You don't have to believe in climate change to buy an electric vehicle. You might believe in energy independence, or you might just think it's going to work out cheaper.
546 karma · joined October 25, 2021
* No discussion of why they were not found by other people in the past.
* No discussion of how these techniques could be used on other problems.
* A lot of calculations which would be left out as trivial by most graph theory papers (for example, calculations about the edge counts of subgraphs)
The fact that this includes arguments which casual practitioners would not be able to confidently use in a crank proof does not evidence its correctness. It just shows us that it's from a different type of person, susceptible to making a different type of error.
The iterative step is z -> z^2 + u, or in components a + bi -> (a^2 - b^2 + c) + (2ab + d)i
Multiplying and adding real numbers between -1 and 1 are fundamentally stable operations when done with floats. The only possible source of instability is if a and b are very close, that a^2 - b^2 will magnify some errors from the limits of numerical accuracy. However, this is mitigated by two things: the region of such numbers is very small, and also if z is in that region, z^2 + u will tend not to be. (The exceptional region, where both are small is now a small dot rather than a thin line) So while doing thousands of iterations, the possibility that for some numbers there are repeated iterations which tend to introduce error is either excluded or just very very unlikely (we don't need to rigorously determine which).
Now remember what we are doing - we're just checking whether the iterated value goes to infinity or to the region where it will stay bounded. We don't need very precise accuracy except if we are on the boundary, as another commenter pointed out. Any region of badly behaved numbers will only tend to break the algorithm if it overlaps the boundary region. So that's one more condition we've placed on our very small region of possibly bad starting values. Furthermore, even if there were lots of bad values located on or very near the boundary, they would only tend to move the boundary by a very small amount. It's easy to check that most values near the boundary quickly either run away to infinity or quickly converge towards the central region (technically towards orbits in the central region rather than limit points). We can quickly check the rough shape of the boundary using a very small number of iterations, fewer than could possibly go wrong using 64-bit floats. If you use say 100 iterations, but keep track of potential large errors, you will plot something that is indistinguishable from the actual Mandelbrot set, with only a very very small set of points where you are 'not sure' of the actual behavior. It's also quite easy to see that points on either side of the boundary will quickly iterate away from the boundary - that is basically the definition of the set.
So although it might be hard to either be extremely sure of the exact boundary details, nor to plot highly zoomed-in details with very good accuracy, it's quite easy to draw the set to a reasonable standard.
A lot of this math was developed by experts in computational and numerical mathematics who looked very hard at questions of stability. In fact lots of fractal and chaotic behavior was dismissed as due to numerical stability before it could be rigorously demonstrated that it was real. (Not the Mandelbrot set to my understanding.)
Putting the cards past a reader or scanner while dealing would alter the flow of the game, and would also introduce other attack vectors.
Suppose there is a service which allows you to watch free porn videos as long as you hand over permissions to star a bunch of repos using your account. Clearly, the service is abusive and should be banned. But isn't it also quite fair for Github to penalize the users? They knew they were handing over something of value when they authorized the access. Either they chose to exchange their genuine 'Github clout' for something they wanted, or their accounts are spammy in the first place (for example, if they created an account solely to access that service).
b) If I had wanted to make merch with this text on it last week but had been deterred by fear of M$ lawyers, I wouldn't really feel any different about it after the author 'releasing the poem under CC'. His claim to own the rights in the first place is totally dubious. He seems erratic and will probably go on to perform other stunts and legalistic trolling before he gets bored.
I agree with other commenters that the author is greedy and petty. He accepted €20,000 for his work, a decent amount. Then he decided that he should make way more money because the game was successful. Then he tried to take advantage of the fact that he hadn't signed a contract, even though he had obviously accepted the terms when he accepted the money. He behaved shittily by not honoring an informal contract. He tried to paint it as some huge company legal dept vs little guy thing based on the fact that it's now Microsoft and yes, work for hire contracts drafted by corporate lawyers do look evil. But he had already reneged on his handshake agreement, after spending the 20K, even before big companies or professional lawyers were involved.
Now he's trying to parlay his brush with fame into Substack subscriptions. Good luck to him.
I know that the restaurant's concerns are not necessarily your concerns, but unlike many other industries, neighbourhood casual dining is competitive enough that the savings probably get passed on to you.
I would expect that in the future, home automation does all the regulation for you without any interaction. You set up a bunch of configuration in advance, and maybe train the device a little bit initially on things like your temperature preferences (because we think we want a certain temp, but actually usually find it slightly too warm or whatever). Then you almost never have to make changes, let alone expend your executive function on deciding what instructions to give the devices.
For example, you consistently buy small ticket household items and rarely return anything: when you do return something they will be helpful and generous to keep you happy.
You buy large amounts of fairly expensive clothes and shoes but return around 50% after trying on. They will accept the returns without issues but won't let you keep anything.
You're a bargain hunter who buys expensive laptops or hard drives whenever the discounts look really good. They will make returning stuff a little harder for you since they know you don't have loyalty, and they don't want to facilitate arbitrage.
Doing this is computationally no more sophisticated than the work they are already doing to detect professional scammers. They aren't supposed to show different customers different prices, but they can freely use things like this to do stealth price differentiation, since many details of how the return policy is implemented are at their discretion.
Although you returned the laptop, the annoying process might have discouraged many others from doing so. The shipping cost and the cost of processing the return are likely much smaller than you expect when accounted for on Amazon's scale. And by making you return and re-order, they are putting the risk on you if the laptop is not the identical product, rather than taking on the costs of administering a price drop refund themselves.
Of all the things that Amazon do, analysing the game theory of customer behavior so that they can do as well as possible out of interactions like this seems like one of their biggest strengths. They certainly have thousands of skilled people working on it.
As for return scams, I would not take what they say at face value. My opinion is that they have quite sophisticated models for analysing returns, both for detection (to distinguish between the behavior professional scammers and regular customers) and economically (to decide that it's cheaper to give the latter the benefit of the doubt, let them keep returned items, etc). The only flaw is if otherwise legitimate customers start to think they can get away with falsely returning 1 in 20 items or whatever. So they 'blather on' about return scams, not because they are material to their business, but to make it clear that if you cross an invisible line, they will go from not caring about your $120 air fryer that you ended up with two of, to pursuing serious legal and criminal consequences.
But if you were accounting for the profit or loss of Alexa specifically, of course you would account for all the AWS services used at the price they are sold for externally.
Have you implemented a system which stores hundreds of billions of pieces of media content and makes different slices of them immediately available to hundreds of millions of users?