2657: Complex Vowels

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Complex Vowels
Pronouncing [ṡṡċċḣḣẇẇȧȧ] is easy; you just say it like the 'x' in 'fire'.
Title text: Pronouncing [ṡṡċċḣḣẇẇȧȧ] is easy; you just say it like the 'x' in 'fire'.


The standard IPA vowel chart.

This is another one of Randall's Tips, this time a Linguistics Tip. The curly-haired linguist, Gretchen McCulloch, manages to produce a cursed sound using complex vowels, which cannot be comprehended by normal humans like Cueball and Megan, who both seem to get a headache from listening to the sound. The sound she makes was produced by extending the IPA vowel plane along an imaginary axis to form the complex vowels.

In phonetics based on the International Phonetic Alphabet (IPA), the space of vocal tract articulators determining vowels is represented as three dimensional, from the position of the tongue and lips. The vertical axis represents vowel height or closedness (i.e., how close or far the tongue is from the top of the mouth), and the horizontal axis represents front-to-back place (i.e., how close or far the top of the tongue is from the teeth.) The position of the tongue, along with the frequency of the vocal cords vibrating in the larynx from air being exhaled by the diaphragm, are the primary determinants of the fundamental and second formant frequencies of vowel sounds. A third dimension of vowel sounds is the "roundedness" of the lips, represented on the IPA vowel chart to the right by pairs of vowel phoneme glyphs. Other higher-dimensional vowel representations include diphthongs, which are simply two different sequential vowels slurred together; diphones, which represent the last half of one phoneme followed by the first half of the next; vowel shift mappings delineating different accents[1][2] and long-term evolution of voiced phone sounds; and cepstral representations such as mel-frequency cepstral coefficients.

Randall suggests increasing the range of vowel sounds available by using complex notation to indicate an additional dimension with an "imaginary" axis. In mathematics, complex numbers are numbers including both real numbers and imaginary numbers. A complex number can be expressed as, "a + bi," where a and b are real numbers, but the latter imaginary part is combined with 'i,' the square root of negative one, as depicted in the central expression in the comic by √-1 indicating a further dimension of coordinates. When expanding the one-dimensional number line with an imaginary axis, it becomes two-dimensional with the "bi" component orthogonal to the original "real" number line. Linguists never use the complex plane to represent vowel roundedness or any other higher-dimensional features of phonemes, although the properties of complex numbers could conceivably support representing physiological features of the vocal tract, such as prior position of the articulators.[citation needed]

This comic conflates complex numbers in mathematics with "complex vowels" in linguistics. Such complex vowels are implied to create sounds which cannot be properly processed by the human brain and represents one with a heavily modified "schwa" Ə phoneme, mirrored vertically and surrounded by multiple diacritics akin to the Zalgo text meme. The sound of this supposedly alien vowel has Cueball and Megan clutching their heads. Overall, Randall's complex vowels bear similarity to the cliché of "black speech" in Lovecraftian horror, a language created by alien beings with different vocal patterns than humans.

In linguistics, 'ə' is the schwa symbol, referred to in the title text and the depiction of complex phonemes, the most common vowel sound in English polysyllabic words (the 'a' in "comma" or the second 'e' in "letter.") Production of the schwa sound takes place with the tongue, jaw, and lips all in a relaxed, central position, and is often entirely optional in many if not most dialects of English. The pronunciation of "[ṡṡċċḣḣẇẇȧȧ]" in the title text is said to sound like the x in the word fire. In fact, there is no x in fire.[citation needed] This is perhaps in line with the idea that complex sounds are incomprehensible to most humans, and likely also impossible to pronounce by anyone other than experts such as Gretchen. Another example of weird diacritics is in 2619: Crêpe, and with Zalgo text in 1647: Diacritics. The use of typography to create psychological stress is explored in 859: (.


[A diagram shows the extrusion of the trapezoidal IPA vowel chart upwards into three dimensions. A point near the center is labeled with an equation that shows "ə + ½√-1 " as being equivalent to a made-up symbol that looks like two schwas mirroring each other with other markings above and below.]
[Below the diagram, a character with shoulder-length dark wavy hair pronounces the new vowel in a speech bubble with unstable lines surrounding it. Two bystanders to her right are bent over slightly, clutching their heads in apparent anguish.]
[Caption below the panel:]
Linguistics tip: Extend the IPA vowel plane along the imaginary axis to produce the complex vowels, cursed sounds which the human mind cannot comprehend.

