# Archive for June, 2014

### Forms and Formulae: Linguistics → Mathematics

This is the second in a series called ‘Forms and Formulae‘ in which I write about articles in the Princeton Companion to Mathematics using poetic forms covered by articles in the Princeton Encyclopedia of Poetry and Poetics. This week’s mathematics article is entitled ‘The Language and Grammar of Mathematics’ and the poetic form is acrostic, which is a superset of last week’s form, the abecedarius.

I’ve already written plenty of apronyms about mathematics that could be considered acrostics, so for this I had to do something else. The following is a double acrostic about the language of mathematics — the first letter of each line spells ‘Linguistics’ and the last letter of each line, read upwards, spells ‘Mathematics’. The line lengths are highly irregular (just as the mapping from linguistics to mathematics can be), which makes that less impressive, but I tried to keep decent enough rhythm and rhyme that it sounds good when read aloud.

Linguistics is mathematics.
Is’ it? Well, that ‘is’ a classic.
Now which ‘is’ is that ‘is’ that you and I
Grammatically understand… wait!
Understand, or understands? It all depends on how that ‘and’ treats data:
I understand ∧ you understand, or you+I is? Are? Am?
Some singular object that understands ambiguous copulae
That may~equivalence relations, ambivalent notations for functions, adjunctions, or ∈ life ∪ death
I ‘am’ and i ‘is’, in a nonempty set?
Cogito, ergo ∀ subjects Ɣ ∈ {sums, numbers, dynamics, …} Ɣ has Grammar s.t. Meaning(s)=Meaning(t)⇔s=t ∀ symbols s,t in Grammar sub gamma.
So, let ‘is’ be a relation where no such equation’s imposed but the intersection of the sets of accepted bijections on the subjects’ grammar sets are nonempty we get (and I don’t have the proof yet to hand, um… It’s trivial, readers with wits understand’em) that linguistics is mathematics, quod erat demonstrandum.

This was a particularly interesting article for me, since I’m very interested in language and grammar in general. It goes into various symbols used in mathematics and talks about which parts of speech they are and how they compare to similar words or parts of speech in English. It turns out mathematics has no adjectives. I had several attempts at different acrostics, and when I figured out the first few lines of this one, I thought I’d move on to explaining a different section of the article every few lines. Then I was inspired to continue it at a time when I didn’t have the book handy, so it ended up focusing on just the first few parts with a nod to something mentioned in a later section. One nice thing I found in the article was:

1. Nothing is better than lifelong happiness.
2. But a cheese sandwich is better than nothing.
3. Therefore, a cheese sandwich is better than lifelong happiness.

Soon after, we get the haiku I found earlier:

For every person
P there exists a drink D
such that P likes D.

It’s really a fun book to read. Next week’s Forms and Formulae will be an air on some fundamental mathematical definitions, which should be interesting because I’m not certain I fully understand the requirements for an air. I may have to dust off the robot choir.

In other news, I got some copies of the They might not be giants poster printed locally, and they look great, even when accidentally printed at twice the intended size. The English pronoun poster is quite readable at about 42x42cm, which is a little less than the size it’s on Zazzle at.

### ‘They might not be giants’ Poster

A while ago I wrote a poem called ‘They might not be giants‘, about the famous phrase, ‘If I have seen further, it is by standing on the shoulders of giants.’ A while later, that poem was published in Offshoots 12, the 2013 anthology of the Geneva Writers’ Group.

Ever since writing it, I’ve been thinking about how great it would be to see a picture of the tower of dwarves described. I’ve also been thinking about which plural of ‘dwarf’ is best, and a couple of grammatical and typographical decisions I made regarding the poem, but mostly I’ve been thinking about the picture. Well, I finally commissioned Len Peralta to draw that picture for me! It is gorgeous.

It is also the real reason I set up a Zazzle store; you can buy it as an 11×17 poster featuring the poem. I’ll have some printed locally as well, so if anyone near Vienna wants one they can buy one directly from me. Maybe you’d like one for yourself, or an aspiring scientist, or an inspiring teacher, or a Len Peralta fan, or an Angela Brett fan (do they exist? Edit: there is one) or even a They Might Be Giants fan who wants their poster collection to cover all possibilities. I think it’s suitable for anyone who has walls. If you know anyone who doesn’t have walls who would like some, see if you can help them find a home.

