> ” This ∞-shaped curve is called a 'leminscate', and ϖ is called the 'lemniscate constant'. I'll show you the leminiscate in my next post.”
This got me confused, so I went to check. Apparently ”lemniscate” is the correct spelling.
johncarlosbaez 27 days ago [-]
Fixed - thanks.
thechao 26 days ago [-]
Hey, John — Matt Parker mentioned in one of his ellipse videos the fact that every elliptical ratio has its own pi-like constant. He just quickly rattles the fact off, but never delves into it. Do you know of any research into trying to characterize the family of pi? I mean, beyond its evil cousins.
klodolph 26 days ago [-]
For a circle, pi is the ratio of the circumference to its diameter. Every ellipse also has a circumference-to-diameter ratio. Well, two ratios, since ellipses have both major and minor diameters. You might think that there would be some kind of clever formula that let you calculate this ratio, but there isn’t! Instead, these pi-like numbers for ellipses are expressed as integrals:
Scroll down to “Complete elliptic integral of the second kind”. That is your search term for looking it up. It is kind of a surprise that there isn’t some neat formula for calculating the circumference of an ellipse. The formula given is:
C = 4 a E(e)
The function E(e) here can be calculated in a few different ways, but it is really just defined as an integral that measures the length of a single ellipse arc.
Here, e is eccentricity. E(0) therefore gives π/4 since a circle has eccentricity 0. E(1) also therefore gives 1. So the E(e) function goes from π/4 to 1 as e goes from 0 to 1.
divbzero 27 days ago [-]
π is derived from the circle, which is defined by distance from a single point.
ϖ is derived from the lemniscate of Bernoulli, which is defined by distances from two points.
Is there an analogous constant that is derived from a shape defined by distances from three points?
dahart 27 days ago [-]
Yes, definitely. Pi is just the perimeter of the circle, and varpi is the perimeter of the lemniscate. If you use three points, you get three tear-drops, and you can compute the perimeter of that.
Let’s call it a trilemniscate. ;)
Here’s a 3d plot of it. If you rotate to view it from +Z downward, then you’ll see the trilemniscate, which is where the volume intersects with the XY plane. Note I subtracted 1 from the product in order to visualize the plane intersection. (And you can turn off the 3 points version and turn on the 2 points version to compare.)
One interesting note about 2 points vs 3 points. The area inside the lemniscate and trilemniscate is the same! (True for more points, as long as they’re evenly space on a circle). The perimeter, of course, goes to infinity as you add more points.
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VHRanger 27 days ago [-]
I mean the concept of distance from 3 points introduces a mess of metrics or even measure theory.
2 points always have a shortest path between each other, so the constant is about this fact. For 3 points you have the whole universe of possible triangle shapes to contend with.
vitus 27 days ago [-]
Shortest path between two points still depends on your metric.
For instance, if you're constrained to travel along the surface of Earth, your shortest path is going to travel along a great circle, rather than pass through the interior of the sphere.
That said, you could, for instance, pick the three vertices of an equilateral triangle (using the Euclidean distance as your metric of choice, as we do in order to derive the lemniscate and the circle), and again deal with the product of the distances from each vertex.
You again start with small circles around each vertex, which eventually expand to a single looping curve, and then into ovals encircling the entire triangle.
it sounds like you are suggesting it might be turtles all the way down?
cl3misch 27 days ago [-]
> I'm not enough of a cultural relativist to believe there's a civilization that cares more about the shape ∞ than the shape ◯.
Maybe these are "logarithmic" beings, as opposed to us "linear" beings? The lemniscate is based on geometric mean, which is basically multiplicative mean and/or mean in log-space -- as opposed to the additive mean in linear space.
If we assume we are linear beings good at intuitive addition but somewhat bad at intuitive multiplication, there could exist beings which live in log-space and whose minds are based on multiplication. Their circle would be the lemniscate.
tibbetts 27 days ago [-]
Humans are actually intuitively log scale thinkers. That is, humans without the kind of early arithmetic training that Westerners get will think more in terms of ratios than differences. There are theories it is more evolutionarily adaptive.
Isn't it also related to our physical perception? Both hearing and vision at least have somewhat logarithmic properties (e.g. response to point-source brightness, and hearing frequency response)
dustingetz 26 days ago [-]
fibonacci retrace shows up in liquid markets a lot
nayuki 27 days ago [-]
Humans have quite a few logarithmic responses: Brightness of light, loudness of sound, musical octaves and relative pitch.
dxbydt 27 days ago [-]
aside: As the Professor points out, the ratio of pi to its evil twin is ~1.198, the arithmetic-geometric mean of sqrt(2) and 1. The geometric part involves a square root, and square roots are expensive. So I was like, well, if the AM converges to GM, then due to AM-GM-HM inequality, it must converge to the harmonic mean as well. And the HM does not need an expensive square root!
Its quite wild that the AM GM convergence is almost immediate - in just 2 steps, whereas to get a decent convergence for the Gauss's constant via HM, you need like 15 steps.You can dispense with expensive operators like square root but you end up paying for it with numerous iterations.
Chinjut 26 days ago [-]
The c value you compute depends on computing the b value, though. It's not a recursion carried out in a way which avoids square roots. It's just carrying out the same AM-GM sequence computation, and then taking a certain weighted harmonic mean over that sequence, which converges just because that original sequence converges anyway.
