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@Steve Donald Knuth certainly does not share your idea that one CFG can be the "real" CFG of another CFG, and it's preposterous for you to claim that he does. Please drop this, it is going nowhere.

@Steve "I'm saying (a) remains the real CFG of (b)" saying that one CFG is the real CFG of another CFG, such that a CFG is not its own real CFG, seems completely meaningless to me. You have some bizarre idiosyncratic ideas about CFGs, and I am not going to edit my answer to address one person. The "structure" you are talking about is meaningful to humans for the purpose of understanding sourse code, but there is no expectation of it being preserved by a compiler; a compiler's output is not source code, by definition. I think you should write a blog instead of further comments here.

... solved for arbitrary CFGs is what makes it difficult. Nonetheless, the fact that a translation is possible even when the CFG is irreducible does not mean that the original CFG was the CFG of some structured program, because the resulting structured program has a different, reducible CFG. It only means that the resulting structured program "represents" the original CFG in the sense that the program has the same behaviour as the original program. If you are still confused, please ask a question like "what is an irreducible CFG?" at CS SE.

@Steve The translation of a CFG into structured control flow will necessarily sometimes produce a program whose CFG is not the same as the original CFG. The class of CFGs for which this is necessary, is the class of irreducible CFGs. But this does not make the translation invalid, because the goal is not for the output program to have the same CFG as the input program, the goal is for it to have the same behaviour as the input program (as is the goal of any compiler). If the problem was only to translate reducible CFGs then it would be much easier, so the fact that the problem must be ...

@Steve "I think what you're calling "preserved behaviour" is what I consider the real CFG of the program" Then you are using the term CFG incorrectly. "it is wrong insofar as you suggest (in the opener) that the "arbitrary CFGs" of gotos are not characteristic of fully structured languages" Then you are wrong, as I have explained, as structured programming only allows for reducible CFGs.

As for "there was no existing jumping code (or "arbitrary CFG") that was unrepresentable in a structured language with a little craftiness in translation", the structured program theorem is about preserving behaviour, not about preserving the CFG; and of course before structured programming was popular, there was plenty of real code which used irreducible control flow. Rewriting that code in a structured way could preserve its behaviour, but not its CFG. Anyway, I'm not able to understand any part of your comments as a suggestion for how my answer can be improved.

@Steve The problems with the "loop and switch" strategy are mentioned in my answer, and the other algorithms which I refer to do not use that strategy, so they do not "end up with [] a processing loop with a control variable" for the whole program. More typically they add boolean flags which each control individual sections of the code, and try to minimise the number of flags added by only using them for irreducible parts of the CFG. As for the "spirit" of structured programming, I think most compiler authors are not too concerned with whether the code their compiler generates has "spirit".

@Steve No, translating from structured control flow to goto (i.e. jumps) is the exact opposite of this question; see even just the title, "How to transpile goto to a language that lacks it?". And at least if you are talking about the standard definition of "structured control flow" (i.e. just sequence, selection and iteration), then programs using only these constructs cannot have arbitrary CFGs; all CFGs of such programs are reducible, so they cannot have irreducible CFGs.

@MSalters "Open source is source code that is made freely available for possible modification and redistribution." (Wikipedia). That certainly includes source code released into the public domain, with or without a formal license. You are making the mistake of conflating "open source code" with "code released under an open source license". That said, releasing something into the public domain means giving others license to use it however they please with no restrictions. The word "license" means a lifting of restrictions, not imposition of them.

All of this is irrelevant because the question says "on the assumption empty passphrases are not allowed". In that scenario, no vulnerability is created by allowing a brute-force attacker to try definitely-wrong passwords quickly. If a million accounts aren't allowed to have empty passwords, then the attacker can discover that by trying the empty password against those million accounts, or they could discover it more easily by reading the password policy, which isn't a secret.

It's a bit like asking how we can consider Newcastle to be in the North of England, when there is no universally agreed line separating the North from the Midlands. That's not a problem when every line people draw still has Newcastle unambiguously in the North. The debate over which line is correct and which cities are on which sides of that line, does not need to be resolved before we can affirm that Newcastle is in the North.

Likewise, there might be debate over which exact line to draw between astrology and science, because some lines might have things on one side which people think should be on the other side. But that isn't a problem for science vs. astrology either, because all the lines being drawn put astrology on one side and science on the other; the disagreement over which line is correct, doesn't impact the conclusion for astrology, even if it might impact the conclusion for other cases.

