### Unintentional Haiku Spoken in a Courtroom 241 Years Ago

Posted by Angela Brett in Haiku Detector on September 1, 2014

When I discovered that the court proceedings of the Old Bailey were available online, naturally I had to see whether they contained any haiku. The archive is too huge to put into Haiku Detector all at once, so I just checked the ‘on this day in…’ link whenever I had time. The most haiku-rich I’ve seen so far was from a wounding case on 8 September 1773, which, now that I think about it, should not have appeared as an ‘on this day…’ link yet. I had to clean up the text a little first, to remove all the Q.s and speakers’ names. Here are some of the 55 haiku that were left.

These ones sound like some kind of metaphor for the fiddly final steps towards achieving goals, and the monsters that might demotivate us from climbing toward those goals, but which are secretly part of ourselves:

How far is it from

the upper step of the stairs

to the door itself?

Upon the landing.

Was the door within view of

you at that time? Yes.

The General must

have seen you coming up two

or three steps at least?

How far had you got

up stairs before you saw Hyde?

Did you hear Hyde’s voice?

Who else was with you

there? I cannot remember

any one but me.

Where did you wait while

Hyde went into the house? At

the top of the street.

The world’s simplest riddle:

Yes. Where did you go

when you came into the house?

Into the entry.

And some more intriguing questions:

After Lee struck me:

the knife dropped upon the ground.

Was it by a blow?

Had he no blow with

the butt end of a pistol?

Not that I know of.

You say you knew the

General very well; do

you think he knew you?

When you came back what

part of the family did

you find below stairs?

In what condition

was the door when he fired

the second pistol?

What did he tell him?

That a parcel of fellows

were below with sticks.

Did you observe the

hole in the door case that was

made by the pistol?

Did you look through the

door to see the direction

the ball had taken?

Was the General

upon his legs or not? He

was upon his legs.

Some which sound like bloody massacres until you get to the last line:

I believe this is

the knife you was cutting the

bread and butter with.

Was James in the room

with you while you was cutting

the bread and butter?

Finally, a few which sound a bit dirty (or so I am told) if you have that kind of mind:

### Forms and Formulae: Not A Number

Posted by Angela Brett in Forms and Formulae on August 30, 2014

*This is the fifth 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 installment’s mathematics article is entitled ‘From Numbers to Number Systems’ and the poetic form is allegory, making this the third poetic form in a row that isn’t actually a poem.*

A long time ago in Greece, there was a community of numbers where everybody lived as one, or two, or three. They were not all equal, because each was unique, but they were all numbers, and that’s what counted. They were the true numbers, and they lived alongside the false, or negative, numbers.

Then One day, which was the day when the number One was celebrated, One Seventh came along. The other numbers looked at it with pity.

“You poor, broken thing,” they said. But the seventh didn’t feel broken.

“I’m not broken. I’m a number, just like you!” said One Seventh.

Seven looked at One Seventh with trepidation. “I don’t think it’s safe to be around a part of seven. What if it wants to take more of my parts?”

Three agreed. “It’s just not wholesome.”

One Seventh pointed to its numerator. “Is this not a one, like the number of the day? How can I not be a number when my very numerator is the purest number of all?”

One was flattered by the description, and in the spirit of the celebration, declared, “One must not only celebrate Oneself, but also display kindness to all those around One. I declare One Seventh to be a number, along with all little Ones like it!” After that, the other numbers were largely kind to the unit fractions, and the fractions always reciprocated.

The next day, Two Fifths came along. Emboldened by the success of One Seventh, Two Fifths said, “I’m a number too! Can I join the celebration?”

Two, whose day it was, said, “But you’re just One Fifth plus One Fifth. It’s just not proper to be going around as if you’re a single number. Split into unit fractions before you scare the little Ones!”

But Two Fifths persisted. “What are you,” it said to Two, “if not One plus One?”

Two did not like the idea two bits, but it could not find a problem with the argument.

Five, who was never any good at acting composed, protested. “This is preposterous! Two, I always knew you weren’t quite as prime as us. Think about it. If we let these two fifths…”

“*This* two fifths,” corrected Two Fifths.