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Spoken symbol bears resemblance to 🜏, https://en.wiktionary.org/wiki/%F0%9F%9C%8F

Not really, it's closer to 'əG.' 01:15, 11 August 2022 (UTC)
Looks like ꬱ to me. Plus some diacritics sprinkled over it, of course. It does look similar to 🜏 when you include the zalgo. 06:53, 11 August 2022 (UTC)

sscchhwwaa is easy, say it like the x in "fire" and the silent p in "bath" 21:42, 10 August 2022 (UTC)

What? There is no 'x' in "fire." 01:17, 11 August 2022 (UTC)
Yes there is, it's the -6th letter! Me[citation needed] 16:53, 11 September 2023 (UTC)

Ideas: bellows-, reed-, and lucite-based voiced phone production tracts typical in science museums; diphones as an alternative to phomemes (a diphone is the second half of one phoneme followed by the first half of the next -- NOT two adjacent phomemes as the Wikipedia article claims. Two adjacent phomemes are a biphone, not a diphone); the relationship of the position of the tongue in two dimensional place × closedeness space to the fundamental and second formant frequencies of speech audio; diphthongs; cepstral representation such as mel-frequency ceptstral coefficients; and Zalgo text IPA. 22:41, 10 August 2022 (UTC)

Roger. 03:25, 11 August 2022 (UTC)

The vowelspace is depicted in two dimensions for convenience, but it has at least three dimensions. Look at the IPA vowel diagram (already added to this page). The third dimension is roundedness.

Yes, of the lips; apart from the two dimensions (out: place, and up: closedeness) of the tongue. 22:59, 10 August 2022 (UTC)
Does roundedness also involve the tongue and cheeks to any extent? 23:36, 10 August 2022 (UTC)
I wonder if Randall is doing this similarly to the way physicists present space-time diagrams with only 2 dimensions of space. We can visualize 3 dimensions using projections on 2-dimensional images, but it's hard to visualize 4 dimensions. Barmar (talk) 15:18, 11 August 2022 (UTC)
If you can't visualize 4-D, play tennis. 03:15, 12 August 2022 (UTC)

This comics reminds me of two good YouTube videos about IPA and vowels: Tom Scott's The Language Sounds That Could Exist, But Don't and Dr Geoff Lindsey The Vowel Space - in the latter the replacement for the mentioned IPA's vowel diagram is proposed, with two dimensions being simply the ratio of two main harmonic components; here the third dimension is sometimes needed to better depict some existing vowels. --JakubNarebski (talk) 08:50, 27 May 2023 (UTC)

This linguist character has appeared 3 times now. Will there be a new character page dedicated to Gretchen or "The Linguist"? 00:21, 11 August 2022 (UTC)

I second this motion. I think it would make more sense to have a generic character called "the Linguist" since, as the explanation for 2381 points out, not every linguist in xkcd is necessarily Gretchen. Plus, it seems like with this comic he's varied the artistic style, with the hair looking slightly less frizzy. 22:15, 11 August 2022 (UTC)

Can someone please create and paste in a zalgostring for the fancy 'əG' ligature shown twice in the comic? 01:10, 11 August 2022 (UTC)

Is this another example of Randall trolling Explainxkcd as in 2619: Crêpe? 01:45, 11 August 2022 (UTC)
This is the best I could do ə ̯̣̌̄̊̇c̵. I added the zalgo marks to a narrow no-break space in between the schwa and a "c" with a line over it (there's no reverse schwa apparently). Obviously it's not a perfect match, but I think that's sort of the point of this comic. RDiMartino (talk) 15:31, 12 August 2022 (UTC)
ꬱ̯̣̌̄̊̇ would work if only I could get the diacritics centered.

Heleatunda (talk) 01:16, 23 November 2022 (UTC)

Someone please remind me how to Zalgo a top horizontal bar over √-1. 02:34, 11 August 2022 (UTC)

