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 Discussion on question by Francesco P…

Imported from a comment discussion on math.stackexchange.com/q...
user46971
Feb 6 19:53
Numerically, $x = e^{W(\ln(2))} \approx 1.5596104694623694$ gives $x^{x^2}+x^{x+x^2} \approx 8.84322729237574$, but I don't know if there's a way to write the exact solution without $W$.
user46971
Feb 6 19:53
$$y = e^{x\ln 2} = (e^{\ln 2})^x = 2^x$$
 

 Discussion between Dan and AstroD

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user46971
Jul 3, 2024 16:32
Anyhow, the essential math that you need to know is:

* An octave is a double of frequency.
* In the standard 12-ET tuning system, the octave is divided logarithmically into 12 equal semitones. Thus, a semitone represents a frequency ratio of 2^(1/12) ≈ 1.059.
* In 12-ET, a perfect fifth (P5) is defined as 7 semitones, for a frequency ratio of 2^(7/12) ≈ 1.498.

All the other math follows from that.
user46971
Jul 3, 2024 16:07
Well, I had assumed that you were using the standard musical intervals, or at least close to it.

For example, consider an interval of 4 semitones (e.g., from C to E). That's probably meant to be a major third. (It *could* be a diminished fourth, e.g. C to F♭, but that's less common.)

By my formula of $f = (7s) \bmod 12$, that works out to 4 Circle of Fifths steps, which is correct (C-G-D-A-E).

But suppose instead that you have an interval of 3.9 semitones. Then my formula says that's only 3.3 CoF steps, because the factor of 7 in the formula multiplies the error (0.1 semitone) by 7.
Dan
Jul 3, 2024 00:35
A fifth is 7 semitones. So 5 fifths are 35 semitones, or 2 octaves + 11 semitones. After octave transposition, that leaves us with 11 semitones.
Dan
Jul 2, 2024 23:58
@AstroD: That's not how 12-ET works. The notes should be 2^(n/12), where $n$ is an integer.
Dan
Jul 2, 2024 23:57
@AstroD: Where did you get those numbers for B♭ and D♭?
Dan
Jul 2, 2024 23:57
@AstroD: Correct. Assuming that the interval is a whole number of 12-ET semitones and not some weird microtonal thing.
Dan
Jul 2, 2024 23:57
@AstroD: It looks like you're correct. except that the frequency ratio should be high/low instead of low/high. But that's just a sign error, giving an interval of -6 semitones instead of +6.
 

 Discussion on question by Citizen and…

Imported from a comment discussion on philosophy.stackexchange...
user46971
Mar 7, 2024 10:41
@CitizenandSociety: It's actually very common among native English speakers to refer to an embryo/fetus as a baby if the mother wants it. See, for example, WebMD's Pregnancy Center, which refers to "your baby" and "a growing baby" prior to birth. And expecting mothers have "baby showers", not "fetus showers". It's only when a woman is seeking an abortion that "humanizing" terms like "baby" or "child" are considered offensive.
 

 Discussion on answer by NotThatGuy: A…

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dan04
Mar 6, 2024 20:04
@barbecue: (1) Crisis pregnancy centers do exist, but the claim that they use deceptive tactics is left-wing propaganda. (2) Perhaps my using quotation marks was a poor choice, and I'm sorry if it confused anyone. That particular phrase was not a direct quote (and I never claimed it to be), but simply my own sarcastic characterization of the argument.
dan04
Mar 6, 2024 20:04
@barbecue: (1) Accusation that pregnancy clinics “trick women”. (2) Use of the "kidnapper demanding a ransom" argument that women are justified in having abortions if lacking financial assistance. (3) Insinuation that anti-abortion people “just care about controlling women's bodies”. All straight out of “pro-choice” propaganda. The bias here is absolutely BLATANT. It may indeed be an “honestly held” bias by the answerer, but IMO it detracts from its usefulness as an answer.
dan04
Mar 6, 2024 20:04
@barbecue: This "answer" is pro-abortion because it makes bad-faith claims about people who hold the opposing position.
 