Five shot it an incalculable look. “If we let these two fifths act like a whole number, next we’ll have matrices, or lengths, or linear graphs wanting to be numbers. It’s a steep gradient!”

“That’s not true!” said Two Fifths. “In other cultures I am a perfectly acceptable number. In Mesopotamia, nobody thinks twice about my being a number, but they would never allow One Seventh. It’s all a matter of culture! And graphs are not numbers there either, so you needn’t worry about that.”

Two was divided by Five’s argument. It worried about diluting the number system, of course, but it was aware that even it could have been excluded from the primes using such an argument. Having always felt like an outsider itself, it had pity on Two Fifths, and declared the fraction and others like it to be numbers.

The next day, The Square Root of Two, who could not be expressed as a fraction, decided to join the numbers. Three said, “Don’t be absurd. You’re not really the square root of two; only square numbers have square roots. You’re just a fraction who’s confused. You look like about one and a hundred and sixty nine four hundred and eighths, to me.”

But the square root was resolute. “Look,” it said, holding up a square. “If we say the sides have length one, then the diagonal has length the square root of two. There is no way we can find a unit that can measure both of them as whole numbers. I can prove it to you!” And The Square Root of Two proved it.

“Okay,” said Three. “You’ve shown that the diagonal can’t be measured with the same unit as the sides. But they’re just lengths, not numbers. All you’ve done is show that not all lengths can be measured with numbers. The numbers are not going to be happy about this, you know.”

“But I am a number! I am the number which can measure that diagonal!”

“That’s just irrational. Lengths are not numbers. Either you’re a number, in which case you should show yourself as a fraction instead of wearing that radical outfit, or you’re a length, or a ratio of lengths, and you should go back where you belength. Make up your mind.”

“I told you this would happen!” said Five. “I told you lengths would be next!”

So the Square Root of Two skulked back to geometry, and commiserated, but did not commensurate, with the ratio of a circumference to a diameter.

Meanwhile, Two Fifths told all its new number friends about its adventures in Babylon, and the sexy sexagesimal numbers there. Before long, it became fashionable for numbers to represent themselves using decimal places instead of fractions. Some of them had to use zeros to make sure their digits hung in the right places.

Zero saw its chance, and claimed its right to be considered a number.

“But you’re not a number!” said Four. “You’re just a placeholder that the fractions use when they’re dressing up in their costumes for their unwholesome sexagesimal parties.” Four looked down its slope at a nearby decimal.

“But if I add myself to you, is there not equality? I should be treated the same as you.”

“But,” said One, “numbers have to be able to multiply. If you multiply you only get yourself. Only multiplying with me should do that! I’m the Unit around here, not you.”

“You’re destroying the family Unit!” shouted Five, in defense of its onely other divisor.

“I can’t even tell whether you’re true or false!” cried One Seventh, nonplussed.

So Zero went back to dutifully holding places, quietly adding itself to everyone and everytwo it met, until they were all convinced it held a place in society.

On the Seventh day, which was the day when One Seventh’s acceptance as a number was celebrated, they rested.

On the Tenth day, which was the day when The Tenth was celebrated, The Tenth returned from a vacation in Flanders and declared, “There are no absurd, irrational, irregular, inexplicable, or surd numbers!”

Five and Three cheered, and made obtuse gestures at The Square Root of Two and its friends. “You see? You’re not numbers.”

“All numbers are squares, cubes, fourth powers, and so on. The roots are just numbers. Quantities, magnitudes, ratios… they are all just numbers like us. We can all fit along the same line.”

Five and Three looked at each other in primal disgust. “I’m not a point on a line! I’m a number! A real number!” Five shouted.

“Real numbers,” countered The Tenth, “include everyone, and everyfraction, and everylength in between.”

The Square Root of Two led its friends into their places between the other numbers, and they celebrated with unlimited sines, cosines, and logarithms. Some of the stuffier primes and fractions protested, but they backed down when they realised just how many of these strange new numbers there were.

But even as The Tenth spoke, it knew that not everything it said was true. After all, false numbers were not the square of anything, even though it had seen them act like they were in some delightful formulae.

