Links: Late May 2013

Interesting

Delightful

Awareness

  • The emptiness of depression, conveyed in cartoon form.

Personal

anim

I’m expecting to become an uncle soon, with my sister’s first child due any day now. I don’t plan to announce the event very promptly on the blog, but I will keep people updated on Twitter. I expect to meet the infant around June 6 or so, and have a 0th birthday present all ready to pass on.

An email from my uncle on May 15 informed me that my father’s father’s mother’s father’s mother’s mother’s father’s grave has been found, just in case that interests you.

I attended my aunt’s 70th birthday party on May 18. Very nice to catch up with people.

It’s been almost two months since I switched Internet providers and changed my email address, and so my old addresses (the ones with ‘netyp’ in the domain name) will expire at the end of May.

Links: Early May 2013

Some links. Not many, but that suits me: it means the blog post doesn’t take long to compose.

Interesting:

  • I didn’t expect to enjoy the NYT article on psychology fraudster Diederik Stapel, but on giving it a chance I found it surprisingly thought-provoking.
  • A fifty minute interview from the Guardian on the origin of life.
  • A brief history of traditional marriage in England. I bet there’s a lot more to be said, but this is an interesting and often surprising take.

Delightful:

  • Cheeky animal video of the month (monkey vs tiger).
  • Everything hangs in the balance in this fantastic work of art.
  • I won’t personally be ordering a copy of Planet of the Apes and Philosophy, but the Amazon page is worth a visit.
  • If you’ve ever dreamed of a utility to convert a Google Street View route into a hyperlapse video, look here. It’s not that utility, but rather a library of Javascript code that can be used to create that utility (hopefully we’ll soon see programmers publishing versions all over the web). The very limited demo version essentially goes to and fro between a start point and an end point, with a third point controlling the camera angle.

A personal postscript: I had a huge scare last night when I lost the message bodies of all 220-ish emails in my Thunderbird inbox! I published a blog post calling for help, and stated that it was a temporary blog post which would be deleted when the crisis was resolved. After a sleepless night and some moral support I did manage to get most of the messages back, and accordingly I’ll delete that blog post shortly after publishing this one.

Herewith a summary. Due to some software glitch (the trigger of which is a complete mystery), the Inbox file (which stores the message bodies) had been wiped clean of content, although the corresponding .msf file (which contains message headers, essentially) was still intact. Hence Thunderbird still displayed the list of messages, but not the messages themselves. To fix the problem, I had to use the Windows 7 restore facility to restore a previous version of the Inbox file (you know: right click on the file, choose Properties, choose Previous Versions, etc). I lost a few days of emails, but these were all receipts and other acknowledgements, nothing critical.

Imaginary musings

Regardless of the school you went to, if you did final year maths then you’ll relate to the following anecdote. Your stories might differ in specifics, but this is pretty much the archetype of what goes on in the classroom. (No doubt it also rings a bell if you’re a teacher.)

  • One day, in passing, I observed that the intelligence quotient of the peer I was talking to was zero.
  • Said peer mentioned, in turn, that my IQ was zero POINT zero.
  • I retorted that his IQ was zero point zero times ten to the minus INFINITY.
  • He returned that my IQ was MINUS zero point zero times ten to the minus infinity.
  • I explained that his IQ was minus zero point zero times ten to the minus infinity *i*.
  • He countered that my IQ was just i — a wholly imaginary quantity — and that at least his was real.

I tell this story as a gentle way to raise the topic of imaginary (and complex) numbers, which I’ve been musing on lately. I think my latest bout of musings were triggered by reading this, which I read via a chain of links that I can’t remember now, but would have included this.

The subject of my muse was why most attempts to explain the applications of complex numbers strike me as unilluminating.

Classroom banter doesn’t count as an application. Neither do pretty fractal patterns — they’re lovely, but like a game, the rules don’t have to mean anything. Neither is it remarkable that one abstraction can be used in the service of another abstraction, as in esoteric results from advanced mathematics. What counts are situations where it’s fruitful to take a quantity derived from real world measurements, and relate it to the square root of a negative number.

I never studied any applications of complex numbers myself, having not done any physics beyond first year university. But I’ve occasionally listened to, or read, people trying to explain how imaginary numbers are useful in their fields, and I almost invariably have no idea what they’re talking about. They might assert that imaginary numbers are useful for such-and-such, but in a way that leaves me no wiser about what said context has to do with squaring something and getting a negative result.

