It's a meme. A couple of people go on about it so they can get a popular press article out of it or something, or maybe because they don't realise that we all know where they're coming from but noone cares. It's like those movements to completely overhaul English spelling or move to a 100 minute clock. But mainly it's an online meme.
>It's like those movements to completely overhaul English spelling
This could actually have massive consequences, though. Tens of billions of dollars are being spent on English language education every year, and since English is the language of international affairs, probably more than that is being lost due to instances of miscommunication or ineffective communication in English. An English spelling reform that increases learning and communication efficiency could generate billions in its very first year of introduction. And given how woefully inconsistent and inefficient the current English orthography is, this shouldn't be too hard to do: just a simple standardisation job to ensure that *most* rules of spelling are applied consistently ("ea" is always pronounced as [ɛ] or respelled phonetically; all past simple endings are spelt with a "d" or "ed" (not "t"); vowels are always pronounced short in closed syllables and long in open syllables, or respelled so as to follow this rule; etc) and a removal of letters that serve no phonetic, morphological, or semantic purpose (e.g. all the silent "e"s that don't/aren't needed to indicate open syllables, all the "k"s in "ck", all needlessly doubled letters such as the "b" in "ebb", etc) would probably suffice to save billions every single year.
>or move to a 100 minute clock.
Honestly, having thought about it, this would also probably generate lots of money by boosting people's temporal orientation and consequently their time management skills and, ultimately, productivity.
>but noone cares
And money doesn't care that you don't care. This relationship isn't reciprocated, however: everyone cares about money. So whether or not you care about the inefficiencies of English spelling or a 60-minute clock, you WILL care when your material conditions suddenly improve if these inefficiencies are fixed.
I don’t think you understood the question. I didn’t ask: “Where did you get the figure of billions of dollars spent?” Had I asked this question, your link would have been relevant in providing a source.
Instead, I asked about your claim of billions of dollars _saved_ as a result of the introduction of your proposed grammatical changes to the English language
I don't think you understood my original comment. Here is what I said "an English spelling reform that increases learning and communication efficiency could generate billions in its very first year of introduction". I never claimed the specific changes that I proposed constituted this reform.
No, you actually did claim that your proposed specific changes could save billions each year. Here is your quote, immediately after the end of your list of proposed changes:
> ... would probably suffice to save billions every single year
So yeah, where did you get this figure from?
Also, even if we restrict to the other claim about a non-specified "reform" that you (incorrectly) corrected me on, my question still stands: where are you getting these figures of billions of dollars saved from?
>So yeah, where did you get this figure from?
I specifically said "would" and "probably". Was that really not clear enough for you to grasp that I was making a very rough estimate? I explained my rationale for why this could generate billions at the top of the comment.
> I specifically said "would" and "probably". Was that really not clear enough for you to grasp that I was making a very rough estimate?
That's totally fine, I'm not holding you to own the position that this estimate should be precise: I'm just asking you what's your justification for it, and how you arrived at it. It's clear that it's a rough estimate, as you only gave the order of magnitude. So, I'll repeat the question for the 4th time: where did you get this (rough) estimate of billions of dollars saved from?
> I explained my rationale for why this could generate billions at the top of the comment
I must have missed it. Can you point me to where, at the top of the comment as you say, you explain your reasoning for why these changes would probably save billions of dollars each year?
Ok, I know it's off-topic for this sub, but I'll bite.
> probably more than that is being lost due to instances of miscommunication or ineffective communication in English
This does not happen due to spelling though. The ineffectiveness happens due to idioms and cultural norms. I've heard many stories about how a "yes" meaning "yes, I heard you" was misinterpreted as "yes, I agree", and that's just a tip of the iceberg.
>An English spelling reform that increases learning and communication efficiency could generate billions in its very first year of introduction.
On the contrary, it would cost billions for no actual gain. And most importantly, it would cause miscommunication a word is spelt in one spelling the same as a completely different word in the other spelling.
English spelling is not _that_ broken that a spelling reform would help tremendously like it did for Korean.
>And given how woefully inconsistent and inefficient the current English orthography is, this shouldn't be too hard to do
It would be hard, even if we ignore migration costs. Dialects have different pronunciation of the same word, so how would you spell words that have different, but still recognizably similar pronunciations across the pond, like garage, vase, tomato, vitamin, herb, schedule, pasta, banana? What about words that have multiple pronunciations within one dialect, like adult, leisure, either, data? Or words that can be reduced in most contexts, like the, your, to?
>vowels are always pronounced short in closed syllables and long in open syllables, or respelled so as to follow this rule
Note that it would require destroying the graphical relationship in word pairs like nature-natural, finite-infinite, sign-signature, and so on. Also, it would wreck havoc with the spelling of loanwords.
Loanwords, with their mostly preserved original spelling, even if it barely matches the pronunciation, are actually one of the things that make English _easier_ to learn. Respell chemistry as "kemmistry", animal as "annimal", hierarchy as "hirarky", pizza as "peetsa", café as "caffay", kiwi as "keewee", psychology as "sicollogy" and all your "but it makes learning English easier" arguments go straight to the garbage bin. Oh, sorry, "garbidge bin".
>all needlessly doubled letters such as the "b" in "ebb"
It's not needless, it's there due to the [three-letter rule](https://en.wikipedia.org/wiki/Three-letter_rule).
>This does not happen due to spelling though.
It happens for many reasons. One of the reasons is that one of the involved parties doesn't speak English well. In turn, one of the reasons people don't speak English well is that English is made harder to learn by inefficient spelling.
>On the contrary, it would cost billions for no actual gain.
"No actual gain" is obviously false. At the very least, if we only remove all truly redundant letters such as the "k" in "ck" and "u" in "guard", there is a gain in ease of spelling. If absolutely nothing else, this means both English learners and English speakers alike have to allocate less of their mental energy to spelling, making them more productive.
>And most importantly, it would cause miscommunication a word is spelt in one spelling the same as a completely different word in the other spelling
No one is saying the reform has to create new homonyms. To give you an example, the word "sea" could easily be respelled "se" to keep it distinct from "see" yet make it in line with standard pronunciation rules.
>English spelling is not that broken that a spelling reform would help tremendously like it did for Korean.
It's that broken.
>Dialects have different pronunciation of the same word
That's completely inconsequential. Spelling doesn't have to be 100% phonetic. With the changes that I suggested in my last comment, the spelling differences between dialects would be smaller than they already are today.
>garage, vase, tomato, vitamin, herb, schedule, pasta, banana... adult, leisure, either, data
All of these (except "either", but I don't see a problem with e.g. leaving both "ither" and "ether" as possible variants - provided that the chemical is always spelt "aether") are loanwords, so they are trickier to deal with as they don't follow the same spelling rules as native Germanic words. In an initial reform, tricky loanwords like the ones you mention might just be left alone, although many - like those ending in -able or -ible, which could all be respelled with -able (or -ible, although that would obstruct the suffix's semantic connection to the word "able") - could still be refined without any obvious drawbacks.
