# Archive for category Uncategorized

### 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.

### 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.

### I have not seen Star Wars, so I wrote some poetry about it.

I have not seen much of the original Star Wars trilogy, unless I saw it when I was too young to remember anything. I was dragged along to Episode 1: The Phantom Menace in the theatre 13 years ago, forced to watch the trilogy back-to-back starting at 2a.m. in around the same time period (I fell asleep before taking much in, but not before the guy who was forcing me to watch it did) and watched as much as I could stand of the Holiday Special with Rifftrax starting at a similar hour (I gave up before the end, but not before Wil Wheaton did.) I played a fair bit of the Episode 1 Racer game on the Nintendo 64 back in the day. Almost everything else I know about Star Wars, I learnt from songs and internet memes. I know quite a lot of factlets from these sources, but I have no idea how they fit together. This Star Wars Day, I had the option of watching the original Star Wars trilogy in the CERN Council Chamber, but I was hesitant to lose my Star Wars virginity when I was one of so few people my age who still knew what it was like not to know the plot. It seemed like that would be wasted if I just saw it. I asked Twitter what to do, and the majority said to write ill-informed poetry about Star Wars before seeing the movies. One suggested haiku. So here’s a haiku, for starters:

“Come to the dark side.”

“Why? You’re not the boss of me.”

The person who suggested writing haiku wanted me to give a title for it, but I can’t decide on one. Maybe something like ‘Star Family Feud’ or ‘Daddy knows best’ or ‘Zo Vader, zo zoon’ (which is Dutch for ‘Like father, like son’.) or ‘Van Vader op Zoon’ (‘From father to son’) Any ideas?

Here is a poem containing most of the things I know about Star Wars that I could think of in the 10 hours or so since I came up with the idea. It amuses me, mainly because it rhymes, but it will probably amuse you more, since you know exactly how wrong it is. I don’t mind if you laugh with me or just at me. I think I’ll just call this one ‘I have not seen Star Wars, so I wrote some poetry about it.’

Long ago, in a galaxy far, far away,
there was light, there was dark, there were no shades of gray.
And a war was beginning, and stars were being made,
though I don’t know their names or the roles that they played.
I know some were ewoks, Storm Troopers and wookiees
And Jedi Knights, padawans, masters and rookies,
but Einstein couldn’t name them, so don’t expect me to.

There were Chewie, and Yoda (the OSV talker)
Han Solo, and Leia, of course, Luke Skywalker.
There were Pod Racers, Falcons, and starships deluxe
and cruisers, and Land Speeders (that and five bucks
will get you a Death Star; it looks like a moon
but it’s some kind of space station dealing out doom.
You would think it would wipe out the good guys, but nup!
For some reason, this one’s a cinch to blow up.)

I digress. There’s a thing called the Force Luke must use,
for the good side or bad? He’s the one who must choose.
(Side note: midi-chlorians, what the Force goes on
are Force mitochondria, some kind of boson.)
So may it be with you, it’s stronger in this
one, whose lack of faith hints that there’s something amiss,
but I think Obi-Wan puts him on the right track.
(That’s a guess. I don’t know who he is. Don’t attack!)

I’m a little unclear how the plot goes from there,
but it’s not like I’m bumbling around unaware.
I know what a mind trick or lightsaber’s for
and I know that they’re not the droids I’m looking for.
If they sleep in a tauntaun, then someone won’t freeze
and for Palpatine’s sake, wookiee’s spelt with two ‘e’s.
And it’s Han that shot first, not… uh… Guido? No, Gweebo!
He couldn’t shoot first at a wounded gazebo.

his wardrobe’s all dark side, you don’t need to ask.
Well he tried to convince the young Luke to turn bad,
And the princess was somehow Luke Skywalker’s sister,
but nobody talked about how he once kissed ‘er.
He vanquished his father, who, looking quite gaunt,
while wheezing could still somehow scream ‘Do not want!’

The End (and I don’t care what anyone thinks;
this poem may suck, but it beats Jar Jar Binks.)

There are a few references to other things in there. OSV refers to Object Subject Verb, the word order Yoda tends to use. Wil Wheaton once traded his Death Star for a Land Speeder and five bucks, which is the only reason I know Land Speeders exist. Gazebos are very hard to wound, but they don’t attack much. And I know Darth Vader screamed ‘Nooooooo!’ rather than ‘do not want‘, but I’m not too sure when or why.

This is not part of the Writing Cards and Letters (have you noticed I’ve been ignoring the letters this time?) project. I’m still planning on publishing a nine of spades by Sunday noon. It will be short and sweet and sour.

May the Fourth be with you, if it still is in your time zone.

Edit: I still haven’t seen Star Wars, and I imperfectly recited this poem at the Open Mic night on JoCo Cruise Crazy 3.