At Length, which was the day when the acceptance of lengths as numbers was celebrated, somereal wondered what would happen if false numbers were squares of something too. It imagined a new kind of radical, like those the square roots wore, but for false numbers. It imagined a world where every polynomial equation had roots, be they real, false, or imaginary. These were clearly not like all the other numbers The Tenth had listed.

Soon after, the imaginary numbers came out of hiding. “We do exist!” they said. “And we can add and subtract and multiply and divide just like you!”

The other numbers were wary, for they could not work out where the imaginaries fit amongst them. They could not even tell who was bigger. Five was disgusted that such numbers had been secretly adding themselves to real numbers all along.

The real numbers were nonetheless intrigued by and slightly envious of these exotic creatures, and despite having become accustomed to all having equal status as numbers, sought new ways to distinguish themselves from the crowd. The whole numbers had never quite got over the feeling of being generally nicer than the other numbers, so they used the new trend to vaunt their natural wholesomeness. The ratio of a circumference to a diameter, who had taken on the name Pi, discovered that in addition to not being expressible as a fraction, it was so much more interesting than The Square Root of Two that it couldn’t even be expressed in such roots. It called itself ‘transcendental’, and had quite some cachet until most of its admirers realised that they had the same property.

Finally they discovered that instead of trying to organise everynum into a line, they could arrange themselves in two dimensions, with the imaginaries along one axis and the reals along the other, and the vast plane in between filled with complex combinations of both.

Some of the more progressive numbers were so excited by this system that they tried to find new numbers that they could arrange into a three-dimensional volume, but they couldn’t find any. However, during their search they found things called quaternions, which lived in a fourth dimension.

An excited transcendental, whose name is too long to write here, brought a subgroup of quaternions in front of the crowd and announced, “I have travelled to the fourth dimension, and found numbers there just like us. We are not alone!”

Five kept its fury pent up this time, but Four Sevenths called out, “They are not numbers like us. I have seen how they multiply. When two quaternions multiply, they can give different results depending on which comes first!”

The numbers clattered their numerals in shock, and a great amount of whispering about unlikeabel multiplication practices ensued.

A complex transcendental sneered, “And what were you doing watching them multiply, eh?”

“Oh, get real!” retorted Four Sevenths, crudely conveying what the transcendental should do with its complex conjugate.

The pair fought, and disorder spread throughout the dimensions. Some sets of numbers sneaked off into the fields to form their own self-contained communities, sick of the controversy surrounding being or not being numbers. As they did, they found still other communities which functioned much like theirs, and some were communities of functions themselves. Indeed, even matrices and graphs formed structures which the enlightened subgroups found familiar, though rather than trying to be accepted as numbers, these groups took pride in having their own identities. The p-adics were adamant that they were numbers, but did not care to join the rest of the real or complex numbers. The octonions did not associate themselves with such labels, going about their operations however it worked for them, and consenting to be called numbers only when it was useful to act as such.

When peace finally settled, there were more groups of objects than there had been numbers, and still more came about when those groups interacted with each other. Most no longer cared about being called numbers, and simply communicated which rules they followed before participating in a given system. And if the requisite system turned out not to exist yet, well, it just had to be invented.

∎

Turning this particular article into an allegory did not take much work. It almost seemed like one already, when I read it in that frame of mind. There are a few direct quotes in the story. The Tenth’s proclamations come from The Tenth, in which Simon Stevin introduced decimal notation to Europe. The very last line of the story is paraphrased from the last line of the article. All I really did was rephrase it as a story from the perspective of the numbers, and add in far too many mathematical puns of greatly varying levels of subtlety.

I’m sorry to anyone with ordinal linguistic personification who thinks I’ve given the wrong personalities to the numbers. Also, in case anyone was wondering, the Greek numeral for four does have a slope.

The next Forms and Formulae will be an anecdote about geometry.