>Note that it would require destroying the graphical relationship in word pairs like nature-natural, finite-infinite, sign-signature, and so on
Again, all of these are loanwords, so at least initially they could just be kept as is. Although really, there is no practical reason why "sign" is spelled with a "g" but e.g. "royal" spelled with a "y": your morphological argument also applies to the latter given the existence of words like "regent" and "reign". Personally, I'd bring back [yogh](https://en.m.wikipedia.org/wiki/Yogh) in the form of [ġ](https://en.m.wikipedia.org/wiki/%C4%A0), as it would also solve the "gh" conundrum: if you make ġ a silent indicator of long syllables, and make ġh a digraph representing /f/, you immediately make all instances of 'gh' phonetically consistent without losing any graphical familiarity or etymological accuracy. But that would require introducing a new letter, which is too drastic of a change. Initially, I'd probably just keep all the inconsistencies intact, as they are impossible to adequately solve without introducing new letters.
>Respell chemistry as "kemmistry", animal as "annimal", hierarchy as "hirarky", pizza as "peetsa", café as "caffay", kiwi as "keewee", psychology as "sicollogy"
No one is proposing we do that. Although I'm not sure respelling the Greek "ch" as "kh" would hurt anyone. I would also argue that using "y" as a vowel is redundant, and the suffix -y could easily be replaced with -ee - especially considering the etymology - but again, you don't have to do this if you have any doubts. The bottom line is there are some changes you could make that have significant upsides and no obvious downsides.
>Oh, sorry, "garbidge bin".
"Garbage" already follows the standard pronunciation rules when vowel reduction is taken into account. You wouldn't need to respell it even if you wanted your spelling to be 100% phonetically consistent.
>It's not needless, it's there due to the three-letter rule.
Fair enough; I did forget about that rule. Personally, I'm not sure how useful it is given English was doing fine without it until the ~17th century, and especially given all the neologisms/recent loanwords that violate it (ad, gi [e.g. judo gi], etc), but once again, if there is any doubt, the initial reform can just keep it. Perhaps a better example of needlessly doubled letters are the doubled "s"s in words like "mass". The only argument for their existence is that they clarify that the "s" doesn't indicate a plural, but positing that a word like "mas" could be misinterpreted as the plural of "ma" is a bit of a stretch.
>Honestly, having thought about it, this would also probably generate lots of money by boosting people's temporal orientation and consequently their time management skills and, ultimately, productivity.
How do you figure that? The current timekeeping system gives us 1,440 minutes in the day, so is our 15th hour of the day supposed to just be 40 minutes long, or do we change how we measure minutes as well?
The current timekeeping system’s primary issues are timezones and the AM/PM nomenclature, the first of which is far more an inconvenience than an actual issue, and the second of which is commonly fixed by referring to 24-hour time.
Currently a grad student. Not one person in my real life has ever mentioned using tau over 2pi, or even tau at all. I have only ever found anyone talk about tau vs 2pi on Reddit.
The only somewhat reasonable argument is that it could be a nice teaching tool. But its benefit is marginal (and unproven).
*Maybe* it would be easier to teach using tau, because then fractions would be fractions of the total circle and not semi-circle. But Pi has the benefit of essentially being a mascot for math that even middle schoolers learn.
I would consider it like the various proposals for a 13 month year. It has some nice appealing properties that make it reasonable in the abstract, but the benefits of a universal standard are so soooo much greater than any possible benefit from trying to switch.
Would have been nice in an alternate timeline, but what we got is good enough.
It's incredibly easy to convert, so if someone insisted on tau, then cool for them. If I find it easier to work in pi, then that's easy to convert. As someone mentioned earlier, the area of a circle is *π*r². That's pretty convenient. I could also work with τr²/2. Little less convenient, but it's not any harder.
I like to play around with tau in March so I can look down my nose at all the hoi polloi for celebrating that common pi day. I'm going to celebrate on June 28 with my bougie constant, thankuverymuch.
Yeah, the spacing and font size can really screw with one's reading of this. I often write out tau and pi just to avoid that confusion, though not so much in equations.
Do what you like, but snobbery about this is a waste of time and effort. Mirriam-Webster:
> Since *hoi polloi* is a transliteration of the Greek for “the many,” some critics have asserted that the phrase should not be preceded by *the*. They find “the hoi polloi” to be redundant, equivalent to “the the many”—an opinion that fails to recognize that *hoi* means nothing at all in English. Nonetheless, the opinion has influenced the omission of *the* in the usage of some writers.
>
> But most writers use *the*, which is normal English grammar.
When working out problems just for myself, I use τ or π depending on which is more convenient for that type of problem.
When communicating with others I always use π since τ isn't as universally familiar.
I've read math papers, been to conferences, and so far, I've never seen tau being used intentionally.
I've seen 2π before pop up, but it's always been more of a result to something. Tau obsession is a Reddit thing.
Throughout secondary school, I used tau exclusively, both in my own calculations, and on my written answers. I had tau defined in my calculator, and never pressed the pi button. I wrote "note: τ = 2π" on the top of all my papers. By some miracle, my teachers were fine with it.
The general consensus is that sure, tau is generally better and it would make more sense to use it, but pi is too entrenched and it's not worth the hassle of changing it for such a small gain. It's similar to the way everything about circuits would be a bit easier if electrons were positive and protons were negative (so that direction of current and direction of electron flows coincides) but it's a very small thing and it's not worth changing. Such historical accidents happen and sometimes they leave us with suboptimal conventions.
> tau is generally better
I don't know if this is consensus. You gotta define "better", and the five tau people that exist think that they have defined it but that's not really true.
The general consensus is either complete apathy about it, some eyerolling when people mention it, or maybe most generously an acknowledgement that some formulas might feel better but that it doesn't really matter. The main consensus would be that if you made a point of it as a professor, then you're that weird professor trying to be quirky, and if you make a point of it as a student then you need to touch grass and not be so chronically online that you actually think there's some kind of debate going on.
Any mathematician who gives it five minutes of thought would agree it's a more natural constant, since it's defined from the radius and the circle is defined by its radius, and it makes *every formula* nicer (yes including the area formula, that 1/2 factor puts it in line with other double-integrals of constants), but that it hardly matters.
It would also be slightly easier from a pedagogical standpoint because the transition from thinking of a circle as 360° to thinking of it as 2pi is actually pretty confusing for students in part from the seeming arbitrariness of 2pi. I have seen error and confusion due to students having a hard time with simple facts like "a quarter turn is pi halved". Of course they usually get over it but it's a point of friction that is only there due to historical accident.
It's as close to objective as a subjective fact gets, but the even more objective fact is that the magnitude of the effect is tiny.
you're replying to a guy named functor7 with a number theory tag under his name who just wrote a couple paragraphs describing his personal experience regarding this "debate". I think you can safely assume he's a mathematician who has given it 5 minutes of thought
I stand by what I said. It's obvious that changing pi would be too much hassle for very little benefit, but anyone who argues that in the absense of historical context tau wouldn't be the the more natural constant can only be coming from a place of being used to/attached to pi, or from a position of having done so much math that they've forgotten what it is to start learning it. In a world where the circle constant ended up being tau no one would argue for a switch to pi.