And some aren't; it's not a list of "commonly encountered" constants, just a list.
yukioikeda 27 days ago [-]
It seems obvious that these are not twins. We can only say that π and ϖ are two among the infinite multitude of siblings ϖₙ.
slippy 27 days ago [-]
Hmm. Why only 2? Why not 3 points? Can you find an interesting curve produced by a constant product of distances from N points? Maybe even in higher dimensions, for 1 point, you have a sphere. What is the shape for 2 points? Is it more like an hourglass-like double droplet?
amelius 27 days ago [-]
There is a generalization:
> Back before Twitter became a Nazi bar, I issued a challenge there: find a whole series of numbers like pi, each with its own bunch of formulas. @duetosymmetry took me up on this and invented the numbers ϖₙ: (...)
plank 27 days ago [-]
Yes. But the question remains: is there a geometrical analogue?
knappa 26 days ago [-]
On the 3 points bit: One and two points are special. In each of these cases, there is, up to translations and uniform scaling, only one configuration. When you have three points, though, there are as many configurations as there are similar triangles. You could probably get a number for each similarity class of triangle, but you shouldn't expect to get a constant across all classes.
metaphor 27 days ago [-]
> This ∞-shaped curve is called a 'leminscate', and ϖ is called the 'lemniscate constant'. I'll show you the leminiscate in my next post.
Two of these...do not belong?
bregma 27 days ago [-]
Shakespeare often spelt the same word differently at different times. If it was good enough for Billy Shakespeare, it should be good enough for modern-day mathematicians, forsooth.
somat 27 days ago [-]
"It is a damn poor mind that can think of only one way to spell a word."
-- Andrew Jackson
Unfortunately Daniel Webster ruined that for the rest of us.
initramfs 27 days ago [-]
I find it hard to believe that Shakespeare would spell the same wird dyfferntli as if heez noom is Sheikhspier een uh deefirind koontri.
stogot 27 days ago [-]
This might feed the “Shakespeare was not one person” theory
zdragnar 27 days ago [-]
The first of Shakespeare plays predate the first published English documentary. It was uncommon for spellings to be inconsistent or change between writings to be easier for a particular audience (in this case, actors) to be able to read.
mckn1ght 27 days ago [-]
I’m still making my way through it, but reading a history of shakespearean/elizabethan england, the first written publications of shakespeare’s plays that were accessible to the general public weren’t written by the man himself (if indeed he was singular).
There were entire efforts put towards pirating the plays by writing them, mostly from memory. It’s believed that someone in the crowd creating a stenographic copy would’ve been noticed so this is a less likely explanation. The memorial effort likely involved both audience and actors. “Official” versions meant to direct the stage productions might have been smuggled out or lost and found.
I haven’t gotten to the part yet that connects to the standard versions we have today. Some official versions were released to correct the record on bad pirated versions. Sometimes theaters would sell official versions to shore up funds.
Maybe this would explain the multiple shakespeare theory as well as writing inconsistencies?
lupire 26 days ago [-]
You wouldn't download Hamlet's pirate story!
drivers99 27 days ago [-]
I guess you mean:
first published English dictionary
and
It wasn't uncommon / It was common
zdragnar 27 days ago [-]
Yes, I was rather tired and typing on my phone required more correcting of the autocorrect feature than I could manage.
Jetrel 26 days ago [-]
Yeah; frankly, in almost all languages, some early works of literature tend to be THE thing that establishes canonical spelling. A lot of this is simply that they act as an argument-settler when two people can't agree how something "ought to be" spelled. In fact, sometimes they go so far as to warp pronunciation, cementing little verbal quirks that only some speakers had.
adrian_b 27 days ago [-]
"Lemniscate" is the correct spelling. All the other variants are mistyped.
yard2010 27 days ago [-]
It's quite funny imo that someday english people were like "forget about latin or german, greek is lit! Let's use greek"
msravi 27 days ago [-]
Why stop at greek or arabic when you can go all the way to sanskrit?
The words for sine and cosine derive from the sanskrit jiva (meaning bowstring, i.e., the chord of a circle)[1]. Sine and cosine were respectively jya and koti-jya, which got transcribed into arabic without the vowel (where it meant nothing). They then pronounced the vowel in the wrong place, calling it jeb (which meant pocket or fold in arabic)[2]. Then this wrong word got translated into latin as sinus (fold), and hence we have sine and cosine!
The wikipedia link has this occurring in the 12th century. But Hellenistic astronomers were already working with sine tables. What did they call the concept?
rsynnott 27 days ago [-]
A healthy mixture was always preferred in maths and science. This is occasionally taken to extremes; the name reverse transcriptase, an enzyme used by retroviruses, is a combo of English, Latin and Greek!
Arabic is also popular, particularly in maths.
flobosg 27 days ago [-]
> Television? The word is half Greek and half Latin. No good will come of this device.
―C. P. Scott
xanderlewis 27 days ago [-]
Is it? I can only think of (the very frequently noted) ‘algebra’ and ‘algorithm’.
rsynnott 27 days ago [-]
Also ‘zero’, and ‘cipher’ (which, oddly, derive from the same word). And ‘average’. There are a few of them.
xanderlewis 26 days ago [-]
Interesting. I'm not sure we can really call these arabic-derived, though. They do seem to ultimately trace back to fairly unrelated arabic words, but their first use in mathematics (much later) seems to have come in the form of a mixture of words from European languages. The two examples I gave seem to be more legitimately Arabic in origin.
dizhn 27 days ago [-]
Not math but I just learned alkali is the word for "ash" in Arabic.
dudeinjapan 27 days ago [-]
And “alcohol”, frequently consumed at science and math conferences
Sharlin 27 days ago [-]
"Alcohol" has a very interesting etymology, too.
