I came to realize that logs don't matter. O(log(n)) and O(1) are effectively the same thing.
The reason is that real computers have memory, accessing memory takes time, and bigger n needs more memory, simply to store the bits that represent the number. Already, we have a factor of O(log(n)) here.
But also each bit of memory takes physical space, we live in a 3D world, so, best case, on average, the distance to a memory cell is proportional to the cube root of the amount of memory cells we will have to access. And since the speed of light is finite, it is also a cube root in time.
So "constant time" is actually cube root on a real computer. And I am generous by saying "real". Real real computers have plenty of stuff going on inside of them, so in practice, complexity analysis at the O(log(n)) level is meaningless without considering the hardware details.
Going from log(n) to log2/3(n) is just an exercise in mathematics, it may lead to practical applications, but by itself, it doesn't mean much for your software.
Please explain to me how you can hash n distinct strings into O(n) buckets in O(1) time. Please note that this process needs to work as n goes to infinity.
Hash tables are O(log n) structures when you don't hand-wave away the "compute a hash" part. The thing is, search trees are far worse than that in practice and you aren't hand-waving away the "compare two elements" part. That's where the real speed savings come from.
What I think you are saying is that computing the hash needs to process the entire string, and the length of that string roughly corresponds to log n, therefore it's O(log n). Not sure I am entirely convinced by that reasoning, but let's roll with it for now.
Because if you apply it to binary search, you need to compare the strings at every step, and by that logic, each of these operations is O(log n), which means your binary search is now O(log^2 n).
I guess the crux is that we are still comparing apples to oranges (or multiplication operations to comparison operations), and at the end what probably makes hashing faster is that we are not branching.
Still I don't think it makes sense to think of both hash tables and binary search as O(log n).
Most of this is very true, except for the one caveat I'll point out that a space complexity O(P(n)) for some function P implies at least a O(cubedroot(P(n))) time complexity, but many algorithms don't have high space complexity. If you have a constant space complexity this doesn't factor in to time complexity at all. Some examples would be exponentiation by squaring, miller-rabin primality testing, pollard-rho factorization, etc.
Of course if you include the log(n) bits required just to store n, then sure you can factor in the log of the cubed root of n in the time complexity, but that's just log(n) / 3, so the cubed root doesn't matter here either.
For example: imagine you have 2 windows, the lower right corner of one window almost touching the upper right corner of the other, so that the bounding rectangles overlap but the graphics don't.
With the inaccurate "false square" corners, you just had to check the bounding rectangles, to know which window to resize, now you have to check the actual graphics (or more likely, a mask).
I am not saying it is the problem, but that's the kind of thing that can happen. Or it may be a simple bug, like a crash, memory corruption, an unhandled exception, the usual stuff, but they couldn't fix it in time and it is better to revert instead of leaving the buggy code or pushing an untested fix.
Just revert the code back to pre-26! This is ridiculous, it can't possibly be this hard and if it is, it just points to the degradation in the quality of Apple software! This is maddening!
This is already the pre-26 bounding box, isn't it? It's the new graphics that don't line up. (Not a great excuse, but the graphics are here to stay at least for a little while.)
> the graphics are here to stay at least for a little while
And that's the reason why I won't buy a new Mac.
Tahoe and Liquid Glass are so horrible that they're going to lose customers because of those. They should realize what they did and just backtrack: it wouldn't be the first time they admit they made a mistake [1].
The magic mouse have been there, almost unchanged, since 2009. That is a lot for a tech product, and retiring a product after 16 years is not admitting to a mistake. For example, the Logitech G5 mouse and its direct evolutions were among the most successful Logitech products, and it didn't last that long.
No, it is not just refusing to admit that the magic mouse was a mistake, it is considering that it is the best ever. That USB port on the underside is still one of the great mysteries though, maybe it is some quirk of evolution, because it is certainly not intelligent design.
In addition to vertical scrolling, the Magic Mouse can do horizontal (or diagonal) scrolling, zooming in and out, and a couple of other tricks. This makes it worthy for the people who need this for their work. There are mice that can do horizontal or vertical scrolling -- but not both at the same time.
People who do their work on large documents (pics in Photoshop, videos, CAD, music, even Excel, etc.) use these capabilities every day, and they like their Magic mice very much. If you are not one of these people (software development, for example, can be done with vertical scroll only, for the most part), it doesn't mean it's a bad product -- all it means it's a product which is not for you.
I don't use Magic Mouse but am very far from expecting Apple to admit "the magic mouse was a mistake" though.