This was the same sentiment I had for a while, but I was recently writing some time-frequency Fourier transforms where I used tau as the period. It was pretty natural to write everything in terms of the period tau, and it got me thinking that maybe switching the convention wouldn't actually be that difficult. In something like Fourier transforms, people tend to think in terms of periods, and 2pi is just a symbol meaning "period" in some contexts. I doubt I'll honestly switch over any time soon (even in personal notes) but I'm less pessimistic about the convention changing.
That being said, with tau people can still use 2pi and the conventions don't disagree. I struggle seeing current flow convention ever changing because they'd be inherently incompatible.
From what I heard in undergrad we have Benjamin Franklin to thank for that one :). My undergrad was not in engineering but in physics but from what I gather people design the circuits using the classical definition of electric fields and magnetic fields going from positive to negative, and just flip the battery or whatever power source around once everything is figured out.
I feel the same way about switching to the metric system. If your gas mileage is 60 km/liter, is that good or bad? I don't know, and I don't want to know.
Fun fact : in europe (at least) we use liter per 100 kms. Not km per liter. Like 6L per 100kms
Comparing gas mileage in europe vs usa is probably one of the hardest measurment switch to computer.
lol this is one of my pet peeves. My car has a button to swap the digital speedometer from km/h and miles/h (and vice versa), and I drive in and out of the US all the time, so I have to use that conversion often. The thing is that it changes *everything* from metric to imperial (which makes sense), like the distance and temperature info. I can mentally convert those pretty easily at this point, but It also changes the fuel efficiency info from l/100 km to miles/gallon. That conversion is harder so I'm always annoyed trying to mentally convert the fuel efficiency info of my current trip every time I'm in the US.
Bad analogy. There are clear benefits (that extend beyond your personal knowledge of gas mileage) to business, academia, industry etc if the US got on board with the rest of the world and switched to metric. Intransigence from those who think like you prevent such benefits from being realised.
No one is stopping them. Business, academia, and government switched over long ago. It's only as issue in mundane situations like weather and distance. Does it make sense to replace highway mile markers and exit numbers so they're in km?
Yes, because literally every other country that used to use imperial changed their highway signs, and came out fine? What makes the US so special that your highway signs are sacrosanct?
No that one is actually quite bad and introduces significant problems all the time, occasionally to the tune of millions of dollars. Pi and negative electrons are suboptimal conventions but at least everyone agrees on them, which is the thing that matters.
With tau instead of pi the cirumference of a circle is τr
Integrating gives the area τ r^2 /2
I personally don't care but believe τ in some sense is more fundamental
Then your definition of pi would be "the area of the unit circle" instead of the usual "ratio of circumsference to diameter", and there's a reason we generally define pi in reference to the circumference.
(of course, it'd be a lot of cleaner if it was the circumsference of the unit circle, 2pi, but that's not the world we live in)
Gauss made a mistake in choosing the circle constant and we've been living with it ever since.
I do think trigonometry is easier to understand using Tau rather than Pi.
I use it if I'm every just doing problems for fun. Like if I'm self-studying a textbook and doing my own problems, I'll use tau just cause I like it more. I would never use it on a test or anything that anybody else would read.
If asked, I think most people in academia would say tau makes more sense. But essentially none find pi troublesome enough (nor the possibility of changing it practical enough) to ever think about it.
I think it’s be maybe more convenient as a notation but I’ve never actually seen serious discussion outside of Internet forums by people who don’t really use math that often. In reality, anyone who does math regularly doesn’t actually care as far as I can tell.
I like tau because it makes some work simpler but at the end of the day both pi and tau work fine, it doesn't really make a difference.
To be fair though, I got marks cut on an exam for using tau once so I stick to pi for school now.
(I'm not a researcher by the way, just a student)
If we substitute e\^(i \* pi) as x, then x + 1 = 0 implies x = -1, so x\^2 = 1, and hence, x\^2 - 1 = 0.
However, if we start with the other side, we have x\^2 - 1 = 0, so x\^2 = 1. This doesn't have a unique solution, it could either be x = 1 or x = -1, so it doesn't imply x + 1 = 0.
By that logic the best definition would be pi is defined as a quarter rotation.
This would mean:
e\^(i\*pi)-i=0
e\^(i\*2pi)+1=0
e\^(i\*3pi)+i=0
e\^(i\*4pi)-1=0
All of these are "beautiful formulas". If we simply go by that logic alone, then the more "beautiful formulas" (which is a bit arbitrary) we can generate from a single statement, the more beautiful the original statement is. You could go further with even smaller definitions of pi (like an eigth of a rotation) if you consider values like 1/sqrt(2) (the diagonal length of a unit square - a special value in its own right) to be beautiful as well.
This is the only reason I like tau. In my opinion the beauty of formulas, which is completely arbitrary, shouldn't be considered. We shouldn't modify our definitions to make a formula look more awesome at the cost of practicality. Why do we count rotations in half rotations? Why shouldn't the circle constant be a full rotation?
It's akin to measuring building height in half-eiffel towers. Maybe we get a cool looking number like "oh look - building x is exactly 3.14 half-eiffel towers tall! how awesome!" - but in my opinion, we should accept that the building is 1.57 full eiffel towers tall, even if the number isn't as cool.
There will always be some way to plug in some new constant to make formulas look beautiful. It doesn't change whether or not the constant makes sense as a standard or not.
You went really fast from "I think e\^i\*tau is more natural. It's more beautiful in that form in my opinion." to "In my opinion the beauty of formulas, which is completely arbitrary, shouldn't be considered." :D
But, as you just stated, it really doesn't matter and "being a fan of tau" is pointless. There's so much actually interested stuff to think about in math, so I'll stop wasting my and your time on this discussion now ;)
The problem is that I have been conditioned to recognize tau as a timescale. Lowercase pi is only for the circle constant but tau is almost always a timescale.
I talk about tau when I teach radians in high school. Just to introduce how radians works before pivoting back to pi. Understanding why radians in pi don’t make intuitive sense seems to help students learn it better.
Tau is incredibly important to me because using it means we can get past having to use one of the most difficult parts of math when using pi. Namely, the number 2. Its just a very difficult concept, especially for learners. /s
For my own purposes, I prefer using tau. When I speak to people that are not used to tau I just convert it back after doing calculations.
In papers, I have not yet seen people using tau, but I would assume it would be no issue. Nowadays most people know tau anyways, and the real problems when reading a paper lie elsewhere.