DiggyJohnson 27 days ago [-]
As others have said, there are a few celestial terms that come to mind:
- azimuth
- zenith
- nadir
Also some chemistry terms, again just from top of brain, might be wrong:
- alchemy
- elixir
- arsenic
- alkali
xanderlewis 26 days ago [-]
Nadir always seemed very obviously Arabic to me. Weirdly, I first encountered it in a book on category theory, and only after that did I start to hear it used in everyday English to mean the opposite of 'apex'.
samatman 26 days ago [-]
It's the opposite of zenith, another word ultimately derived from Arabic.
The difference between an apex and a zenith is that an apex exists as a point in space, while a zenith is a direction, with no fixed point which may be said to be "the" zenith. There are other differences given that apex has a few related meanings, but this is the main one.
xanderlewis 23 days ago [-]
Ah, yes. I knew it wasn’t quite the right word.
pfdietz 26 days ago [-]
Sofa!
27 days ago [-]
ajmurmann 27 days ago [-]
Dolphin, music (from muse), logic, ethics, physics, mathematics, pharmacy, angel, comedy, drama. The list of Greek loan words that are shared by many European languages goes on and on
Edit: I think almost every word with "ph" in it is from Greek and "th" in languages other than English.
lolinder 27 days ago [-]
They're asking about Arabic loanwords.
FredPret 27 days ago [-]
If you add all Latin words with Greek origins, most European languages are really forms of Greek
nicwilson 27 days ago [-]
azimuth is the only other one I can think of off the top of my head
dredmorbius 26 days ago [-]
You'll find "zenith" at your feet.
samatman 26 days ago [-]
You're thinking of nadir, also Arabic. The zenith is in the opposite direction.
dredmorbius 25 days ago [-]
Gah! So much for my wit.
jjtheblunt 27 days ago [-]
The sheriff says "hold my beer".
mikhailfranco 26 days ago [-]
A funny false or convergent etymology - shire reeve not sharif.
Here's another false trail from a real conversation:
Q: What US state's name comes from the title of an Arabic ruler?
A: Al Abama?
Of course, the correct answer is California from Khalifa transliterated through a Spanish novel:
I understand the confusion. Lemons smell good. The second root, on the other hand, far less pleasant.
Netcob 27 days ago [-]
Not to be confused with the "lemonscape", a hallucinated world you enter when you've eaten too many lemons.
mst 27 days ago [-]
Having that shape become more important to a civilisation than the circle because it has something to do with the geometry of hyperspace seems like it could be an interesting conceit for a sci-fi setting.
pavel_lishin 27 days ago [-]
The Anvil of the Stars, by Greg Bear, featured a race of aliens whose mathematics weren't based on integers.
mst 26 days ago [-]
This somehow reminds me of Egyptian mathematics where they refused to admit to the existence of any fraction with a numerator other than 1 (except for 2/3).
Learning how to expand e.g. 3/7 into 1/n + 1/m + ... using their methods was a fascinating experience.
I wouldn't want to suffer under such constraints day to day but it was one of the most memorable parts of the History of Mathematics course I took alongside what was other a mostly pure maths degree.
tibbetts 27 days ago [-]
Sounds like a Greg Egan writing prompt.
dmd 27 days ago [-]
Baez and Egan are close friends, so don’t be surprised if you see it pop up.
mst 26 days ago [-]
Egan would probably be my first thought of somebody who could take a concept like that and make something well worth reading out of it.
Second thought would probably be Derek Künsken. (no claim he's necessarily the second best option but he's definitely the second author I've read recently enough to have the name of in brain cache to come to mind as "could almost certainly pull it off")
szundi 27 days ago [-]
People just prompt themselves
TuringTest 27 days ago [-]
Bob Shaw's Night Walk has something like that as a major plot point.
It's not aliens but humans, and it's not an 8-loop geometry, but without spoiling it too much it's safe to say that discovering how hyperspace works is the central concept guiding the story.
mst 26 days ago [-]
Kindle Edition: £2.99
Sounds like at least £2.99's worth of fun to me from the blurb, so it's now queued up.
I swear I'll get to it eventually.
... honest.
antonvs 27 days ago [-]
[flagged]
dang 27 days ago [-]
Please don't do this here.
antonvs 26 days ago [-]
Can you really call yourself a hacker if you’ve never spelled 80085 on a calculator?
bowsamic 26 days ago [-]
[flagged]
dang 25 days ago [-]
Lots of things are right.
sundarurfriend 27 days ago [-]
[flagged]
sapphicsnail 27 days ago [-]
If I saw ϖ in the wild I would have assumed it was an omega (ω) with a macron over it. Makes me wonder how many more varient Greek letters are out there.
wombatpm 27 days ago [-]
Ancient, Ancient Greek had three additional letters: an F like character, a double lambda character, and P sounding character that looked like a lollipop. In case you need some additional symbols
Interesting! I can see it in two ways: (1) as elongated U-shaped ellipsis that rotates sideways and (2) as bent lemniscate that rotates vertically.
