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cmaster - reinstate monica

 Discussion on answer by Mozibur Ullah…

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cmaster - reinstate monica
Sep 28, 2024 04:06
Interesting. It feels weird to me, but I'm just one person, and I do not know many mathematicians. So I'll accept that. It just leaves me wondering why people trained in abstract thinking would choose to restrict their thoughts in such a way. It feels so unnecessary. And limiting. And it leaves me wondering: What do they gain from caring about reality to make up for these restrictions? Are they even aware that they are restricting themselves?
cmaster - reinstate monica
Sep 28, 2024 04:06
Likewise, the famous spectre tile (de.wikipedia.org/wiki/Einstein-Problem_(Geometrie)) was discovered by pure curiosity by an amateur mathematician, not because of any possible application. True, that one did not bend any axiomatic systems, it merely discovered an example that answered the question for its possibility of existence. My point is that his curiosity was the only driving force behind him exploring the tiling of shapes. And when I explore math, my curiosity is also frequently the only driving force. And I really don't care about reality when I do so.
cmaster - reinstate monica
Sep 28, 2024 04:06
@MoziburUllah Are you a mathematician? My impression is that the only thing required for jumping into a rabit hole is curiosity about what may be found. For instance, you look at numerical systems, ask yourself what properties we usually assume for the digit set, and then check what happens if you relax a condition. You will find that it is not necessary that all digits are positive. Which leads to you realizing that there are actually ten different base ten systems. And odd bases allow the zero to be in the middle, leading to balanced systems (en.wikipedia.org/wiki/Balanced_ternary).
cmaster - reinstate monica
Sep 28, 2024 04:06
I'd put it a bit differently: Mathematicians are frequently inspired by real world problems. However, they are not restricted to reality. They might just as well pursue an idea (of arbitrarily changing an axiom, for instance) and see where it leads. That's frequently where true inovation happens.
 

 Discussion on answer by Miss_Understa…

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cmaster - reinstate monica
Aug 8, 2024 09:24
@kaya3 Easy to reach something in finite local time when your clock slows to a stop...
 

 Discussion on question by Mikhail Kat…

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cmaster - reinstate monica
Aug 4, 2024 17:31
@Hudjefa is exactly right, the question of Thomson's lamp is ill-posed: If you observe a state of the light bulb after an infinite number of switches have been performed, it requires that a last switch has been performed. And that last switch can never happen, because infinity means that there must be a following switch. The disappointing answer is that the limit of the infinitely switching light bulb is simply not defined.
 

 Discussion on answer by causative: Th…

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cmaster - reinstate monica
Aug 3, 2024 05:37
@causative Funny how everything in math about infinities is about series, sets and limits, and then someone comes along and says "forget about convergence". It simply makes no sense. But he's not the only one who gets that wrong. I guess there's an infinite supply of people using faulty intuition to assign false results to undefined limits...
 

 Discussion between MichaelK and cmast…

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cmaster - reinstate monica
Jun 26, 2024 13:21
Bummer. You just failed Logic 101.
cmaster - reinstate monica
Jun 26, 2024 12:19
However, what you seem to be taking issue with, is the contents of that precondition. And I get the impression that this is more personal than logical. Because you do not get down to actually and calmly exchanging arguments, actually trying to understand what they are saying. What I sadly see in your comments, however, is that you simply restate your definition as if it were the only correct one, and by implication ignore all those believers in the diverse religions (Abrahamic, polytheist, whatever) around the earth that all associated supernatural powers with the term "god".
cmaster - reinstate monica
Jun 26, 2024 12:19
@MichaelK The point of that leading sentence is, that it makes the rest of the answer perfectly correct no matter how you define "god". If you define it the way I do, you can look at the rest of the reasoning, check its validity, and all is well. If you do not define the word "god" to imply any of the things I listed, the rest of my answer is just an implication with an unmet precondition. And that's true by definition of "implication". So there's absolutely nothing that falls apart.
cmaster - reinstate monica
Jun 26, 2024 12:19
@MichaelK "absolute authority over its adherents" - well, that description applies to any absolutistic monarch or dictator. That has absolutely nothing to do with being a god. Also, I can ask the exact same questions to you: According to you and what authority? Were you there when the word was created? And exactly what entries of the taxonomy list would you think are not supposed to possess divine powers? (Apart from the last class of demigods and culture heros, which are obviously not gods, that is?) If you want me to play your game, you need to play too!
cmaster - reinstate monica
Jun 26, 2024 12:19
Btw, Q from the Star Trek universe does possess divine powers. From the wikipedia page: "possesses immeasurable power over time, space, the laws of physics", emphasis mine. And while a science fiction writer is always able to handwave away pretty much everything, you can only have power over the laws of physics when you are not subject to the laws of physics. And, quite consequently, Q does not exist within the realm of time and space as we know it...
cmaster - reinstate monica
Jun 26, 2024 12:19
@MichaelK Ok, I didn't know that. Protected speech does indeed vary wildly across the nations. In Europe you wouldn't be as lucky, here the cops would proceed precisely by the protocol I gave. Nevertheless, the term "god" was created precisely to mean supernatural beings that were thought to have some special power over something, and most people do still understand it in this way. There's no point in calling something a god and worshiping it, when it has no powers anyway. Atheistic versions of "gods" are a science fiction trope, but not the meaning of the word "god" in general usage.
cmaster - reinstate monica
Jun 26, 2024 12:19
@MichaelK May I propose a little experiment? Tell a cop "you are a bastard" and then explain to them, that the term does not imply any slander. What will happen? Exactly. He'll get your name, by force if need be, and you will either pay a hefty fine or go to jail. And I'll say: Please, use the terms in the way that the majority of people understand them. There's just as much use in denying the term "bastard" to be slander as denying the term "god" to imply divine powers. Whatever you mean, if there's no divine powers, it's not a god.
cmaster - reinstate monica
Jun 26, 2024 12:19
@MichaelK And what about divine powers? Unless there's anything transcendental and supernatural about a being, it simply does not qualify for the term "god".
 