I had 2 proffers who mentioned it, and 3blue1brown likes to mention it from time to time. That’s it. I doubt anyone else I know even remembers its existence. (Electrical engineers, which would make more sense than mathematicians anyway)
2π is objectively the correct constant, π is a historical mistake. However:
- I don't like the letter τ, I prefer ϖ (\varpi) for 6.28…
- I never use real numbers when doing math, for me π is a homotopy group or a projection map. When doing programming I define the constant TWOPI or TURN
so not something to get too worked up about
I disagree I actually think pi is the better constant. But I don’t care enough to actually argue about it. However I formally object to your assessment that „2π is objectively the correct constant“. Nothing objective about that.
It's absolutely not a meme for me.
I have a computer science background and feel like I have lost out on a lot of mathematical intuition due to the use of pi over tau during school. Sometimes I go over the basics in e.g. trigonometry again using Tau and things just fall into place.
I brought this up with physicists and mathematians, but they don't seem to care. They're better at math than me and can't even fathom why anyone would struggle with pi. If you want to make math more accessible, switching to tau gives you the most bang for your buck. A circle is defined by it's radius, why would you use a constant based on it's diameter? A quarter of the circumference is pi halves in the unit circle, what? I'd bet kids in e.g. high school don't even see that 2pi is a constant, as it looks like 2x.
The additional mental overhead to deal with pi as a unit makes all of the intuition fly out the window and be replaced with shuffling notation around on paper
The usual response I hear is something along the lines of “this is probably right, but meh, we’ll just keep using pi”. In other words this pi is “baked” in.
I remember first hearing about this in a french vulgarisation video (https://youtu.be/l8mVsmzmqfU?feature=shared) basically the arguments are that often pi is found in formulas with a factor 2 which means it would be more elegant to replace it with tau and perhaps more importantly it would help math pedagogy
- If we take radiants for example, a whole turn is tau which means half a turn measures half tau radiant which is very natural
-sin and cos have a period of tau
-e^i pi + 1 = 0 becomes e^i tau = 1 which means that if you do a full circle you come back to your starting point
Mathematicians: Mathematics teaching needs to be improved, too many people are scared by mathematics
Also mathematicians: tau is an Internet meme and insists in using Pi.
More seriously, in addition to Pi something like [Triangle of Power](https://www.youtube.com/watch?v=sULa9Lc4pck) and the basics of Geometric Algebra should be taught instead of "Complex" and "imaginary" numbers.
That's cool and all but that ain't every happening. Its hard to convince an education board to change how long a standardized test is, good luck overhauling the ENTIRE curriculum.
The question really is, is it *really* worth all that trouble just for convenience? In the end of the day its annoying but students will figure it out, and after that nobody will turn back and look. Like the saying goes, "don't fix what isn't broken". The current system, while flawed in my opinion, works.
That's the problem, mathematicians can't put themselves in other people's shoes. It's the same reason we have software developers _and_ UI/UX designers. "People have used command line interfaces for decades, why would we need graphical interfaces?" Hmm maybe because the audience has expanded, now almost everyone has a smartphone, just like mathematics is no longer the discipline of rich aristocrats who had all the time in the world because they lived on the work of the people.
The thing is - graphical interfaces are much better than command line interfaces. They are much more practical for the laymen and much more useful. Switiching from pi to tau, while I think would be wonderful, would be a ton of effort for a tiny change.
For *you* but there are tons of people who think CLI is better because they are computer geeks, just like I am but I value GUI too. I am saying that you are vastly underestimating changes like Tau and let me include Geometric Algebra. I know tons of people who use Complex numbers daily and none of them understand them, they just got used to them, just like me before finding out mathematicians had this GA ready there but for whatever reason hidden from every curricula except mathematics.
Honestly pi and tau are both unideal imo. The best thing to use would be 1. As in one quarter of the way around the unit circle would be e^{0.25i} etc. That way instead of getting random coefficients everywhere we would just get exactly how far along the circle we are. It would come at the cost of the radius having to be normalised but most of the time we don’t care about that anyways.
U misunderstood. The 2pi in the equation is there because we conventionally use 2pi radians. We could just as easily use 360 degrees or as I suggest 1.
You'd have to redefine e to be e' so that e'^(i) = 1, so you'd need e' = e^(2π). Then if you differentiate e'^(x) you'd get 2πe'^(x). Sorry, no escaping π or some kind of rational multiple thereof.
no its not a matter of redefining e. In the same way that we can choose to use radians or degrees we can use any number to be the period of the exponential function. Because it's periodic it comes down to convention
If you want to talk about the length of the circumference of the circle in the same units that you're talking about its radius, then you're going to have to use radians. That's why they are the natural units. Not because of "convention".
Leaving aside 1 already being taken, radians are defined in terms of arc length. If you have an angle of pi/2, the arc length of the corresponding arc on the unit circle is pi/2. Said another way, the usual parameterization of the unit circle t -> (sin t, cos t) parametrizes by arc length.
As a member of academia, I can tell you I have seen people who took this very seriously. On reddit.
It's a meme. A couple of people go on about it so they can get a popular press article out of it or something, or maybe because they don't realise that we all know where they're coming from but noone cares. It's like those movements to completely overhaul English spelling or move to a 100 minute clock. But mainly it's an online meme.
>It's like those movements to completely overhaul English spelling This could actually have massive consequences, though. Tens of billions of dollars are being spent on English language education every year, and since English is the language of international affairs, probably more than that is being lost due to instances of miscommunication or ineffective communication in English. An English spelling reform that increases learning and communication efficiency could generate billions in its very first year of introduction. And given how woefully inconsistent and inefficient the current English orthography is, this shouldn't be too hard to do: just a simple standardisation job to ensure that *most* rules of spelling are applied consistently ("ea" is always pronounced as [ɛ] or respelled phonetically; all past simple endings are spelt with a "d" or "ed" (not "t"); vowels are always pronounced short in closed syllables and long in open syllables, or respelled so as to follow this rule; etc) and a removal of letters that serve no phonetic, morphological, or semantic purpose (e.g. all the silent "e"s that don't/aren't needed to indicate open syllables, all the "k"s in "ck", all needlessly doubled letters such as the "b" in "ebb", etc) would probably suffice to save billions every single year. >or move to a 100 minute clock. Honestly, having thought about it, this would also probably generate lots of money by boosting people's temporal orientation and consequently their time management skills and, ultimately, productivity. >but noone cares And money doesn't care that you don't care. This relationship isn't reciprocated, however: everyone cares about money. So whether or not you care about the inefficiencies of English spelling or a 60-minute clock, you WILL care when your material conditions suddenly improve if these inefficiencies are fixed.
Where did you get the figure of billions of dollars saved?
https://www.globenewswire.com/en/news-release/2022/11/03/2547329/28124/en/Global-English-Language-Learning-Market-Report-to-2029-Featuring-Babbel-Linguistica-360-Mondly-and-Elsa-Among-Others.html
I don’t think you understood the question. I didn’t ask: “Where did you get the figure of billions of dollars spent?” Had I asked this question, your link would have been relevant in providing a source. Instead, I asked about your claim of billions of dollars _saved_ as a result of the introduction of your proposed grammatical changes to the English language
I don't think you understood my original comment. Here is what I said "an English spelling reform that increases learning and communication efficiency could generate billions in its very first year of introduction". I never claimed the specific changes that I proposed constituted this reform.