Sure, each demarcation line you might draw between astrology and science will have its debatable edge cases, which means that there may be a demarcation problem for those edge cases. It doesn't mean the same problem applies for astrology, because astrology isn't one of those debatable edge cases.

The "demarcation problem" means it can be difficult to classify items which do not clearly fall on either side of a demarcation line, or where the choice of demarcation line is controversial in some way. Neither of those problems actually exists in the demarcation between astrology and science.

It does not appear that I have had any trouble reconciling with your observation, since there is no other observation which it would need to be reconciled with anyway.

As I said, c = 1 in natural units, is certainly not equal to your calculation in units of m/s, and could equal anything you like if humans were to choose different units than metres and seconds. c could equal pi if we wanted it to, but we don't. No explanation is needed for the fact that you can combine arbitrary numbers together in an arbitrary way and get a close approximation for c; on the contrary, an explanation would be needed if the number 299,735,540 did have some cosmic significance, because this number really just describes the units of "metre" and "second" invented by humans.

For example, pi^2 / 3 is a very close approximation to Rydberg's constant, with an error of about 0.0008% - much better than your result, and I'm sure if you put your mind to it you could tell just as fanciful a story about why pi^2 / 3 is a very natural calculation to do. But likewise, we have measured Rydberg's constant precisely enough to know that it is not pi^2 / 3, it is different by about 0.0008%.

Humanity has, in fact, seen this many times.

There is no coincidence, there are just two numbers which are fairly close but definitely not equal. They do not actually coincide.

The idea that physicists might have gotten the speed of light wrong by 0.02% is almost as laughable as the idea that mathematicians might have gotten pi wrong by 0.02%.

In fact, we measured it so precisely that nowadays the metre is defined as the distance light travels in 1/c seconds. So in some sense the speed of light is known perfectly accurately and cannot be measured, and any error when attempting to measure it is really an error in your metre or your second.

I think it is also worth mentioning that if your computed value for the speed of light has an error of 0.02% compared to the measured speed of light, then your computed value is simply wrong by 0.02%. We have measured the speed of light much more accurately than that.

And yours is arbitrarily derived from the fact that humans have 10 fingers and measure things in metres and seconds. The only universal value for the speed of light, ignoring arbitrary human units, is 1.

The speed of light is 1 Planck length per Planck time. No need for numerology.

@Servaes I said "to suffer, be harmed, be sinned against, or so on".

Moral agency is the wrong thing to consider here. Moral agency is about one's capacity to make decisions or perform actions with moral status or moral consequences. What matters here is one's capacity to suffer, be harmed, be sinned against, or so on. I don't know of a moral framework which says that agency is a necessary condition for suffering.

AFAICT, this question boils down to a simple one: "if change only happens with time, how could change happen without time?" And then the answer is obvious: these two notions are in plain contradiction and you must reject one. Supposing (as the question does) that we don't reject the latter, then we must reject the former by adopting a broader definition of "change" that doesn't require time. For instance, if you are comfortable with the idea of a gradient's colour changing over space rather than time, then it seems you can have change without time.

@Steve The only way for you to assert that you have given enough information for a sensible person to understand what you mean, is if you say everyone commenting or answering here is not sensible, because it seems nobody other than you understands what you are asking.

There is no difference between the type system of SQL and the type system of SQL, though. What about SQL makes it not an answer to your question? Yes, clearly, I'm not understanding something about what you want to know, which is why you need to clarify. You are asking "about some unspecified language which, although presumably not SQL, nevertheless aligns sufficiently with SQL concepts that there is no "impedance mismatch"". If it's only presumably not SQL, then you haven't ruled out SQL as a possible answer. And I don't see anything else which rules out SQL.

@Steve Well, as I said, there are lots of languages where there is no "object-relational impedance mismatch", as that is only a feature of OO languages. And SQL itself is a non-OO language which is used clientside.

Of course, the other answer is that a lot of applications do use client-side SQL databases. For example, Google Chrome stores your history, cookies etc. in an SQLite database; SQLite is also used by the rpm and Nix package managers on the client-side.

Basically, because SQL is not as expressive as other paradigms. You can resolve the "object-relational impedance mismatch" by adopting other paradigms besides OO without just writing everything in SQL, and if you do stick with OO then the "impedance mismatch" is often an acceptable cost.

