[HN Gopher] The number pi has an evil twin
       ___________________________________________________________________
        
       The number pi has an evil twin
        
       Author : pkaeding
       Score  : 412 points
       Date   : 2024-12-24 03:41 UTC (19 hours ago)
        
 (HTM) web link (mathstodon.xyz)
 (TXT) w3m dump (mathstodon.xyz)
        
       | BeetleB wrote:
       | I follow John on Mastodon. He never fails to disappoint.
        
         | hinkley wrote:
         | Then why do you follow him?
        
           | barrell wrote:
           | 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
        
             | jrmann100 wrote:
             | Here's a StackExchange thread on this exact mix-up (a
             | "misnegation"):
             | 
             | https://english.stackexchange.com/questions/139448/never-
             | fai...
        
             | heresie-dabord wrote:
             | 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".
             | 
             | https://english.stackexchange.com/questions/139448/never-
             | fai...
             | 
             | https://en.m.wikipedia.org/wiki/Irregardless
        
               | kazinator wrote:
               | 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.
        
               | barrell wrote:
               | 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 wrote:
               | 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 wrote:
               | Only in the same sense that "could care less" is
               | understandable but also means the opposite of the
               | intention.
        
               | ftmch wrote:
               | 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.
        
               | scubbo wrote:
               | Frankly, I could care less
        
               | hinkley wrote:
               | I have only ever heard it used as a high brow burn, and a
               | wickedly hard one at that.
        
             | reshlo wrote:
             | > can have the meaning "never disappoints"
             | 
             | How?
        
               | kazinator wrote:
               | 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.
        
               | seba_dos1 wrote:
               | > 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"
        
               | reshlo wrote:
               | > 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 wrote:
               | > 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".
        
               | nuancebydefault wrote:
               | They said they were a follower of them though.
        
               | barrell wrote:
               | -\\_(tsu)_/- linguistic drift. Technically it means you
               | routinely disappoint, but it's often used idiomatically
               | to mean the opposite
        
             | ykonstant wrote:
             | What a country!
        
             | jacknews wrote:
             | 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 wrote:
               | 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.
        
             | Agingcoder wrote:
             | 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 wrote:
               | 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?
        
         | BeetleB wrote:
         | Heh. This comment blew up on me. Yes, it was a typo.
        
       | metaphor wrote:
       | > This [?]-shaped curve is called a ' _leminscate_ ', and p is
       | called the ' _lemniscate_ constant '. I'll show you the
       | _leminiscate_ in my next post.
       | 
       | Two of these...do not belong?
        
         | brookst wrote:
         | Even the word has evil twins
        
         | saghm wrote:
         | It's so evil that it defies spelling
        
         | thaumasiotes wrote:
         | Lemniscate.
         | 
         | https://en.wiktionary.org/wiki/%CE%BB%CE%B7%CE%BC%CE%BD%CE%A...
        
         | adrian_b wrote:
         | "Lemniscate" is the correct spelling. All the other variants
         | are mistyped.
        
           | yard2010 wrote:
           | It's quite funny imo that someday english people were like
           | "forget about latin or german, greek is lit! Let's use greek"
        
             | laurent_du wrote:
             | What makes you think it was the English? I am pretty sure
             | it comes from continental Europe.
        
             | cgio wrote:
             | Latin is lemniscus, so someday Latin people were like
             | "let's use Greek"
        
               | dmurray wrote:
               | Latin writers have been like "let's use Greek" at least
               | since Virgil, so modern writers can be excused for
               | getting their roots mixed up.
        
             | rsynnott wrote:
             | 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.
        
               | xanderlewis wrote:
               | Is it? I can only think of (the very frequently noted)
               | 'algebra' and 'algorithm'.
        
               | nicwilson wrote:
               | azimuth is the only other one I can think of off the top
               | of my head
        
               | rsynnott wrote:
               | Also 'zero', and 'cipher' (which, oddly, derive from the
               | same word). And 'average'. There are a few of them.
        
