Posts Tagged found haiku

Unintentional Haiku in New Scientist’s Medical Frontiers: The Movie


How else can you stare at an empty canvas and see a work of art?I’ve made a new version of Haiku Detector. The main changes are:

  • Performance improvements
  • Tweaks to which haiku are identified when punctuation is pronounced differently depending on line breaks and other factors (this includes a workaround for the ‘all numbers pronounced as zero’ bug I found in the speech synthesiser.) In my test data the list of haiku identified is better now.
  • Bug fixes.

To celebrate the new release, I fed in the text from the latest New Scientist ‘Collection’ issue, on medical frontiers. The funniest haiku arose when the last sentence of one article joined up with the headline and byline of the next. For example, this looks like the tagline of a movie about an underappreciated superhero, fighting to save anti-vaxxers from diseases of yore:

They will not thank you.
Dan Jones FIGHTING INFECTION
Small shot, big impact

After the opening credits, we see our hero Dan Jones in his lab, and the subtitle announcing his first challenge.

DRUG: Chlorotoxin
SOURCE: Deathstalker scorpion
CONDITION: Cancer

His superpowers come, of course, from vaccines:

Some vaccines seem to
provide us with a host of
extra benefits

But not everybody is happy with that:

Several groups have been
trying to develop drugs
that block these signals.

These groups spread propaganda:

Half an hour or
so later, you’ll feel a lot
better. Or will you?

They work around rules:

“Because we use cells,
not field-grown plants, we don’t come
under the same rules.”

And they target humanity by zapping the very microorganisms they’re made up of. Here’s a quote from the evil mastermind:

There are more cells in
your body than there are stars
in the galaxy.

These cells can then be
killed using a laser that
penetrates the skin.

And just when Dan thought he had the solution, the problems compounded to the point of suspension of disbelief, precipitating a crisis. The mastermind had cooked up her own microbial minions:

Those microbes can be
in the environment or
a vaccine syringe.

To make matters worse,
there is a shortage of new
antibiotics.

The sequel, which may or may not be a Doctor Who crossover, features a heroine who will live forever:

“Just endless.” Helen
Thomson REGENERATION
Let’s get physical

Yep, it’s definitely a Doctor Who crossover. Here’s a quote from that movie:

“I’m the doctor. I’m
going to tell you what your
feelings really mean.”

She discovered that time, and specifically time travel, is the best cure for a broken heart:

If we can’t fix hearts
with stem cells there might be an
even better way

As the animal
was slowly warmed, it began
to return to life.

But however clever the TARDIS is, there’s one thing Helen Thomson isn’t sure she can do:

But can we ever
turn the clock back to a world
without HIV?

It turned out, weirdly enough, that the answer was in making sure there was enough shelf space for one’s awards. So she went home to Britain to save the Officers of the British Empire:

On her return home,
she applied those lessons in
British hospitals.

So far, two patients
have had OBEs, but neither in
a room with a shelf…

While we’re making sequels, let’s revive an old favourite, which never had any sequels:

The matrix holds a
dazzling array of future
possibilities.

But what is the matrix?

Normally, matrix
is harvested from human
or pig cadavers.

I guess you have to see it for yourself.

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Another Haiku Detector Update, and Some Observations on Mac Speech Synthesis


Screenshot of Haiku Detector

I subjected Haiku Detector to some serious stress-testing with a 29MB text file (that’s 671481 sentences, containing 16810 haiku, of which some are intentional) a few days ago, and kept finding more things that needed fixing or could do with improvement. A few days in a nerdsniped daze later, I have a new version, and some interesting tidbits about the way Mac speech synthesis pronounces things. Here’s some of what I did:

  • Tweaked the user interface a bit, partly to improve responsiveness after 10000 or so haiku have been found.
  • Made the list of haiku stay scrolled to the bottom so you can see the new ones as they’re found.
  • Added a progress bar instead of the spinner that was there before.
  • Fixed a memory issue.
  • Changed a setting so it should work in Mac OS X 10.6, as I said here it would, but I didn’t have a 10.6 system to test it on, and it turns out it does not run on one. I think 10.7 (Lion) is the lowest version it will run on.
  • Added some example text on startup so that it’s easier to know what to do.
  • Made it a Developer ID signed application, because now that I have a bit more time to do Mac development (since I don’t have a day job; would you like to hire me?), it was worth signing up to the paid Mac Developer Program again. Once I get an icon for Haiku Detector, I’ll put it on the app store.
  • Fixed a few bugs and made a few other changes relating to how syllables are counted, which lines certain punctuation goes on, and which things are counted as haiku.