@WeatherVane See Guidance on the use of domestic CCTV. One requirement is "putting up a notice informing people that recording is taking place". In the scenario described by this question, that isn't done; Bob records Sue without her knowledge.

The two wrongs described in the question are the filming without consent, and the false accusation. But neither party can plausibly say that their criminal act was justified by the other's criminal act, because each party committed their crime without knowledge of the other crime. Bob recorded the film before Sue made her false accusation, and Sue made her false accusation before she knew about the film. In the usual sense of the phrase "two wrongs don't make a right", the second wrong is done with the intention to correct the first wrong, but that isn't the case here.

It is not question begging, you are just reading my words as if they are an argument for a different conclusion than what I have stated. It doesn't matter how the individual dice are able to obey a distribution; so long as you accept that the distribution of the sum of the two dice is different to the distributions of the individual dice, then there is a new distribution with no physical entity keeping track of that distribution. Even if you believe the individual dice "keep track" of their own distributions, what physical entity keeps track of the distribution of their sum?

Then, given that a distribution can be obeyed without anything keeping track for that distribution, why should we suppose it is necessary that anything keeps track for any other distribution? We have already shown that it is not necessary for this particular distribution, therefore you cannot claim it is necessary for distributions in general.

@user80226 The point is to show that distributions don't need anything "kept track of" in order to be followed. A system of two dice obeys a distribution which neither die individually obeys, neither die is responsible for or capable of "keeping track" of what that distribution is supposed to produce in the long run, and a human adding the result of the two dice in their head doesn't magically create some other physical entity which "keeps track" of the dice together to ensure the distribution is obeyed in the long run. So a distribution is followed without any "keeping track".

But even if a real, non-ideal, physical die does not roll independent, identically distributed outcomes, there is still a probability distribution associated with each separate roll of that die. It's just that the distributions for each separate roll might be different, and we don't necessarily know what those distributions are, and it might not be physically possible to sample any individual one of those distributions more than once (if doing so somehow changes the physical state of the die, or the universe in which the die is rolled). But they are distributions nonetheless.

When you don't abstract away the usual physical details, it may well be the case that repeated rolls of a real, non-ideal, physical die are not independent or identically distributed. Nonetheless, that doesn't refute the concept of a probability distribution, because a probability distribution is an abstract mathematical object, not something which exists in reality. Just as the number 17 exists in the ontology of mathematics, so does the uniform discrete distribution on six elements. How can we know a physical die exhibits that distribution? Only by statistical tests and inductive reasoning.

I think the part you are hung up on is the idea that probability distributions must be manifested in physical objects, such as dice. The answer is that they don't need to be, because "random processes" are not the same thing as "probability distributions". As the last part of my answer states, "It also doesn't have to be physically possible to take independent samples from a distribution."

@user80226 It doesn't matter where your random inputs come from. If you don't believe in dice, add the radioactive decay times of two unstable nuclei, or whatever else you prefer. You are picking at things which are not relevant to the point.

@user80226 The thought experiment doesn't change if the dice aren't fair, only the numbers (perhaps 7 could be five or sixteen times as likely as 12, with unfair dice). Either way, it is the numbers you get on the two dice, and the rule for combining those into one outcome, which determines the result - not some kind of hidden state remembered by the system of two dice which is somehow separate to the individual dice. And if no "keeping track" is required for the system of two dice to obey a probability distribution, why should any "keeping track" be required for the individual dice?

@keshlam I guess you mean "no more improbable"? Yes, all of that exactly.

Enjoy your day.

Anyway, I am going to eat

Forget about the future, forget about repeated trials, probabilities don't have to mean that and usually don't

No, you are confusing the statement "F(X) follows a distribution Y" with "F(X) follows a distribution Y and I know exactly what Y is"

The number 0.2 doesn't need to be interpreted as representing anything about repeated trials. It could be interpreted as meaning, if I were forced to offer bets on the outcome to other people who have the same knowledge as me, then I'd offer odds of 1 in 5.

And it is meaningless to talk about the long-run distribution of outcomes, because this whole scenario is a setup and nobody is ever going to put us in a room with five apples again.

And it is not wrong for me to assign those numbers! Nor is it wrong for someone else who knows more than me to assign the numbers 0 and 1 instead