# Wau (Digamma) **URL:** \ **Category:** Factual Questions\ **Created:** [December 10, 2016, 4:01am UTC](https://boards.straightdope.com/t/wau-digamma/774325 "2016-12-10T04:01:31Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Enola\_Straight](https://avatars.discourse-cdn.com/v4/letter/e/dec6dc/32.png) [@Enola\_Straight](https://boards.straightdope.com/u/Enola_Straight)\ **Post date:** [December 10, 2016, 4:01am UTC](https://boards.straightdope.com/t/wau-digamma/774325/1 "2016-12-10T04:01:31Z")
[https://www.youtube.com/results?search\_query=wau](https://www.youtube.com/results?search_query=wau) According to the links above, this neat little number (which I never before heard of:dubious:) was known to the ancients. Is it a constant like sqrt2, pi, and e, with an expressable value? What equasions/formulas is it used in? ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [December 10, 2016, 4:16am UTC](https://boards.straightdope.com/t/wau-digamma/774325/2 "2016-12-10T04:16:58Z")
[spoiler]One of her expressions was: F = 5/6 + (5/6 + (5/6 + …)/6)/6 Which is equivalent to (since that part to the upper-right is equal to F itself): F = 5/6 + F/6 Solve: 6F = 5 + F 5F = 5 F = 1 Or is it really 0.9999…? :)[/spoiler] ---
**Author:** ![septimus](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/septimus/32/410_2.png) [@septimus](https://boards.straightdope.com/u/septimus)\ **Post date:** [December 10, 2016, 9:25am UTC](https://boards.straightdope.com/t/wau-digamma/774325/3 "2016-12-10T09:25:59Z")
> [@Dr.Strangelove](#): > > F = 1 > > Or is it really 0.9999…? Reported. ---
**Author:** ![Quartz](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/quartz/32/267_2.png) [@Quartz](https://boards.straightdope.com/u/Quartz)\ **Post date:** [December 10, 2016, 10:40am UTC](https://boards.straightdope.com/t/wau-digamma/774325/4 "2016-12-10T10:40:01Z")
The digamma was not only a number but a letter in ancient (pre-classical) Greek. [Wiki](https://en.wikipedia.org/wiki/Digamma) has the lowdown. ---
**Author:** ![pulykamell](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/pulykamell/32/3166_2.png) [@pulykamell](https://boards.straightdope.com/u/pulykamell)\ **Post date:** [December 10, 2016, 2:10pm UTC](https://boards.straightdope.com/t/wau-digamma/774325/5 "2016-12-10T14:10:24Z")
Assuming I’m not being whooshed: It’s a bit of a math joke. Wau (WOW!) is the number one. Maybe not a joke exactly, as all the properties of one are true in the videos, she’s just presenting them is an obfuscated way to show how cool (WOW!) the number one is. And how strange and mystical it seems when you present it in this manner. ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [December 10, 2016, 2:35pm UTC](https://boards.straightdope.com/t/wau-digamma/774325/6 "2016-12-10T14:35:45Z")
Y’know, as soon as I saw **Dr. Strangelove** refer to the video-presenter as “her”, I said to myself “I’ll bet that’s Vi Hart”. The video is a bit trollish, but she just might succeed at tricking some folks into thinking. ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [December 10, 2016, 3:52pm UTC](https://boards.straightdope.com/t/wau-digamma/774325/7 "2016-12-10T15:52:53Z")
On the bright side, Miss Hart is certainly making mathematics cool for young women … and that’s gotta be a good thing. **Quartz’** Wikilink gives the value of wau as six … so does that mean 0.999…∞… = 6 (= Ϝ) once we get “beyond infinity”? ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [December 10, 2016, 10:30pm UTC](https://boards.straightdope.com/t/wau-digamma/774325/8 "2016-12-10T22:30:24Z")
> [@septimus](#): > > Reported. I… but I didn’t mean… it was just a jo… aaaaaahhhhhh! (trapdoor to lava pit slides closed) ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [December 11, 2016, 11:08am UTC](https://boards.straightdope.com/t/wau-digamma/774325/9 "2016-12-11T11:08:28Z")
> [@Dr.Strangelove](#): > > Or is it really 0.9999…? > > 🙂 It’s really -…999999.0 ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [December 11, 2016, 2:08pm UTC](https://boards.straightdope.com/t/wau-digamma/774325/10 "2016-12-11T14:08:08Z")
Three’s [another video](https://www.youtube.com/watch?v=-eS8-1A47Z0) that makes the argument that wau = 1 or 0, given the properties she gave. (I think there may be a couple exceptions.) ---
