simiones
For example, the special theory of relativity doesn't work if space-time has any "lowest scale" (i.e. if the distance between any two events can be expressed as n * min_dist, where n is an integer and min_dist is a constant that has the same value for all observers), it you can't infinitely sub-divide it, since then lengths couldn't contract the way that the Lorrentz transforms predicts. Lots of math in QM and QFT also requires space and time to be continuous for other reasons as well.
Also, none of our current laws put any kind of limit on the life span of the Universe as a whole, so space-time is also infinitely increasing, even if heat death or big crunch models are correct.
Of course, none of this is provable per se - it is fundamentally impossible to run an experiment in finite time that proves whether something is finite or infinite. It could be that SR and QFT are wrong in their continuous space assumptions, but only in ways that are too subtle to measure. Still, as it stands, we don't have any theory of how the world works which allows for a discrete space-time, even as an approximation - we need space-time to be continuous for our current theories to work at all.
Exponential complexity is what you automatically get when your algorithm is "generate a possible solution, verify if it's correct, repeat if it's not". Polynomial complexity is what you get when the problem itself has some kind of structure that you can exploit to either directly construct a solution, or to generate a very small set (relative to the problem size) of possible solutions that have to be checked by hand.
Now, it is true that for all practical problem-solving purposes, "P = NP but only with algorithms that require n^10^80 or more time (with this as a proven lower bound for even the typical case, no hope of improving)" would be exactly equivalent to "P != NP". However, it would still be a mathematically extremely interesting result, as it would tell you that any problem where it is easy to verify if a solution is correct carries some hidden structure that makes it "easy" to generate the solutions. And it could still open the door to finding new sub-classes of actually easy instances of these problems that are not known today, even if the worse case remains just as intractable.
Now, note the refutation of ETH with the new algorithm found by AI is not really that impressive, it doesn't seem to have that deep of an implication. Sub-exponential running times are not that fundamentally different from exponential ones - they basically just tell you that the problem has just enough structure to eliminate a certain class of possible solutions outright, instead of spending the time to actually verify them. If the algorithm found had been polynomial, even of a huge degree, this would have been a completely different discussion. As it is, we'll just replace the ETH with a "nearly-E"TH and nothing much changes.
The way I view this, there are three separate things: processes, applications, and windows. In all versions of Windows, a single process/application, that the user launched exactly once, was able to have one main window and multiple other windows that could be independently manipulated, closed etc. Since Alt+F4 was added as a keyboard shortcut, it closed the currently active window, which might happen to be a confirmation dialog or anything else. If it was used to close the main window, the application/process might choose to shut down, automatically closing other windows it owned, but this was never a requirement.
Now, for the process / application distinction. By my understanding, in traditional Windows, the concept of an application is essentially an executable whose main function is WinMain. A user can spawn one or more processes from the same application executable, and these are handled differently in 16-bit vs 32-bit Windows - but they have always existed as separate copies, within the technical limitations of the time. Even in Windows 1.0, the second execution of WinMain did indeed receive a hPrevInstance and could use it to access resources of the already running instance - but it was still a separate thing, with its own window and its own event loop. Ultimately it wasn't all that different from a new process spawned from the same executable - except that memory and compute constraints at the time made it important to have a way to share certain parts of the parent (and the lack of memory isolation made it trivial to access the memory of any other thing running on the system anyway).
The concept that an application can only have 0 or 1 instances running is a very weird concept that MacOS shares only with mobile OSs and Windows Metro/Universal/UWP/whatever MS calls their mobile-style store apps today.
Edit to add a note: it's actually quite common on Windows today for programs to not actually launch, or at least not use, a second process when running the executable again. What they do instead is that during startup they check if the process is already running by checking some named mutex or other similar mechanism, and if it is, they ask that process to open a new top-level window, maybe with the new document loaded into it if you were actually opening a doc, and then the new process just exits, while the old process start a new window that for all intents and purposes looks just like a new copy of the process to the user.
Feeding on nutrients from an animal that died and was then broken down by other beings into base elements in the same area as your roots doesn't qualify these trees in any way as either "carnivorous" nor even "necrophage". Carnivorous plants are those that trap and kill animals that they then directly digest, such as a venus fly trap. Those don't just benefit from animals dying around them and being consumed by bacteria - they have mechanisms that cause the death of the animal and then secrete substances that directly convert the animal into plant nutrients.
Now, Alt+F4 didn't exist as a standard keyboard shortcut in Windows 1.0 - it was added later, but certainly by Windows 95 at the latest. And already in Windows 95, Alt+F4 was the "Close Active Window" shortcut, which would close the window or dialog that was currently active - not the entire application whose window this was. So pressing Alt+F4 on your keyboard while a "Save As" dialog was present in Word 95 would close that "Save As" dialog, it wouldn't close your Word document.
You can check the Windows Programming Guide to see how to create dialog windows or popup windows in the same app that already had a main window in Windows 1.03: https://archive.org/details/win103-sdk-manuals/5%20-%20Windo...
Though I should note that this would be the "SSSR" since I was clearly using the latin alphabet, even if I had chosen to use the Russian name of the USSR.