So it occurred to me that perhaps most explanations fail because they show the audience an imaginary-shaped peg without first cutting an imaginary-shaped hole. Let me illustrate the point with reference to negative numbers, and then relate it to imaginary/complex ones later on.

Once upon a time, negative numbers were widely regarded as an affront to common sense. Quantities less than nothing? Crazy. But applications soon became apparent, and those applications tended to fit very particular patterns. One can sensibly answer questions like: if you’re looking for a scenario that lends itself to being modelled with negative numbers, then what sort of characteristics should you look for?

In my metaphor, the answer to that question is the negative-shaped hole, and a particular scenario which has those characteristics is the negative-shaped peg. And here’s the answer: you look for a scenario where every quantity has a corresponding opposite. The opposite of having a particular speed is having the same speed in the opposite direction. The opposite of being so high off the ground is being so far under it (and, preferably, upside down). The opposite of having so much money is being so far in debt. And so on.

If you have a scenario in which various quantities have corresponding opposites, then you have a scenario that lends itself to being modelled with the aid of negative numbers. There’s your hole, and you’ll find any number of pegs to fit. Note also that negative numbers don’t measure anything mysterious; simply flip the coordinate system around and they become positive.

If we carry this pedagogical approach over to the imaginary case, the question becomes as follows. Suppose you’re looking for a scenario that lends itself to being modelled with imaginary numbers. What characteristics would you look for?

And for a pretty good answer, consider that in the world of imaginary numbers, there exists a function such that f(f(x)) = -x. In fact there are two such functions (multiplying by i and multiplying by -i), but the point is made by translating that formula into everyday language. It means there is something you can do to a quantity twice and always get back the opposite of what you started with.

That’s probably the simplest imaginary-shaped hole you can find. If you have a scenario in which there’s something you can do to a quantity twice and always get back the opposite of the quantity you started with, then you have a scenario that lends itself to being modelled with the aid of imaginary numbers. As for pegs, no problem. Try anything involving rotations and waves.

In the case of rotations, the thing you can do twice and end up with the opposite of what you started with is to rotate a quarter of the way around. In the case of waves, it’s to wait for a quarter of a wavelength to go by. Given such tools, if a physicist’s eyes roll at an elementary blunder in this blog post, you can calculate what that physicist will be looking at by the end of it. You can almost as simply calculate the same thing using old-fashioned real numbers, of course, but with a good i you can fit into a single formula what otherwise requires an algorithm. And you can show that the principle neatly carries over to finer intervals — less than a quarter of the whole.

I haven’t mentioned Euler’s equation — an oft-celebrated result of a very clever procedure that makes it meaningful to raise numbers to imaginary powers, and is typically taught in first year mathematics at university. The relevant consequence is that i can be re-written as e to the power of πi/2, and hence that i to the power of some number n is the same as e to the power of nπi/2 [note: π is pi -- but my blog happens to use a font that doesn't draw it very well]. Re-writing everything as exponents of e may make things more complicated for algebra, but simplifies things for calculus. But because I haven’t done any calculus since the 1990s (and wasn’t much good at it then), I won’t go there.

(Exponents of e are also neater if you measure angles in radians rather than quarter-revolutions, but I’m pretty sure the reason mathematicians measure angles in radians is because it leads to trigonometric functions having neat power series and hence Euler’s equation etc, so the causality is kind of inverted there.)

I’m definitely not going to mention quantum physics. If you’re interested, try a blog by someone who understands it. You didn’t come here for that.

Links: Late April 2013

This collection of links is short, but I hope the quality pleases you.

Interesting/Awareness:

Useful/Delightful:

A lizard, a wedding and a painting

A least three things have happened in the last week that are worth sharing. The most important is my second cousin’s wedding, which we’ll get to in a moment. But first, here’s a photo of a gecko I saw on my kitchen window last Thursday evening:

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I’ve never seen a gecko at this address before, and — although I’ve read about it often enough — I’ve never seen a gecko climbing glass before. Amazing.

On Saturday, my second cousin Simon married Jemima, who I hadn’t met before. The wedding took place in the Lutheran Church at Strathalbyn, a largish town about 50km southeast of Adelaide. Here are my photos from the service:

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And from outside the church:

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Everybody taking photographs at the same time:

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Between the service and the reception, my parents and I explored the town of Strathalbyn, which features a very nice park in the middle. Here’s my best photograph:

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The reception was held back in the church hall. On display was the official wedding cake, which is almost certainly the best-decorated cake at any wedding I’ve been to. Simon is a tractor fanatic, hence the farm-themed decorations as seen in the first photo below.