 Discussion between Obie 2.0 and Pete W

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user46971
Mar 1, 2024 21:29
@PeteW: The reason that the world allowed Germany to exist as a sovereign state again was that the Germans admitted defeat and renounced their genocidal ideology. Whereas Hamas still openly desires a Judenrein state "from the river to the sea", which Israel can obviously never accept.
 

 Discussion on question by feldentm: S…

Imported from a comment discussion on langdev.stackexchange.co...
user46971
Dec 11, 2023 20:55
@supercat: True. The correspondence between "character" and "byte" broke as soon as people wanted to represent Chinese or Japanese on a computer.
user46971
Dec 11, 2023 20:55
@chrysante: It depends on what the language's equivalent of byte all1s = ~0; print(int(all1s)); does. If it prints -1, then bytes are signed. If it prints 255 (or some other positive number), then bytes are unsigned. If it produces an error because byte can't be converted to int, then "signedness" isn't meaningful.
 

 Discussion on answer by Keiji: Why do…

Imported from a comment discussion on langdev.stackexchange.co...
user46971
Nov 14, 2023 01:34
You can work around factorial's range limitation (at the cost of precision) by having it return a floating-point value instead of an integer. For IEEE 754 double-precision, this is good up through 170! = 7.257415615307999e+306. Of course, if you're going to bring floating-point into this, you might as well generalize it and define the gamma function.
 

 Discussion on question by Nike Dattan…

Imported from a comment discussion on langdev.stackexchange.co...
user46971
Nov 13, 2023 19:29
Python does have math.factorial, but it was added in 2008, fairly late in the development of the language.
 

 Discussion on answer by o.m.: What ki…

Imported from a comment discussion on politics.stackexchange.c...
user46971
Nov 10, 2023 08:54
@ohwilleke: Yeah, one of the Founder (I forgot who) wrote that he expected 95% of Presidential elections to be decided by the House. In effect making the contingent election the real election, and the Electoral College just a qualifying primary.
user46971
Nov 10, 2023 08:54
@gerrit: US government shutdowns aren't so much due to our election system, as to our unique "debt ceiling" laws that allow Congress to pass a deficit budget without having authorized borrowing enough money to cover it.
user46971
Nov 10, 2023 08:54
There's no inherent reason why proportional representation (per state) in the House of Representatives would require changing to parliamentary system. Yes, under the presidential system, there'd be the possibility of the President being from a different party than the Congressional majority, but that's already the case now.
user46971
Nov 10, 2023 08:54
@gerrit: "negotiations dragging on forever" is already possible with the FPTP system: See the recent struggle to elect a Speaker of the House.
 

 Discussion on answer by sfxedit: Is t…

Imported from a comment discussion on politics.stackexchange.c...
user46971
Nov 4, 2023 21:48
@Obie2.0: When did the IRA ever express a desire to genocide the entire British population and resettle Great Britain with Irish people? Because that would be the direct equivalent to what Hamas wants for Israel.
 

 Discussion on question by JockM: Look…

Imported from a comment discussion on retrocomputing.stackexch...
user46971
Oct 28, 2023 09:07
"Conversational paragraph style" is a prominent feature of COBOL, so perhaps this language was some kind of FORTRAN/COBOL hybrid. I'd suggest COMTRAN, but that one seems to use SET instead of PUT for assignment.
 

 Discussion on answer by Machavity: Wh…

Imported from a comment discussion on politics.stackexchange.c...
user46971
Oct 18, 2023 21:51
@MissSkooter For comparison, the NSDAP got 43.9% of the vote in Germany's March 1933 election (even with significant voter intimidation against other parties). Would you have called them "not representative" of Germany at the time?
 