That last item is more difficult than you’d think, because the Mac speech synthesis engine (which I use to count syllables for Haiku Detector) is very clever, and pronounces words differently depending on context and punctuation. Going through words until the right number of syllables for a given line of the haiku are reached can produce different results depending on which punctuation you keep, and a sentence or group of sentences which is pronounced with 17 syllables as a whole might not have words in it which add up to 17 syllables, or it might, but only if you keep a given punctuation mark at the start of one line or the end of the previous. There are therefore many cases where the speech synthesis says the syllable count of each line is wrong but the sum of the words is correct, or vice versa, and I had to make some decisions on which of those to keep. I’ve made better decisions in this version than the last one, but I may well change things in the next version if it gives better results.

Here are some interesting examples of words which are pronounced differently depending on punctuation or context:

ooohh Pronounced with one syllable, as you would expect
ooohh. Pronounced with one syllable, as you would expect
ooohh.. Spelled out (Oh oh oh aitch aitch)
ooohh… Pronounced with one syllable, as you would expect
H H Pronounced aitch aitch
H H H Pronounced aitch aitch aitch
H H H H H H H H Pronounced aitch aitch aitch
Da-da-de-de-da Pronounced with five syllables, roughly as you would expect
Da-da-de-de-da- Pronounced dee-ay-dash-di-dash-di-dash-di-dash-di-dash. The dashes are pronounced for anything with hyphens in it that also ends in a hyphen, despite the fact that when splitting Da-da-de-de-da-de-da-de-da-de-da-de-da-da-de-da-da into a haiku, it’s correct punctuation to leave the hyphen at the end of the line:

Da-da-de-de-da-
de-da-de-da-de-da-de-
da-da-de-da-da

Though in a different context, where – is a minus sign, and meant to be pronounced, it might need to go at the start of the next line. Greater-than and less-than signs have the same ambiguity, as they are not pronounced when they surround a single word as in an html tag, but are if they are unmatched or surround multiple words separated by spaces. Incidentally, surrounding da-da in angle brackets causes the dash to be pronounced where it otherwise wouldn’t be.

U.S or u.s Pronounced you dot es (this way, domain names such as angelastic.com are pronounced correctly.)
U.S. or u.s. Pronounced you es
US Pronounced you es, unless in a capitalised sentence such as ‘TAKE US AWAY’, where it’s pronounced ‘us’

I also discovered what I’m pretty sure is a bug, and I’ve reported it to Apple. If two carriage returns (not newlines) are followed by any integer, then a dot, then a space, the number is pronounced ‘zero’ no matter what it is. You can try it with this file; download the file, open it in TextEdit, select the entire text of the file, then go to the Edit menu, Speech submenu, and choose ‘Start Speaking’. Quite a few haiku were missed or spuriously found due to that bug, but I happened to find it when trimming out harmless whitespace.

Apart from that bug, it’s all very clever. Note how even without the correct punctuation, it pronounces the ‘dr’s and ‘st’s in this sentence correctly:

the dr who lives on rodeo dr who is better than the dr I met on the st john’s st turnpike

However, it pronounces the second ‘st’ as ‘saint’ in the following:

the dr who lives on rodeo dr who is better than the dr I met in the st john’s st john

This is not just because it knows there is a saint called John; strangely enough, it also gets this one wrong:

the dr who lives on rodeo dr who is better than the dr I met in the st john’s st park

I could play with this all day, or all night, and indeed I have for the last couple of days, but now it’s your turn. Download the new Haiku Detector and paste your favourite novels, theses, holy texts or discussion threads into it.

If you don’t have a Mac, you’ll have to make do with a few more haiku from the New Scientist special issue on the brain which I mentioned in the last post:

Being a baby
is like paying attention
with most of our brain.

But that doesn’t mean
there isn’t a sex difference
in the brain,” he says.

They may even be
a different kind of cell that
just looks similar.

It is easy to
see how the mind and the brain
became equated.

We like to think of
ourselves as rational and
logical creatures.

It didn’t seem to
matter that the content of
these dreams was obtuse.

I’d like to thank the people of the xkcd Time discussion thread for writing so much in so many strange ways, and especially Sciscitor for exporting the entire thread as text. It was the test data set that kept on giving.

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Haiku Detector Update


I’ve been sitting on some improvements to Haiku Detector for a while, and it’s about time I released the new version. I had been planning to put this version on the app store, but I’m waiting to hear back from somebody about an icon for it. So for now, you can download it without going through the store. It should work on Mac OS X 10.6 or later.

