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)
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".
in australia workers seem to have more rights. they have industry awards that specify minimum wage and safety conditions etc, they have the legal right to strike and the legal right for union/collective bargaining if they choose it, aka freedom of association. when i look at employment conditions in the US, it boggles my mind how workers there basically have zero safety net. its an extreme example of giving all the power to the employer.
Maybe Americans get higher incomes because US companies structurally sell to larger markets than Australian companies, so - at least for those roles with scale / leverage - the role is more productive & the absolute value that the employee can extract is high, even if the proportion of the overall value extracted by the worker is similar to or lower than the proportion extracted by an Australian worker.
Maybe if Americans had stronger unions, perhaps American workers could benefit from both higher incomes - due to the increased scale & opportunities of the US market - & increased protections relative to Australian workers.
Another thing that is quite different between the US & Australia is that in the US, the public is generally a lot more trusting of business over government. US business interests have a long history of influencing US public opinion- there's examples of stuff like business interest groups creating educational materials & getting them into schools, so kids learn early about the wonders of capitalism & free markets. It's unsurprising that you might not find unions so popular in such an environment. A book that details quite a lot of that history is Kerryn Higgs' book Collision Course: Endless Growth on a Finite Planet [1].
One of the reasons that unions in the US are unpopular because they function as the funding arm of one of the political parties. In some states you have to join these unions to get a job at a state agency or at a government funded school. This is obviously incredibly corrupting, where the unions donate huge amounts of money to politicians who then feed back more money to the union members, and it's all paid for by taxpayers.
There's also ridiculous rules that many of them have adopted. My favorite example is that in my state a teacher was awarded the "Teacher of the Year" award, which is a pretty prestigious award, and requires you to be nominated by your students. Before the next school year she was fired because they had to make some cuts and the union had set it up so it was a Last In-First Out arrangement. So the teacher of the year was let go as that was her first or second year teaching. The teachers union prioritized its older members at the cost of that school losing their best teacher.
American unions are very different, in my experience, from what I saw from the European companies I've worked for. Those employee unions seemed solely focused on the people working at the company and did a good job representing their interests and solely their interests. If that's how unions in the US functioned, many people would have a much different opinion of them.
There are plenty of legal "safety nets" for American employees, regardless of if you're in a union or not. Could they be better? Sure, anything can be improved, just like every other country on Earth.
What kind of boggles my mind is that people online think they have an understanding of almost every part of American society because of what they read online or saw in the news. I wouldn't for the slightest second think I would have a clue about the working conditions in Australia, nor would I think I have the ability to read stuff online and get an actual understanding of it.
The most glaring example of this were all the people who came here for the world cup, afraid of all the crime and all that nonsense, and realized that living in America is actually pretty fucking great.
> its an extreme example of giving all the power to the employer
And yet, we make the most money, which seems to kind of go against that idea. If all the power was with the employer, you'd expect low wages, not high ones.
Apologies if that was a harsh response, it's just tiresome reading all of these foreign online "experts" on American society.
Comparing US safety nets to those of “any other country on Earth” is just patently absurd and disingenuous. EU has mandated - mandated - 4 week paid leave. In the US you are obligated to exactly 0 days of paid leave.
I get that this is HN and most people here haven’t worked the bottom-of-the-barrel retail jobs that this applies to, but there is very little difference in take home pay for this income regime after accounting for necessary expenses such as housing, transportation, and food; in some cases EU take home is even higher. https://boundlesshq.com/blog/us-vs-europe-employment-costs-s...
Like, sure, if you want to larp as a low income oligarch the US is the best place to do that. Otherwise, you’re going to be regularly crying after 10 hour shifts because you’re in the red each month after necessary expenses. Most people would like tech talent fall into the latter category out of schadenfreude or profit motive.
What's disingenuous is comparing government mandated minimums and acting like that has any reflection on what the situation is for the vast majority of people. In addition, plenty of states and localities have their own requirements for PTO, sick pay, etc. You act as if the US is some homogenous place.
> I get that this is HN and most people here haven’t worked the bottom-of-the-barrel retail jobs
I worked 50+ hours a week while pursuing my CompSci degree. The place I worked was officially commission based (Circuit City) so it didn't matter how many hours they put me on the schedule. I was frequently working 9am - 9pm retail shifts. My easy shifts were 10am-9pm or 12-9:30. Life is hard, but somehow I managed to get my degree while working that schedule for years. My favorite thing was when we did entire store inventories. It was required to be there, but we didn't get paid. Was it legal? Who knows!
I wish I had the pay and benefits that every single major big box store provides now. It would have been glorious. $15-$20 an hour to start, plus full benefits, PTO, sick days, paid breaks(!), etc etc? Heck, quite a few would have helped pay for my tuition too!
> Tech needs to unionize.
There is no job sector in the US that needs unions less than tech. I'm not sure how you can go from talking about "hard" retail jobs to the absolute cushy profession we enjoy. Sitting around in a comfortable office or working from home, poking at a keyboard, attending meetings, stock awards, ridiculously high pay for the amount of effort it requires - the list goes on and on.
reply