when israel and america both went on their insane run through gaza, venezuela and iran, the second thing i thought after feeling sorry for those people, was feeling sorry for israelis and americans. its going to be a rough ride getting out of this for both nations' people.
edit: and indeed the west in general, that has largely said and done nothing while watching events unfold.
nice intuition there, this comment prompted me to consider a simpler example, 2d embedded within 3d. does the 2d plane (embedded in 3d) go through the 3d origin (where 0 maps to 0) and is thus a linear transformation in 3d but a 2d affine transform in 2d? it feels like this is the case?
No, the 2d x-y plane in your example cannot pass through the 3d space’s origin because that would imply that you fixed the z coordinate at zero. The plane must be fixed at some nonzero z because you need to be able move x and y values by some scaled version of z to make translation happen. If z is zero, that scheme does not work.
Consider a transformation f where we wish to move x-y coordinates s units to the right. In 2d, we could express it as:
f(x, y) = (x + s, y)
But that transformation is affine not linear. There is no way to generate the value s as a linear combination of the inputs x and y. So, our workaround is to embed the x-y plane into 3d space at z=1. Then we can move (x,y,1) points in that plane s units to the right using this transformation:
f(x, y, z) = (x + s*z, y, z)
This new transformation is linear: it maps (0,0,0) to itself. But it maps our embedded 2d plane's origin (0,0,1) to (s,0,1), shifting it right by s units, as we want.
The matrix form of that transformation is:
[[1 0 s]
[0 1 0]
[0 0 1]]
The same scheme would work if we had embedded the plane at any fixed z=r for nonzero r. We would only have to rescale the s in the matrix to s/r. Again, however, if r=0, this scheme will not work, as 1/r has gone to infinity.
ive been thinking -- if i have a 3x3 matrix [1 0 q; 0 1 r; 0 0 1], when dotted with x, those rows are planes in 3d with normals n1=(1 0 q), n2=(0 1 r) and n3=(0 0 1). plane 3 is parallel to the x-y plane and 1 unit up. plane 1 is tilted by q and parallel to the y-axis, plane 2 is tilted by r and parallel to the x-axis. the intersection of those planes (i.e. the solution x) when calculating Ax=b gives an output vector b sitting in 3d space at b=(x+qz, y+rz, 1*z). since we always specify z=1 we have b=(x+q, y+r, 1). in 3d this is a linear shear because we are translating proportionally by z but because z always equals 1 in this case we effectively get a translation in 2d.
so as the other 2 helpful commenters also just said: 3d shears using linear algebra degenerate to 2d affine transformations when z=1 (or w in 4d)
re-read this a day later and ofc it still makes sense to me but really most of it is barking up the wrong tree, focusing on solutions (which we already know) rather than outputs. if i could delete it i would but oh well.
In the 50's there were predictions that in 10 years no-one will have to work again because of the advances made in automation, like the washing machine for example. Any predictions of less work this time around are a complete joke.
That's the point, those jobs went away, the need for a job didn't. No one seems to know what long term opportunities are going to be created by AI, we only know that it is going to erode existing opportunities.
For thousands of years humans have dreamed of reaching the stars.
Imagine if the astronaut taking Earthrise had looked down upon his planet with such scorn. Human aspirations frequently exceed our capacity for timely predictions. It doesn't make the aspiration any less worthwhile.
On a cosmic scale human life is a "complete joke". It is a feature of humanity (which we should cherish) that we nevertheless pursue our lives with interest anyway.
You work less than your counterparts centuries ago... on what understanding of history do you imagine your life would be better in the past? Is your life with a washing machine worse? Is the perfect the enemy of the good? What part of "glimpse" is escaping you?
Like this scene from Pirates of Silicon Valley between Bill Gates and Steve Jobs: https://www.youtube.com/watch?v=CBri-xgYvHQ Bill was saying that Steve was stealing from Xerox so it's okay if Bill stole from Xerox first.
Games I cant play on Linux are kernel level anti-cheat shooters. Anti cheat should be handled on the server anyway, no one should be installing that on their machines. Everything else works great!
Math is not dead, it (and i guess programming to a lesser degree?) is something people do to better themselves, akin to meditation. Just because AI can meditate (it cant) doesnt mean humans will stop meditating. We may become irrelevant in that AI can generate results and proofs that it doesnt need us for, but then AI will make itself irrelevant to us! The slippery slope slides both ways.