 Discussion on question by Rushi: Term…

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cmaster - reinstate monica
May 17, 2024 20:01
@DikranMarsupial Whether an objects address needs to be stored (in memory) or not does not so much depend on whether it's declared a pointer or a reference (that distinction is only relevant for the semantics of the virtual machine), but rather on whether the compiler knows how to compute the address without the stored value. But we are getting seriously off-topic here, we'd better cut this discussion short.
cmaster - reinstate monica
May 17, 2024 20:01
@DikranMarsupial Oh, I saw that. And I know the C++ standard parlance around it with references being "aliases" of the object itself, etc. And, of course, they do not need to be stored anywhere if the compiler knows where the object itself can be found. Nevertheless, the same goes for a declared pointer variable. And references do need to be stored when they are a) function arguments, b) non-static class members, or c) function return values. In all three cases, a register or memory chunk needs to be reserved to store a value that is the address of the referenced object.
cmaster - reinstate monica
May 17, 2024 20:01
@DikranMarsupial The compiler is free to remove any local variable that's not actually needed. Whether that's a reference or a pointer is irrelevant. Reference semantics make it easier to avoid storing the pointer's value on the stack, though. However, any reference argument does have a place where it is passed, be it stack or register. And any reference within an object adds to the size of that object. That you cannot take the address of a reference does not mean that it doesn't have one (no memory storage without an address). It only means that C++ does not allow you to get your hands on it.
cmaster - reinstate monica
May 17, 2024 20:01
@DikranMarsupial You are blinded by the abstractions according to the C++ standard. What you need to understand is the actual machine code that your compiler spits out. And when you do that, you find that there is actually zero difference between pointers and references, that both are stored within the same amount of bytes, that null references are dead simple to create, and that it's only the thin abstract language surface that waves its hand saying "references are not pointers". Please take a bit of time to thoroughly read the answer I linked in my last comment for details.
cmaster - reinstate monica
May 17, 2024 20:01
Btw, a good deal of the reasons why I would always call C++ references "pointers in disguise" can be found in the second part of my answer to a question about null references (stackoverflow.com/a/42520025/2445184). It's basically that the "reference" abstraction is so leaky that they are in no way easier to handle than C++ pointers.
cmaster - reinstate monica
May 17, 2024 20:01
Actually, I like the term "ontological evasion". Perhaps because I'm firmly in the camp of "if it walks like a pointer, quacks like a pointer, flies like a pointer, I'll call it a pointer!" camp. And because I think that this term actually describes quite precisely what C++ & co. are doing when they talk about "references": They actually mean to say "pointer", but the term got so burned in the flame wars that they give the beast different names, trying to tame it a bit in the process.
 

 Discussion on question by Baby_philos…

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cmaster - reinstate monica
Mar 26, 2024 17:19
All existence is the ultimate miracle. Because there cannot be an explanation for why there is anything at all. Whether "anything" includes a god or not is irrelevant to this miracle. All we can do is to acknowledge that something exists, as dissatisfactory as that may be.
 