I’ve always been fascinated by Len’s videos of himself drawing, so I paid a little extra to get this mesmerising speedpaint video, which doubles as a great way to get an idea of what the poster looks like close-up. Note that the final poster has the title of the poem on it, and a few other small changes to the text.

I still can’t watch it without squeeing. It took him 2 hours, 36 minutes, which is about how long it would take me to draw a stick figure version indistinguishable from a Christmas tree.

This is actually not the first time I’ve commissioned Len to draw something for me; he also drew the picture of Jonathan Coulton transforming into an internet superstar at the beginning of a video I made to celebrate Jonathan’s Thing A Week by summarising each song in the form of a ‘roses are red’ poem. He drew most of the rest of the art in the video, too, but that was done already as part of his Visual Thing A Week project, which is the reason I know he exists.

That’s all from me. Go have fun, and tune in tomorrow for the next exciting installment of Forms and Formulae.

### Forms and Formulae: Y Lines About X Letters of the Alphabets (an Abecedarius of Math(s))

This is the first in a series called ‘Forms and Formulae‘ in which I write about articles in the Princeton Companion to Mathematics using poetic forms covered by articles in the Princeton Encyclopedia of Poetry and Poetics, even though the Companion already contains plenty of poems. The first entry in the former is entitled ‘What is Mathematics About?’ and the first entry in the latter is abecedarius.

The following is an abecedarius of what mathematics is about — an ABC of mathematics, if you like. You can also try reading it along to  ’88 Lines About 44 Women’ (which you might be familiar with from The Brunching Shuttlecocks’ ‘88 Lines About 42 Presidents‘ or the great Luke Ski’s ‘88 Lines About 44 Simpsons‘) though the rhyme scheme is different. It only coincidentally has a similar meter, but once I saw it I decided to go along with it.

Axioms are how you ask ‘what if’; just pick some — you decide.
Break it down and every branch of math(s) depends on these.
Differentiating the conditions at the boundaries.

Elements of Euclid was a textbook for millennia.
Functions follow formulae to map domain to range.
Gödel showed some true things can’t be proven, but still many are,
Held without theology as truths that never change.

Inconsistent axioms will prove all and its opposite,
Jeopardising hopes the formal system will be sending forward
Knowledge for deriving knowledge-prime or knowledge-composite.
Logic’s only limits are the ones that something’s tending toward.

Manifold(s) are ways to bring such limits to geometry.
Numerous are non-numeric methods that we use.
Often are two manifolds the same, up to isometry,
Proving that(,) there’s gobs of generality to lose.

Quod Erat Demonstrandum quoth inerrant understander,
Rigorously rational and rooted in the real,
Symbol-shuffling spanning such solution sets with candor,
Theorem after theorem or conjecture from ideal.

Universal sets have mathematicians quite inside themselves;
Vector spaces set a basis they can build upon.
Wolfram’s Weisstein’s MathWorld’s website rivals books on many shelves.
X rules the domain that functions are dependent on.

Y‘s home on the range is the solution set that many seek.
Zeno cuts each line in half so drawing it is undefined.
Alphabet is insufficient;
Beta hurry onto Greek.
Gamma raises complex powers.
Delta changes Zeno’s mind.

Epsilon‘s so small that
Zeta covers the prime landscape sole.
Eta‘s very many things;
Theta‘s varied just by one
Iota in the calculus where
Kappa played a founding role.
Lambda has a calculus.
Mu (micron)’s small, but not-none.

Nu math(s) is Tom Lehrer’s nightmare.
Xi‘s that universal set.
Omicron‘s a small big-O.
Rho‘s a row (zeros-out) rank.
Sigma sum is all you get.
Tau is sometimes phi, 2pi.
Upsilon, we wonder, ‘Y?’

