Forms and Formulae: Self-Avoiding Walk


A picture of the Sun peeking over the spine of The Princeton Companion to Mathematics as it rests on top of The Princeton Encyclopedia of Poetry & PoeticsThis 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, lauzengiers or 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 »

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


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 Casio digital watch displaying Sunday, 3 August, at 13:37:59 daylight savings time, set against a backdrop of The Ultimate Hitchhikers' GuideA 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.

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The First Attack


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.

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Unintentional Haiku from New Scientist on The Unknown Universe


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.

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Forms and Formulae: The Numbers Are Not Enough


A picture of the Sun peeking over the spine of The Princeton Companion to Mathematics as it rests on top of The Princeton Encyclopedia of Poetry & PoeticsThis 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.

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Forms and Formulae: Linguistics → Mathematics


A picture of the Sun peeking over the spine of The Princeton Companion to Mathematics as it rests on top of The Princeton Encyclopedia of Poetry & PoeticsThis 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.

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‘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.

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


A picture of the Sun peeking over the spine of The Princeton Companion to Mathematics as it rests on top of The Princeton Encyclopedia of Poetry & PoeticsThis 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.
Calculus will help you count the branches that you can’t divide,
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.
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.
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.

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.

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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
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.

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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:

Poster preview

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.

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