## 1292: Pi vs. Tau

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cellocgw
Posts: 2068
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### Re: 1292: Pi vs. Tau

orthogon wrote:
PolakoVoador wrote:¹I couldn't find a definitive IPA transcription for ão. It seems it can be transcribed as [ɐ̃w̃], [ãw̃], [ãʊ̃], and maybe some other variants.

If even professional cunning linguists can't agree on how to pronounce it, I don't feel quite so bad.
This reminds me that, to a Frenchman, the difference between love and death is just a pout of the lips. (It's the same as the difference between plenty and a nice backside).

FTFY, with Rule34 in effect
resume
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peewee_RotA
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### Re: 1292: Pi vs. Tau

cellocgw wrote:
orthogon wrote:
PolakoVoador wrote:¹I couldn't find a definitive IPA transcription for ão. It seems it can be transcribed as [ɐ̃w̃], [ãw̃], [ãʊ̃], and maybe some other variants.

If even professional cunning linguists can't agree on how to pronounce it, I don't feel quite so bad.
This reminds me that, to a Frenchman, the difference between love and death is just a pout of the lips. (It's the same as the difference between plenty and a nice backside).

FTFY, with Rule34 in effect

Hopefully this doesn't lead to any fallatious arguments.
"Vowels have trouble getting married in Canada. They can’t pronounce their O’s."

Palmstroem
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### Re: 1292: Pi vs. Tau

So this is really a bad kind of joke.
If ever, PAU could only be 0.75 TAU but NEVER EVER 1.5 PI. What a mess of an idea!!!

Moonfish
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### Re: 1292: Pi vs. Tau

typo wrote:
Moonfish wrote:The compromise should be the Chinese symbol for Rooster: 酉.

Here are the numbers to go with the traditional symbols.
Spoiler:

Notice how the rat pushes the cat off the ox.

Shouldn't sin(tau) = cos(rooster) = exactly zero? Or is roundoff error part of the tradition?

Yes, Microsoft Excel doesn't use trig-identities or a lookup table so it has a round-off error. Last night I made the chart quickly because it was late and I wanted my post to be near the top.

Really, the chart should indicate that there does not exist an animal which can accompany the Rat, Horse or Cat in a way that will meet the Roster or the Rabbit or vice-versa.
• sin(子)=0
• cos(酉)=0
• sin(午)=0
• cos(卯)=0
• sin(猫)=0

cream wobbly
Posts: 170
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### Re: 1292: Pi vs. Tau

PolakoVoador wrote:Pau is actually the slang/crude word for it, like dick or cock.

Obviously a sly reference to Moonfish's suggestion to use "the Chinese symbol for Rooster: 酉", or cock.

Klear
Posts: 1965
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### Re: 1292: Pi vs. Tau

peewee_RotA wrote:
cellocgw wrote:
orthogon wrote:
PolakoVoador wrote:¹I couldn't find a definitive IPA transcription for ão. It seems it can be transcribed as [ɐ̃w̃], [ãw̃], [ãʊ̃], and maybe some other variants.

If even professional cunning linguists can't agree on how to pronounce it, I don't feel quite so bad.
This reminds me that, to a Frenchman, the difference between love and death is just a pout of the lips. (It's the same as the difference between plenty and a nice backside).

FTFY, with Rule34 in effect

Hopefully this doesn't lead to any fallatious arguments.

That would suck.

jc
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### Re: 1292: Pi vs. Tau

Moonfish wrote:The compromise should be the Chinese symbol for Rooster: 酉.

I've seen this before, but those charts are sorta baffling. 酉 isn't the Chinese symbol for rooster; it's pronounced yóu in Mandarin, and is a radical that means wine. (More often you'd see 酒.) It would be pronounced differently in other dialects/languages that use Chinese characters, but would still mean fermented juices. Rooster is 公鸡 (gōng jī) or 雄鸡 (xióng jī), where the second symbol of course means chicken. There are any number of Chinese dictionaries online now, so you can easily look this up. Most of the other symbols in the charts are as badly wrong. Is there some (semi-)sensible explanation of why they did this? Is there some sort of metaphorical connection between male chickens and wine that I'm not seeing?