Phi‘s the golden ratio.
Chi-squared ballpark’s on the ball.
Psi‘s a polygammous one.
Omegahd, there is no end;
Aleph-null can yet extend;
Aleph one is still too small;
Beth one, too, still isn’t all;
Beth-two, one can yet transcend.

Gimel still can bring you some,
Daleth beats continuum.

Out you go to maybe see (oh, mathematicality!)
That math(s) is an infinity (for all things there exists a key!)
And cast it as a trinity (a singular plurality!)

When I decided to do this, I don’t think I realised how many Greek letters there were. In the time it would have taken to finish a normal abecedarius, I was only halfway there, and further motion seemed impossible. Luckily, Zeno was there to sympathise. I also didn’t realise any Hebrew letters after bet were used in mathematics. Apparently Cantor used gimel and daleth for yet bigger infinities. I hope to write a new Forms and Formulae each week, so the later forms had better not be this long. I didn’t always stick to things from the ‘What is Mathematics About’ article, or even that subject. However, I think I conformed to the abecedarius form fairly well; the abecedarius is often used for religious purposes, and I was able to work in that mathematics requires no faith (‘held without theology’) and extends beyond alpha and omega, and also that the differing ways of abbreviating the word in different countries (with or without ‘s’) makes it similar to the three-in-one Christian trinity.

### Pronoun Flowchart Update and Poster

It occurred to me that now that I have a Zazzle store, I could print posters of the inadvertently-Zork-themed English pronoun flowchart I made at the start of the year. The image I used for the background has no ‘noncommercial’ condition on the license, after all. So I fixed a typo, fixed the alignment of the text in the boxes, thickened the lines, nudged a few things into better positions, and before I knew it I was moving a whole lot of things around to get it into more of a square shape to make better use of the space and fit onto a standard poster size. I think the result looks much tidier, and what’s more, in the process of doing that I noticed I’d somehow forgotten to add an example sentence for the pronoun ‘he’.

Now it is available as a 24″x24″ poster. You can order it at a smaller size if you like, but I think the text would be quite small (though still readable) in that case. I’ve also made an updated pdf of it, so if you want you could print that as a poster instead, or just read it on your screen; I don’t mind. The background might look slightly different from the Zazzle version due to resolution issues, but it’s only a faint background image so it doesn’t matter that much. I have yet to try either option.

Zork-themed English Pronoun Flowchart by Angelastic
Browse more Grammar Posters at Zazzle

It still doesn’t include relative, possessive or interrogative pronouns. Picking a pronoun is complicated enough without them. It does include we, ourselves, us, they, themselves, them, he, she, himself, him, herself, her, I, itself, it, myself, me, oneself, one, yourself, yourselves, you, and advice on when to look up a more exotic gender-neutral pronoun or dialectal plural ‘you’. Most of these rules will be obvious to native English speakers, but if you like grammar or flowcharts it’s interesting to see them written explicitly, and the example sentences may be entertaining. It could also be useful to people or robots whose native language is not English.

As with the other poster, if I get enough money that Zazzle actually pays me, I will lend it on Kiva, since I currently have enough money from my day job to live on.

### Creative Output Posters and Postcards

Almost five years ago, I took a photo of the audio input and output ports of my then-new MacBook Pro, and edited it to have various things I’ve written and drawn streaming out of the output port, as a pun on the idea of ‘creative output’. I then renamed the blog to go with it, since the old title no longer encompassed everything I was doing. I said I might make posters of it some day, but all I did was use it on my contact cards. However, I recently decided to set up a Zazzle store so I can sell another thing I have in the works, so I’ve just made that picture available as a poster and postcards. The postcards are eligible for a 20% discount for a Father’s Day promotion Zazzle has going on, which I think ends some time today. [Edit: It turns out they pretty much always have some kind of discount that applies to certain things.]