 Discussion on answer by Ted Wrigley: …

Imported from a comment discussion on politics.stackexchange.c...
user46971
Oct 18, 2023 00:11
Anyhow, back to the original topics:

* "Antisemitism" is generally understood to mean hatred of Jews, even if Arabs (including Palestinians), Ethiopians, and Maltese people are also "semites" (linguistically speaking).
* Ted's answer asserts that "to classify human beings into undifferentiated groups representing competing power blocks" is a right-wing tendency, while others (including myself) believe that it's a left-wing tendency.
user46971
Oct 17, 2023 16:04
@wizzwizz4 No, we on the political Right do NOT agree with Wilhoit's proposition. We want the same laws to apply to everyone. It's the Left who wants to give certain groups of people a pass for any crimes they commit, because they're just lashing out at an "oppressive" system.
2
user46971
Oct 16, 2023 14:58
@KarlKnechtel: I agree. The first paragraph of this answer is exactly backwards. The Right sees morality as a matter of individual actions. The Left sees it in terms of classes (differentiated by power, privilege, or wealth) and takes it as axiomatic that the less-powerful group is right (a view that detractors call "underdogma").
 

 Discussion on answer by Raffzahn: Why…

Imported from a comment discussion on retrocomputing.stackexch...
user46971
Oct 11, 2023 08:15
Also, the conventional BASIC way of generating a random integer between A and B inclusive was INT(RND(0) * (B - A + 1)) + A. This wouldn't have worked right for negative numbers if INT truncated instead of floored. (The argument to RND is a dummy. Atari BASIC required it because its parser didn't support zero-length argument lists, but GW-BASIC just let you write RND.)
 

 Discussion on answer by adam.baker: W…

Imported from a comment discussion on politics.stackexchange.c...
user46971
Oct 6, 2023 08:12
It's a one-sided question. If the OP had asked "Does the ADA decrease employment among disabled people?", then a side-by-side comparison would be useful. But they didn't.
 

 Discussion on question by Hashim Aziz…

Imported from a comment discussion on langdev.stackexchange.co...
user46971
Sep 23, 2023 18:41
@supercat: Or for that matter, using - for both hyphen and minus, or " for both opening and closing quotation marks (versus separate “ or ”). There's only so many characters you can reasonably fit on a keyboard (or in a single-byte character encoding), so some compromises had to be made.
user46971
Sep 23, 2023 18:41
@Andrew: / had already-established use as a fraction bar (e.g., in ¼, ½, ¾) by 1718, so using it as a division operator was a natural extension.
 

 Discussion on answer by ohwilleke: To…

Imported from a comment discussion on politics.stackexchange.c...
user46971
Jul 28, 2023 20:19
To be fair, the average German doesn't need air conditioning, because the country doesn't have any ultra-hot climates like the US has with Phoenix.
user46971
Jul 28, 2023 15:34
@JamesK What you're proposing is called the "median" taxpayer. The conventional usage of "average" refers to the mean.
 

 Discussion on answer by Timur Shtatla…

Imported from a comment discussion on politics.stackexchange.c...
user46971
May 20, 2023 23:44
@vsz: Do you remember which SE site it was?
user46971
May 20, 2023 21:41
The 54-24% liberal lean of people with postgrad degrees is significant, but doesn't in itself explain the overwhelming 97-3% bias of professors claimed by OP. It also doesn't explain journalists.
 

 Discussion on answer by Steve: Is it …

Imported from a comment discussion on law.stackexchange.com/qu...
user46971
Mar 17, 2023 07:58
@Steve: Indeed, the perception of drunkenness as a male vice (and one that enabled domestic violence) was why the 1800's Temperance movement, and then Prohibition activism, was dominated by women.
 

 Discussion on question by wokopa: How…

Imported from a comment discussion on worldbuilding.stackexcha...
user46971
Feb 15, 2023 04:07
Do you have a specific goal for how many horsepower this improved horse should get?
 