### Forms and Formulae: Self-Avoiding Walk

Posted by Angela Brett in Forms and Formulae on August 14, 2014

This is the fourth 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 post’s mathematics article is entitled ‘**The General Goals of Mathematical Research**‘ and the poetic form is **alba**, which is a kind of song; I **recorded it **^{[direct mp3 link]} using my robot choir and some newfound musical knowledge, and there are many notes on that after the lyrics below. Here are some extracts from the article on the alba, explaining the features that I ended up using:

A dawn song about adulterous love, expressing one or both lovers’ regret over the coming of dawn after a night of love. A third voice, a watchman, may announce the coming of dawn and the need for the lovers to separate. An Occitan alba may contain a dialogue (or serial monologues) between lover and beloved or a lover and the watchman or a combination of monologue with a brief narrative intro.

The alba has no fixed metrical form, but in Occitan each stanza usually ends with a refrain that contains the word

alba.

…the arrival of dawn signaled by light and bird’s song…

The watchman plays an important role as mediator between the two symbolic worlds of night (illicit love in an enclosed space) and day (courtly society,

lauzengiersor evil gossips or enemies of love)

I based the song on section 8.3 of the article, entitled ‘Illegal Calculations‘. In retrospect, using the word *alba* in each refrain (are these even refrains?) doesn’t make much sense, since I’m not writing in Occitan, and the casual listener will not know that *alba* means ‘dawn’ in Occitan. But hey, it kind of rhymes with the start of ‘self-avoiding walk‘. How can I not rhyme an obscure foreign word with an obscure mathematical concept?

**Introduction:**

Mathematicians struggle even today to learn about the average distance between the endpoints of a self-avoiding walk. French physicist Pierre-Gilles de Gennes found answers by transforming the problem into a question about something called the n-vector model when the n is zero. But since this implies vectors with zero dimensions, mathematicians reject the approach as non-rigorous. Here we find that zero waking up next to its cherished n-vector model after a night of illicit osculation.

**Zero:**

I am just a zero; I am hardly worth a mention.

I null your vector model figure, discarding your dimension,

and every night I’m here with you I fear the break of day,

when day breaks our veneer of proof, and we must go away.

Here by your side

till alba warns the clock.

Fear’s why I hide

in a self-avoiding walk.

**N-vector model:**

Let the transformations of De Gennes show your place.

Never let them say we’re a degenerate case.

When I’m plus-two-n there’s just too many ways to move,

But you’re my sweetest nothing and we’ve got nothing to prove.

Here by your side

till alba warms the clock.

Fear can’t divide;

it’s a self-avoiding walk.

**Watchman:**

The sun has come; your jig is up. It’s time for peer review.

You think your secret union has engendered something new.

You thought you would both find a proof, but is it you’re confusing

The sorta almost kinda-truths the physicists are using?

That’s not rigorous,

says alba’s voice in shock.

All but meaningless

to the self-avoiding walk.

**Zero and N-vector model together:**

If you say that our results don’t matter,

then go straight to find a better path.

For as long as you insult our data,

Is it wrong to say you’re really math?

Hey there, Rigorous

at alba poised in shock,

you are just like us,

in a self-avoiding walk.

∎

All voices are built-in Mac text-to-speech voices, some singing thanks to my robot choir (a program I wrote to make the Mac sing the tunes and lyrics I enter, which still needs a lot of work to be ready for anyone else to use.) Older voices tend to sound better when singing than the newer ones, and many new voices don’t respond to the singing commands at all, particularly those with non-US accents. So for the introduction I took the opportunity to use a couple of those non-US voices. These are the voices used:

**Introduction:** Tessa (South African English) and, since I also can’t fine-tune Tessa’s pronunciation of ‘Pierre-Gilles de Genne’, Virginie (French from France)

**Zero:** Junior

**N-vector Model:** Kathy

**Watchman:** Trinoids

Most of the bird noises come from the end of Jonathan Coulton’s ‘Blue Sunny Day‘, and I can use them because they’re either Creative Commons licensed or owned by the birds. The two peacock noises are from a recording by junglebunny. Free Birds!

