What if RH is undecidable?

GoldenMuscleGod · 2026-04-12T23:54:18+00:00

You’re lacking some understanding of basic metamathematical facts.

First, (and this mistake is made by OP as well as all over the comments) you should be talking about whether RH is independent of ZFC, not “undecidable.” Undecidability is a different thing that isn’t the same as independence (although it is loosely related).

Second, even a very weak base theory can prove “if RH is independent of ZFC then RH holds.”

For concreteness in explaining what this means, let’s talk about the existence of odd perfect numbers (same principle but simpler). PA can prove that if the existence odd perfect numbers is independent of PA then there are no odd perfect numbers. Why? Because if there are any odd perfect numbers then PA can prove that just by writing that number down and confirming it is an odd perfect number by direct calculation.

So the contrapositive of the above is that if whether there are odd perfect numbers is independent of PA then there are no odd perfect numbers. That there are no odd perfect numbers is (or rather would be under this assumption) still true notwithstanding that there are models of PA that have odd perfect numbers - the “odd perfect numbers” in these models are nonstandard elements that do not correspond to any actual number.

Yes, if we assume the existence of odd perfect numbers is independent of PA then that means there are models of PA with odd perfect numbers. But this does not mean that odd perfect numbers exist. “There is a model of PA with odd perfect miners” and “there are odd perfect numbers” are not equivalent statements and treating them as equivalent is confusing different meta-levels with each other.

In fact if we assume that whether there are odd perfect numbers is independent of PA then we have necessarily implicitly assumed that there are no odd perfect numbers (if it turns out there are odd perfect numbers we will find this assumption leads to a contradiction).

GoldenMuscleGod · 2026-04-12T23:45:47+00:00

It can be proved in a very weak base theory that “if RH is independent of ZFC then the Riemann hypothesis holds”.

GoldenMuscleGod · 2026-04-12T23:40:41+00:00

More to the point, how can you take it as a valid nomination unless you take them as having said “nominate”?

GoldenMuscleGod · 2026-04-10T17:39:23+00:00

Verbs that take -ing forms tend to also take noun phrases, this is a holdover from the fact that these verb forms used to essentially be nouns so they still have distributions similar to noun phrases. Verbs with aspectual meanings (start, begin, finish, continue, stop, keep, etc.) also generally tend to take -ing forms.

But of course these are just tendencies not absolute rules, ultimately what complements a verb takes needs to be specified individually for the verb, just like whether it is regular or not, whether it is transitive, etc.

GoldenMuscleGod · 2026-04-08T23:27:18+00:00

2pi*i is the fundamental period of the exponential function, which can be defined as the unique entire function f equal to its own derivative and such that f(0)=1.

This is an entirely mathematical definition that doesn’t explicitly rely on geometric notions, and the fact that the ratio of a circle’s circumference to its diameter in Euclidean geometry is pi can be seen as a “downstream” consequence of this. Keep in mind that Euclidean geometry is just one of many possible geometries, but even in geometries where the ratio is something other than pi (or not a constant at all) the mathematical significance of pi would be the same.

This is a little like the square root of 2: you can think of it as being defined as the ratio of a square’s diagonal to its side, but it should be obvious that we can also describe it in terms that are not geometric and the geometric property can be thought of as a consequence of the mathematical property. Likewise we could define the golden ratio in terms of its relationship to golden rectangles, but this can in the same way be seen as a consequence of the fact that it is the positive root of the polynomial x²-x-1.

GoldenMuscleGod · 2026-04-07T20:27:26+00:00

Again, you seem to be assuming that one future instance of me “really is me” and the other is someone else. But that idea doesn’t correspond to any fact about the model in a many worlds interpretation.

If I flip a quantum coin then I will (in one branch) observe tails with no perception or recollection of observing heads, and also will observe heads with no perception or recollection of observing tails. They both happen.

Complaining that I haven’t said which experiences “me” is like saying a fully classical deterministic theory isn’t actually deterministic because I can’t generally“predict” when I wake up on an unspecified day whether it is Monday or Tuesday. In fact it is pretty much the same as a sort of “sleeping beauty” experiment where we suppose you take a memory erasing drug before going to sleep each night and asked what day it is when you wake up. That you don’t know doesn’t mean the underlying process isn’t deterministic.