I am using Sequoia and the windows are definitely rounded! Though the radius is pretty small (the curved region is about a quarter of the mouse cursor area), so the fact you can drag it from outside the window doesn't look ridiculous.
When Tesla debuted, the cost of batteries made electric cars more like an expensive novelty. The Tesla roadster certainly was fun, but it wasn't a practical car for day-to-day use.
Of course, things have changed.
Had Tesla gone all-in on Lidar, they could have turned the technology into a commodity, they are a trillion dollar company producing a million cars a year. Lidar is already present on cheap robot vacuum cleaners, and we have time-of-flight cameras in smartphones, I don't believe it would have been a problem to equip $50k cars with Lidar.
On this topic, I think it is worth mentioning Framasoft [1]
It is a French organization that offers plenty of alternatives to Google and other big tech products. A lot of them are just rebranded and hosted open source software, but they also develop their own, such as PeerTube and Framaprout (the last one is a joke, but PeerTube isn't).
Yup, I'm surprised this wasn't mentioned earlier but they're the ones behind PeerTube (which I see posted on HN a lot) and many other tools. They've been building google alternatives for over two decades now and many of their tools are quite mature
I don't think they can win over large company, they are just a small nonprofit organization, large companies want to work with other large companies.
Where they can make a difference is for fellow organizations and maybe small companies. A lot of them go to Google because that's the most convenient, even if it sometimes against their principles, they are proposing an alternative.
One minor criticism I have is that while they are not hiding the fact that they are rebranding off-the-shelf free software, they could give them a bit more visibility, should users want to self host at some point.
One tradeoff is that one of the tradeoffs graphics programmers do is about security. They typically work with raw pointers, using custom memory allocation strategies, memory safety comes after performance. There is not much in terms of sandboxing, bounds checking, etc... these things are costly in terms of performance, so they don't do it if they don't have to.
That's because performance is critical to games (where the graphics programmers usually are), and if the game crashes, no big deal as long as it doesn't happen so often as to seriously impact normal gameplay experience. Exploits are to be expected and sometimes kept deliberately if it leads to interesting gameplay, it is a staple of speedruns. Infinite money is fun in a game, but not in serious banking software...
I am all for performance, and I think the current situation is a shame, but there are tradeoffs, we need people who care about both performance and security, maybe embedded software developers who work on critical systems, but expect a 10x increase in costs.
An interesting example, because your body is literally something you have to hide. That is, it is illegal not to.
Personally, I hide it because that's what society is telling me, especially if children are around, and I have no real reason to go against that. I mean, who wants to see what I do in the bathroom? But should the government want to, I will gladly let them as it will nicely illustrate what I think of them.
There are many things I want to hide more than my body functions. It is a social taboo, not something that has to do with personal safety and security, which is what privacy advocates usually point to. Arguably, it is the opposite problem: something you have to hide, but for personal freedom, you shouldn't have to.
Information asymmetry has always been a thing, wars have been though over this.
But I think that in our age, information asymmetry is particularly low, at least in western countries. Each one of us has access to a tremendous amount of data, sure the powerful have access to more, but I have a feeling that the relative difference is shrinking.
I will always remember when a police investigator was interviewed, the context was a controversy about police files. The investigator said: "police files? not very useful, when we want to investigate someone, we browse Facebook". It means that the police doesn't have much as much of an information advantage compared to you and me.
Journalism, world events, etc... Most of the times, we have all sorts of first hand reports, photos, videos, news sources from enemy countries, etc... Not all of them reliable, and factchecking enough to see through that mess takes work, but it is possible in a way that wasn't before. A lot is available on open data platforms, plus all the shady stuff like Wikileaks, darknets, etc... that are not that hard to access either.
Should you want to, you can be your own Palantir, because most of what Palantir does is standard data analysis that can be done with open source tools, and most of the data sources are public, private data is just the cherry on top.
Of course it takes work, but it is possible with limited resources, mostly a computer, an internet connection, and time. No need to travel around the world to meet contacts and get access to paper archives.
No one really says that in an absolute sense, it is always in context, what it usually means is "I trust a particular institution with the data they collect", not "I will give my credit card number to everyone who asks".
For example, let's say you approve of installing security cameras monitored by police in your residence, if you say "I have nothing to hide" what you are actually meaning is "there is nothing these cameras can see that I would want to hide from the police". I think it is obvious that it doesn't mean you approve of having the same cameras installed in your bathroom.