ComputerGuru 27 days ago [-]
The post mentions that ϖ is called “varpi”; I just wanted to add that this is actually short for “variant of pi”, also known as an “archaic form of pi” from old Greek writing.
flatline 27 days ago [-]
I read it as “omega-bar.”
thoughtcritical 26 days ago [-]
"figure of eight" curves .... perhaps the simplest is the lemniscate of Gerono, which has the parametrization:
However, the lemniscate of Bernoulli may be visually more pleasing; it has a parametrization very similar to the lemniscate of Gerono, except that both axes are scaled by a factor of 1/(sin(t)^2 + 1) = 2/(3 - cos(2t)):
scale = 2 / (3 - cos(2t));
x = scale cos(t);
y = scale * sin(2*t) / 2;
It looks like this:
Wish people wouldn’t inject weird social jabs into stuff like this
kolbe 26 days ago [-]
Just like advertising--if they have earned my attention by saying things I want to read, then they have the right to dilute its quality with whatever else they want, up until it net doesn't interest me anymore. In this case, the jab is tiny and the quality content is bountiful.
whamlastxmas 25 days ago [-]
The author isn’t going to convince anyone or change anything with a random jab and it detracts from what they’re communicating
Is there an evil twin to the set of prime numbers?
OscarCunningham 27 days ago [-]
There are the Lucky Numbers https://en.wikipedia.org/wiki/Lucky_number. Generated by a variant of the Sieve of Eratosthenes, they're believed to have a similar distribution to the primes while not having similar multiplicative properties.
There are the anti prime numbers (also called highly composite numbers).
block_dagger 27 days ago [-]
Every even number?
ralusek 27 days ago [-]
2?
pwdisswordfishz 26 days ago [-]
Well, this one is pretty evil as prime numbers go.
sourcepluck 27 days ago [-]
> This ∞-shaped curve is called a 'leminscate', and ϖ is called the 'lemniscate constant'. I'll show you the leminiscate in my next post.
I think others have commented, but this three-way spelling certainly got a chuckle from me.
mettamage 26 days ago [-]
So are there an infinite amount of constants like this? In terms of pi, e and this number?
Just wondering, there are an infinite number of shapes I suppose? But does that mean there is an infinite amount of constants?
dwaltrip 26 days ago [-]
There are infinite integers [1]. So even if we just look at basic polygons — shapes formed by connecting some (integer) number of points with straight lines — we easily get infinite shapes.
Math is crazy. The universe is crazy. Happy holidays!
———
[1] At least, that’s what they tell us… :p
Morizero 27 days ago [-]
Is there an abstraction of a leminscate/consonant with 3+ center points?
The lemniscate really looks like a homoclinic orbit in a 2d dynamics problem
27 days ago [-]
BearOso 27 days ago [-]
I thought it might be e. e is often used to model unbounded growth, so it's chaotic, while pi is harmonic.
Plus, evil starts with 'e', so why not.
"Laugh with me Jocko!"
"Eeeeeeeeeeeeee!"
anyfoo 27 days ago [-]
Can’t have harmonics (i.e. harmonic oscillations, or any oscillations really) without e, though. sine and cosine are both sums of e, and if you look at the beauty of analytical sinusoid signals (which only have one component in the entire spectrum, lacking their negative frequency one) it’s just one exponential and nothing else.
upvote for tau, the one really running the show while pi gets the fame & fortune
layer8 27 days ago [-]
Is there something like ThreadReaderApp for Mastodon?
TomK32 27 days ago [-]
Am I the only one who expected the evil twin to be 3 ?
incognito124 27 days ago [-]
For some reason, I imagined a number where every digit of pi was transformed into a [9-digit] and that it has special properties. This one is more magical, though.
aap_ 27 days ago [-]
Wow, pomega is such a terrible name for it!
babbledabbler 26 days ago [-]
Woah it even has a w for wa-pi-rio.
Bengalilol 27 days ago [-]
mupi (mutant pi) or piet (pi evil twin) would be better names
Qem 27 days ago [-]
Pizarro = Pi + Bizarro. Also there was an evil person that beared this name, Francisco Pizarro, the conquistador that kickstarted the genocide against the Incas. See https://en.m.wikipedia.org/wiki/Francisco_Pizarro
waldrews 27 days ago [-]
Seems like a fine number, but I bet there's quite a few more irrational computable numbers out there.
nektro 26 days ago [-]
how close is ϖ to e?
notpushkin 27 days ago [-]
> I'm not enough of a cultural relativist to believe there's a civilization that cares more about the shape ∞ than the shape ◯.
Rumor has it there is one civilization of lizard-people out there. One is in fact running a company here on Earth with this shape as a logo!
Curiously that made the thread better for me and the author's opinion about Twitter is exactly as true as the opposite opinion, that it is now the unfiltered source of objective truth. Or do you believe your opinions on the threads value or twitters reputation is special?
veltas 27 days ago [-]
I also found it extremely helpful that the author virtue signalled to agree with me, so I know whether I am supposed to like it or not.
pera 27 days ago [-]
What's more likely: (i) famous mathematician expressing his frustration regarding how his previous internet community is now full of Nazis, or (ii) famous mathematician casually saying Nazis suck so to be perceived as morally superior by some random readers?