(Yeah, 公鸡 is a bit bizarre if you look up the pieces, but 雄鸡 literally means "male chicken".)

(And pay no attention to my avatar; she knows nothing about chickens.

Red Hal
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### Re: 1292: Pi vs. Tau

Coq au vin?
Lost Greatest Silent Baby X Y Z. "There is no one who loves pain itself, who seeks after it and wants to have it, simply because it is pain..."

tijis421
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### Re: 1292: Pi vs. Tau

jc wrote:
Moonfish wrote:The compromise should be the Chinese symbol for Rooster: 酉.

I've seen this before, but those charts are sorta baffling. 酉 isn't the Chinese symbol for rooster; it's pronounced yóu in Mandarin, and is a radical that means wine. (More often you'd see 酒.) It would be pronounced differently in other dialects/languages that use Chinese characters, but would still mean fermented juices. Rooster is 公鸡 (gōng jī) or 雄鸡 (xióng jī), where the second symbol of course means chicken. There are any number of Chinese dictionaries online now, so you can easily look this up. Most of the other symbols in the charts are as badly wrong. Is there some (semi-)sensible explanation of why they did this? Is there some sort of metaphorical connection between male chickens and wine that I'm not seeing?

(Yeah, 公鸡 is a bit bizarre if you look up the pieces, but 雄鸡 literally means "male chicken".)

(And pay no attention to my avatar; she knows nothing about chickens.

Did a little digging, and apparently that symbol references specifically The Year of the Rooster (in the Chinese zodiac), and not the animal itself. http://en.wikipedia.org/wiki/Rooster_(zodiac)

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### Re: 1292: Pi vs. Tau

It really bugs me this obsession with the arithmetic mean. Everyone knows the compromise solution should be (approximately):

4.4428829381583662470158809900606936986146216893756902230853956069564347930994739105753269347647652373634102126852287913643595985183456274923753463596744150232792788197558775331134536611013065221276530194774425487210754103171084527094816028497839310744451018693349370376912502367662868965278459072338293537027968341334261390132571999513151920932970571280772320536651610302756426072196089526770753011078898123946053600601266609761083123933162167957116257394014233745839574936725248532023239776421097324180690297438357604026048774308323656925324071117930277294812528886328259145471099304920717804917268521860513184011650433338124264825037685666242833416484508325374460570658685811163152238933907947870006312834522943221506476856815227748095072579099603143898138603547688754059187856080338167869286047803138691757815707248164765512869327582115023660724139750872509310515861675793274942840999372565997699832638888087983353491441570958154980781032652885213669573597840246487776291167652324697770833097280113...

thevicente
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### Re: 1292: Pi vs. Tau

Just because people here seem interested, in Brazil the word "pau" depends heavily on context and can mean a lot of the things, not just the one that first came to Polako's mouth.

For example, in computer jargon, crash. As in "the app crashed", " the app gave a pau"

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### Re: 1292: Pi vs. Tau

I know about those algorithms which generate the number pi. But how do we know this isn't the *actual* value of the ratio of a circle's circumference to its diameter?

3.1415926535897932384626433832795028841971693993751058209749445923078164062862089986280348253421170679821480865132823066470938446095505822317253594081000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000... and so on.

At the end of Carl Sagan's Contact, somebody generates pi in binary to billions and billions of digits. Then they arrange the digits in a square, and find a perfect circle of...either 0's in a field of 1's, or vice versa, I forget which.

This suggests another interesting possibility. In base 10, or any other base, let each digit represent a different color. Then generate pi to a Graham's number of digits. Arrange various groups of digits in a square, or a cube. Eventually, the (apparently) random numbers, represented as colors, will reveal famous paintings, or photos of exotic locales. Arrange the digits as a cube and you might get 3D images of scenes of your favorite movies. Or if 0 is black and 1 is white, and you get long sequences of 0 and 1, you get black and white images of pages from Google Books, or lengthy sequences of frames of film from famous black-and-white movies. Of course, you'd also be getting images from alien worlds as well.