Slow way = Windows Character Map --> Group by: unicode subrange... Group By: Combining Diacritical Marks. 6th character from the top left (U+0305:Overline) yields √-̅1̅.
Fast way = HTML character entities, {character it combines with}&#{character number code}; (773:Overline) yields √-̅1̅
Ignore other codes as they are either non-combining or have height relative to combining character (ie Macron) -- 04:35, 11 August 2022 (UTC)
Are you sure? Those aren't wide enough to connect along the top for me. 07:57, 11 August 2022 (UTC)
[same person as previous above] looks great now, let me check innthe browser that it had issues in.... 02:24, 12 August 2022 (UTC)
[different person...] It's never looked Ok for me, on multiple browsers and platforms it always rendered as two separate overstrikes, and even the first does not connect to the √ bit. As an extended root-overstrike is more useful for visually bracketting ambiguities, like the central bit in "(-b±√(b²-4ac))/(2a)" I consider it superfluous for what would be "√(-1)" but cannot be "√(-).1". Nice try, though.
Related, I've exchanged "1/2" for ½. On this device it looks similar (slanted numerator/denominator bar and still an offset, unlike the drawn comic which is vertically aligned), but it might look better or even direct over-under with the correct font rendered into. And, like the former, probably read better as screen-readers process the Transcript for the visually impaired.
If it weren't for that latter point, I'd take the idea used in 2614 for the in-Explanation
(<table style="display: inline-table; line-height: 0.6em; vertical-align: middle; font-size:7pt; text-size-adjust: none;"><tr><td>2</td></tr><tr><td>2</td></tr></table>) and put it as:
2 10:41, 12 August 2022 (UTC)
Ok, back to the 'root' bit: the (Explanation, not Transcript) current use of √<span style="border-top: 1px solid currentColor">-1</span> is okish but hovers the line above the "√" top by about ¾ of the initial down-tick's height (as rendered here... Chrome on Android, for reference), which is clearly not pixel-perfect. Maybe this is an outlier (obscure browser and OS that applies to hardly anyone, right?) so not gonna edit it away, but "√-1" is already unambiguous for anyone who knows what "√" is actually used for. Do we absolutely need to solve this rendering problem at all? At least until we persuade Unicode to release a special arbitrary-width over-kerning version of the √-character. 09:09, 15 August 2022 (UTC)

I don’t think what Randall is trying to do is provide a “roundness” dimension, but that’s how the explanation reads to me right now (“such” a dimension, e.g.) Szeth Pancakes (talk) 05:13, 11 August 2022 (UTC)

Agreed - rearranged it a bit to deal with the real-life dimensions first, then be more explicit that the proposal is to add to the existing dimensions in a way analogous to how imaginary numbers expand the domain of real numbers. 08:19, 11 August 2022 (UTC)

Being an Englishman of a certain age, I had a panic flash back to the ITA. Arachrah (talk) 12:55, 11 August 2022 (UTC)

What was wrong with the Independant Television Authority?
(Seriously, though, the Initial Teaching Alphabet was very bad... It insisted that "book" had a different vowel in it to "up", contrary to everyone's experience, including the teacher who tried to use it. - Ironically, though, when a few years later we were in 'big school' and being taught our first French lesson we got confused by being told at the very start that the words "un" and "une" (written on the board) were the equivalent to the English word "uh" (spoken)... Uh? What's "uh"?... "You know, as in 'uh book', 'uh table', 'uh chair'...") 14:37, 11 August 2022 (UTC)
I'm curious how you pronounce them if they *aren't* different vowels: is it uhp and b'uhk (^p and b^k in IPA), the Near-close near-back rounded vowel (not sure how to describe it or get the upside down omega to render, or something entirely different? 21:57, 11 August 2022 (UTC)
Quite possibly, but I'm never entirely confident that I have the right impression of what a given IPA means, from my particular regional accent as a baseline. Definitely the same (excepting the phonemic ending each of "-uck/-upp" and the presence or not of another initial element).
A good comparative linguist could probably name the various zones (encompassed by various isogloss lines) where this is true. And, by actually hearing me, perhaps narrow down the one from which I actually hail, quite accurately. At least one set of my grandparents always said "book" (or "look") more like the longer "ew" than "uh", and they were pretty much always local to another town just 10-15 miles away from the one of my own birth/upbringing (don't remember much of the other grandparents, but they were also from a village more in the other area than my own, but making an almost equilateral triangle on the map). Traces of this kind of 'elsewhere' accent from my parents probably did make me stand out a little bit from my "nth generation local" peers. But still up≈book applies.
If I had a cat, by now it would be staring up at me, wondering why I've been saying "up book book up look whup uck luck suck tuck muck Krup ... (etc)" to myself, trying to detect any changes and all similarities. While imaging myself in various social situations that demand broader or more RPified pronunciations... ;) ((Plus trying to calculate my exact tongue-placement/etc.)) 23:09, 11 August 2022 (UTC)
Blast from the past! I remember ITA from when I was in elementary school on Long Island in the 60's. In my later years I frequently confused this with IPA. Barmar (talk) 15:18, 11 August 2022 (UTC)

Not sure what the text "There is one unique such function and the new mathematics is consistent." - in current version, with similarly bad historic variations - is supposed to mean. The point of sqrt(-1) is that it never had a valid result on the Real number-line, and only by imagining a non-real dimension can you start to work with such a number (alone or in combination with real values) with a consistency that allows even nth-roots and exponentiation. The "unique (...) function" bit sounds strange. And note that -1 does not have a single unique root (which I can't help feeling is what is trying to be said, still)... its two roots are i and -i, for much the same reason that sqrt(1)=±1. But maybe the statement I'm wondering about is written under some branch of functional number-theory that I'm not familiar with, so could the relevent editor(s) please do it in a way that won't so confuse/trouble me or mislead others? 22:03, 11 August 2022 (UTC)