To me the second option is an extremely bizarre take and I cannot imagine why anyone would even consider it.
mnsc 26 days ago [-]
Interpretation 1 is more likely and made the dry mathematician more relatable/human which made the writing better imo.
nthingtohide 27 days ago [-]
> Hence neither a man's contemporaries nor the man himself can form any final estimate of him or of his fitting position, because their knowledge is too imperfect. History often reverses the decision of contemporaries.
Probably true about Elon.
I_complete_me 27 days ago [-]
But I think mainly in the direction of demotion. Offhand I can't think of examples of someone ... oh, wait Van Gogh.
nthingtohide 27 days ago [-]
Baruch Spinoza is another. He was excommunicated.
27 days ago [-]
rsynnott 27 days ago [-]
It’s a metaphor (ironically originating _on_ Twitter, not _about_ Twitter, pre-Musk); essentially, once you allow Nazis in a bar, they metastasize, and pretty soon you’re a Nazi bar. It’s perfectly applicable to the current state of twitter.
gosub100 27 days ago [-]
what metaphor was it called back when they allowed far-left hate speech but censored, shadow-banned or otherwise slowed stories that their secret thought-control departments didn't like? what would you call that?
xigoi 27 days ago [-]
Twitter already contained a lot of hateful speech before Elon acquired it.
lern_too_spel 27 days ago [-]
Those tweets would typically be demoted instead of promoted.
veltas 27 days ago [-]
I absolutely agree, a dead 1920's German nationalist movement is exactly why we shouldn't allow free speech online.
himgl 27 days ago [-]
[flagged]
rsynnott 27 days ago [-]
I was a Twitter user from 2007 to late 2022. That idiot wasted no time in ruining it; by Dec 2022 it was very clearly time to go.
nuancebydefault 27 days ago [-]
Nobody uses twitter these days.
himgl 27 days ago [-]
What a daft claim to make. A simple web search would have informed you that Twitter has over half a billion monthly active users.
nuancebydefault 27 days ago [-]
Hmm you mean X right?
himgl 27 days ago [-]
Same thing.
johnp314 27 days ago [-]
Since it's an "evil twin" should we not expect to find it in an alleged Nazi bar?
mongol 27 days ago [-]
Yes, that is when I stopped reading. I left Twitter recently, but I would not call it a Nazi bar. It is just not for me, any longer.
Johanx64 27 days ago [-]
[flagged]
d_burfoot 27 days ago [-]
[flagged]
ryanmcgarvey 27 days ago [-]
Is it a political statement if it's also a statement of fact? Sure, the comment has some color to it, I'll concede that, but one can no longer post these kinds of things on Twitter and get the honest engagement from community members one used to. It's no longer a welcoming place for this kind of discussion.
BearOso 27 days ago [-]
With no account, I can no longer read comment chains on Twitter. It will only show the direct comment linked to. If you go to the user's page, all you see are the promoted tweets. There's no way to access the timeline sequentially anymore.
With those restrictions, you're writing only to a captive audience if you post on Twitter.
So you are technically correct, you literally cannot post these things on Twitter.
foogazi 27 days ago [-]
> Why does this guy think it's acceptable to bitterly insult so many people,
Won’t someone think of the people?
My mom is on X - I don’t see how that offhand remark insults her
> I think HN should have a policy for submitted content that is along the lines of the policies in place for comments
We can already flag and vote - what more censorship do you want ?
veltas 27 days ago [-]
[flagged]
yason 27 days ago [-]
[flagged]
pwdisswordfishz 26 days ago [-]
Same here. I have to install a userscript to restore usable scrolling:
> Up/down arrows jump to the next post and page up/down isn't too helpful for reading.
I didn't experience this at all on Firefox, up/down and page up/down scrolled in the normal way.
davorak 27 days ago [-]
The issue existed from me in both firefox and chrome. Click on outside columns will result in normal scroll. Click or highlight in the center column will result in the jumpy scroll that does not quite scroll one comment at a time with up/down arrow.
RobotToaster 27 days ago [-]
It kinda happens to me on firefox, one press of the down arrow scrolls so "Here's a formula for the lemniscate in polar coordinates" in the first reply is at the top of the screen, not helpful.
kuschkufan 27 days ago [-]
here's a nickel, get a new browser.
no idea why i even go for bait like this. because i like doing unpaid support work i guess. i tested in firefox and chrome. both work fine and don't do it like op decribes - no keybinds, keys behave normal.
maybe one of the dudes from yesterdays thread that had his own chatgpt programmed browser extensions installed that break the web for him.
BeetleB 27 days ago [-]
I follow John on Mastodon. He never fails to disappoint.
hinkley 27 days ago [-]
Then why do you follow him?
barrell 27 days ago [-]
Oddly enough, “never fails to disappoint” can have the meaning “never disappoints” as well as “routinely disappoints”. I’ve never thought about that one before
heresie-dabord 27 days ago [-]
Native EN parser here. I would never consider this usage correct except as a rhetorical (facetious) insult. People may well repeat it without understanding the original nor their mistake. Although if enough people bust the syntax, it may attract descriptivist reporting, as with the widely observed malapropism "irregardless".
It’s not a matter of correctness, but of understanding. OP definitely intended to imply the content does not disappoint, and used a colloquialism most native speakers would understand
slippy 27 days ago [-]
I am a native speaker and got the gist and saw the paradox, and found the phrasing a bit tortured by the triple negative. Thank you for explaining that this was a colloquialism. Now I have to go look up the etymology... And upon further inspection, this usage is actually a misnegation.