               | dizhn wrote:
               | Not math but I just learned alkali is the word for "ash"
               | in Arabic.
        
               | ajmurmann wrote:
               | 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 wrote:
               | They're asking about Arabic loanwords.
        
               | FredPret wrote:
               | If you add all Latin words with Greek origins, most
               | European languages are really forms of Greek
        
               | dudeinjapan wrote:
               | And "alcohol", frequently consumed at science and math
               | conferences
        
               | Sharlin wrote:
               | "Alcohol" has a very interesting etymology, too.
        
               | DiggyJohnson wrote:
               | 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
        
               | flobosg wrote:
               | > _Television? The word is half Greek and half Latin. No
               | good will come of this device._
               | 
               | --C. P. Scott
        
               | jjtheblunt wrote:
               | The sheriff says "hold my beer".
        
             | ajmurmann wrote:
             | Don't most European languages use Landis loan words from
             | both Latin and Greek? Both used to be taught in classical
             | education.
        
             | msravi wrote:
             | 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!
             | 
             | 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
        
         | dotancohen wrote:
         | I understand the confusion. Lemons smell good. The second root,
         | on the other hand, far less pleasant.
        
         | bregma wrote:
         | 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.
        
           | stogot wrote:
           | This might feed the "Shakespeare was not one person" theory
        
             | zdragnar wrote:
             | 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.
        
               | drivers99 wrote:
               | I guess you mean:
               | 
               | first published English dictionary
               | 
               | and
               | 
               | It wasn't uncommon / It was common
        
               | zdragnar wrote:
               | Yes, I was rather tired and typing on my phone required
               | more correcting of the autocorrect feature than I could
               | manage.
        
               | mckn1ght wrote:
               | 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?
        
           | somat wrote:
           | "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 wrote:
           | I find it hard to believe that Shakespeare would spell the
           | same wird dyfferntli as if heez noom is Sheikhspier een uh
           | deefirind koontri.
        
         | Netcob wrote:
         | Not to be confused with the "lemonscape", a hallucinated world
         | you enter when you've eaten too many lemons.
        
       | notpushkin wrote:
       | > I'm not enough of a cultural relativist to believe there's a
       | civilization that cares more about the shape [?] than the shape
       | O.
       | 
       | 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
        
         | kvdveer wrote:
         | You mean Arduino is ran by the Illuminate?
        
           | ta988 wrote:
           | yes you can blink leds
        
       | sapphicsnail wrote:
       | If I saw p in the wild I would have assumed it was an omega (o)
       | with a macron over it. Makes me wonder how many more varient
       | Greek letters are out there.
        
         | wombatpm wrote:
         | 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
        
           | rsynnott wrote:
           | Considerate of them; very helpful for future mathematicians.
        
           | perihelions wrote:
           | I guess these are the letters?
           | 
           | https://en.wikipedia.org/wiki/Archaic_Greek_alphabets
           | 
           | W Digamma
           | 
           | [?] Heta
           | 
           | [?] San
           | 
           | [?] Koppa
           | 
           | [?] Tsan, Digamma
           | 
           | [?] Sampi
        
         | Pinus wrote:
         | Any actual Greeks around here? I always wondered what p looks
         | like when jotted down in, say, a shopping list...
        
           | xico wrote:
           | This is actually a normal manuscript p as taught in Greek
           | school. See https://www.typotheque.com/articles/modern-
           | handwriting-a-his...
        
         | nuancebydefault wrote:
         | As psted now and then on HN:our alphabet has a variant as well:
         | ampersand (per se: and).
        
       | big-green-man wrote:
       | You just blew my mind. I'm taking a dive on this.
        
       | Morizero wrote:
       | Is there an abstraction of a leminscate/consonant with 3+ center
       | points?
        