Wikipedia has a discussion of why the Bible implies pi is 3. The scribe was probably just rounding off to the nearest whole number.

Coyoty
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### Re: 1292: Pi vs. Tau

webdude wrote:DOUBLE ENTENDRE, ANYONE?

In Hawaiian, pau means finished. As in done, finito, case closed. As in the L.A. Lakers without Kobe? Pau.

Pau FTW!

So the climax of the movie "American Hawaiian Portuguese 1.5 Pi" would be a pau pau pau?

Klear
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### Re: 1292: Pi vs. Tau

Hmmm... this reminds me of a discussion I had with my friend once. Given some sensible mapping of numbers to letters, there is the whole Hamlet contained somewhere within pi, right? So what we were wondering is whether Hamlet is likely to be found sooner than Graham number-th digit of pi, or not. None of us had any idea how it even begin to estimate that. I just reasoned that one of the numbers must be quite extremely smaller than the other.

gladiolas' post seems to suggest that Graham's number wins by far. Is that so? I was leaning towards that option as well...

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### Re: 1292: Pi vs. Tau

thevicente wrote:Just because people here seem interested, in Brazil the word "pau" depends heavily on context and can mean a lot of the things, not just the one that first came to Polako's mouth.

For example, in computer jargon, crash. As in "the app crashed", " the app gave a pau"

It also means "wood", but what is the fun in that?

JohnTheWysard
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### Re: 1292: Pi vs. Tau

danhaas wrote:Pau means "Penis" in portuguese, so this discussion is quite cringesworthy for me.

Interesting. If I remember aright, "pau" is Hawaiian for "nothing, negligible", for instance "Is there any beer left?" "Pau!"

gmalivuk
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### Re: 1292: Pi vs. Tau

gladiolas wrote:I know about those algorithms which generate the number pi. But how do we know this isn't the *actual* value of the ratio of a circle's circumference to its diameter?
Some of the algorithms are derived directly from the definition of a (Euclidean) circle, and the rest of them can be proven to converge on the same number.

Klear wrote:Hmmm... this reminds me of a discussion I had with my friend once. Given some sensible mapping of numbers to letters, there is the whole Hamlet contained somewhere within pi, right? So what we were wondering is whether Hamlet is likely to be found sooner than Graham number-th digit of pi, or not. None of us had any idea how it even begin to estimate that. I just reasoned that one of the numbers must be quite extremely smaller than the other.

gladiolas' post seems to suggest that Graham's number wins by far. Is that so? I was leaning towards that option as well...
Graham's number is so much larger than anything you could possibly wrap your head around that it is very, very likely that the whole of all the text produced in the history of humanity, once encoded with some appropriate scheme, appears not once but millions of times in the first Graham's number of digits of a normal number (which pi is believed but not proven to be).

The expected position of a subsequence N characters long in a random string from an alphabet of B characters is B^N. So, converting a normal number to base-128 and using ASCII, we can expect the 250,000 or so characters of Hamlet to show up somewhere around the 128250000th position. This seems like a lot, but relative to Graham's number it's basically indistinguishable from the number of thumbs I have on my left hand.
Last edited by gmalivuk on Mon Nov 18, 2013 9:06 pm UTC, edited 1 time in total.
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Moonfish
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### Re: 1292: Pi vs. Tau

tijis421 wrote:
jc wrote:
Moonfish wrote:The compromise should be the Chinese symbol for Rooster: 酉.

I've seen this before, but those charts are sorta baffling. 酉 isn't the Chinese symbol for rooster; it's pronounced yóu in Mandarin, and is a radical that means wine. (More often you'd see 酒.)

I did my best with the chart. However while I've tried to learn Mandarin a few times, I still only speak English. It's possible I've gotten some things wrong. Can someone help me find more information about these symbols?

In my research, I first found information in pages about the Chinese Zodiac
Particularly of note was the following wikimedia picture about the 24 cardinal directions used in Chinese navigation:

I then consulted some friends in China. (And also bought some World of Warcraft gold so that their boss wouldn't get mad about the chatting.)
My friends had similar notes that 酉 doesn't typically mean "Rooster" but agreed that the picture seemed legitimate.