Beside it is a photograph of the balcony where the married couple and selected company sat during the reception.

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Below are two more photos. The first is a close-up from our table, starring Mum, and the second shows the view toward the balcony. The light levels in the room were too low for my camera to focus properly, but I’m sure you’ll forgive that.

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During the proceedings, the microphone coordinator gave us half an hour to compose messages to be read aloud. My parents remember this was a common thing at weddings a generation ago, but almost unknown these days — perhaps it’s coming back into fashion, but more likely Simon and Jemima heard about it from old folk and thought it was a good idea.

Anyway, with assistance from family — because I couldn’t figure out the last line on my own — I composed the following limerick:

When Simon did marry Jemima
He couldn’t find anyone finer.
She doesn’t have wheels
Yet somehow appeals
And we hope that he’ll often remind her.

To my mind, the reception was a lot more enjoyable than the service. However it did run late (so many speeches), and we didn’t stay till the very end. I never did find out if the cake tasted as good as it looked, but the rest of the food was beyond criticism.

It was great to catch up with Simon and meet Jemima, but of course it wasn’t the place for an extended chat. I look forward to having that opportunity another time.

The third event worth sharing from the last week is the delivery — yesterday evening — of the painting I bought last month on Kangaroo Island. The painting is called Southern Swell, and the artist is Suzanne Trethewey. Here is a picture of it hanging above my living room table, followed by two complementary close-ups:

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Links: Early April 2013

My pick of the Internet’s best links from the last month or so. As ever, leave a comment if you’d like to have a conversation about any of them.

Interesting

Delightful

Awareness

Personal

  • I didn’t do the final version, but I had a hand in this design (mostly in choosing the component images).
  • Was recently reminded of this gravity simulator. Last time I played with it I couldn’t get a secondary body in stable orbit, but this time I succeeded. Tell me in a comment if you can do the same.
  • When I was in Kangaroo Island I bought a bottle of this honey liqueur. The best cocktail recipe I’ve come up with is as follows: One part honey liqueur, one part orange juice, two parts coconut water (about 5% alcohol per volume, as the liqueur is 20%). Incidentally, the oil painting I bought on Kangaroo Island will be delivered next Monday.

Kán yu andastánd wot aim seiing?

Whatever you think of the complexities and ambiguities of English spelling, reforming it is not a realistic prospect this side of an independently-governed moon colony.

Or, to put it another way: Woteva yu think ov dhi kompleksitíz ánd ámbigyúitíz ov Inglish speling, rifōming it iz not a rialistik prospekt dhis said ov an indipendentli-gavand mún koloni.

Because however unattainable reform might be in the real world, everything is possible in the imagination. Only very boring people permit their actions to be governed by the question, “Is it practical” when they could be asking, “Is it fun?”. So here’s my question: Suppose you were the governor of that moon colony. How would you propose a more-or-less phonemic English could be spelt?

Bikoz haoeva anateinabul rifōm mait bi in dhi rial wǎld, evríthing iz posibul in dhi imájineishon. Ounli veri bōring pípul pǎmit dhe ákshonz tu bi gavand bai dhi kweschon, “Iz it práktikul” wen dhei kud bi āsking, “Iz it fan?”. Sou hiaz mai kweschon: Sapouz yu wǎ dhi gavana ov dhát mún koloni. Hao wud yu propouz a mo-o-les fonemik Inglish kud bi spelt?

In this blog post I’ll present a system of my own, and for comparison also refer to a quite different system I designed a number of years ago.

In dhis blog poust ail prizent a sistem ov mai oun, ánd fo kompárison ōlsou rifǎ tu a kwait difrent sistem ai dizaind a namba ov yiaz agou.