         | fisian wrote:
         | Yes, the Lissajous
         | https://en.wikipedia.org/wiki/Lissajous_curve which also can be
         | turned vertical (to look like an 8 instead of [?]).
        
           | mandarax8 wrote:
           | But this doesnt have the property that the product of the
           | distances to the focal points is constant no?
        
         | mandarax8 wrote:
         | Heres two examples for 3 and 6 points in 2D, 3D respectively:
         | https://en.wikipedia.org/wiki/Cassini_oval#Generalizations
         | 
         | These are symmetric as well though.
        
       | SubiculumCode wrote:
       | Is there an evil twin to the set of prime numbers?
        
         | block_dagger wrote:
         | Every even number?
        
           | ralusek wrote:
           | 2?
        
         | fisian wrote:
         | There are the anti prime numbers (also called highly composite
         | numbers).
        
         | OscarCunningham wrote:
         | 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.
        
         | amai wrote:
         | The opposite of prime numbers are
         | 
         | https://en.wikipedia.org/wiki/Highly_composite_number
         | 
         | But I'm not sure if these ones are evil.
        
       | GistNoesis wrote:
       | And to protect you from it, you can use the following lucky
       | clover charm (polar plot r=cos(2 _theta)
       | ):https://www.wolframalpha.com/input?i=+plot+r%3Dcos%282theta%...
       | whose perimeter can also define a constant 4*E(-3) ~ 4 * 2.4221
       | 
       | https://www.wolframalpha.com/input?i=plot+r%3Dcos%282theta%2..._
        
       | divbzero wrote:
       | p is derived from the circle, which is defined by distance from a
       | single point.
       | 
       | p 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?
        
         | clort wrote:
         | it sounds like you are suggesting it might be turtles all the
         | way down?
        
         | VHRanger wrote:
         | 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.
        
           | jovial_cavalier wrote:
           | It's easy to generalize this to more points.
           | 
           | https://www.desmos.com/calculator/fo7tqlfjgo
        
           | vitus wrote:
           | 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.
           | 
           | https://en.wikipedia.org/wiki/Cassini_oval#Generalizations
           | 
           | https://en.wikipedia.org/wiki/Polynomial_lemniscate#Erd%C5%9.
           | ..
        
         | dahart wrote:
         | 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.)
         | 
         | 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.
        
       | divbzero wrote:
       | The Fourier transform is composed of trigonometric sines and
       | cosines.
       | 
       | There must be an analogous transform composed of lemniscate sines
       | and cosines?
        
         | ttoinou wrote:
         | You could try to make a transform based on a sum of lemniscates
         | in the complex plane
        
       | yukioikeda wrote:
       | It seems obvious that these are not twins. We can only say that p
       | and p are two among the infinite multitude of siblings p[?].
        
       | efortis wrote:
       | Infinity symbol with Lissajous curve:
       | 
       | x = A _sin(at + delta)
       | 
       | y = B_sin(bt)
       | 
       | https://ericfortis.github.io/lissajous/?preset=Infinity
        
         | jan_g wrote:
         | 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.
        
       | TomK32 wrote:
       | Am I the only one who expected the evil twin to be 3 ?
        
         | incognito124 wrote:
         | 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.
        
       | nthingtohide wrote:
       | Change pi to p in this setup.
       | 
       | 2022 - Non-Euclidean Doom: What happens to a game when pi is not
       | 3.14159... https://youtu.be/_ZSFRWJCUY4?t=406
        
         | seba_dos1 wrote:
         | Such a promising yet disappointing talk.
        
       | AlecBG wrote:
       | The lemniscate really looks like a homoclinic orbit in a 2d
       | dynamics problem
        
       | doffen wrote:
       | > _Back before Twitter became a Nazi bar,_
       | 
       | Would've been a better thread without this irrelevant aside,
       | which isn't even true anyway.
        
         | mongol wrote:
         | 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.
        