"It is a veiled insult: an ironic form of insult delivery which is misinterpreted as flattery to the buffoon who is targeted by it, much to the entertainment of anyone else within earshot who understands the true meaning."
hinkley 27 days ago [-]
Only in the same sense that “could care less” is understandable but also means the opposite of the intention.
ftmch 26 days ago [-]
There are East European languages, mostly Slavic ones, that have these weird double negatives which are grammatically correct and mean the opposite. A sentance such as: "I haven't never been there" means you've never been there.
hinkley 27 days ago [-]
I have only ever heard it used as a high brow burn, and a wickedly hard one at that.
kazinator 27 days ago [-]
I've never failed to win a game of mahjong against a bunch of grannies a Chinatown back room joint.
I've never tried such a thing; therefore, I've never failed.
scubbo 27 days ago [-]
Frankly, I could care less
Agingcoder 27 days ago [-]
This is the first time I come across this mistake / non-mistake so I misunderstood your comment. Are you sure it’s a common enough misnegation for people to understand what you meant ?
barrell 27 days ago [-]
I didn’t use the expression, I don’t think I would have myself, but it didn’t even strike me as odd until I read the comment by hinkley. Did you read the original comment and think BeetleB follows John and thinks all of his content is disappointing?
jrmann100 27 days ago [-]
Here's a StackExchange thread on this exact mix-up (a "misnegation"):
Never heard that one, but maybe it's like 'could care less', which has acquired the opposite of it's actual meaning (the phrase should be 'could not care less') by repeated incorrect use.
hinkley 27 days ago [-]
I’d say that’s more tolerated than embraced. We know what you meant, you just didn’t say what you meant. Not everyone tolerates it.
reshlo 27 days ago [-]
> can have the meaning “never disappoints”
How?
kazinator 27 days ago [-]
A complete stranger who has nothing whatsoever to do with you, who has never tried to do anything for you, nor has been expected to, has never disappointed you. They've also never failed to disappoint you, because they have not failed in any regard whatsoever.
This is an example of a vacuous truth.
I've never failed an airliner landing. While that may sound like I'm boasting of being a good pilot, in fact I'm not a pilot at all, and I've never attempted such a thing.
Another vacuous truth.
Every crow in an empty set of crows is white.
Also, every crow in an empty set of crows is black.
Propositions universally quantified over an empty set are all vacuously true.
Statements with always and never are universally quantified over some set of events. If that set is empty it leads to vacuous truths.
"Every time I've seen a crow, it has always been white" is vacuously true if I've never seen a crow. I.e. the set of crows I've seen is empty, and consequently is a true statement that they're all white.
reshlo 27 days ago [-]
> A complete stranger who has nothing whatsoever to do with you, who has never tried to do anything for you, nor has been expected to, has never disappointed you. They've also never failed to disappoint you, because they have not failed in any regard whatsoever.
Nobody who uses the phrase ever means it in this way. The point of using the statement is to convey that you are familiar with the person’s history.
As another commenter has already pointed out, “has never failed to disappoint” is not the same statement as “never fails to disappoint”. The habitual present can’t refer to empty sets, as it is only used to refer to repeated actions.
kazinator 27 days ago [-]
> Nobody who uses the phrase ever means it in this way.
That is true. Outside of formal logic situations, deliberately uttered vacuous truths are only ever used by nerds to be clever, or for sarcasm, or insult and such.
Someone habitually using "never fails to disappoint" intended as a compliment has somehow latched onto an incorrect idiom; they likely intend something slightly funny like "never manages to disappoint" (tries hard to disappoint, but never does, due to being so good!). Or maybe it's supposed to be a deliberately funny mixup of "never fails" and "never disappoints".
seba_dos1 27 days ago [-]
> A complete stranger who has nothing whatsoever to do with you, who has never tried to do anything for you, nor has been expected to, has never disappointed you. They've also never failed to disappoint you, because they have not failed in any regard whatsoever.
"never failed" != "never fails"
nuancebydefault 27 days ago [-]
They said they were a follower of them though.
barrell 27 days ago [-]
¯\_(ツ)_/¯ linguistic drift. Technically it means you routinely disappoint, but it’s often used idiomatically to mean the opposite
ykonstant 27 days ago [-]
What a country!
BeetleB 27 days ago [-]
Heh. This comment blew up on me. Yes, it was a typo.
For a more festive example see Berghaus star projection on page 156.
[1]: https://pubs.usgs.gov/pp/1453/report.pdf (1989)
https://www.wolframalpha.com/input?i=plot+r%3Dcos%282theta%2...
This got me confused, so I went to check. Apparently ”lemniscate” is the correct spelling.
https://en.wikipedia.org/wiki/Elliptic_integral
Scroll down to “Complete elliptic integral of the second kind”. That is your search term for looking it up. It is kind of a surprise that there isn’t some neat formula for calculating the circumference of an ellipse. The formula given is:
The function E(e) here can be calculated in a few different ways, but it is really just defined as an integral that measures the length of a single ellipse arc.Here, e is eccentricity. E(0) therefore gives π/4 since a circle has eccentricity 0. E(1) also therefore gives 1. So the E(e) function goes from π/4 to 1 as e goes from 0 to 1.
ϖ is derived from the lemniscate of Bernoulli, which is defined by distances from two points.
Is there an analogous constant that is derived from a shape defined by distances from three points?
