[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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