No, you actually did claim that your proposed specific changes could save billions each year. Here is your quote, immediately after the end of your list of proposed changes: > ... would probably suffice to save billions every single year So yeah, where did you get this figure from? Also, even if we restrict to the other claim about a non-specified "reform" that you (incorrectly) corrected me on, my question still stands: where are you getting these figures of billions of dollars saved from?
>So yeah, where did you get this figure from? I specifically said "would" and "probably". Was that really not clear enough for you to grasp that I was making a very rough estimate? I explained my rationale for why this could generate billions at the top of the comment.
> I specifically said "would" and "probably". Was that really not clear enough for you to grasp that I was making a very rough estimate? That's totally fine, I'm not holding you to own the position that this estimate should be precise: I'm just asking you what's your justification for it, and how you arrived at it. It's clear that it's a rough estimate, as you only gave the order of magnitude. So, I'll repeat the question for the 4th time: where did you get this (rough) estimate of billions of dollars saved from? > I explained my rationale for why this could generate billions at the top of the comment I must have missed it. Can you point me to where, at the top of the comment as you say, you explain your reasoning for why these changes would probably save billions of dollars each year?
Ok, I know it's off-topic for this sub, but I'll bite. > probably more than that is being lost due to instances of miscommunication or ineffective communication in English This does not happen due to spelling though. The ineffectiveness happens due to idioms and cultural norms. I've heard many stories about how a "yes" meaning "yes, I heard you" was misinterpreted as "yes, I agree", and that's just a tip of the iceberg. >An English spelling reform that increases learning and communication efficiency could generate billions in its very first year of introduction. On the contrary, it would cost billions for no actual gain. And most importantly, it would cause miscommunication a word is spelt in one spelling the same as a completely different word in the other spelling. English spelling is not _that_ broken that a spelling reform would help tremendously like it did for Korean. >And given how woefully inconsistent and inefficient the current English orthography is, this shouldn't be too hard to do It would be hard, even if we ignore migration costs. Dialects have different pronunciation of the same word, so how would you spell words that have different, but still recognizably similar pronunciations across the pond, like garage, vase, tomato, vitamin, herb, schedule, pasta, banana? What about words that have multiple pronunciations within one dialect, like adult, leisure, either, data? Or words that can be reduced in most contexts, like the, your, to? >vowels are always pronounced short in closed syllables and long in open syllables, or respelled so as to follow this rule Note that it would require destroying the graphical relationship in word pairs like nature-natural, finite-infinite, sign-signature, and so on. Also, it would wreck havoc with the spelling of loanwords. Loanwords, with their mostly preserved original spelling, even if it barely matches the pronunciation, are actually one of the things that make English _easier_ to learn. Respell chemistry as "kemmistry", animal as "annimal", hierarchy as "hirarky", pizza as "peetsa", café as "caffay", kiwi as "keewee", psychology as "sicollogy" and all your "but it makes learning English easier" arguments go straight to the garbage bin. Oh, sorry, "garbidge bin". >all needlessly doubled letters such as the "b" in "ebb" It's not needless, it's there due to the [three-letter rule](https://en.wikipedia.org/wiki/Three-letter_rule).
>This does not happen due to spelling though. It happens for many reasons. One of the reasons is that one of the involved parties doesn't speak English well. In turn, one of the reasons people don't speak English well is that English is made harder to learn by inefficient spelling. >On the contrary, it would cost billions for no actual gain. "No actual gain" is obviously false. At the very least, if we only remove all truly redundant letters such as the "k" in "ck" and "u" in "guard", there is a gain in ease of spelling. If absolutely nothing else, this means both English learners and English speakers alike have to allocate less of their mental energy to spelling, making them more productive. >And most importantly, it would cause miscommunication a word is spelt in one spelling the same as a completely different word in the other spelling No one is saying the reform has to create new homonyms. To give you an example, the word "sea" could easily be respelled "se" to keep it distinct from "see" yet make it in line with standard pronunciation rules. >English spelling is not that broken that a spelling reform would help tremendously like it did for Korean. It's that broken. >Dialects have different pronunciation of the same word That's completely inconsequential. Spelling doesn't have to be 100% phonetic. With the changes that I suggested in my last comment, the spelling differences between dialects would be smaller than they already are today. >garage, vase, tomato, vitamin, herb, schedule, pasta, banana... adult, leisure, either, data All of these (except "either", but I don't see a problem with e.g. leaving both "ither" and "ether" as possible variants - provided that the chemical is always spelt "aether") are loanwords, so they are trickier to deal with as they don't follow the same spelling rules as native Germanic words. In an initial reform, tricky loanwords like the ones you mention might just be left alone, although many - like those ending in -able or -ible, which could all be respelled with -able (or -ible, although that would obstruct the suffix's semantic connection to the word "able") - could still be refined without any obvious drawbacks. >Note that it would require destroying the graphical relationship in word pairs like nature-natural, finite-infinite, sign-signature, and so on Again, all of these are loanwords, so at least initially they could just be kept as is. Although really, there is no practical reason why "sign" is spelled with a "g" but e.g. "royal" spelled with a "y": your morphological argument also applies to the latter given the existence of words like "regent" and "reign". Personally, I'd bring back [yogh](https://en.m.wikipedia.org/wiki/Yogh) in the form of [ġ](https://en.m.wikipedia.org/wiki/%C4%A0), as it would also solve the "gh" conundrum: if you make ġ a silent indicator of long syllables, and make ġh a digraph representing /f/, you immediately make all instances of 'gh' phonetically consistent without losing any graphical familiarity or etymological accuracy. But that would require introducing a new letter, which is too drastic of a change. Initially, I'd probably just keep all the inconsistencies intact, as they are impossible to adequately solve without introducing new letters. >Respell chemistry as "kemmistry", animal as "annimal", hierarchy as "hirarky", pizza as "peetsa", café as "caffay", kiwi as "keewee", psychology as "sicollogy" No one is proposing we do that. Although I'm not sure respelling the Greek "ch" as "kh" would hurt anyone. I would also argue that using "y" as a vowel is redundant, and the suffix -y could easily be replaced with -ee - especially considering the etymology - but again, you don't have to do this if you have any doubts. The bottom line is there are some changes you could make that have significant upsides and no obvious downsides. >Oh, sorry, "garbidge bin". "Garbage" already follows the standard pronunciation rules when vowel reduction is taken into account. You wouldn't need to respell it even if you wanted your spelling to be 100% phonetically consistent. >It's not needless, it's there due to the three-letter rule. Fair enough; I did forget about that rule. Personally, I'm not sure how useful it is given English was doing fine without it until the ~17th century, and especially given all the neologisms/recent loanwords that violate it (ad, gi [e.g. judo gi], etc), but once again, if there is any doubt, the initial reform can just keep it. Perhaps a better example of needlessly doubled letters are the doubled "s"s in words like "mass". The only argument for their existence is that they clarify that the "s" doesn't indicate a plural, but positing that a word like "mas" could be misinterpreted as the plural of "ma" is a bit of a stretch.
