one thing, it’s a massive liability for the utility. Power is produced on an as needed just in time fashion. Putting extra power onto the grid just means that the load is less predictable, and if the utility doesn’t have storage, this extra power could be excess, and there isn’t a convenient and safe way to dump persistent excess power on a grid level, and they can’t phone you up to ask you to shut down your solar arrays either.
This is why you see negative energy prices from time to time. Oversupply is a problem and it can wreck equipment.
For those curious: Gothic 1.
I’ve never heard of it before and it doesn’t look like my type of game. Anyone played it?
Cassette Beasts not Beats ;)
What about Elisa? I was under the (potentially mistaken) assumption that Elisa was the successor of Amarok.
I am sorryI am sorryI am sorryI…
So like, it’s really easy to armchair and just say that they should ignore the haters and so on, but having been on the opposite end of a small Internet hate mob, even if you only have like a dozen people telling you that you’re a crook, or a piece of shit, or your stupid or dishonest, or whatever, it doesn’t really matter how accurate any of that is, it really does start to get to you, no matter who you are.
The only healthy option is to log out at that point.
Oh, I’ll try to describe Euler’s formula in a way that is intuitive, and maybe you could have come up with it too.
So one way to think about complex numbers, and perhaps an intuitive one, is as a generalization of “positiveness” and “negativeness” from a binary to a continuous thing. Notice that if we multiply -1 with -1 we get 1, so we might think that maybe we don’t have a straight line of positiveness and negativeness, but perhaps it is periodic in some manner.
We can envision that perhaps the imaginary unit, i, is “halfway between” positive and negative, because if we think about what √(-1) could possibly be, the only thing that makes sense is it’s some form of 1 where you have to use it twice to make something negative instead of just once. Then it stands to reason that √i is “halfway between” i and 1 in this scale of positive and negative.
If we figure out what number √i we get √2/2 + √2/2 i
(We can find this by saying (a + bi)^(2) = i, which gives us (a^(2) - b^(2) = 0 and 2ab = 1) we get a = b from the first, and a^(2) = 1/2)
The keen eyed observer might notice that this value is also equal to sin(45°) and we start to get some ideas about how all of the complex numbers with radius 1 might be somewhat special and carry their own amount of “positiveness” or “negativeness” that is somehow unique to it.
So let’s represent these values with R ∠ θ where the θ represents the amount of positiveness or negativeness in some way.
Since we’ve observed that √i is located at the point 45° from the positive real axis, and i is on the imaginary axis, 90° from the positive real axis, and -1 is 180° from the positive real axis, and if we examine each of these we find that if we use cos to represent the real axis and sin to represent the imaginary axis. That’s really neat. It means we can represent any complex number as R ∠ θ = cos θ + i sin θ.
What happens if we multiply two complex numbers in this form? Well, it turns out if you remember your trigonometry, you exactly get the angle addition formulas for sin and cos. So R ∠ θ * S ∠ φ = RS ∠ θ + φ. But wait a second. That’s turning multiplication into an addition? Where have we seen something like this before? Exponent rules.
We have a^(n) * a^(m) = a^(n+m) what if, somehow, this angle formula is also an exponent in disguise?
Then you’re learning calculus and you come across Taylor Series and you learn a funny thing, the Taylor series of e^x looks a lot like the Taylor series of sine and cosine.
And actually, if we look at the Taylor series for e^(ix) is exactly matches the Taylor series for cos x + i sin x. So our supposition was correct, it was an exponent in disguise. How wild. Finally we get:
R ∠ θ = Re^(iθ) = cos θ + i sin θ