The majority of people walking in the worse neighborhoods of LA or Chicago never have a single crime happen to them. But that doesn't mean that it's safe to go in a bad neighborhood - and it really doesn't mean it's safe to go there wearing designer clothing, gold watches, diamond rings and wearing your Apple VR device.
The same is true for travel. It's perfectly safe for the vast majority - but it's very important to be aware what may make you a target and what can happen to you if you are. Tens of millions of people visit the UK or China every year with no incident. But if you're a public active supporter of Palestine Action, or an active demonstrator against the CCCP respectively, be aware that you personally face a real risk from this travel, and your devices are actually very likely to be searched at those borders. Vice versa though (anti-CCCP activist traveling to UK, PA activist traveling to China) is perfectly safe, though.
Plenty of times. Perhaps the worse is pushing Manifest v3 with no support for real ad blockers in Chrome. Not to mention no support for ad blockers in Chrome mobile.
Also, their stealing of newspaper content.
Their new push for AI summaries instead of actual search in their search product, stealing even more clicks from sites that actually produce information.
YouTube pushing Shorts to everyone, and now the weird text posts that you can't hide.
In general their gigantic push for ads everywhere all of the time.
The way the law is structured, you are never buying copies of digital goods, regardless of the format in which you obtain them. Instead, you buy a license to use the digital good under the specific terms and conditions of that license. That is why if you get a disk with GNU utils on it from the FSF, you are still bound by the GPL in what you can do with the data on that disk.
Just like they obviously did the research on the Apple VisionPro and that is inevitably going to be the next big computing device, right?
I think the research is exactly what's happening right now (or will once it launches).
Now, as to how plausible this is, we'll actually get into semantics. To me, saying that "gravity is quantum" would mean that it is a real force/interaction, and that this force obeys the Heisenberg uncertainty principle. So, I wouldn't say "gravity is quantum" if it turns out that the Entropic gravity theory is true, as in that theory gravity is only an apparent interaction. However, I admit that this may only be my perception of what these terms mean together, and that others may use "gravity is quantum" to refer to any theory that explains the macroscopic effects we call gravity in a way that matches quantum theories.
A: If gravity is quantum, then (B) there must be some particle-like think that we call a graviton that mediates the interactions, and then seeing a rubidium atom fall must have been an interaction with this particle.
not A: If gravity is not quantum, then they are making no claims about a graviton.
If you think gravity is not quantum, then you go to the "not A" branch, and they make no claims about that branch - so there is no contradiction with their IF.
Now, say we have an experiment where two different sources each fire one electron in some direction; and say the electrons have the same spin and other properties except for their initial position and momentum. We can meaningfully say that for a certain location between the two sources there is some > 0 probability for either electron to be there, so the amplitude of each electron's wavefunction at that position is > 0. However, that doesn't mean we can ever find both electrons at that same postion at the same time: the individual wavefunctions are just parts of the two-electron system's wavefunction, and, per the Pauli exclusion principle, that one will be 0 for any state of the form "electron A at position x and electron B at position x". So, for any position, you can find either electron there, but never both.
An additional wrinkle is that this only applies for two identical electrons. If the electrons have different spins, then they can actually be found at the same location at the same time. You can have a spin-up and a spin-down electron in the same place at the same time, but not two spin-up electrons. This is the fundamental property of fermions. However, you can have any number of identical photons at the same location - that's the fundamental property of bosons.
The only way this statement could be false would be to have quantum gravity but no particle that mediates this interaction - which doesn't seem plausible almost by definition.
Many trademarks are indeed more or less global.
> A lot of companies also don't trade under their full name. Apple, famously, wasn't founded as Apple but as Apple Computer, and was only able to rename after achieving a deal with Apple Records.
That's irrelevant - Apple Computers owns the Apple trademark (for certain industries).
> The lack of more namespaces also led to things like nissan.com being owned by Uzi Nissan (and now his family, I assume) rather than the car company.
It's not perfect and not guaranteed to be unique, yes. But people's names have many orders of magnitude more collisions.
> <firstname>@<lastname>.name as an email address.
No, you'd at best get `[email protected]` as your email address. Which, again, is irrelevant, as it's impossible to say which of the many thousands of Firstname Lastname people this might belong to.
> (The cultural aspect is irrelevant - it was not enforcing a specific order. If people wanted to register lastname.firstname.com, nothing would stop that)
I wasn't referring to a specific order, but to the cultural idea that people have 1 firstname and 1 lastname. In Spain, for example, people typically have 1 first name and 2 last names - but you couldn't get `a.b.c.name` as an address. Having a first name, a middle name, and a last name is also very common.
There are also cultures where people simply have one name, not first + last. For example, a person's full legal name in Tibet might just be "Woeser".
That's a silly idea. While there are laws that ensure to a decent extent that there is a single company called "Google", so that it's relatively unambiguous who `google.com` should refer to, there is no uniqueness whatsoever to personal name. There are likely hundreds of thousands of people called "John Smith", so the FQDN `john.smith.name.` would not really tell you anything.
This is without even going into the fact that "first-name.last-name" is culturally specific (though, to be fair, a large proportion of cultures in the world use this format).