Done. 23:09, 11 August 2022 (UTC)

Since when does a completely generic orthogonal projection from 2- to 3-D invoke the Gell-Mann quark model? Unicode needs a glyph to tell physicists to settle down. Removed: "The multi-plane scheme of the comic seems inspired by the representation of the Gell-Mann quark model used in particle physics (you can see one on page 4 of the Particle Data Group quark model review)." 02:02, 12 August 2022 (UTC)

Reminds me of Battle of the Linguist Mages - Punctuation marks are alien invaders from another dimension, and magic consists of pronouncing "power morphemes" (assuming learning them doesn't drive you mad, first). --Bobson (talk) 02:43, 12 August 2022 (UTC)

The symbol reminds me of the Mandelbrot Set but turned on its side. 07:17, 12 August 2022 (UTC)

Not sure about the most common vowel sound in English polysyllabic words (the 'a' in "comma" or the second 'e' in "letter.") - those are pronounced completely differently (unless perhaps you are from the south of England and pronounce 'letter' as 'lettah'). 07:32, 12 August 2022 (UTC)

I would pronounce them 'commuh' and 'lettuh', with a very short 'uh', which would fit with it being the most common vowel sound, given people say 'uh?' quite a lot. Although that's about as unpolysyllabic as you could get. 09:02, 12 August 2022 (UTC)
Again, probably multiple isoglosses apply. I'm an "uh"-common person from the North and recognise "ah"-common accents as (certain bits of) the South, but it's possible that "lettah"<->"lettuh" and "commah"<->"commuh" transition at different boundaries across/around/through the Midlands, thus confusing many people. I think RP goes more "commah" and "lettuh(r)". Checking Wiktionary, though, IPA is given as /ˈkɒm.ə/ (UK, otherwise unspecified) and /ˈlɛtə(ɹ)/ (RP), but there's not much info on direct comparisons between, say, East London/East Midlands/East Yorkshire/East Anglia/East Kilbride/Dwyran... 11:36, 12 August 2022 (UTC)

You could do something like this comic with the embeddings of a language model trained on IPA and human responses. Stuff like https://towardsdatascience.com/introduction-to-word-embedding-and-word2vec-652d0c2060fa http://www.isle.illinois.edu/speech_web_lg/pubs/2021/gao2021zero.pdf . A speech generating reinforcement learning system rewarded on human response would almost certainly discover complex vowels: sounds humans recognise partly, possibly impossible mixes of normal vowels, that produce erratic or novel human behavior. This has likely happened in some kind of marketing or attention research. 19:20, 12 August 2022 (UTC)

To add on to this, when playing with or demoing powerful neural networks, people often give the networks impossible prompts (like dall-e’s original example of an armchair in the shape of an avocado, a contradiction as avocados are never shaped like something that is a chair) —- and surprisingly a strong model will actually produce a result humans believe meets the request. This is like the example of “x in fire" —- mainstream neural networks usually do not reject input, they just solve it the best they can, producing an output that best matches everything they learned, or is an extrapolation from what they learned along their internal dimensions. 19:26, 12 August 2022 (UTC)

"the properties of complex numbers could conceivably support representing physiological features of the vocal tract" - not sure about this - the properties of complex numbers stem from imaginary numbers being defined in relation to the square root of -1 - it's not obvious how a value of -1 would have any meaning in vocalspace (since it's a limited scale, not a continuous plane), never mind its square root, so how would the interactions between real and imaginary numbers read across to those between tongue movements and other vocal tract features? 10:10, 15 August 2022 (UTC)

Well... Although I never liked the way it was worded, I envisaged it as depicting extradimensional movements/displacements, possibly introducing resonances of air beyond the current three dimensions (and time) of movement. Such as compressive waves in a further imaginary dimension. (For transverse/tortional-waves, in media that support them, moments of movement/wbatever perpendicular/hyperradial to any 'real' version, but in air tbat's probably moot. Unless it isn't..?)
Or you could consider, as you say, a limited scale of 0..1 being the distance of the tongue-tip between roof-touching and floor-touching (-1 would be a tongue embedded in whichever surface is zero, somehow phased through and creating a 'nevative cavity' of resonance, somehow, and an i-ward position would be... Well, not 'sideways' (though that does change things) but hyper-sideways (again those other dimensions, probably requiring muscles/etc we don't normally consider), and all that implies.
...that's if you want my assumptions about how an entirely ficticious and frankly esoteric scenario might 'really' be implemented. I won't say it's the way it would be, and there are limely many other (mis)interpretations of how it might happen, these were just my first thoughts on initially reading the comic (but it used less words in my head, as I could more easily imagine the necessary illustrative diagrams that did most of the heavy lifting). 11:52, 15 August 2022 (UTC)