

And following up on that threat was obviously going to be horrible for the people in Gaza.
But please continue patting yourself on your back…


And following up on that threat was obviously going to be horrible for the people in Gaza.
But please continue patting yourself on your back…


Good. I remember my parents boycotting South Africa over apartheid. Israel is acting much worse than they were.


Obviously wrong.


As far as I can tell, his involvement is investing in a rare earth mineral company as part of a green energy initiative. I don’t see anything connecting him to some “freedom city”. That’s Peter Thiel: https://www.insidehook.com/internet/peter-thiel-praxis-next-great-city-greenland


Moving the goalposts is an informal fallacy in which evidence presented in response to a specific claim is dismissed and some other (often greater) evidence is demanded.


Your original argument was that this conflict was opened by kidnapping the head of a state.
Faced with a counterpoint, you’re arguing it’s not like a much more serious invasion.
True, but that’s not invalidating the fact that it was not opened by a kidnapping.


Have you heard about the expression “moving the goalposts”?


Also cementing USA’s new reputation as an unreliable business partner.


“roughly five weeks”
Since weeks are counted from the beginning of her last period, not conception, this operation must have happened within one week of her missed period. Perhaps it wasn’t so clearly within the law.


I pasted 1k line C++ file into Gemini, along with a screenshot and a trace log and asked it to find the bug. It reasoned for about 5 minutes. Extract of the solution:
There has to be an issue in this sequence for i=21:
V_to_next_xy (norm) is (5.00004113497265e-08, -0.999999999999999, 0). (Correct)
Unnormalized perpendicular P_un = Vec3(V_to_next_xy.y(), -V_to_next_xy.x(), 0.0) should be (-0.999999999999999, -5.00004113497265e-08, 0).
temp_bisector becomes P_un.
temp_bisector.normalize() is called.
The result of this normalization is logged as temp_bisector (result of collinear path): (-1.78813934326169e-07, -0.999999999999984, 0).
This step (5) is where the numerical error occurs. The vector (-0.999…, -5e-8, 0) when normalized should not become (-1.78e-7, -0.999…, 0).
The latter is almost parallel to (0, -1, 0), while the former is almost parallel to (-1, 0, 0).
It’s as if temp_bisector.normalize() for the input (-0.999…, -5e-8, 0) is producing something wildly incorrect, or the vector being normalized was actually (-1.78e-7 * L, -0.999… * L, 0) for some L.
What if temp_bisector = Vec3(V_to_next_xy.y(), -V_to_next_xy.x(), 0.0); itself has precision issues?
If V_to_next_xy.y() is -0.999999999999999 (16 nines), this is -(1.0 - 1e-15).
If V_to_next_xy.x() is 5.00004113497265e-08.
Vec3 tmp = Vec3(-(1.0-1e-15), -5.00004113497265e-08, 0.0).
This should be fine.
The most plausible candidate is Vec3::normalize() failing on this specific input vector (-0.999999999999999, -5.00004113497265e-08, 0).
Perhaps length() computes sqrt(xx + yy + zz).
xx = (-(1.0-1e-15))^2 = (1.0-1e-15)^2 = 1.0 - 2e-15 + 1e-30.
yy = (-5e-8)^2 = 2.5e-15.
xx + y*y = 1.0 - 2e-15 + 1e-30 + 2.5e-15 = 1.0 + 0.5e-15 + 1e-30.
length = sqrt(1.0 + 0.5e-15 + 1e-30). This is extremely close to 1.0.
If this length calculation has any error causing it to be, for example, abs(y) by mistake, then x/length would become x/abs(y) and y/length would become y/abs(y) = sign(y).
x/abs(y) = -1.0 / 5e-8 = -2e7. This is not what’s happening.
The logged value for temp_bisector (-1.78813934326169e-07, -0.999999999999984, 0)
is suspicious because its X component -1.78813934326169e-07 is very close to the X component of V_to_prev_xy (norm) from loop i=21, which is -5.00004113497265e-08, divided by a factor. Or perhaps V_to_next_xy.x() itself was somehow used more directly than -V_to_next_xy.x() in the Y component of the vector passed to normalize.
The logged temp_bisector (result of collinear path) for i=21 is (-1.78813934326169e-07, -0.999999999999984, 0).
Consider Loop i=20: temp_bisector (result of collinear path): (1, 0, 0). Its input for perpendicular construction was V_to_next_xy (norm) = (X_v: 4.9999318885022e-08, Y_v: -0.999999999999999, Z_v: 0).
Perpendicular from this is (Y_v, -X_v, 0) = (-0.999…, -4.999…e-8, 0). Normalizing this gives (-1, -4.999…e-8, 0).
The log for i=20 says it becomes (1,0,0). This is also wrong. It should be (-1, -very_small_y, 0).
The fallback temp_bisector = Vec3(1,0,0) only happens if temp_bisector.normalize() (the one on the perpendicular) also fails.
It seems the normalize() call for the vector constructed as Vec3(V_to_next_xy.y(), -V_to_next_xy.x(), 0.0) is problematic when one component is very small.
It correctly identified that sqrt(_v[0]*_v[0] + _v[1]*_v[1] + _v[2]*_v[2]); had too low precision and using std::hypot(_v[0], _v[1], _v[2]) would likely solve it.
If this is just autocomplete, then I agree that it’s a pretty fancy one.


They installed some sort of sound isolating suspended/floating (?) ceiling in my apartment. I absolutely love it. In my neighbors apartment I could constantly hear people above, but in mine it’s almost always silent.


The US started using mailboxes 14 years after the UK
In 1849, the Royal Mail first encouraged people to install letterboxes to facilitate the delivery of mail. Before then, letterboxes of a similar design had been installed in the doors and walls of post offices for people to drop off outgoing mail.
In 1863, with the creation of Free City Delivery, the US Post Office Department began delivering mail to home addresses.


I read newspapers in several languages and see your strawman in comments all over the world: Criticizing Israel means supporting Hamas.
In reality pretty much everyone is explicitly not supporting Hamas terrorists while arguing for a stop to the Israeli atrocities.


It’s not supporting Hamas to point out that Israel is doing horrible things.


If being against murder, war crimes, and genocide is being an antisemite, then so be it. I will be a proud antisemite. It will be a badge of honor.
Maybe it’s something about not knowing if the last element is the top of the stack or the bottom of the stack?
Trump was not ever going to try to stop it, he supports genocide and war crimes. Remember him telling Israel to “finish the job in Gaza”?