**Author:** ![correlophus](https://avatars.discourse-cdn.com/v4/letter/c/58956e/32.png) [@correlophus](https://boards.straightdope.com/u/correlophus)\ **Post date:** [December 11, 2016, 5:16pm UTC](https://boards.straightdope.com/t/wau-digamma/774325/11 "2016-12-11T17:16:57Z")
The letter wau was an actual letter of the greek alphabet which was used in many older, preclassical dialects to represent the indo-european w sound, and comes from the semitic letter of the same name. It was called digamma only after it stopped being used for a long time due to its resemblance to two gamma letters. It is the sixth leter of the greek alphabet and just signifies the number 6, nothing mystical or obscure. It lies between the letter epsilon, the number five, and the letter zeta, the number 7. Later in byzantine times the new letter stigma, an abreviation for the st consonant cluster, was used for the number six. Nowadays stigma is no longer used, and six is symbolized with st. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [December 11, 2016, 9:29pm UTC](https://boards.straightdope.com/t/wau-digamma/774325/12 "2016-12-11T21:29:19Z")
To be clear, the ancient use of wau to represent 6 and Vi Hart’s cheeky use of wau to represent 1 have nothing to do with each other. (And Hart does indeed use wau to represent 1 and not 0; while a few of the properties she gives are satisfied by not just 1 but also 0 or other values, other properties she notes are satisfied only by 1, and indeed, thus 1 is the only value simultaneously satisfying ALL the properties she notes) ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [December 11, 2016, 9:47pm UTC](https://boards.straightdope.com/t/wau-digamma/774325/13 "2016-12-11T21:47:17Z")
> [@Indistinguishable](#): > > It’s really -…999999.0 I disagree. I think it’s really the sum of -1 + -2 + -4 + -8 + … ---
**Author:** ![watchwolf49](https://avatars.discourse-cdn.com/v4/letter/w/e9c0ed/32.png) [@watchwolf49](https://boards.straightdope.com/u/watchwolf49)\ **Post date:** [December 11, 2016, 10:09pm UTC](https://boards.straightdope.com/t/wau-digamma/774325/14 "2016-12-11T22:09:01Z")
[“One Is The Loneliest Number”](https://www.youtube.com/watch?v=d5ab8BOu4LE) {Youtube video 3’06"} ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [December 11, 2016, 11:57pm UTC](https://boards.straightdope.com/t/wau-digamma/774325/15 "2016-12-11T23:57:52Z")
> [@](#): > > Quoth **Dr. Strangelove** : > > Or is it really 0.9999…? Which is of course one of the properties of wau she mentions, that it doesn’t have a unique decimal representation. Incidentally, this is one of the properties which rules out wau=0. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [December 12, 2016, 12:10am UTC](https://boards.straightdope.com/t/wau-digamma/774325/16 "2016-12-12T00:10:46Z")
Perhaps the least ambiguous property she ever notes is the straight up definition “e[sup]2iπ[/sup] = ϝ”, which is satisfied by 1 and only 1. ---
**Author:** ![Dr.Strangelove](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/dr.strangelove/32/6613_2.png) [@Dr.Strangelove](https://boards.straightdope.com/u/Dr.Strangelove)\ **Post date:** [December 12, 2016, 12:47am UTC](https://boards.straightdope.com/t/wau-digamma/774325/17 "2016-12-12T00:47:17Z")
> [@Chronos](#): > > Which is of course one of the properties of wau she mentions, that it doesn’t have a unique decimal representation. Incidentally, this is one of the properties which rules out wau=0. Unless you’re using IEEE 754. Then, negative zero is a possibility :). ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [December 12, 2016, 1:14am UTC](https://boards.straightdope.com/t/wau-digamma/774325/18 "2016-12-12T01:14:50Z")
Also, …9999.9999… (and for that matter …1111.1111…) and such things. 🙂 ---
**Author:** ![Chronos](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/chronos/32/134_2.png) [@Chronos](https://boards.straightdope.com/u/Chronos)\ **Post date:** [December 12, 2016, 4:18am UTC](https://boards.straightdope.com/t/wau-digamma/774325/19 "2016-12-12T04:18:30Z")
I was leaving implicit that by “decimal representation”, I meant “according to the standard conventions for such”. I mean, I could invent a convention that 1.0 represented 0, and 2.0 represents one, and 4.0 represents two, and so on, and in that convention 0 would have two representations, but nobody would ever actually use that convention. ---
**Author:** ![Indistinguishable](https://avatars.discourse-cdn.com/v4/letter/i/90ced4/32.png) [@Indistinguishable](https://boards.straightdope.com/u/Indistinguishable)\ **Post date:** [December 12, 2016, 4:34am UTC](https://boards.straightdope.com/t/wau-digamma/774325/20 "2016-12-12T04:34:43Z")
Yes, of course. I’m just joking around, as we all are. [Next page](https://boards.straightdope.com/t/wau-digamma/774325.md?page=2)