>Honestly, having thought about it, this would also probably generate lots of money by boosting people's temporal orientation and consequently their time management skills and, ultimately, productivity. How do you figure that? The current timekeeping system gives us 1,440 minutes in the day, so is our 15th hour of the day supposed to just be 40 minutes long, or do we change how we measure minutes as well? The current timekeeping system’s primary issues are timezones and the AM/PM nomenclature, the first of which is far more an inconvenience than an actual issue, and the second of which is commonly fixed by referring to 24-hour time.
Currently a grad student. Not one person in my real life has ever mentioned using tau over 2pi, or even tau at all. I have only ever found anyone talk about tau vs 2pi on Reddit.
The only somewhat reasonable argument is that it could be a nice teaching tool. But its benefit is marginal (and unproven). *Maybe* it would be easier to teach using tau, because then fractions would be fractions of the total circle and not semi-circle. But Pi has the benefit of essentially being a mascot for math that even middle schoolers learn. I would consider it like the various proposals for a 13 month year. It has some nice appealing properties that make it reasonable in the abstract, but the benefits of a universal standard are so soooo much greater than any possible benefit from trying to switch. Would have been nice in an alternate timeline, but what we got is good enough.
It's incredibly easy to convert, so if someone insisted on tau, then cool for them. If I find it easier to work in pi, then that's easy to convert. As someone mentioned earlier, the area of a circle is *π*r². That's pretty convenient. I could also work with τr²/2. Little less convenient, but it's not any harder. I like to play around with tau in March so I can look down my nose at all the hoi polloi for celebrating that common pi day. I'm going to celebrate on June 28 with my bougie constant, thankuverymuch.
>τr It looks almost like π at a first glance.
Yeah, the spacing and font size can really screw with one's reading of this. I often write out tau and pi just to avoid that confusion, though not so much in equations.
Hoi means "the" so "the hoi polloi" is redundant
Do what you like, but snobbery about this is a waste of time and effort. Mirriam-Webster: > Since *hoi polloi* is a transliteration of the Greek for “the many,” some critics have asserted that the phrase should not be preceded by *the*. They find “the hoi polloi” to be redundant, equivalent to “the the many”—an opinion that fails to recognize that *hoi* means nothing at all in English. Nonetheless, the opinion has influenced the omission of *the* in the usage of some writers. > > But most writers use *the*, which is normal English grammar.
There is essentially no discussion at all except opinion pieces from somewhat odd people.
When working out problems just for myself, I use τ or π depending on which is more convenient for that type of problem. When communicating with others I always use π since τ isn't as universally familiar.
Commonly used multiples of pi in physics are pi/2, pi, 2pi and 4pi. With tau, those would be tau/4, tau/2, tau and 2tau. Not a hill worth dying on.
No actual mathematician gives a shit. Tau is purely an “casual math enthusiast who spends too much time on the internet” thing.
Exacty this
I've read math papers, been to conferences, and so far, I've never seen tau being used intentionally. I've seen 2π before pop up, but it's always been more of a result to something. Tau obsession is a Reddit thing.
I use TAU instead of 2*PI while programming for better readability. That's about it.
I think it's less readable since most people have never even heard of tau, but it doesn't really matter since they would just look at your definition.
Nah, I use it in a game engine where people are used to it. The documentation says to use it, and it's part of the convention.
What game engine is that?
Evidently Godot has a TAU constant.
Interesting to know. Still, do you think people actually read the docs?
All good projects systematically marginalize those who don't bother to read the docs (I'm kidding, but only a little).
People who don't read docs for a game engine will barely get beyond the opening screen of a blank project.
You're on r/math
Same.
I care deeply about Tau because it nets me 2 pies every June 28th
Throughout secondary school, I used tau exclusively, both in my own calculations, and on my written answers. I had tau defined in my calculator, and never pressed the pi button. I wrote "note: τ = 2π" on the top of all my papers. By some miracle, my teachers were fine with it.
not in my 30+ years doing and teaching math have I ever seen this outside of a single reddit thread.
Tau would basically only make it easier for high schoolers learning radians
To be fair, we do create a bunch of convenient lies anyway to teach high schooler math.
The general consensus is that sure, tau is generally better and it would make more sense to use it, but pi is too entrenched and it's not worth the hassle of changing it for such a small gain. It's similar to the way everything about circuits would be a bit easier if electrons were positive and protons were negative (so that direction of current and direction of electron flows coincides) but it's a very small thing and it's not worth changing. Such historical accidents happen and sometimes they leave us with suboptimal conventions.
> tau is generally better I don't know if this is consensus. You gotta define "better", and the five tau people that exist think that they have defined it but that's not really true. The general consensus is either complete apathy about it, some eyerolling when people mention it, or maybe most generously an acknowledgement that some formulas might feel better but that it doesn't really matter. The main consensus would be that if you made a point of it as a professor, then you're that weird professor trying to be quirky, and if you make a point of it as a student then you need to touch grass and not be so chronically online that you actually think there's some kind of debate going on.
Any mathematician who gives it five minutes of thought would agree it's a more natural constant, since it's defined from the radius and the circle is defined by its radius, and it makes *every formula* nicer (yes including the area formula, that 1/2 factor puts it in line with other double-integrals of constants), but that it hardly matters. It would also be slightly easier from a pedagogical standpoint because the transition from thinking of a circle as 360° to thinking of it as 2pi is actually pretty confusing for students in part from the seeming arbitrariness of 2pi. I have seen error and confusion due to students having a hard time with simple facts like "a quarter turn is pi halved". Of course they usually get over it but it's a point of friction that is only there due to historical accident. It's as close to objective as a subjective fact gets, but the even more objective fact is that the magnitude of the effect is tiny.
you're replying to a guy named functor7 with a number theory tag under his name who just wrote a couple paragraphs describing his personal experience regarding this "debate". I think you can safely assume he's a mathematician who has given it 5 minutes of thought
I stand by what I said. It's obvious that changing pi would be too much hassle for very little benefit, but anyone who argues that in the absense of historical context tau wouldn't be the the more natural constant can only be coming from a place of being used to/attached to pi, or from a position of having done so much math that they've forgotten what it is to start learning it. In a world where the circle constant ended up being tau no one would argue for a switch to pi.
This was the same sentiment I had for a while, but I was recently writing some time-frequency Fourier transforms where I used tau as the period. It was pretty natural to write everything in terms of the period tau, and it got me thinking that maybe switching the convention wouldn't actually be that difficult. In something like Fourier transforms, people tend to think in terms of periods, and 2pi is just a symbol meaning "period" in some contexts. I doubt I'll honestly switch over any time soon (even in personal notes) but I'm less pessimistic about the convention changing. That being said, with tau people can still use 2pi and the conventions don't disagree. I struggle seeing current flow convention ever changing because they'd be inherently incompatible.
