Unfortunately it seems their proof already had the Pythagorean Theorem embedded within its implicit assumptions - they define measure of an angle through rotation of a circle. They don't explicitly define circle, but from their diagram they hint at the "understood" definition, namely a set of points equidistance from a central point, while using Euclidean distance as the metric.
It depends on how long you're willing to roll back US interventionism. If you're talking about pre-WW1, maybe. But even by the mid-late 19th century the US started sticking its nose in the Pacific (which alarmed Japan, which contributed to that countries subsequent militarism). So I'd say you'd have to go back even further.
If not the US, it would probably be Europe and/or the Soviet Union. China and the Soviet Union nearly came to blows in the 60s.
Europe decolonized largely because Hitler wrecked major continental colonial powers France and the Netherlands) and put Britain with their backs against the wall such that it had to partially abandon its empire in order to defend itself and avoid a complete disaster. So they let India go, but tried to hold on elsewhere. This worked to some extent, but not in others. What remained tried to morph into the Commonwealth, this was only partially successful.
The US assumed the crown, this time with a different model, hegemony vs. colonialism. They had a rival in the Soviet Union, which funded Communist revolutions in many parts of the developing world. With the exception of Vietnam, something the Chinese did not do. They valued North Vietnam as a buffer against Wester imposition, but were not too keen on a reunified Vietnam, indeed they invaded a few years after South Vietnam collapsed.
Hm. The biggest problem there are the definition of "diagonal" and "box".
I mean non-square sudokus are still in NP. If a solution can be validated in polynomial time, a problem is in NP.
And to validate a (x, y) sized sudoku, you need to check (x * y) [ number of total squares] * (x [row] + y [column] + max(x, y)ish [diagonal-ish] + ((x/3) + (y/3)) [box]). The boxes might be weird, but boxes are smaller than the overall sudoku, so we are looking at some max(x, y)^4 or so. Same for the diagonals. The input is x*y numbers, so max(x, y)^2. Very much polynomial in the size of the input[1]
And it should also be easy to show that if an (n, n) sized sudoku has a solution, an (n+k, n+k) sized sudoku has a solution. You kinda shove in the new numbers in knights-kinda moves and that's it.
1: this can be a bit weird, because you need to be careful "what you're polynomial in". If your input is a number or two, you might be polynomial in the magnitude of the number, which however is exponential with the input length.
In this case however, we wouldn't have encoding shenanigans, since we're just placing abstract symbols from the turing machine's alphabet onto an imagined grid.
> But What I don’t understand about this is why is “time” framed as observer based? In my mind, the events do happen at the same time and just are unable to be observed as such. I feel like time is a figment of our imagination, it’s just a measurement. In my pea brain time makes sense more as a constant and the other things are something else that impacts the latency of observance
Its a logical consequence of the speed of light being constant in all inertial reference frames, regardless of the velocity.
This is an axiom of special relativity, but it has also been verified at (admittedly low) relative velocities.
That in itself is somewhat absurd, but it leads to further absurdities when you do the math. In order for the speed of light to remain invariant, you can no longer speak of an absolute (preferred) frame of reference.
You can of course, privilege certain reference frames e.g. Earth, but its rather arbitrary.
The data centers themselves with all the supporting infrastructure (telecom/power), as well as all the chip fabs needed to build the hardware, even if the hardware itself becomes obsolete / breaks down on a 4-5 year time scale.
In the same way the rights of way obtained with all the railroads were, even if the rails / engines themselves had to be replaced every decade or so
But some hardware does last quite a long while. Fiber laid from 25 years ago is still pretty useful.
English is a Germanic language with a Latin alphabet, as spoken by Celts, after being ruled by people from France who were originally from Norway (or maybe Denmark)
Is the point that any var declared in between the braces automatically goes out of scope, to minimize potential duplication of var names and unintended behavior ?
The worst I've seen is old school C programmers who insisted on reusing loop variables in other loops. Even worse, those loop variables were declared inside the loop declaration, which old C standards allowed to visible outside of it.
Later versions of C++ disallowed this, which led to some interesting compile failures, which led to insistence of the old stubborn programmers that new compilers simply not be used
Those drones are getting lost / shot down / missing their targets at high rate. But since they are relatively cheap, they almost effectively artillery shells right now. Don't need a high kill rate when you have lots of them.
That is true, not every drone hits the target. But the same with any other weapon. How many 155 shells are needed to actually hit the target? A moving target?
And one regular 155mm shell is 5x more expensive than FPV drone.
Drone prices everyone mentioning are without warheads. And depends on capabilities. Mainly how far it flies and how heavy payload is. I would say kamikadze drone manufactured in Ukraine costs 300-1000$
BTW Russia and the US at least, saw this coming decades ago. Which was the reason behind the intermediate range missile treaty, which was sadly ripped up in the early 2000s.
They likely are useful now, given their costs are going down and can be used in saturation attacks like Iran just did. A single ICBM with a dozen 500lb bombs can take out an fleet of fighters.
If launched from a nuclear country, the attacked country would have to assume nuclear payload. In the case of another nuclear country, this means nuclear retaliation.
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