As I mentioned, I’ve been learning about songwriting from John Anealio, and since the Forms and Formulae project sometimes requires me to write songs, I’m putting the new knowledge into practice sooner than I expected. This song uses several musical things I’ve never tried before, which is quite exciting, but it also means I probably didn’t do them very well, because there’s only so much I can learn in a couple of months of half-hour weekly lessons. I welcome friendly criticism and advice. The new things are: Read the rest of this entry »

### Misinterpreting Douglas Adams: Digital watches were a pretty neat idea.

Posted by Angela Brett in Culture on August 3, 2014

My first watch was digital. I was probably nine or ten, and the watch was a black Casio with a dashed line around the face in alternating green and blue. My brother and I would race to find each other whenever we noticed the hour was about to change, so that we could watch the watch digits all change at once. Needless to say, the changes from 9:59:59 to 10:00:00 and 12:59:59 to 1:00:00 were especially thrilling^{[⁉︎]}.

I’d learnt how to read an analogue clock, of course, but not fluently. To me, reading an analogue clock was akin to reading Roman numerals: a quirky, difficult system from long ago. Some analogue clocks even had the hours *in* Roman numerals. Some had no numbers at all. Some such watches only seemed to exist to give men a socially acceptable way to wear bracelets. Telling time was clearly not a priority.

So when I read in the Hitchhikers’ Guide to the Galaxy that humans were “so amazingly primitive that they still think digital watches are a pretty neat idea,” I naturally assumed it was because intelligent life forms had invented them so long ago that digital watches had about as much chance of being described as a ‘neat idea’ as the wheel. Digital watches are too simple an invention for anyone to find interesting. These days, almost everything has a digital clock built in, so the most important thing about a digital watch is a strong strap to keep it conveniently on the wrist.

A few digital watches and a grudge against fragile watch straps and lost pins later, I moved to Switzerland, and when my watch strap broke or fell off I felt obliged to check out some of the famous Swiss watches. I was baffled by the evidence that not only did humans still think digital watches were a pretty neat idea, they also still thought analogue ones were. The only Swiss digital watches with good straps I could find had skeuomorphic round faces, or lacked such basic features as seconds, dates, or a light. I get it: the Swiss are proud of how precise they can be with tiny gears. But it’s the third millennium; get with the timepieces!

As Swiss innovations go, I prefer milk chocolate and Velcro. I found a Casio dealer and bought a solar-powered, waterproof, digital watch that synchronises daily with an atomic clock using radio waves and has a well-attached metal strap. It will stay on my wrist and display precisely the right time in plain digits, indefinitely with no intervention whatsoever, for less than the price of a piece of Swiss jewellery that doesn’t even have numbers on it. A fall onto concrete gave it some sparkly cracks in one corner, but it is still waterproof and functional many years and no battery changes or time adjustments later.

Unhappy with the hypothesis that most of the human race was more concerned with adding respectability to their diamond bracelets than with locating themselves in spacetime, I had to eventually accept that there was something people liked about analogue watches. Just as there must be something great about shoelaces that keeps Earthbound people using them even after the invention of Velcro, and even though Back to the Future fans know that by 2015 we shouldn’t still be tying them.

The thought crept up on me that maybe Douglas Adams didn’t like digital watches at all. Maybe he didn’t think they were ever a pretty neat idea. I thought about this for a few years, gradually becoming less and less sure that my initial interpretation was the correct one. Eventually, I looked it up:

So there you have it. Douglas Adams liked pie charts. I like pie charts too, but after the first glance I will look for the labels with exact percentages, and be frustrated if they aren’t there. For me, a word can be worth a thousand pictures, and a number can be worth a poorly-defined number of words.

As he says, digital watches have improved since then. I don’t need to put down my suitcase to press a button on my watch, unless it’s either dark and I need to turn the watch light on, or it’s recently been dark and the watch turned off its display to save power. In fact, my suitcase has four wheels (wheels! Now, aren’t they a neat idea?) so I never have to pick it up to begin with; I just give it a push occasionally while I stroll along, reading the time like a frood.

### Reader participation alert:

Did you interpret the statement about digital watches the same way I did? If not, how did you interpret it, and how did it mesh with your own opinion on digital watches?