 Discussion on answer by Robert Rapple…

Imported from a comment discussion on worldbuilding.stackexcha...
cmaster - reinstate monica
Aug 5, 2023 20:50
@Yakk I don't know where you got those numbers from. The wikipedia (en.wikipedia.org/wiki/Speed_of_electricity) says: "In everyday electrical and electronic devices, the signals travel as electromagnetic waves typically at 50%–99% of the speed of light in vacuum". Those "electrical and electronic devices" mostly rely on copper conductors just like your average electric cable.
cmaster - reinstate monica
Aug 5, 2023 20:50
@Yakk Precisely. Electrical cable. Signal speed on the order of the speed of light. Far better than any computer clock synchronization. The only feasible way to get even more precise timing would be the use of GPS signals.
cmaster - reinstate monica
Aug 5, 2023 20:50
@Yakk Even simpler: Just run a long cable with an igniter every few meters through the entire stock pile. Or create a cable tree if the added amperage gets too high. But a single igniter at the very center of the pile would do the trick just as nicely.
 

 Discussion on question by Ethan Mille…

Imported from a comment discussion on bicycles.stackexchange.c...
cmaster - reinstate monica
Apr 14, 2023 12:14
Well, I'd much rather hear an uncomfortable truth than a nice lie. I don't know about other people, they might prefer getting lied at, I for one would always prefer the truth. In this case, the truth is that while I would gladly answer your question, I cannot do so without further information. Preferably in the form of pictures of the brake in question, as Eric has said already. I strongly believe that I would be doing you a grave disservice if I just made up an answer without any idea of what has happened to your brake.
cmaster - reinstate monica
Apr 14, 2023 12:14
This video explains the details about why ChatGPT may be outright lying to you: youtube.com/watch?v=viJt_DXTfwA The really interesting part starts around minute 16.
cmaster - reinstate monica
Apr 14, 2023 12:14
@EthanMiller Truthfulness is nothing that ChatGPT has been trained for. Do not use it for answers. If you need correct answers, especially when they are safety critical like your coaster brake question, ask the experts like you did here. The Wikipedia is also a much, much better source of truth than ChatGPT. ChatGPT can't even correctly compare numbers and dates, how do you expect it to know anything about bikes?
cmaster - reinstate monica
Apr 14, 2023 12:14
@ojs More to the point: Think of ChatGPT as an eloquent imposter. Because that's what it's actually trained for. The training aims to get confirmation votes by people who are not experts, so when ChatGPT and other such language models produce something that sounds sensible to the average non-expert, that's a 99% score. When an expert asks questions, the performance of these programs seems to disintegrate rather quickly. With hilarious consequences. The Youtube channel computerphile has some very enlightening videos on this.
 

 Discussion on answer by Marco Ocram: …

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cmaster - reinstate monica
Feb 22, 2023 11:51
@justhalf You can have countably infinitely many points of non-zero probability within the domain of a continuous random variable. And the remaining uncountably many possible outcomes of zero probability can still have a non-zero probability as a whole.
 

 Discussion on answer by Dale: Is ther…

Imported from a comment discussion on physics.stackexchange.co...
cmaster - reinstate monica
Sep 26, 2022 01:18
@Dale That last comment of yours is gold. Would be nice if you edited its content into your answer, somehow.
cmaster - reinstate monica
Sep 26, 2022 01:18
@BobD When two black holes merge, the resulting gravitational waves may carry away a tremendous amount of momentum. So much, that the resulting larger black hole is accelerated by hundreds of kilometers per second. Since there is no third object involved, the entire situation looks like two BHs spiraling in to each other until they touch, and the next moment, the resulting BH is speeding away from the scene. This is, of course, in stark violation of Newton's third law, for there is no other massive body on the scene that is accelerated in the opposite direction.
cmaster - reinstate monica
Sep 26, 2022 01:18
@BobD The strongest "violation" of conservation of momentum is the case when two black holes of opposite spin merge. en.wikipedia.org/wiki/… says "the center of gravity can add over 1000 km/s of kick velocity. The greatest kick velocities (approaching 5000 km/s) occur for equal-mass and equal-spin-magnitude black-hole binaries, when the spins directions are optimally oriented to be counter-aligned, parallel to the orbital plane or nearly aligned with the orbital angular momentum." Of course, the momentum is carried away as gravitational waves.
 

 Discussion on answer by BillOnne: Why…

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cmaster - reinstate monica
Sep 13, 2022 14:50
@eclipz905 Moral Relativism and Appeal to Tradition may fall apart when exposed to some scrutiny, but the vast majority of people never apply any scrutiny to any moral view they've grown accustomed to. So, while it's not a good idea to try to defend eating meat based on tradition, the correct answer to why people are eating meat is because they've been taught by their parents to do so. And because they've internalized the BS about meat eating being a necessity that people tend to tell their kids when they find out where all that delicious meat is actually coming from.
cmaster - reinstate monica
Sep 13, 2022 14:50
This. Ever seen the unbelieving looks when you tell someone you're vegetarian? Ever heard the "but people must eat meat to stay healthy"? Truth is, you can live quite a healthy life without eating animals (provided you take your B12), but those people have seen their parents eat meat, their teachers eat meat, their peers eat meat, and everyone say's it's a good thing. And they've grown to like the taste. They only learned about the source of their meat long after the habit was established. When they had something to loose. Who's going to question that? Yeah, those vegetarians again...
 