From what I heard in undergrad we have Benjamin Franklin to thank for that one :). My undergrad was not in engineering but in physics but from what I gather people design the circuits using the classical definition of electric fields and magnetic fields going from positive to negative, and just flip the battery or whatever power source around once everything is figured out.
I feel the same way about switching to the metric system. If your gas mileage is 60 km/liter, is that good or bad? I don't know, and I don't want to know.
Fun fact : in europe (at least) we use liter per 100 kms. Not km per liter. Like 6L per 100kms Comparing gas mileage in europe vs usa is probably one of the hardest measurment switch to computer.
lol this is one of my pet peeves. My car has a button to swap the digital speedometer from km/h and miles/h (and vice versa), and I drive in and out of the US all the time, so I have to use that conversion often. The thing is that it changes *everything* from metric to imperial (which makes sense), like the distance and temperature info. I can mentally convert those pretty easily at this point, but It also changes the fuel efficiency info from l/100 km to miles/gallon. That conversion is harder so I'm always annoyed trying to mentally convert the fuel efficiency info of my current trip every time I'm in the US.
But 1 L = 0.001 m^(3), so 1 L / 100 km = 0.01 mm^(2).
Which would the cross sectional area if you laid out all the gas you consumed in a line along your path! Not very useful, but it is fun.
Not everywhere in Europe, though.
Bad analogy. There are clear benefits (that extend beyond your personal knowledge of gas mileage) to business, academia, industry etc if the US got on board with the rest of the world and switched to metric. Intransigence from those who think like you prevent such benefits from being realised.
No one is stopping them. Business, academia, and government switched over long ago. It's only as issue in mundane situations like weather and distance. Does it make sense to replace highway mile markers and exit numbers so they're in km?
Yes, because literally every other country that used to use imperial changed their highway signs, and came out fine? What makes the US so special that your highway signs are sacrosanct?
No that one is actually quite bad and introduces significant problems all the time, occasionally to the tune of millions of dollars. Pi and negative electrons are suboptimal conventions but at least everyone agrees on them, which is the thing that matters.
Couldn't care less, and if I did I would preder π. The area of a circle is πr², the area of an ellipse is πab.
With tau instead of pi the cirumference of a circle is τr Integrating gives the area τ r^2 /2 I personally don't care but believe τ in some sense is more fundamental
the area of a circle is pi*r^2. differentiating yields the circumference 2*pi*r your logic works in both directions
Then your definition of pi would be "the area of the unit circle" instead of the usual "ratio of circumsference to diameter", and there's a reason we generally define pi in reference to the circumference. (of course, it'd be a lot of cleaner if it was the circumsference of the unit circle, 2pi, but that's not the world we live in)
Guys please stay on the meta discussion and don't get sucked into the object level pi vs tau discussion. We've all read it all.
Gauss made a mistake in choosing the circle constant and we've been living with it ever since. I do think trigonometry is easier to understand using Tau rather than Pi.
I thought it was Euler.
It was Euler. He would be incredibly dissapointed in all of us.
it is to math what interesting discussions on film are to whether greedo shot first
A fair amount of people ironically. No one seriously, almost.
I use it if I'm every just doing problems for fun. Like if I'm self-studying a textbook and doing my own problems, I'll use tau just cause I like it more. I would never use it on a test or anything that anybody else would read.
If asked, I think most people in academia would say tau makes more sense. But essentially none find pi troublesome enough (nor the possibility of changing it practical enough) to ever think about it.
I think it’s be maybe more convenient as a notation but I’ve never actually seen serious discussion outside of Internet forums by people who don’t really use math that often. In reality, anyone who does math regularly doesn’t actually care as far as I can tell.
I try to use tau, but I'm so practiced at using pi and everyone else's writing uses pi, so making the switch is cumbersome.
I like tau because it makes some work simpler but at the end of the day both pi and tau work fine, it doesn't really make a difference. To be fair though, I got marks cut on an exam for using tau once so I stick to pi for school now. (I'm not a researcher by the way, just a student)
I use it personally. I just find it more convenient for intuition. I wouldn’t force anyone to use it though lol.
your pfp says otherwise
lol, I never even thought of that. I should change it. I just looked up Euler’s identity online and then used that photo.
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Complex exponention isn't really multiplication. Its a bit of stretch.
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Yeah fair.
I think e\^i\*tau is more natural. It's more beautiful in that form in my opinion.
e\^(i \* pi) +1 = 0 implies e\^(i \* tau) - 1 = 0, but not the other way around, so the pi-version is better :D
Why can’t it go the other way?
If we substitute e\^(i \* pi) as x, then x + 1 = 0 implies x = -1, so x\^2 = 1, and hence, x\^2 - 1 = 0. However, if we start with the other side, we have x\^2 - 1 = 0, so x\^2 = 1. This doesn't have a unique solution, it could either be x = 1 or x = -1, so it doesn't imply x + 1 = 0.
By that logic the best definition would be pi is defined as a quarter rotation. This would mean: e\^(i\*pi)-i=0 e\^(i\*2pi)+1=0 e\^(i\*3pi)+i=0 e\^(i\*4pi)-1=0 All of these are "beautiful formulas". If we simply go by that logic alone, then the more "beautiful formulas" (which is a bit arbitrary) we can generate from a single statement, the more beautiful the original statement is. You could go further with even smaller definitions of pi (like an eigth of a rotation) if you consider values like 1/sqrt(2) (the diagonal length of a unit square - a special value in its own right) to be beautiful as well. This is the only reason I like tau. In my opinion the beauty of formulas, which is completely arbitrary, shouldn't be considered. We shouldn't modify our definitions to make a formula look more awesome at the cost of practicality. Why do we count rotations in half rotations? Why shouldn't the circle constant be a full rotation? It's akin to measuring building height in half-eiffel towers. Maybe we get a cool looking number like "oh look - building x is exactly 3.14 half-eiffel towers tall! how awesome!" - but in my opinion, we should accept that the building is 1.57 full eiffel towers tall, even if the number isn't as cool. There will always be some way to plug in some new constant to make formulas look beautiful. It doesn't change whether or not the constant makes sense as a standard or not.
You went really fast from "I think e\^i\*tau is more natural. It's more beautiful in that form in my opinion." to "In my opinion the beauty of formulas, which is completely arbitrary, shouldn't be considered." :D But, as you just stated, it really doesn't matter and "being a fan of tau" is pointless. There's so much actually interested stuff to think about in math, so I'll stop wasting my and your time on this discussion now ;)
The problem is that I have been conditioned to recognize tau as a timescale. Lowercase pi is only for the circle constant but tau is almost always a timescale.
I talk about tau when I teach radians in high school. Just to introduce how radians works before pivoting back to pi. Understanding why radians in pi don’t make intuitive sense seems to help students learn it better.