— Where to Start —

To begin, you need to make a number of decisions. These include:

Tu bigin, yu níd tu meik a namba ov disizhonz. Dhíz inklúd:

  • Which dialects is your system intended for? Perhaps all of them (good luck with that), perhaps only your specific accent, or perhaps something in between. The system herein aspires to work for most non-rhotic dialects of English.
  • Wich daialekts iz yo sistem intended fo? Paháps ōl ov dhem (gud lak widh dhat), paháps ounli yo spesifik aksent, o paháps samthing in bitwín. Dhi sistem hiarin aspaiaz tu wǎk fo moust non-rotik daialekts ov Inglish.
  • Do you wish to exploit familiar spellings to keep your system easy to learn, or do you want to give English spelling a clean start by building a consistent, sensible system from the ground up? Herein, I’ve gone for the familiarity approach, up to a point.
  • Du yu wish tu eksploit familya spelingz tu kíp yo sistem ízi tu lǎn, o du yu wont to giv Inglish speling a klín stāt bai bilding a konsistent, sensibul sistem from dhi graond ap? Hiarin, aiv goon fo dhi familíáriti aprouch, ap tu a point.
  • Will there be a symbol reserved for schwa, and if so, which? You could re-use an existing letter to ensure it flows easily under the pen, but at the cost of making the remaining letters work that much harder to fill the gap. If not, people will go on misspelling separate as they always have. In this case I’ve chosen not to represent schwa.
  • Wil dhe bi a simbol rizǎvd fo shwā, ánd if sou, wich? Yu kud ríyúz an egzisting leta tu ensho it flouz ízili anda dhi pen, bat át dhi kost ov meiking dhi rimeining letaz wǎk dhat much hāda tu fil dhi gáp. If not, pípul wil gou on misspeling separeit az dhei ōlweiz háv. In dhis keis aiv chousen not tu reprizent shwā.
  • Will you have exactly one spelling per pronunciation, or will you build in some redundancy? Also, perhaps you’d like to use spelling to indicate which syllable is stressed. Here I’ll keep things simple for the most part, but discuss possible extensions at the end.
  • Wil yu háv egzáktli wan speling pǎ pronansíeishon, o wil yu bild in sam ridandansi? Ōlsou, paháps yúd laik tu yúz speling tu indikeit wich silabul iz strest. Hia ail kíp thingz simpul fo dhi moust pāt, bat diskas posibul ekstenshonz át dhi end.

My previous system was tailor-made for my specific dialect, was considerably more radical at the expense of being hard to remember, reserved the letter i for schwa, and included a rather convoluted system for marking stressed syllables.

Mai prívios sistem woz teila-meid fo mai spesifik daialekt, woz konsidarabli mo rádikul át dhi ekspens ov bíing hād tu rimemba, rizǎvd dhi leta i for shwā, ánd inklúded a rādha konvolúted sistem fo māking strest silabulz.

[The self-translations will cease at this point. They've been proofread a few times, but errors may remain.]

— Consonants —

In English, n becomes a velar nasal when followed by g or k (as in anger, angle, ankle, anchor, etc), and in those cases it makes sense to spell the combination ng or nk as we normally do (since the velar nasal can be regarded as an allophone of n). But we also use the spelling ng to represent a velar nasal on its own, leading to the ambiguity whereby the g in anger is pronounced but that in hanger is not.

In my old system, I decided that a velar nasal not followed by g or k would be spelt yn, resolving the ambiguity and taking advantage of the fact that the letter y (always a consonant) cannot occur immediately before another consonant. This time, however, I’ve decided that the anger/hanger ambiguity is a tolerable one, and to simply spell the velar nasal ng as English speakers are used to.

Similarly, in English the spelling th sometimes denotes the unvoiced fricative of thieves, sometimes the voiced fricative of these, and sometimes simply the sequence of sounds represented by the letters t and h (the famous-to-the-point-of-being-a-cliche example being pothole).

In my old system I used the spellings hs and hz for unvoiced and voiced th respectively, taking advantage of the fact that the h sound never occurs immediately before another consonant, and having the second half of the digraph be something that normally represents a sound of the some phonological category (unvoiced and voiced fricatives respectively). This time I’ve decided to spell the unvoiced th simply as such, and (borrowing from some other languages) to use the spelling dh for its voiced equivalent.

In this system, the letter j has the pronunciation that English speakers would expect, and the same goes for the digraphs ch, sh and zh. The letter c never occurs on its own (as its two main pronunciations are spelt s and k), but only as part of the digraph ch. One can envisage a later reform of the reform in which the surplus h is dispensed with, but for the sake of familiarity I’ve decided to leave ch alone. The letters q and x do not exist in my alphabet at all.

— Vowels —

That’s enough about consonants. The real fun is with the vowels, which I’ll describe with reference to John Wells’s lexical sets.