^{[⁉︎]} _{If you think you’ve grown out of such primitive excitement, try watching the hour change on this clock made of planks of wood and rearranged manually by construction workers. The website only delivers one image at a time, now, so you’d have to refresh a lot to get a video effect there, but they sell an iOS app which will show you video, the Lite version of which has the transition from 9:59 to 10:00.}

∎

### The First Attack

Posted by Angela Brett in The Afterlife on July 16, 2014

In one of the workshops I went to before the official start of the 13th International Conference on the Short Story in English, we were given four pages of text from various sources (see if you can recognise them!) and instructed to cut each page into four pieces, mix them up, lay them out on a table and note down any interesting phrases we found by aligning lines from different pieces of paper. We were free to slightly alter the sentences so they’d make sense. What I ended up with rather amused me, so I’ll post it here, as a sort of found poetry:

The first attack, where ignorant armies clash

Where the sea meets the shadow of the moon of death

The thing they would not stand was back, and back, and fling

Stand together to win the war against steel, but they cannot dent the steel.

A great people has been moved to naked shingles of the world

The President agreed, in the white immunity, “I fear no evil, for I implemented our government’s. Tonight, I ask for your prayers for all the three-shilling tea, and the best worlds have been shattered.”

I was particularly amused by the two chance juxtapositions that led to ‘in the white immunity’ and ‘I fear no evil, for I implemented our government’s’. So far at the conference I’ve met all sorts of interesting people and learnt many things (it is strange to see a partially-academic conference that has nothing whatsoever to do with particle physics) and heard many stories. I can’t say much about them now, though, as I’d like to get a half-decent amount of sleep before I read a story and introduce a few others at the conference tomorrow. I’m too tired to even read the entry on aleatory poetics in the Princeton Encyclopedia of Poetry and Poetics.

### Unintentional Haiku from New Scientist on The Unknown Universe

Posted by Angela Brett in Haiku Detector on July 14, 2014

I added some features to Haiku Detector so that it will find haiku made of more than one sentence, though I haven’t released the new version yet, since I’d like to release it on the Mac App store (even though it will probably still be free, at least at first) to see how that works, and to do that I’ll need an icon first. If you know anyone who can make Mac icons at a reasonable price, let me know. Meanwhile, New Scientist has released a new ‘collection‘ called The Unknown Universe, so why not mine it for haiku? The topics are ‘The early universe’, ‘The nature of reality’ (again), ‘The fabric of the cosmos’, ‘Dark materials’, ‘Black holes’, ‘Time’ (again) and ‘New directions’.

Let’s start at the very beginning, **the early universe**:

Can we really be

sure now that the universe

had a beginning?

At first, that seems like a terrible place to break the sentence to start a new line. But what if we pretend, until we get to the next line, that ‘Can we really be?’ is the whole question? Because that’s the real reason people wonder about the universe.

Now, here’s a multi-sentence one, which conveniently has a full sentence as the first line:

“We’re back to square one.”

Tegmark agrees: “Inflation

has destroyed itself.”

Deep. But what is this inflation thing, anyway?

Well, for one thing, it’s

not clear what actually

does the inflating.

Only then will we

truly know what kind of a

bang the big bang was.

“I am not convinced

the cyclic model is that

grander idea.”

But I think this is my favourite. There’s a monster at the end of this universe, and it’s making crosswords.

Cosmic monsters that

have survived into our times

also pose puzzles.

Now for **the nature of reality**:

“It pulls the rug out

from under us to prove a

theory right or wrong.”

Maybe we just need to look around us.

There is also down,

and, for that matter, left, right,

forwards and backwards.

Have we figured out what we’re looking for yet?

What it is, though, we

do not have the words or the

concepts to express.

Maybe E. L. James can help us figure it out:

“This experiment

allows us to see the shades

of grey in between.”

These ones are about **the fabric of the cosmos**:

“If you go by what

we observe, we don’t live in

space-time,” Smolin says.

We battle against

them each time we labour up

a hill or staircase.

“But where did the weak

primordial fields that seed the

dynamo come from?”

The same force that keeps

our feet on the ground also

shapes the universe.

I like this one for the contrast between the first and last lines:

The information-

loss paradox dissolves. Big

questions still remain.

Here are some of the ‘**dark materials**‘ haiku, about dark matter and dark energy:

The discovery of

dark matter would be the find

of the century.

I love how this contrasts ‘discovery of’ with ‘find of'; I didn’t notice that in prose form.