I was particularly interested in a number symbol for Cat. I thought it was interesting that the story of the Zodiac made note of both a Rat as the minimum, 0% turn element and a Cat as the maximum, 100% turn element but recognized that the two were the same thing and the system would have problems if both where included.

I would like to know more about what the symbols in the picture actually mean and also how trigonometry works in classic Chinese cartography and navigation.

I also think that pi is stuck in a futile 18th century attempt to mathematically prove the existence of God. Tau is better but requires a more modern approach to the concept of a maximum and infinity.

orthogon
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### Re: 1292: Pi vs. Tau

Klear wrote: Given some sensible mapping of numbers to letters, there is the whole Hamlet contained somewhere within pi, right?

... or even given some non-sensible mapping, such as UTF-8 </troll>

ETA: Of course, Hindi speakers would have to wait considerably longer for the translation to appear in Devanagari script.
xtifr wrote:... and orthogon merely sounds undecided.

Zowayix
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### Re: 1292: Pi vs. Tau

To those who haven't heard about tau before, feel free to look up the Tau Manifesto.

Personally, I will always be an advocate for tau. Given how fundamental the circle constant is, I'm honestly surprised Randall apparently isn't.

alanbbent
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### Re: 1292: Pi vs. Tau

PolakoVoador wrote:It also means "wood", but what is the fun in that?

Yes, I remember learning the translation as "wood" or "stick," but then while I was living in Brazil, I heard "quem toma Fanta, o pau levanta." and I learned a little more Portuguese that day.

gmalivuk
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### Re: 1292: Pi vs. Tau

Or maybe they were just telling you that Fanta makes good tree fertilizer.

Zowayix wrote:To those who haven't heard about tau before, feel free to look up the Tau Manifesto.

Personally, I will always be an advocate for tau. Given how fundamental the circle constant is, I'm honestly surprised Randall apparently isn't.
Given how few tauists work with advanced mathematics compared to things like math education, I'm not surprised at all.
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rmsgrey
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### Re: 1292: Pi vs. Tau

Zowayix wrote:To those who haven't heard about tau before, feel free to look up the Tau Manifesto.

Personally, I will always be an advocate for tau. Given how fundamental the circle constant is, I'm honestly surprised Randall apparently isn't.

There are some situations where Pi is more convenient - for example, the formula (T*r^2)/2 (using T for tau because I'm too lazy to figure out how to extort Greek letters out of this keyboard) is less appealing than the pi-based equivalent.

lgw
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### Re: 1292: Pi vs. Tau

orthogon wrote:
Klear wrote: Given some sensible mapping of numbers to letters, there is the whole Hamlet contained somewhere within pi, right?

... or even given some non-sensible mapping, such as UTF-8 </troll>

ETA: Of course, Hindi speakers would have to wait considerably longer for the translation to appear in Devanagari script.

Is there a Unicode codeplane for Klingon yet, to encode Hamlet as originally written?

(BTW, the "Hamlet in Klingon" I've seen is pretty bad - Hamlet is so crammed full of alliterative poetry and wordplay that it's just not the same in translation.)
"In no set of physics laws do you get two cats." - doogly

mschmidt62
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### Re: 1292: Pi vs. Tau

rmsgrey wrote:
There are some situations where Pi is more convenient - for example, the formula (T*r^2)/2 (using T for tau because I'm too lazy to figure out how to extort Greek letters out of this keyboard) is less appealing than the pi-based equivalent.

Michael Hartl argues that, while the formula for the area of a circle make look neater with π than with tau, the 2 in the denominator for the tau formula shows up in other integrations with a quadratic dimension. So the 2 in the denominator reminds us of the integral nature of the area calculation. See his earlier-referenced Tau Manifesto.

I am glad Randall brought this whole issue to my attention. I will be a tau advocate from now on.

Copper Bezel
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### Re: 1292: Pi vs. Tau

Yeah, I guess if you've not seen this before, here is as good a place to gush as any.