         | nthingtohide wrote:
         | > 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 wrote:
           | But I think mainly in the direction of demotion. Offhand I
           | can't think of examples of someone ... oh, wait Van Gogh.
        
             | nthingtohide wrote:
             | Baruch Spinoza is another. He was excommunicated.
        
         | Johanx64 wrote:
         | Crikey! The dude can't even write a maths article without
         | delving into tribal politics garbage halfway through. This is
         | depressing.
        
         | mnsc wrote:
         | 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 wrote:
           | 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 wrote:
             | 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 wrote:
               | Interpretation 1 is more likely and made the dry
               | mathematician more relatable/human which made the writing
               | better imo.
        
         | rsynnott wrote:
         | 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.
        
           | veltas wrote:
           | I absolutely agree, a dead 1920's German nationalist movement
           | is exactly why we shouldn't allow free speech online.
        
           | xigoi wrote:
           | Twitter already contained a lot of hateful speech before Elon
           | acquired it.
        
             | lern_too_spel wrote:
             | Those tweets would typically be demoted instead of
             | promoted.
        
           | himgl wrote:
           | It's not at all applicable. Makes me wonder if you even use
           | Twitter if you're making claims like that. More likely you're
           | just parroting nonsense from your echo chamber.
        
             | nuancebydefault wrote:
             | Nobody uses twitter these days.
        
               | himgl wrote:
               | 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 wrote:
               | Hmm you mean X right?
        
               | himgl wrote:
               | Same thing.
        
             | rsynnott wrote:
             | 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.
        
           | gosub100 wrote:
           | 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?
        
         | johnp314 wrote:
         | Since it's an "evil twin" should we not expect to find it in an
         | alleged Nazi bar?
        
       | slippy wrote:
       | 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 wrote:
         | 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 p[?]: (...)
        
           | plank wrote:
           | Yes. But the question remains: is there a geometrical
           | analogue?
        
       | Bengalilol wrote:
       | mupi (mutant pi) or piet (pi evil twin) would be better names
        
         | Qem wrote:
         | 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
        
       | mst wrote:
       | 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.
        
         | tibbetts wrote:
         | Sounds like a Greg Egan writing prompt.
        
           | dmd wrote:
           | Baez and Egan are close friends, so don't be surprised if you
           | see it pop up.
        
           | szundi wrote:
           | People just prompt themselves
        
           | mst wrote:
           | 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 Kunsken. (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")
        
         | pavel_lishin wrote:
         | The Anvil of the Stars, by Greg Bear, featured a race of aliens
         | whose mathematics weren't based on integers.
        
           | mst wrote:
           | 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.
        
         | TuringTest wrote:
         | 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 wrote:
           | Kindle Edition: PS2.99
           | 
           | Sounds like at least PS2.99's worth of fun to me from the
           | blurb, so it's now queued up.
           | 
           | I swear I'll get to it eventually.
           | 
           | ... honest.
        
       | sourcepluck wrote:
       | > This [?]-shaped curve is called a 'leminscate', and p 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.
        
       | yason wrote:
       | Offtopic but oh boy was that page difficult to scroll. Up/down
       | arrows jump to the next post and page up/down isn't too helpful
       | for reading. I have the keyboard overrides forbidden in my
       | browser but obviously the web page can still bind events to keys
       | not usually reserved for browser shortcuts... So, the usual
       | navigation breaks up, leaving me to learn one particular site's
       | idiosyncratic behaviour in the user interface space. No thanks, I
       | just left.
       | 
       | Some people saw this right from the start. I remember the time
       | when disallowing javascript would mostly spare you from
       | unnecessary and irritating opt-ins, and you could still consume
       | the actual content of the page using the browser as basically a
       | text reader with hyperlinks, like originally intended. Now you
       | can no longer, in effect, do that as pages consider the browser a
       | VM to present themselves, and this just leads to a tug of war
       | between the browser and its users vs the page creators. Both
       | assume a level of control of a more than Turing complete medium
       | and there's no compromise into that. The working solutions I see
       | are either you write programs that run in the browser-VM to
       | implement web stores etc. or you write effectively HTML 1.0 level
       | structured documents to deliver information and leave the
       | presentation to the browser-reader.
       | 
       | Back in the old days HTML was a huge step up from text files and
       | proprietary hypertext documents but these days I'm more like
       | hoping everything was ultimately, mostly plaintext.
        