Before putting it up for sale, I updated it. I added the Wordles from everything I’ve written since then, as well as various images from the Cantor Ternary Set Cantor Ternary Set, the arrow poems, and the Post-It decorations in my temporary apartment. I’ve added things to almost the entire output stream, but you might need help from Myopic Person to make some of them out amongst the general mess of output. Apart from that, I made a few cosmetic improvements using new features in a much more recent version of Acorn (which I’ve just noticed still isn’t the latest), which no longer crashes when dealing with a file that size. I also made use of the graphics tablet and fonts I’ve acquired in the mean time. I added the words ‘Creative Output’ and the URL of the blog, since the whole picture was based on that pun and may not have any artistic merit without it.

This is what the poster looks like:

The postcards show a bit more of the Mac at the top, due to the different aspect ratio.

For the poster I chose the ‘standard’ size with the closest aspect ratio to the original picture, since a standard size will make it cheaper for anyone who wants to order a framed version. The poster is 19″x13″, and at that size it should be about 210ppi; I can’t do much better than that since it was based on a 12 megapixel photo. This is higher than Zazzle recommends for a good-quality print, and it should be fine for a poster, but if you’re a real print aficionado who prefers higher ppi, you can choose the ‘extra small’ option in the Size menu.

I don’t need extra money at the moment, since I still have a day job (though I will be looking for a new one next year; does anybody need a programmer who knows some things about accelerating particles and also occasionally writes, studies linguistics, and doodles on photos?) and since the payments from Zazzle will go into my PayPal account anyway, I will lend them on Kiva until such time as I need them.

### Wordles: Just, like… know things, okay?

I realised that I never created a Wordle for the second run of Writing Cards and Letters, like I did for the first run. For that matter, I haven’t written a second joker for it either. But first things first. Here’s a Wordle for all the words used in the things I wrote for the second Writing Cards and Letters, not including diagrams, videos, or those speculative card games, but including the text of ISS vs. LHC that’s directly on the blog.

I usually look for related words that are coincidentally near each other. The big words don’t leap out to me as saying anything much, apart from ‘just know’, I guess, but I like the ‘much writing, one head’ which could even be continued as ‘much writing, one head, two HeartValet feel things.’ Is that how to get intense emotion into writing? Having two HeartValet implants instead of one? Then there’s the LHC baby and the time dealer. But which is true of my writing? Is it ‘Find story, keep.’ or ‘years lost’?

Anyway, I’ve written many other things since that first year of Writing Cards and Letters, some just because I felt like it, and some because of NaPoWriMo. Here’s the Wordle for all the poems I posted for NaPoWriMo, which I participated in for about half a month before realising I had a short story to write:

Gave one internet? Judged? Just like (better) things! Loud feminine? Masculine wrong? Awesome never? Doctor McFly?! Don’t be concerned by the large ‘die want’; the ‘die’ is mostly the German word. Or it’s a result of ‘clear verse, soul worse (perhaps.)’

Here’s the Wordle of the various things I’ve written and posted to my blog since the end of the first Writing Cards and Letters that didn’t fit into either project. I did not include the Mozartpuffreissnitten recipe, since that’s more of a blog post than a piece of writing, and again I didn’t include the text of things I made videos or audio recordings for in that time.

Well, this is interesting. Clearly I’m a CERN princess. Or a time chameleon; wouldn’t that be cool? A chameleon that has chronophore cells instead of chromatophore cells, so it can resemble (or presemble) any time? Eyes spread is just unreasonable, though. This one has a lot of names of real people in it, which probably came from my origin story.

I find it amusing that this one is all about a princess and the others are just, like, things. So I decided to see what the relative weights were when I put the text for all three things in one Wordle:

Just know. One time, like, love, okay? People, think! Die, baby dealer! Got thulium? Story, song, chlorine… really?! Life: Make Something. There are a lot of names in here, which is interesting considering each name is usually only used in one story. Is it a bad thing to refer to somebody by name often? I tend to get lost in stories where characters are referred to in too many different ways.

I may have to challenge myself to write something about the word combinations found in these, or write something that doesn’t contain any of my most common words.