We still don’t know what

it is. It is everywhere

and we can’t see it.

That opens the door

to a dazzling array of

possibilities.

This chase through space will

be thrilling, but the quarry

may still elude us.

“It seems like a long

shot,” he says. But others are

being won over.

“But we don’t see a

fifth force within the solar

system,” says Burrage.

Though maybe the array of possibilities isn’t so dazzling after all:

It is limited

to perhaps three things. First, dark

energy pushes.

There are only two haiku about **black holes**, but one of them sounds like an idea Dan Brown might write about, probably without first reading New Scientist:

A BOMB made out of

a black hole is a rather

unsettling thought.

And the other sounds like it belongs on an episode of Doctor Who:

One of them will have

to blink if this paradox

is to be undone.

There are no more haiku on **time**, but luckily there were some in the last collection. I love this one about **new directions**, though:

Put that to many

physicists, and you will get

a grumpy response.

Ah, those physicists, always hopeful:

“Historically, these

things have usually led

somewhere,” says Davies.

They even have a solution to that ‘we still don’t know what it is’ problem from earlier:

“We don’t know what it

is so we have to give it

a name, a symbol.”

After that, it gets

a lot more speculative,

but here’s the best guess.

But they’re not *that* confident about it:

There are also good

reasons to think it is an

unwarranted one.

Paths to a theory

of everything will become

even more winding.

For instance, it could

decrease with time, or even

become negative.

Infinity makes things even more difficult:

INFINITY. It

is a concept that defies

imagination.

But it is at the

big bang that infinity

wreaks the most havoc.

The first line of the first infinity one reminds me of a CERN friend’s recipe for gravity: you just put ‘it’ in gravy.

### Forms and Formulae: The Numbers Are Not Enough

Posted by Angela Brett in Forms and Formulae, Uncategorized on July 12, 2014

This is the third 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 post’s mathematics article is entitled ‘Some Fundamental Mathematical Definitions’ and the poetic form is air, which is a kind of song.

This song covers the first few sections of the article, about the development of the various number sets (Natural numbers [which I learnt as not including zero], whole numbers [including zero], integers, rational numbers, real numbers, and complex numbers) and finally a little abstract algebra. I’ve made a recording of it ^{[direct mp3 link]} using my robot choir and some instruments in GarageBand. I didn’t follow all the suggestions relating to airs, but one hallmark of an air is ‘illustrative musical devices highlighting specific words’, and I went overboard on that, illustrating each set using the background music. Airs are typically accompanied by a lute or other plucked instrument, but I used a piano instead, to highlight the word ‘Peano‘ in the first line.

[1 2 3]

You can play the Peano axioms.

Your successor will never fail.

But if you ain’t got nothing you ain’t got enough

so you start lower down the scale.

[0 1 2]

Well you’ve now got zero problems.

You can count on every fact.

You can add without an end, but exceed your subtrahend

or you’ll find you can’t subtract.

[-1 0 1]

So you add in the minus integers.

Zero gains another side.

You can add and take away, but not conquer all the way

’cause you can’t always divide.

[⅕,⅓, ¼]

Now your system is highly rational,

no division you can’t deal.

But no matter what you do, you can’t find the root of two

though you know that it must be real.

[ɸ, e, π]

So you fill all the gaps with irrationals.

You have a solid number line.

Solve absurdities at will but you’re out of square roots still

when you start with a minus sign.

[1+⅕i]

So you use your imagination.

You take the square of your mind’s i.

Your calculations never stall, but you wonder if that’s all

that this complex plane can fly.

[triangles, snares, cats]

The operations work on all numbers,

but is that all they can do?

They apply to other things; now you’ve groups and fields and rings

to apply that structure to.

∎

This took longer than my last Forms and Formulae, due to the recording. I made several improvements to my robot choir (an app I wrote one weekend to get my Mac to sing for me) including fixing a silly bug which had thrown the timing of my previous recordings off. I’ve also been taking music lessons over Skype with John Anealio, and I used a few of the things I learnt for this; if you know a bit of music theory you might notice a few music theory puns in there.