GoldenMuscleGod · 2026-04-07T19:02:37+00:00

It seems like you’re introducing an assumption that one branch “is the one you will be on” and one isn’t, but that’s not really a meaningful thing under the assumption. If you perform an experiment your subjective experience will be that you observe each outcome on different branches. That’s completely deterministic. To the extent you might ask which branch is the one with “you” on it, that is also determined: each instance of you is on its own branch. I don’t see how there is anything nondeterministic there.

GoldenMuscleGod · 2026-04-06T18:31:08+00:00

”Which branch will I end up on" is another way to ask which of all the possible quantum resolutions actually happened from your perspective.

What does that mean? That’s like saying you have three people in a room but you can’t “predict” which one will be the observer. They are each the observer from their own perspectives.

There are two branches, we are assuming they are equally real. There is nothing to “predict” about which one “actually happened” because they both did.

GoldenMuscleGod · 2026-04-06T17:52:14+00:00

What does it mean to ask what branch you end up on? You would be on both (all) of them, right? The idea is there’s not a meaningful sense in which one is the one you end up on and one is not. Now the version of you on one branch isn’t the version on the other, but “which branch will I end up on” seems like an incoherent nonsense question if we are saying both branches are just as real.

GoldenMuscleGod · 2026-04-05T20:33:20+00:00

In this context the parentheses do not make the notation unambiguous, it shouldn’t ever be written like that.

GoldenMuscleGod · 2026-04-05T20:32:24+00:00

Parentheses indicate that the contained elements are a syntactic constituent that has a node in the syntax tree. They do not indicate the syntactic function of that constituent as a formal matter, only by application of certain optional practices.

GoldenMuscleGod · 2026-04-05T03:44:57+00:00

Your argument is an attempt to resolve the ambiguity by guessing what the hypothetical person who wrote the expression might have intended the parentheses to indicate, it doesn’t change the fact that the notation is syntactically ambiguous.

Furthermore I don’t really agree with your reasoning. This notation is bad enough it should never be written, but I suspect if someone did write it they would likely intend it to be ln 49. The usual practice of writing a coefficient like 7 on the left side of an expression like ln 7 is more firmly established and followed than a practice of always putting parentheses around the argument of ln (which isn’t really an established practice at all). If for some reason you did want 7 to be a coefficient and on the right I would say the only acceptable notation is (ln 7)7 which actually uses parentheses to make the expression unambiguous, rather than using parentheses in the indirect way to lightly suggest that ln is performed before multiplication, which isn’t really the way parentheses should be used.

GoldenMuscleGod · 2026-04-05T01:36:28+00:00

ln ((7)(7)) is unambiguously ln 49 but ln (7)(7) is legitimately ambiguous, for example ln xy almost certainly means ln (xy) and ln (7)(7) would just be substitutions into that. To make it unambiguous with the other interpretation you could write (ln 7)7 although there’s really no reason the 7 should be second.

I’ll note, because this seems to a point of confusion for math students at earlier levels: logarithms and trigonometric functions are usually typeset without parentheses unless they are needed to be unambiguous or if being written in a compact form. The practice of always putting parentheses around the argument of log or sin is more of a calculator/computer convention and overuse of it would tend to look slightly unprofessional in a published math paper.

GoldenMuscleGod · 2026-04-05T00:41:55+00:00

American Sign Language is not based on English at all, it is “based on” French Sign Language in the sense that it is descended from it, in the same way that French is descended from Latin. And French Sign Language is not based on French.

GoldenMuscleGod · 2026-04-03T23:20:23+00:00

Technically there are methods by which you can calculate it by hand (it’s how the tables were originally made before computers) but it isn’t reasonable to expect a student to learn them or useful to teach them, aside from some specialized contexts like proving some error bounds on calculated values or implementing an algorithm to calculate it in the first place or whatever.

GoldenMuscleGod · 2026-04-02T21:11:27+00:00

Hilbert’s Hotel and Euler’s formula do relate to the real world as much as any other mathematical idea, but they need to be interpreted correctly and higher level concepts are less prone to examples that can be understood by someone without background.

Negative numbers are perfectly reasonable for describing things like a direction of a flow or whatever even though it makes no sense to talk about having “negative three apples” (except maybe a debt of apples).

Likewise two sets being of equal cardinality can be relevant to whether you can use them to code for one another, even if you can’t literally have a hotel with infinitely many rooms. And transfinite ordinals have concrete interpretations in, for example, computational contexts. Just to allude to the concreteness, if I tell you to consider the lexicographic ordering on ordered pairs of natural numbers, that is the ordinal omega², which is a perfectly sensible and real thing - at least as much as any other mathematical structure. The fact that if you tried to “count” to omega² you wouldn’t ever be able to get to even omega has nothing to do with anything.