You can be mad at America and ignore Iran's role if you want, but that doesn't lead you to anywhere productive. The United States like any country is an actor on the world stage that has interests and can take action to defend or assert those interests. If the world thinks this is a problem, they should have mediated between the United States and Iran and helped to prevent conflict. Instead they did next to nothing. War happened. Cue surprise and condemnation.
I think the world will start mediating but not in the way you think/want. They will just divest from the U.S., slowly but surely so that when the next U.S clown start messing around they don’t have to flatter it anymore.
They are divesting. Moving gold away from the US, selling US bonds, the EU creating an investment mechanism meant to pull EU investment away from the US and into EU companies, etc.
The Netherlands still maintains gold in the US and also divested from Canada. It's also like, $80 billion dollars which is maybe a lot to a tiny country with the GDP of Florida but it's an inconsequential amount to, say, the American economy. Second there are mechanical and legal reasons you might want to have more gold in London where it is more easily tradable.
> the EU creating an investment mechanism meant to pull EU investment away from the US and into EU companies
If you claim this is a divestment from the US (the most important market for many European countries) then you also have to claim the EU is divesting away from China.
Arming all their proxies in the region so they can indisriminately kill people ? Firing balistic missiles and drones on cities ? Atacking civilian ships & killing many sailors just doing their job ?
I know. It was a rhetorical question. I want the person I was replying to, to admit to these non-defensive activities, or admit to their not following the events closely.
I think the rhetorical answer is why should we care if Iran is doing bad stuff around? Is that enough to start a war with Iran?
We don’t care if Trump is doing a deal with criminals to steal oil from Venezuela either so why should the world be so eager to help him steal oil from Iran as well?(and perhaps do a deal with the meanest of them all)
Why should we care that Israel is doing bad stuff around? Or Russia?
> We don’t care if Trump is doing a deal with criminals to steal oil from Venezuela either so why should the world be so eager to help him steal oil from Iran as well?(and perhaps do a deal with the meanest of them all)
Not stealing oil. Let’s set that aside.
The reason nobody cares is because Maduro was a criminal and was responsible for economic devastation in Venezuela resulting in 1/3rd of the country fleeing!
Russia-Ukraine war is important for Europe and perhaps should for the US as well but you can well see that’s not that important for Israel for example.
Nobody cares about Maduro saga because it’s not worth it to upset the U.S for obvious no real gain. On the other hand the Greenland saga for example played out differently. You may see a pattern if you look close enough: Greenland and Venezuela are pretty much the same situation and taking down the bad guy had nothing to do with it. You may also remember the U.S released the convicted drug dealer from Honduras because it played ball with the U.S.
> Russia-Ukraine war is important for Europe and perhaps should for the US as well but you can well see that’s not that important for Israel for example.
We just decide it's not important then like Europe decides Iran isn't important. No difference.
> Nobody cares about Maduro saga because it’s not worth it to upset the U.S for obvious no real gain.
Well it's not that there's some "let's not upset the US" thing here, it's because they know it was a good thing for global security and good for the Venezuelan people.
> On the other hand the Greenland saga for example played out differently. You may see a pattern if you look close enough: Greenland and Venezuela are pretty much the same situation and taking down the bad guy had nothing to do with it.
That doesn't make any sense lol. How in the world are you arriving at a pattern match where you see Maduro, a guy helping Russia evade sanctions, destroying the Venezuelan economy, and creating a humanitarian disaster as 1/3rd of the country fled with Greenland, a country the US operates military bases on and has a population of like 20 people?
> You may also remember the U.S released the convicted drug dealer from Honduras because it played ball with the U.S.
I'm not familiar with the exact circumstances here. Maybe I agree or disagree with the action, but if they were doing something that was more helpful than the punishment for the crimes they committed maybe it makes sense to do.
> The reason nobody cares is because Maduro was a criminal and was responsible for economic devastation in Venezuela resulting in 1/3rd of the country fleeing!
And now it's even worse but USA gets free oil so it's all fine!
No, it's better now. Most Venezuelans are glad that Maduro is gone and their economy will improve greatly over the next decade or so. The US isn't "getting oil for free".
edit: and indeed the west in general, that has largely said and done nothing while watching events unfold.
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