Let’s call it a trilemniscate. ;)
Here’s a 3d plot of it. If you rotate to view it from +Z downward, then you’ll see the trilemniscate, which is where the volume intersects with the XY plane. Note I subtracted 1 from the product in order to visualize the plane intersection. (And you can turn off the 3 points version and turn on the 2 points version to compare.)
https://www.desmos.com/3d/dl9v2vqbqb
One interesting note about 2 points vs 3 points. The area inside the lemniscate and trilemniscate is the same! (True for more points, as long as they’re evenly space on a circle). The perimeter, of course, goes to infinity as you add more points.
2 points always have a shortest path between each other, so the constant is about this fact. For 3 points you have the whole universe of possible triangle shapes to contend with.
For instance, if you're constrained to travel along the surface of Earth, your shortest path is going to travel along a great circle, rather than pass through the interior of the sphere.
That said, you could, for instance, pick the three vertices of an equilateral triangle (using the Euclidean distance as your metric of choice, as we do in order to derive the lemniscate and the circle), and again deal with the product of the distances from each vertex.
You again start with small circles around each vertex, which eventually expand to a single looping curve, and then into ovals encircling the entire triangle.
https://en.wikipedia.org/wiki/Cassini_oval#Generalizations
https://en.wikipedia.org/wiki/Polynomial_lemniscate#Erd%C5%9...
https://www.desmos.com/calculator/fo7tqlfjgo
Maybe these are "logarithmic" beings, as opposed to us "linear" beings? The lemniscate is based on geometric mean, which is basically multiplicative mean and/or mean in log-space -- as opposed to the additive mean in linear space.
If we assume we are linear beings good at intuitive addition but somewhat bad at intuitive multiplication, there could exist beings which live in log-space and whose minds are based on multiplication. Their circle would be the lemniscate.
https://www.scientificamerican.com/article/a-natural-log/
https://imgur.com/a/UkxkPzW
Its quite wild that the AM GM convergence is almost immediate - in just 2 steps, whereas to get a decent convergence for the Gauss's constant via HM, you need like 15 steps.You can dispense with expensive operators like square root but you end up paying for it with numerous iterations.
Note that the arithmetic-harmonic mean I think you were going for is just the geometric mean (not the arithmetic-geometric mean, just the geometric mean simpliciter; see https://mathworld.wolfram.com/Arithmetic-HarmonicMean.html).
Euler–Mascheroni Constant (integrals and sums involving the harmonic series, Gamma functions)
Catalan’s Constant (certain trigonometric series, lattice Green’s function)
Feigenbaum Constants (logistic map, chaos in dynamical systems)
Khinchin’s Constant (partial quotients in simple continued fractions)
Glaisher–Kinkelin Constant (asymptotic expansions of the Barnes G-function, combinatorial limits and certain product expansions)
Ramanujan’s Constant (complex multiplication of elliptic curves)
Omega Constant (Omega times e to the power of Omega = 1, Lambert W function, x^x^x^... = 2)
f(x,1) = x
c_n is such that f(c_n,n) = 2
c = lim c_n
See also: https://en.wikipedia.org/wiki/List_of_mathematical_constants
> Back before Twitter became a Nazi bar, I issued a challenge there: find a whole series of numbers like pi, each with its own bunch of formulas. @duetosymmetry took me up on this and invented the numbers ϖₙ: (...)
Two of these...do not belong?
There were entire efforts put towards pirating the plays by writing them, mostly from memory. It’s believed that someone in the crowd creating a stenographic copy would’ve been noticed so this is a less likely explanation. The memorial effort likely involved both audience and actors. “Official” versions meant to direct the stage productions might have been smuggled out or lost and found.
I haven’t gotten to the part yet that connects to the standard versions we have today. Some official versions were released to correct the record on bad pirated versions. Sometimes theaters would sell official versions to shore up funds.
Maybe this would explain the multiple shakespeare theory as well as writing inconsistencies?
first published English dictionary
and
It wasn't uncommon / It was common
The words for sine and cosine derive from the sanskrit jiva (meaning bowstring, i.e., the chord of a circle)[1]. Sine and cosine were respectively jya and koti-jya, which got transcribed into arabic without the vowel (where it meant nothing). They then pronounced the vowel in the wrong place, calling it jeb (which meant pocket or fold in arabic)[2]. Then this wrong word got translated into latin as sinus (fold), and hence we have sine and cosine!
1. https://en.m.wikipedia.org/wiki/Jy%C4%81,_koti-jy%C4%81_and_...
2. https://en.m.wikipedia.org/wiki/Sine_and_cosine#Etymology
Arabic is also popular, particularly in maths.
―C. P. Scott
The difference between an apex and a zenith is that an apex exists as a point in space, while a zenith is a direction, with no fixed point which may be said to be "the" zenith. There are other differences given that apex has a few related meanings, but this is the main one.
Edit: I think almost every word with "ph" in it is from Greek and "th" in languages other than English.
Here's another false trail from a real conversation:
Of course, the correct answer is California from Khalifa transliterated through a Spanish novel:https://en.wikipedia.org/wiki/Etymology_of_California#Las_Se...
https://en.wikipedia.org/wiki/Calafia
https://en.wiktionary.org/wiki/%CE%BB%CE%B7%CE%BC%CE%BD%CE%A...
Learning how to expand e.g. 3/7 into 1/n + 1/m + ... using their methods was a fascinating experience.