I certainly prefer tau, and I wouldn't have to think about radians using it, but it's pretty obvious irk it's not changing....
So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

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JustMe
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### Re: 1292: Pi vs. Tau

I think when the formula's easier with pi, you should use pi. When it's easier with tau, you should use tau.

That's why I'm an engineer and not a mathematician.
I have traveled from 1963 to be a member of the unofficial board Council of Elders. Phear M3

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### Re: 1292: Pi vs. Tau

A Triple Couplet on the pau Identity

Once Euler doth on thee raise up his eye,
Who knoweth what ill end betides? Not I!
Dost thou turn three quadrants to the south?
Thou mean twixt half-baked pi and fulsome tau!
I say but \phi on thee, thou parlous pau!

ei pau = -i

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### Re: 1292: Pi vs. Tau

A Triple Couplet on the pau Identity

Once Euler doth on thee raise up his eye,
Who knoweth what ill end betides? Not I!
Dost thou turn three quadrants to the south?
Thou mean twixt half-baked pi and fulsome tau!
I say but \phi on thee, thou parlous pau!

ei pau = -i

mschmidt62
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### Re: 1292: Pi vs. Tau

Copper Bezel wrote:Yeah, I guess if you've not seen this before, here is as good a place to gush as any.

It's such a shame that they let the common folk post in these message boards.

keithl
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### Re: 1292: Pi vs. Tau

MathUhhhSaurus wrote:This reminds me of how the inverse of an ohm was referred to as a mho before they changed it.
I still like to call them mhos. Reminds me that electrical engineers can actually be funny on occasion.

Agreed. Larry, Siemens, and Curly just doesn't sound right.

Elmach
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### Re: 1292: Pi vs. Tau

I like sqrt(tau) or sqrt(2pi) as the fundamental circle constant; a lot of things become so much nicer. I'll just use the symbol ռ for it.

See, it has all the advantages of tau whenever you need it, but it also has the added benefit of

EDIT: Wow, I just looked up stuff I thought would look better with this, and I can't find anything.

But still, ռ is a goodish idea. Better than 2ռ2/3, anyways.

Bernkastel
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### Re: 1292: Pi vs. Tau

Moonfish wrote:The compromise should be the Chinese symbol for Rooster: 酉.

Math is always running out of symbols and it should be more culturally inclusive anyway.

There is a wonderful story about animals racing across a river that helps people remember the order.

Here are the numbers to go with the traditional symbols.

Notice how the rat pushes the cat off the ox.

I second this notion.

Kit.
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### Re: 1292: Pi vs. Tau

thevicente wrote:Just because people here seem interested, in Brazil the word "pau" depends heavily on context and can mean a lot of the things, not just the one that first came to Polako's mouth.

For example, in computer jargon, crash. As in "the app crashed", " the app gave a pau"

"The app gave a dick"

Seems legit.

BlueSloth
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### Re: 1292: Pi vs. Tau

Ok, wait..

Octal digits of pau according to bc (with a few extra digits beyond 200 since bc was having trouble getting the last 3 digits right):

Code: Select all

echo "scale=190; obase=8; 6*a(1)" | bc -l4.554574376314416443236234514475050122425471573015650314763354527003\04316771261165505467475703133125234035147165764643331727311243102010\76447270723624573721640220437652155065544220143116155742515634462136\362517430

Octal digits of pau according to sage:

Code: Select all

echo "floor((3/2)*pi*8^200).digits(base=8, padto=201)" | sage | grep "\[" | tr -cd "[:digit:]" | rev455457437631441644323623451447505012242547157301565031476335452700304316771261165505467475703133125234035147165764643331727311243102010764472707236245737216402204376521550655442201431161557425156344621

Those agree with each other, but only agree with Tasrayryn's number up to the 18th digit. And they don't have 666 in them anywhere

Which one of us is wrong?

Also, does anybody know an easier way to get octal digits out of sage?

BTW, here's e+2 in octal. Also no 666.