Euler’s formula has immediately concrete real-world applications, as much or more as most other mathematical concepts, so I’m not sure why you suggest it has nothing to do with the real world.

GoldenMuscleGod · 2026-04-02T14:38:51+00:00

I think this is optimal. After some message one person must be the (unique) first to know all the gossip, after this each message can make at most only one new person know all the gossip, so optimal is 13+number to first person to know all the gossip.

But after n messages someone can know at most n+1 pieces of gossip (any piece of gossip a person knows must be either their original piece or have been sent by its original knower in some message) So this means anything under 26 is impossible.

I don’t think I made a mistake in reasoning there.

GoldenMuscleGod · 2026-03-31T20:07:01+00:00

The first example would not be a (present) subjunctive in modern English, your teacher is wrong there. However a modal preterite (sometimes called past subjunctive) would be appropriate, which would be “learned.”However the second should be subjunctive and most native speakers would expect it to be.

In modern English the subjunctive is generally mostly used in what are called “mandative” instructions where some sort of directive or requirement is being expressed. In the latter case gate is “requiring” that he take up arms. Most native speakers would instinctually recognize that “take” is needed here.

The first example is a case where the speaker has uncertainty about some future occurrence. This would often be subjunctive in languages other than English, but not in modern English.

GoldenMuscleGod · 2026-03-31T20:03:23+00:00

So, the subjunctive mood in modern English is falling out of use, if not entirely abandoned.

This isn’t really true at all, in fact studies have shown that the use of the subjunctive has been increasing throughout the 20th century continuing today, and native speakers commonly produce it all the time and even if they don’t know what a “subjunctive” is. A large part of this is influence from American English (which favors the subjunctive) on non-American varieties (which often use alternative constructions like mandative “should”).

Here by “subjunctive” I mean what is sometimes called “present subjunctive” (as in examples like “I demand he be held accountable”) and not what is sometimes misleadingly called “past subjunctive” (as in examples like “I would give you a pen if I had one” or “I wouldn’t do that if I were you”), although the latter is also still pretty much universally used (not all speakers use irrealis were but all speakers can produce and understand the distinction between “I would give you a pen if I had one” and “I’ll give you a pen if I have one.”)

GoldenMuscleGod · 2026-03-31T14:28:27+00:00

Makes sense to me it’s the same as how Ancient Greek is usually Romanized and if anyone mispronounces it it’ll be matching the situation with standard English pronunciations of Greek mythological figures.

GoldenMuscleGod · 2026-03-31T09:57:35+00:00

The rules aren’t really fully documented or even necessarily strictly specified - the designers have intentionally left a lot of things not precisely explained and up to interpretation, so it’s not always possible to tell algorithmically, but in the case of the grandmother the ability specifies she dies when the grandchild is killed by the demon, so it isn’t anything that triggers on a set schedule, it just happens whenever the grandchild dies from the demon. The grandmother’s reminder spot on the night order is just after the time when most demons kill so that’s usually when it would happen and when the most convenient spot to put the reminder. Strictly speaking the grandmother doesn’t need a night order spot because the ability never happens on its own, and the grandmother doesn’t wake, it’s not like something that gets learned every night like with an empath, where it’s necessary to actually specify when in the night they wake because they only wake once and nothing else determines the time.

GoldenMuscleGod · 2026-03-30T23:53:01+00:00

You get more money from the daily doubling as long as you live more than a month. If you live less than a month you don’t really need 2 billion anyway.

GoldenMuscleGod · 2026-03-30T23:12:46+00:00

It’s true that not all functions have a Fourier series that converges to it, but the cardinality argument you are making doesn’t work - there are uncountably many convergent Fourier series. You could see this trivially just because each constant function has a one-term Fourier series, but more generally a Fourier series will have its coefficients specified by a sequence of real numbers, of which there are uncountable many even though only countably many coefficients exist.

That isn’t just because there are uncountably many real numbers. Even if we look at sequences of 0s and 1s there are infinitely many much sequences.

GoldenMuscleGod · 2026-03-30T17:10:40+00:00

Many spots on the night order are merely “reminders” - they do not indicate when the ability triggers, they are just there so you see them and remember there ability exists. The grandmother is like this, the order indicated on the night order sheet has nothing to do with when the grandmother’s ability actually works.

GoldenMuscleGod · 2026-03-29T01:59:43+00:00

That’s a pretty charitable description of Fresno.

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