I wouldn't want to suffer under such constraints day to day but it was one of the most memorable parts of the History of Mathematics course I took alongside what was other a mostly pure maths degree.
Second thought would probably be Derek Künsken. (no claim he's necessarily the second best option but he's definitely the second author I've read recently enough to have the name of in brain cache to come to mind as "could almost certainly pull it off")
It's not aliens but humans, and it's not an 8-loop geometry, but without spoiling it too much it's safe to say that discovering how hyperspace works is the central concept guiding the story.
Sounds like at least £2.99's worth of fun to me from the blurb, so it's now queued up.
I swear I'll get to it eventually.
... honest.
https://en.wikipedia.org/wiki/Archaic_Greek_alphabets
Ϝ Digamma
Ͱ Heta
Ϻ San
Ϙ Koppa
Ͷ Tsan, Digamma
Ͳ Sampi
There must be an analogous transform composed of lemniscate sines and cosines?
x = Asin(at + delta)
y = Bsin(bt)
https://ericfortis.github.io/lissajous/?preset=Infinity
x = cos(t); y = sin(2t) / 2; and looks like this:
Lemniscate of Gerono animation https://i.sstatic.net/VKBgs.gif
However, the lemniscate of Bernoulli may be visually more pleasing; it has a parametrization very similar to the lemniscate of Gerono, except that both axes are scaled by a factor of 1/(sin(t)^2 + 1) = 2/(3 - cos(2t)):
scale = 2 / (3 - cos(2t)); x = scale cos(t); y = scale * sin(2*t) / 2; It looks like this:
Lemniscate of Bernoulli animation https://i.sstatic.net/nOPMx.gif
per: https://gamedev.stackexchange.com/questions/43691/how-can-i-...
2022 - Non-Euclidean Doom: What happens to a game when pi is not 3.14159… https://youtu.be/_ZSFRWJCUY4?t=406
https://en.wikipedia.org/wiki/Highly_composite_number
But I'm not sure if these ones are evil.
I think others have commented, but this three-way spelling certainly got a chuckle from me.
Just wondering, there are an infinite number of shapes I suppose? But does that mean there is an infinite amount of constants?
Math is crazy. The universe is crazy. Happy holidays!
———
[1] At least, that’s what they tell us… :p
These are symmetric as well though.
Plus, evil starts with 'e', so why not.
"Laugh with me Jocko!" "Eeeeeeeeeeeeee!"
You don't say. Newton must have been sick that day.
https://tauday.com/tau-manifesto
Rumor has it there is one civilization of lizard-people out there. One is in fact running a company here on Earth with this shape as a logo!
/s
But I was actually alluding to Meta and the memes about Mark Zuckerberg being a lizard: https://www.youtube.com/watch?v=jiudBq7z8wk
To me the second option is an extremely bizarre take and I cannot imagine why anyone would even consider it.
Probably true about Elon.
With those restrictions, you're writing only to a captive audience if you post on Twitter.
So you are technically correct, you literally cannot post these things on Twitter.
Won’t someone think of the people?
My mom is on X - I don’t see how that offhand remark insults her
> I think HN should have a policy for submitted content that is along the lines of the policies in place for comments
We can already flag and vote - what more censorship do you want ?
I didn't experience this at all on Firefox, up/down and page up/down scrolled in the normal way.
no idea why i even go for bait like this. because i like doing unpaid support work i guess. i tested in firefox and chrome. both work fine and don't do it like op decribes - no keybinds, keys behave normal.
maybe one of the dudes from yesterdays thread that had his own chatgpt programmed browser extensions installed that break the web for him.
https://english.stackexchange.com/questions/139448/never-fai...
https://en.m.wikipedia.org/wiki/Irregardless
"It is a veiled insult: an ironic form of insult delivery which is misinterpreted as flattery to the buffoon who is targeted by it, much to the entertainment of anyone else within earshot who understands the true meaning."
I've never tried such a thing; therefore, I've never failed.
https://english.stackexchange.com/questions/139448/never-fai...
How?
This is an example of a vacuous truth.
I've never failed an airliner landing. While that may sound like I'm boasting of being a good pilot, in fact I'm not a pilot at all, and I've never attempted such a thing.
Another vacuous truth.
Every crow in an empty set of crows is white.
Also, every crow in an empty set of crows is black.
Propositions universally quantified over an empty set are all vacuously true.
Statements with always and never are universally quantified over some set of events. If that set is empty it leads to vacuous truths.
"Every time I've seen a crow, it has always been white" is vacuously true if I've never seen a crow. I.e. the set of crows I've seen is empty, and consequently is a true statement that they're all white.
Nobody who uses the phrase ever means it in this way. The point of using the statement is to convey that you are familiar with the person’s history.
As another commenter has already pointed out, “has never failed to disappoint” is not the same statement as “never fails to disappoint”. The habitual present can’t refer to empty sets, as it is only used to refer to repeated actions.
That is true. Outside of formal logic situations, deliberately uttered vacuous truths are only ever used by nerds to be clever, or for sarcasm, or insult and such.
Someone habitually using "never fails to disappoint" intended as a compliment has somehow latched onto an incorrect idiom; they likely intend something slightly funny like "never manages to disappoint" (tries hard to disappoint, but never does, due to being so good!). Or maybe it's supposed to be a deliberately funny mixup of "never fails" and "never disappoints".
"never failed" != "never fails"