### Recipe: Mozartpuffreisschnitten

In 2009 in Geneva, I made a pavlova for my birthday. In 2012 in Sweden, some friends made me a pancake cake. This year, in Vienna, I went to two concerts between the time my birthday started in New Zealand and the time it ended in Austria. When Sara Chicazul goes to a concert on her birthday, she makes cake, Nanaimo bars, cupcakes, or Nanaimo bar cupcakes, for the entire audience, so I decided I’d have to do the same. While I did help Sara with Nanaimo bar cupcakes before JoCo Cruise Crazy 4, I was a minion rather than an evil genius, so I don’t really have the expertise to make a lot of cupcakes myself. What’s more, I had a French exam the day of the first concert, so I didn’t have a lot of time. Instead, I made about the third simplest food that can be made with puffed rice (a.k.a. Rice Krispies, Rice Bubbles, Ricies.) I made Rice Krispies Treats (a.k.a. Rice Bubbles Squares, or some other combination of a word for puffed rice and either ‘treats’ or ‘squares’) with Austria’s famous (i.e. I’d never heard of them until a tour guide told us about them the first time I visited Austria) Mozartkugeln (a.k.a. Mozart balls, followed by sniggering) mixed in.

So here is the recipe for what I’m going to call Mozartpuffreisschnitten. Serves two concert audiences including performers (bigger than Viertel, smaller than the first JoCo Cruise Crazy, which the Nanaimo bars were made for) with enough left over for a peckish post-birthday girl.

• One 300g bag of marshmallows — I used a bag of white ones, but the ones pictured here are multicoloured because I took the picture of my spare pack after making them.
• One 170g bag of Mozartkugeln Minis.
• About six cups of puffed rice cereal. It turns out, going by my quick look in a few shops and the word of a few locals, that there is no such cereal available in Austria. Luckily, I had enough that I’d brought with me from Switzerland, but I had hoped to get some more to be sure, and was quite surprised by this lack. Probably any light cereal that isn’t too sweet would work. I saw several cereals that seemed like good candidates, but they were 30% honey, which seems like overkill when you’re adding 470g of candy. But hey, it’s your birthday, you’re allowed twice as much redundantly superfluous overkill as you want.
• A little bit of some kind of oil (probably optional.) I found a recipe online that said to use butter, but I didn’t have any, so I used sunflower oil. I don’t think the oil is really necessary anyway.
• Some non-stick baking paper.
• Cornflakes to garnish (optional.) I’d bought them as an emergency filler in case of insufficient puffed rice, and decided to stick them on for decoration and to reduce stickiness.

Pour the oil, marshmallows and Mozartkugeln into a pan, and put it on a medium heat.

The chocolate will melt first. It turns out there’s no solid, unmeltable centre in Mozart balls.

Soon the marshmallows will start to get gooey. Have fun mixing them with the melted chocolate.

Soon enough the marshmallows will be fairly smooth, and you can make streaky patterns in them with the chocolate. Take a note of how you feel at this moment: this is what it was like to create Jupiter.

But eventually you’ll have to say goodbye to Jupiter and say hello to smooth, uniform, light brown goo. Don’t worry, Zeno, you don’t have to say hello and goodbye every time the streakiness changes.

Turn off the heat and pour in the puffed rice, stopping to mix it in a couple of times. Add more if there still seems to be enough goo to hold it. You’d be surprised at how much can still be mixed in when it already looks fairly dry. Pour it all onto the baking paper such that it’s a few centimetres high. Or make it into a giant Mozart ball; I don’t care. Add cornflakes or whatever garnish you like that will stick on.

Once it’s cooled, cut it into squares, or rectangles, or smaller balls, so it’s easier for people to eat. Don’t worry about it too much; it’s easy to tear into smaller chunks with your hands, so if your concertgoers want smaller pieces they can have them.

Everybody who tried the ones I made said they liked them. Some had tried Rice Krispie treats in the USA and missed them. In my opinion, the finished product didn’t taste too much like Mozartkugeln, so if I did this again I’d use more of them. The only other time I’ve made Rice Krispie Treats, I added Sprüngli chocolat chaud grand cru and it made it really chocolatey. The classic recipe is just puffed rice and marshmallows, so of course it’s good with any amount of Mozartkugeln, including zero.

I almost forgot: the other thing that happened on my birthday was the song I wrote to sing with Worm Quartet went live on The FuMP sideshow.