Code: Select all

echo "scale=190; obase=8; e(1)+2" | bc -l4.557605213050535512465277342542004717236361661347054074705515512651\70233101050620637674622347347044466373713722774330661414353543664033\10025354214136551737075527257726254111031765076574063355020530662525\173664324

nwm
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### Re: 1292: Pi vs. Tau

BlueSloth wrote:Ok, wait..

Octal digits of pau according to bc (with a few extra digits beyond 200 since bc was having trouble getting the last 3 digits right):

Code: Select all

echo "scale=190; obase=8; 6*a(1)" | bc -l4.554574376314416443236234514475050122425471573015650314763354527003\04316771261165505467475703133125234035147165764643331727311243102010\76447270723624573721640220437652155065544220143116155742515634462136\362517430

Octal digits of pau according to sage:

Code: Select all

echo "floor((3/2)*pi*8^200).digits(base=8, padto=201)" | sage | grep "\[" | tr -cd "[:digit:]" | rev455457437631441644323623451447505012242547157301565031476335452700304316771261165505467475703133125234035147165764643331727311243102010764472707236245737216402204376521550655442201431161557425156344621

Those agree with each other, but only agree with Tasrayryn's number up to the 18th digit. And they don't have 666 in them anywhere

Which one of us is wrong?

Also, does anybody know an easier way to get octal digits out of sage?

BTW, here's e+2 in octal. Also no 666.

Code: Select all

echo "scale=190; obase=8; e(1)+2" | bc -l4.557605213050535512465277342542004717236361661347054074705515512651\70233101050620637674622347347044466373713722774330661414353543664033\10025354214136551737075527257726254111031765076574063355020530662525\173664324

According to my calculations you are correct. Also I have no idea how Tasrayryn could have arrived at the digits he has. The first 501 octal digits are:

Code: Select all

4.55457437631441644323623451447505012242547157301565031476335452700304316771261165505467475703133125234035147165764643331727311243102010764472707236245737216402204376521550655442201431161557425156344621363625174410110777026111560241174471252241762037163367420573533032164702576626667446275343255043345060027305171025475041452166612112500275317166412767657355633417212140135534536541060452450664011414377406267077573054507036064406511117752700327100355213521015136220621644573043264505244325316526666260

So there are triplets of 3 at the 116th, of 7 at the 216th, of 1 at the 222th and of 6 at the 278th and 325th decimal place, but there are also quadruplets of 1th at the 430th and of 6th at the 494th decimal place. It seems the title text was already changed once, but it is still incorrect even considering the first 500 digits.

Copper Bezel
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### Re: 1292: Pi vs. Tau

mschmidt62 wrote:
Copper Bezel wrote:Yeah, I guess if you've not seen this before, here is as good a place to gush as any.

It's such a shame that they let the common folk post in these message boards.

I actually meant it - I wasn't trying at being elitist. I don't know maths, for one thing. = ) Lucky 10,000, right?
So much depends upon a red wheel barrow (>= XXII) but it is not going to be installed.

she / her / her

Shamino
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### Re: 1292: Pi vs. Tau

So would a compromise between Pau and Tau (1.75 Pi) be the Vulcan constant T'Pau?

(Ducking and running away now...)

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### Re: 1292: Pi vs. Tau

Bah! I'd say throw both out for most situations. Change our units to reflect the transformations we're making; when we actually need to fill a circular areas with squares, or circumscribe it with straight line segments. use a formula that accounts for the heuristic nature of what you're doing.

m = one meter of distance, not distance projected onto a curve.
mc = one meter circled (formerly pi m2)
mc = the border of one meter circled, aka the circumference (formerly 2 pi m)
ms = one meter sphered (formerly 4/3 pi m3)
ms = the border of one meter sphered, aka the surface area (formerly 4 pi m2)
m2 = Area constructed of rectangles (between one and any tractable number)
The thing about recursion problems is that they tend to contain other recursion problems.

brenok
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Location: Brazil

### Re: 1292: Pi vs. Tau

Shamino wrote:So would a compromise between Pau and Tau (1.75 Pi) be the Vulcan constant T'Pau?

(Ducking and running away now...)

You're toying with powerful forces here...