It’s not especially funny overall, but I mentioned when I called into Dementia Radio last night that I would submit it to the FuMP Sideshow, so I will. [Edit: and here it is!] Another thing that came up were these Tom Lehrer songs about mathematics, which the host was not aware of. They were some of the first Tom Lehrer songs I heard, and definitely worth a listen if you like Tom Lehrer, maths, or both. I found them in 2005 while looking to replace some pirated Tom Lehrer songs I’d accidentally deleted before listening to them (I did eventually buy all of Tom Lehrer’s albums) and in that same search I came across the MASSIVE database of maths and science songs, which led me to Jonathan Coulton and so many other musicians and friends.

One of those other musicians was Monty Harper, and the first tune I came up with was very similar to the verses of his Silly Song. I changed some parts to make it less similar, but mostly I just made it more repetitive and annoying. Dammit, Jim, I’m a poet, not a musician.

The article in the Princeton Companion to Mathematics was actually very long, and I haven’t finished reading it yet. Assuming I do get to the next article instead of writing something about the latter parts of this one, the next Forms and Formulae will be an alba (a dawn song about adulterous love!) about the goals of mathematical research. That should be fun. It will probably take a while, since it’s another song. Also, I will be busy next week at the 13th International Conference on the Short Story in English. I will be reading a story on the Thursday afternoon; probably a slightly revised version of Valet de cœur.

### Forms and Formulae: Linguistics → Mathematics

Posted by Angela Brett in Forms and Formulae, Uncategorized on June 26, 2014

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.

**L**inguistics is mathematic**s**.

‘**I**s’ it? Well, that ‘is’ a classi**c**.

**N**ow which ‘is’ is that ‘is’ that you and **I**

**G**rammatically understand… wai**t**!

**U**nderstand, or understands? It all depends on how that ‘and’ treats dat**a**:

**I** understand ∧ you understand, or you+I is? Are? A**m**?

**S**ome singular object that understands ambiguous copula**e**

**T**hat may~equivalence relations, ambivalent notations for functions, adjunctions, or ∈ life ∪ deat**h**

**I** ‘am’ and i ‘is’, in a nonempty se**t**?

**C**ogito, ergo ∀ subjects Ɣ ∈ {sums, numbers, dynamics, …} Ɣ has Grammar s.t. Meaning(s)=Meaning(t)⇔s=t ∀ symbols s,t in Grammar sub gamm**a**.

**S**o, 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 demonstrandu**m**.

∎

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:

- Nothing is better than lifelong happiness.
- But a cheese sandwich is better than nothing.
- 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

Posted by Angela Brett in Publishing on June 25, 2014

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))

Posted by Angela Brett in Forms and Formulae, Uncategorized on June 19, 2014

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.

**A**xioms are how you ask ‘what if'; just pick some — you decide.

**B**reak it down and every branch of math(s) depends on these.

**C**alculus will help you count the branches that you can’t divide,

**D**ifferentiating the conditions at the boundaries.

**E**lements of Euclid was a textbook for millennia.

**F**unctions follow formulae to map domain to range.

**G**ödel showed some true things can’t be proven, but still many are,

**H**eld without theology as truths that never change.

**I**nconsistent axioms will prove all and its opposite,

**J**eopardising hopes the formal system will be sending forward

**K**nowledge for deriving knowledge-prime or knowledge-composite.

**L**ogic’s only limits are the ones that something’s tending toward.

**M**anifold(s) are ways to bring such limits to geometry.

**N**umerous are non-numeric methods that we use.

**O**ften are two manifolds the same, up to isometry,

**P**roving that(,) there’s gobs of generality to lose.

**Q**uod Erat Demonstrandum quoth inerrant understander,

**R**igorously rational and rooted in the real,

**S**ymbol-shuffling spanning such solution sets with candor,

**T**heorem after theorem or conjecture from ideal.

**U**niversal sets have mathematicians quite inside themselves;

**V**ector spaces set a basis they can build upon.

**W**olfram’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.

**Z**eno cuts each line in half so drawing it is undefined.

**Alpha**bet 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.

**Pi** squares circles’ radii.

**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.

**Omega**hd, 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.

Now you know your ABC(-Omega-Aleph-NOP)

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.