 Discussion on answer by Speakpigeon: …

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cmaster - reinstate monica
May 18, 2022 21:26
@Speakpigeon Ok. I don't think that it's any use to continue arguing with someone who thinks "set theory is wrong". Have a good day.
cmaster - reinstate monica
May 18, 2022 21:26
@Speakpigeon Well, the empty set is the zero-element of set theory, you can hardly avoid calling that "being at its core". You can just as well say that zero is not a number, and I'd simply write you off as not knowing what you are talking about. Of course, mathematicians know set theory, and of course they talk about the empty set a lot. Just like you talk about zero a lot when you learn about arithmetic. It's arguably the most important number of them all.
cmaster - reinstate monica
May 18, 2022 21:26
Try explaining that to a mathematician. And not be seen as not knowing what you are talking about afterwards. The notion of the one and only empty set is at the core of set theory.
 

♦  Basic Mathematics

This room is meant for all basic mathematical discussion, incl...
cmaster - reinstate monica
May 18, 2022 16:33
Indeed, interesting read. When I learned about Russel's paradox, I had a hunch that it could be resolved using 3-valued logic, but never got to the system you explained in that answer. I will definitely add these thoughts to my mental library :-)
cmaster - reinstate monica
May 18, 2022 16:12
Ah, ok.
cmaster - reinstate monica
May 18, 2022 16:10
Hi. I've never been here before, are there any rules for using this room?
 

 Discussion on answer by Dawood ibn Ka…

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cmaster - reinstate monica
May 18, 2022 16:01
@DoubleKnot Indeed, I was thinking of something like a top and bottom element. However, user21820 correctly pointed out that the top element cannot exist (the set of well-defined sets is not well-defined, contrary to my gut feeling :-( ). Nevertheless, we need the empty set to give meaning to {1}∩{2}. So, while we cannot have (and do not need) the set of well-defined sets, we do need the empty set, and not just because it's the zero element for the union operation.
cmaster - reinstate monica
May 18, 2022 15:54
Any yes, I agree that there are other possible definitions for the natural numbers, which do not even touch on set theory.
cmaster - reinstate monica
May 18, 2022 15:51
Note that the same does not hold for the set of all well-defined sets, because there is no way to get to that set by combining some two well-defined sets A∪B. I thought we would need it in analogy to how we need the empty set, but that thought was broken. So, learned something today :-)
cmaster - reinstate monica
May 18, 2022 15:47
@user21820 Good catch, I didn't see that. So, obviously, we do not have a well-defined one-element for the intersection operation. On the other hand, we absolutely must include the empty set to close the intersection operation: Consider a set A = {1} and a set B = {2}. The intersection A∩B = {} must yield the empty set. We need to include this in the theory, lest we be left with a hole in the definition of A∩B.
cmaster - reinstate monica
May 17, 2022 05:45
@DawoodibnKareem A non-well-defined set would be the set of all sets that do not contain themselves. Because such a set would contain itself exactly if it does not contain itself. As such, that's not a valid definition of a set. But that's not the case with the set of all well-defined sets.
cmaster - reinstate monica
May 17, 2022 05:45
@DawoodibnKareem Does it lead to contradictions? Unless you forbid sets that contain themselves, I don't see any contradictions. As such, it looks like that set is well-defined.
cmaster - reinstate monica
May 17, 2022 05:45
@DoubleKnot Maybe set theory is not a Ring structure, but sets form an algebra similar to the boolean algebra with the union and intersection operations. Both operations are commutative and associative, and you actually get two distributive laws. As you might guess, the empty set is the zero-element for the union operations, while the set of all well-defined sets is the one-element for the intersection operation. I wouldn't say these are indespensable, but sure nice to have. It's definitely enough structure for me to want these two sets included in the theory.
cmaster - reinstate monica
May 17, 2022 05:45
@DoubleKnot Even to the mathematician, theories are tools to be used when they come in handy, and set theory is no exception. As such, usefulness is an excellent reason to include something in math, as long as it does not lead to contradictions. Another heuristic in math is that no unnecessary rules should be imposed. Explicitly excluding the empty set is both of questionable usefulness, and adds unnecessary complexity to the system. The empty set simply falls out of all minimal Axiom sets for set theory and is useful in the vast majority of (mathematical) use cases. Just like the number zero
cmaster - reinstate monica
May 17, 2022 05:45
@DoubleKnot That said, there's nothing wrong with studying theories which differ in key parts from the mainstream theories. Like studying a set theory without an empty set, or arithmetic without the natural number zero. Nevertheless, unless these pursuits prove useful in some contexts, they will never gain the status of a well-known theory.