         | NoboruWataya wrote:
         | > 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.
        
           | RobotToaster wrote:
           | 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.
        
           | davorak wrote:
           | 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.
        
         | kuschkufan wrote:
         | 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.
        
       | soneca wrote:
       | > _" This [?]-shaped curve is called a 'leminscate', and p 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 wrote:
         | Fixed - thanks.
        
       | candlemas wrote:
       | >On our planet, it was Bernoulli, Euler and Gauss who discovered
       | this math.
       | 
       | You don't say. Newton must have been sick that day.
        
       | cl3misch wrote:
       | > I'm not enough of a cultural relativist to believe there's a
       | civilization that cares more about the shape [?] than the shape
       | O.
       | 
       | 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 wrote:
         | 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.
         | 
         | https://www.scientificamerican.com/article/a-natural-log/
        
           | jcelerier wrote:
           | 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 wrote:
           | fibonacci retrace shows up in liquid markets a lot
        
         | nayuki wrote:
         | Humans have quite a few logarithmic responses: Brightness of
         | light, loudness of sound, musical octaves and relative pitch.
        
       | d_burfoot wrote:
       | > Back before Twitter became a Nazi bar
       | 
       | Why does this guy think it's acceptable to bitterly insult so
       | many people, in an offhand way, by making comments like this?
       | What does he think he's gaining?
       | 
       | I think HN should have a policy for submitted content that is
       | along the lines of the policies in place for comments. If the
       | content violates the rules ("Please don't use Hacker News for
       | political or ideological battle") it should be flagged and
       | removed, like a comment would be.
        
         | ryanmcgarvey wrote:
         | 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 wrote:
           | 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 wrote:
         | > 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
         | ?
        
       | cluckindan wrote:
       | Side by side, there is a clear parallel to monopolar and bipolar
       | fields. Is this found in any version of Maxwell's equations?
        
       | layer8 wrote:
       | Is there something like ThreadReaderApp for Mastodon?
        
       | BearOso wrote:
       | 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 wrote:
         | 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.
        
       | aap_ wrote:
       | Wow, pomega is such a terrible name for it!
        
       | dclaw wrote:
       | This discussion helped me discover my new favorite map.
       | https://en.wikipedia.org/wiki/File:Peirce_Quincuncial_Projec...
        
         | _steady wrote:
         | oh wow that's a lot like a maximally extended penrose diagram
        
       | dxbydt wrote:
       | 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!
       | 
       | 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.
        
       | ComputerGuru wrote:
       | The post mentions that p 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 wrote:
         | I read it as "omega-bar."
        
       | initramfs wrote:
       | https://en.wikipedia.org/wiki/Bizarro
        
       | avalys wrote:
       | I thought this was going to be about tau, which is not pi's evil
       | twin, but rather, the One True Circle Constant.
       | 
       | https://tauday.com/tau-manifesto
        
         | ssalka wrote:
         | upvote for tau, the one really running the show while pi gets
         | the fame & fortune
        
       | waldrews wrote:
       | Seems like a fine number, but I bet there's quite a few more
       | irrational computable numbers out there.
        
       | TaurenHunter wrote:
       | Other notable constants and where they show up:
       | 
       | 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)
        
         | ctrlrsf wrote:
         | How do you even know this?
        
       | mettamage wrote:
       | 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?
        
       | whamlastxmas wrote:
       | Wish people wouldn't inject weird social jabs into stuff like
       | this
        
         | kolbe wrote:
         | 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.
        
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