The real question is one of trust and risk assessment. Are the risks of revealing a piece of information worth it? how much do you trust the other party? not the literal meaning of "nothing to hide".
The point is that the data you're sharing may look banal to you now, but you have no idea how it might get used in the future, and by whom. You should assume that all data you share is available to everybody. Thus everybody should prefer privacy by default.
> but you have no idea how it might get used in the future, and by whom.
This is the part a lot of people, including the idiot politicians who push for surveillance laws, do not underestand. Political regimes do not rule forever, even in the US, and what is permited/acceptable today, might not be permited/acceptable tommorrow.
Indeed. And there's risk-reward tradeoff. The debated argument says "have all my data if you want for no reason". The stronger case is, "what do I get in return"?
Often in this discussion it's about a society-wide standard. The benefit to "me" might be that e.g. the police can do their job well, hopefully protecting me from criminals, while sticking to reasonable and trusted privacy controls (e.g. intrusive data collection requires a court warrant, and I trust the courts enough to do a good job). That's very different to uploading all social media conversations logs to NSA because "nothing to hide".
Looping back to this article, it is unclear if there was ever ant good reason to record religion in Amsterdam. Nor would I exclusively blame administrative procedures on the Holocaust - though I'm sure it made matters worse.
If that's all it is, it's logically sounder than what it is raised in defense against, the multifallacious "I have nothing to hide" that implies those who oppose a policy do have something to hide and sidesteps the actual question of privacy.
Like everyone else, I am very skeptical that it is somehow related, for several reasons.
- He is just a small time streamer, I didn't watch his videos but it looks like typical clickbait content playing on people's paranoia. Why would Palantir care about it?
- I didn't watch the videos in question, but I suppose that he says that Palentir is evil because it is used by police forces to attack poor migrants, that kind of thing. Not only he is saying what everyone is saying, but it may be good advertising for Palantir, as it shows that they are good at their (evil) job.
- Streisand effect, I am sure that even the idiots at Palantir know that it may not be a good idea to give attention to a streamer who annoys them.
- Speaking of attention, it is highly likely that the streamer in question was unbanked for a completely unrelated reason but saw the opportunity to make buzz, and it seems to be working!
- There seem to be no further evidence connecting the two.
> I am sure that even the idiots at Palantir know that it may not be a good idea to give attention to a streamer who annoys them.
Thiel has proved that he can hold a grudge. After Gawker outed him, he spent years shopping for anyone who could sue them, and found his guy in Hulk Hogan. He financed the lawsuit that led to Gawker Media's bankruptcy and closure.
>Thiel has proved that he can hold a grudge. After Gawker outed him, [...]
That might be true, but it's a stretch to go from this to "Thiel had a grudge for this specific streamer and was responsible for him getting banned". For one, Gawker has orders of magnitude more visibility than this guy.
Oh he does. But he uses the Streisand effect to his benefit to sell his product. Maybe you could argue it is not the Streisand effect if you want exposure by quenching stuff, though?
This can be very frustrating when it's a false positive, but these 'neobanks' have a tendency to be very "trigger happy" and quickly close accounts whenever they have a reason to think there is fraud involved. And there's a lot of automation involved of course.
When that happens, they won't tell you the reason of course, because that would help fraudsters improve their fraud skills.
There is no reason to believe this bank actually have humans who are aware of this customer's Twitter handle, and who read it, and didn't like what they saw.
There should really be a rule banning these types of comments.
The response to someone’s comment regarding “x” is not “why are you defending x?”. It’s a rebuttal of “x”. Respond to the argument on its merits. Don’t dodge it.
Do you lot ever get tired of saying this type of stuff? There’s nothing new or interesting in this comment. This isn’t a fresh perspective. You’re just saying the same one liner that have been said hundreds of thousands of times before. Let’s move on.
The reason is that real computers have memory, accessing memory takes time, and bigger n needs more memory, simply to store the bits that represent the number. Already, we have a factor of O(log(n)) here.
But also each bit of memory takes physical space, we live in a 3D world, so, best case, on average, the distance to a memory cell is proportional to the cube root of the amount of memory cells we will have to access. And since the speed of light is finite, it is also a cube root in time.
So "constant time" is actually cube root on a real computer. And I am generous by saying "real". Real real computers have plenty of stuff going on inside of them, so in practice, complexity analysis at the O(log(n)) level is meaningless without considering the hardware details.
Going from log(n) to log2/3(n) is just an exercise in mathematics, it may lead to practical applications, but by itself, it doesn't mean much for your software.
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