 Discussion on question by Schezuk: Di…

Imported from a comment discussion on retrocomputing.stackexch...
user46971
Feb 12, 2023 18:03
@DrSheldon: When I took the AP Computer Science exam in 2000, it was in C++.
 

 Discussion on answer by supercat: Whe…

Imported from a comment discussion on retrocomputing.stackexch...
user46971
Feb 1, 2023 09:35
@supercat: Basically, the Committee's intention was to make C programs run on any useful computer architecture, even the ones that do "weird" things like having multiple sizes of pointers. Behaviors were left "undefined" if there was at least one platform on which "the obvious thing to do" couldn't be implemented efficiently.
 

 Discussion on answer by ohwilleke: Wh…

Imported from a comment discussion on politics.stackexchange.c...
user46971
Nov 30, 2022 21:44
Regardless of his opinions on other prior Court rulings, I highly doubt that Clarence Thomas would want to reconsider Loving v. Virginia.
 

 Discussion on answer by littleadv: Wh…

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user46971
Nov 10, 2022 20:07
@littleadv: You seem to be assuming that the educational "bar" for English text-based signs is inherently higher than that for non-text-based signs. I'm not sure I agree with that.

*If* you can read English, then when you see a sign that says "no stopping any time", you don't stop. OTOH, if you see a circular sign with a blue background and big red X on it, you'd have no clue what it means *unless you have explicitly been taught* that it prohibits stopping.
user46971
Nov 10, 2022 18:19
@littleadv: The Jim Crow "literacy" tests were often designed with trick questions to ensure that nobody could actually pass them.

US road signs contain straightforward driver-relevant information like "do not pass", "no stopping any time", "road narrows", "hill", or "draw bridge". Yes, you do need to have basic English literacy to read the signs. But that doesn't constitute a deliberately-exclusionary literacy test.

But what you are claiming is that:

* At the time the signs were designed, there was a significant number of people in the US who were either illiterate or non-English spea…
user46971
Nov 9, 2022 21:01
Back to the original topic: Citation needed on @littleadv's claim that US text-based road signs were designed to be exclusionary. If you don't want poor people to drive, a *much* simpler way to accomplish that is to impose high taxes on cars and gasoline.

As I see it, the US refusal to adopt Vienna road signs is simply because nobody wants to spend a ton of money and time replacing signage just to make things more convenient for a few foreigners.
 

 Discussion on question by Paul Omans:…

Imported from a comment discussion on law.stackexchange.com/qu...
user46971
Oct 14, 2022 17:23
Hello, my name is David\b\b\bniel. Don't forget the backspaces.
user46971
Oct 14, 2022 17:23
Are you Elon Musk?
 

 Discussion on answer by Justme: What …

Imported from a comment discussion on retrocomputing.stackexch...
user46971
Sep 25, 2022 07:40
Note that “deleting” a file merely marks its directory entry as deleted; the disk blocks containing the file's actual data are unaffected. This is what allows UNDELETE to work. There are “secure delete” utilities that overwrite the disk with zeroes or random garbage if you need a file to really be deleted.
 

 Discussion on question by user1094359…

Imported from a comment discussion on math.stackexchange.com/q...
user46971
Sep 15, 2022 20:44
In case it's helpful to anyone, the numerical solution (to double precision) is $x \in \{ -1.4889457526134013 \pm 0.25350154536444197i, 0.42318354674129005 \pm 0.3398852191091182 i, 1.0657622058721112 \pm 0.5933867644735602 i\}$.
user46971
Sep 15, 2022 20:44
Maybe it can, but WolframAlpha only gives numerical approximations.
 

 Discussion on answer by Sola Gratia: …

Imported from a comment discussion on hermeneutics.stackexchan...
user46971
Aug 16, 2022 00:00
Nitpick: Spanish verb conjugation isn't gendered. But it's true that nouns and adjectives referring to mixed groups use the masculine -os ending.