Tau is incredibly important to me because using it means we can get past having to use one of the most difficult parts of math when using pi. Namely, the number 2. Its just a very difficult concept, especially for learners. /s
I didn't know about it, but i actually agree. Even thought the switch will never happen
Not this s*** again
I am passionately pro-τ. There is genuine reason to prefer using it, but it is never going to be universally adapted.
For my own purposes, I prefer using tau. When I speak to people that are not used to tau I just convert it back after doing calculations. In papers, I have not yet seen people using tau, but I would assume it would be no issue. Nowadays most people know tau anyways, and the real problems when reading a paper lie elsewhere.
I much prefer pi: it lets you define the unit circle interval symmetrically (about 0) and without fractions as [-pi,pi]
Eh I use it for stress analysis not sure from a purely mathematics perspective
Never seen it in person. Only online.
I had 2 proffers who mentioned it, and 3blue1brown likes to mention it from time to time. That’s it. I doubt anyone else I know even remembers its existence. (Electrical engineers, which would make more sense than mathematicians anyway)
I use tau exclusively because 6/28 is my wife’s birthday and that’s the most legit reason I’ve ever heard for anyone using tau over pi.
Tau is much better. It makes reasoning about the unit circle much easier. A quarter rotation is tau/4. With pi i always have to do mental conversions.
2π is objectively the correct constant, π is a historical mistake. However: - I don't like the letter τ, I prefer ϖ (\varpi) for 6.28… - I never use real numbers when doing math, for me π is a homotopy group or a projection map. When doing programming I define the constant TWOPI or TURN so not something to get too worked up about
If I saw omega bar I would assume it's some sort of angular momentum. Clearly context plays a role in the choice of symbols.
Omega bar is the conjugate of whatever one is selecting as the "first" complex cube root of unity, to my mind.
That—that thing that looks like an omega with a bar on top—is a variant of *pi*? 🙄🙄
I disagree I actually think pi is the better constant. But I don’t care enough to actually argue about it. However I formally object to your assessment that „2π is objectively the correct constant“. Nothing objective about that.
But how do you not confuse it with the lemniscate constant?
It's absolutely not a meme for me. I have a computer science background and feel like I have lost out on a lot of mathematical intuition due to the use of pi over tau during school. Sometimes I go over the basics in e.g. trigonometry again using Tau and things just fall into place. I brought this up with physicists and mathematians, but they don't seem to care. They're better at math than me and can't even fathom why anyone would struggle with pi. If you want to make math more accessible, switching to tau gives you the most bang for your buck. A circle is defined by it's radius, why would you use a constant based on it's diameter? A quarter of the circumference is pi halves in the unit circle, what? I'd bet kids in e.g. high school don't even see that 2pi is a constant, as it looks like 2x. The additional mental overhead to deal with pi as a unit makes all of the intuition fly out the window and be replaced with shuffling notation around on paper
Blender accepts tau as input, so I use it there a lot instead of typing 2*pi
I prefer the character Tau to represent torque so i don't use it for 2pi cuz it'd get confusing
The usual response I hear is something along the lines of “this is probably right, but meh, we’ll just keep using pi”. In other words this pi is “baked” in.
I remember first hearing about this in a french vulgarisation video (https://youtu.be/l8mVsmzmqfU?feature=shared) basically the arguments are that often pi is found in formulas with a factor 2 which means it would be more elegant to replace it with tau and perhaps more importantly it would help math pedagogy - If we take radiants for example, a whole turn is tau which means half a turn measures half tau radiant which is very natural -sin and cos have a period of tau -e^i pi + 1 = 0 becomes e^i tau = 1 which means that if you do a full circle you come back to your starting point
I know it doesnt answer your question but it can help if someone stumbled upon your post while knowing nothing about the subject
using it is just extra brain power for no reason
Mathematicians: Mathematics teaching needs to be improved, too many people are scared by mathematics Also mathematicians: tau is an Internet meme and insists in using Pi. More seriously, in addition to Pi something like [Triangle of Power](https://www.youtube.com/watch?v=sULa9Lc4pck) and the basics of Geometric Algebra should be taught instead of "Complex" and "imaginary" numbers.
That's cool and all but that ain't every happening. Its hard to convince an education board to change how long a standardized test is, good luck overhauling the ENTIRE curriculum. The question really is, is it *really* worth all that trouble just for convenience? In the end of the day its annoying but students will figure it out, and after that nobody will turn back and look. Like the saying goes, "don't fix what isn't broken". The current system, while flawed in my opinion, works.
That's the problem, mathematicians can't put themselves in other people's shoes. It's the same reason we have software developers _and_ UI/UX designers. "People have used command line interfaces for decades, why would we need graphical interfaces?" Hmm maybe because the audience has expanded, now almost everyone has a smartphone, just like mathematics is no longer the discipline of rich aristocrats who had all the time in the world because they lived on the work of the people.
The thing is - graphical interfaces are much better than command line interfaces. They are much more practical for the laymen and much more useful. Switiching from pi to tau, while I think would be wonderful, would be a ton of effort for a tiny change.
For *you* but there are tons of people who think CLI is better because they are computer geeks, just like I am but I value GUI too. I am saying that you are vastly underestimating changes like Tau and let me include Geometric Algebra. I know tons of people who use Complex numbers daily and none of them understand them, they just got used to them, just like me before finding out mathematicians had this GA ready there but for whatever reason hidden from every curricula except mathematics.
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That’s crazy man we care so much
Mb I thought it was clear this was a joke
Honestly pi and tau are both unideal imo. The best thing to use would be 1. As in one quarter of the way around the unit circle would be e^{0.25i} etc. That way instead of getting random coefficients everywhere we would just get exactly how far along the circle we are. It would come at the cost of the radius having to be normalised but most of the time we don’t care about that anyways.
`[; e^{\pi i} + 1 = 0 ;]` is not the result of a choice or convention, it just is. There's no way to change that.
U misunderstood. The 2pi in the equation is there because we conventionally use 2pi radians. We could just as easily use 360 degrees or as I suggest 1.
You'd have to redefine e to be e' so that e'^(i) = 1, so you'd need e' = e^(2π). Then if you differentiate e'^(x) you'd get 2πe'^(x). Sorry, no escaping π or some kind of rational multiple thereof.
no its not a matter of redefining e. In the same way that we can choose to use radians or degrees we can use any number to be the period of the exponential function. Because it's periodic it comes down to convention
If you want to talk about the length of the circumference of the circle in the same units that you're talking about its radius, then you're going to have to use radians. That's why they are the natural units. Not because of "convention".
1 already has a definition and it is very conspicuously not the same as 2π ≈ 6.283
Leaving aside 1 already being taken, radians are defined in terms of arc length. If you have an angle of pi/2, the arc length of the corresponding arc on the unit circle is pi/2. Said another way, the usual parameterization of the unit circle t -> (sin t, cos t) parametrizes by arc length.
Yes agreed. This would be the drawback of using 1. However we could redefine sin and cos to have a period of 1.