In my dialect, the PALM/BATH/START sets are merged, as are the LOT/CLOTH sets, and THOUGHT/NORTH/FORCE sets. If your dialect has slightly different mergers (e.g. BATH merged with TRAP instead of PALM), you might have to modify the system slightly and use alternative spellings for some words, but we’d still be able to understand each other. If you dialect has significantly different mergers, then my system may not be suitable for your dialect. I expect that nearly all non-rhotic dialects of English would — with minor adjustments — find it workable.

Here’s my list of vowel spellings and the corresponding lexical sets:

a … STRUT
á … TRAP
ā … PALM/BATH/START
ǎ … NURSE [was ü in earlier drafts]
e … DRESS
ē … SQUARE
i … KIT
í … FLEECE
o … LOT/CLOTH
ō … THOUGHT/NORTH/FORCE
u … FOOT
ú … GOOSE
ai … PRICE
ao … MOUTH
ei … FACE
ia … NEAR
oi … CHOICE
ou … GOAT

In my old system. I chose spellings for vowels and diphthongs that closely mirror their pronunciations in Australian English (e.g. reserving certain symbols for front, central and back vowels respectively). In this new system, I’ve stuck more closely to traditional and familiar values that are not tied to a specific accent. That said, I’ve referred to accents I’m familiar with in order to make sure diacritics change vowel quality in reasonably consistent ways.

There is no symbol for schwa. To represent schwa, one should choose the vowel best suited to the role in the context (taking into account the pronunciation used when the word is overarticulated or sung, the pronunciation used in more conservative accents, the traditional spelling, the etymology, and so on). I do have one rule, though: to keep things simple, vowels that are frequently reduced to schwa should normally be represented with one of the basic five symbols a, e, i, o, u — no diacritics, no digraphs. For example, the re in reform contains the FLEECE vowel (í) when clearly articulated, but because it is often reduced to schwa, we compromise and use the KIT vowel symbol (i) instead.

(The indefinite article a would be spelt ei when there is a reason to emphasise it, but otherwise I favour a rather than e for several reasons. These include familiarity, maintaining the similarity between a & an, and avoiding confusion with the word air. Even the most consistent languages in the world have exceptions for some of their most common words. The word and maintains its diacritic because, although the vowel is often reduced in a sentence, it is always articulated when the word is spoken in isolation.)

Because the DRESS, KIT, LOT, CLOTH and FOOT vowels (also TRAP, but that’s unimportant here) never occur word-finally in English, you may omit the diacritics on ē, í, ō, ú when they occur as the final letter of a word (i.e. spell them e, i, o, u respectively).

A comment on my use of diacritics. Although I’ve tried to keep the spellings of phonemes reasonably familiar, I think this can be taken too far. A system based entirely on the most common correspondences between spelling and sound in English (say, komyoonikayshun for communication) risks being perceived as juvenile. I think diacritics are widely perceived as sophisticated, so may help counteract that effect. However, they do place an extra burden on handwriting and risk being confused with commas from the line above, so it pays not to overdo them. That’s why I’ve outlawed diacritics on reduced vowels, advised omitting most of them from word-final vowels, and made a point not to include them in digraphs.

— Extensions —

As an optional extra, here’s a suggestion for how my system might be extended to include stress marking:

  • Add a h or y between the nucleus and coda of the stressed syllable (aesthetically, I generally favour h after ao, u, and y after e, i). For example, communication without stress marking is komyúnikeishon. With stress marking, it becomes komyúhnikeiyshon.
  • To mark stress on a syllable that lacks a coda, represent the coda with an apostrophe. Without stress marking, ambiguity would be ámbigyúiti. With: ámbigyúh’iti.

This could be used routinely, or only when potential for confusion exists. Redundant stress marking might be used to differentiate between homophones.

(Note: I do not use apostrophes in other contexts, e.g. no apostrophes for common contractions or possession. Apostrophes and diacritics seem a little too fly-specky in conjunction.)

We might use etymological spellings as well as redundant stress marking to differentiate between some homophones. Perhaps dhe for there, dhēy for their, and dheia for they’re, for example. If a system such as this were actually used, the community would soon develop some conventions.

— Postscript —

I’d like to end by reiterating what I said at the beginning: that this is not a serious proposal for an English spelling reform, but is intended as entertainment. Please feel free to use the comments section appropriately as a playground.

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