This version finds haiku made up of multiple sentences rather than only those made of 17-syllable sentences. I also fixed the bug which caused it to crash occasionally when dealing with very long texts. To celebrate, I’ll go through some of the same texts I did when I first released Haiku Detector, and see what new haiku are discovered. To start with, John Scalzi‘s Old Man’s War. This version of Haiku Detector finds 304 haiku in it. Sometimes, sentences can be included in more than one haiku:

“I’m sorry. My sense
of humor was surgically
removed as a child.”

“My sense of humor
was surgically removed as
a child.” “Oh,” I said.

“Oh,” I said. “That was
a joke,” she said, and stood up,
extending her hand.

Here are some of my favourites of the multi-sentence haiku:

She asked, still without
actually looking up
at me. “Pardon me?”

“Okay,” I said. “Mind
if I ask you a question?”
“I’m married,” she said.

“Well, she doesn’t have
to live with you, now does she.”
“How was the cookie?”

“Our friend Thomas would
make it to mile six before
his heart imploded.”

This one sounds like it could be a metaphysical statement about what consciousness is in general:

Your consciousness is
perceiving the small time lag
between there and here.

“I would not presume
to assume, Master Sergeant!”
‘Presume to assume’?

My wife’s out here, sure.
But she’s happy to live her
new life without me.

“Let me see.” Silence.
The familiar voice again.
“Get this log off him.”

“The question now is
what is really going on.”
“Any thoughts on it?”

I think this one is my favourite:

I can just be me.
But I think you could love me
if you wanted to.

I found a lot of new haiku in the CMS paper announcing the discovery of the Higgs boson, but they were all combinations of names from the stupendous author list. Since I included some from New Scientist last time, here are some from the issue of New Scientist that I am currently reading, a special issue on the human brain:

Imaging techniques
are allowing us to see
the brain in action.

The sound waves broke up
the synchronous firing,
ending the seizure.

Thought experiments
Sometimes an experiment
is impossible.

The ancient Greeks knew
about thought experiments
in mathematics.

These two go together:

Does that mean we should
revise our definition
of intelligence?

Until recently,
the same one had been used since
the 1950s.

I have many ideas for improving Haiku Detector, and I’d still like to see if I can detect the best-sounding haiku using linguistic tagging, but before that I’m thinking of rewriting the whole thing in Swift as a learning exercise. Since I don’t have a day job at the moment, I have a bit of free time if I strategically ignore sections of my to-do list. Actually, on that note, here are some particularly obvious haiku from the Mac OS X and iOS Human Interface guidelines:

At a minimum,
a menu displays a list
of menu items.

A picker displays
a set of values from which
a user picks one.

That will do for now. I hope you enjoy playing with the new version of Haiku Detector.

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Unintentional Haiku from New Scientist on A Better You


It’s been a while since I’ve run an issue of New Scientist through Haiku Detector. Since I’m far behind on holidailies, here are some of the unintentional haiku in their collection issue, A Better You. There were 40 haiku all up, many of which were bylines or captions. Many others were rather underwhelming as haiku, but here are the at-least-passably-whelming ones. First, some about getting smart:

We kick off with the
most important organ in
your body: your brain.

These brain areas
are very active when you
play an instrument.

Then you have to have
the motivation to do
something about it.

Now some about what not to eat:

As a result, health
bodies are gearing up for
a “war on sugar”.

Its conclusion: there
is “no evidence” that food
can be addictive.

Is it simply that
too much sugar equals too
many calories?

Unfortunately,
recent research casts doubt on
their effectiveness.

Headlines have appeared
questioning the benefits
of eating less salt.

The last one on that topic echoes Hank Green’s thoughts on picking the right addiction:

Assuming you will
have some vices, the trick is
to choose them wisely.

Some about growing old gracefully:

Some think the effect
is simply about having
a long way to fall.

What you need is a
bit of excitement along
the way. Take some risks.

What on earth was he
doing differently? What was
cushioning the blow?

Not surprisingly,
one of the most important
is intelligence.

Learning like a child
is easy if you know how,
says David Robson

Whatever you want
to learn, it’s never too late
to charge those grey cells.

He recently took
up Chinese, and has no plans
to stop after that.

Some under the heading ‘Get physical’:

They just haven’t been
very good at telling us
what they’ve discovered.

Could exercise be
a killer lying in wait
for the unwary?

Pain may return on
finishing the exercise,
or the next morning.

So if exercise
is so beneficial, why
won’t people take it?

“I’m sorry,” he says
when I ask about the noise.
“I’m on a treadmill.”

and some recipes for success:

It seems that anger
can make us impetuous,
selfish and risk-prone.

Concentrating in
itself is not enough to
screen out distractions.

Instead of nuking
your friendly bacteria
you should nurture them.

Their wounds were slower
to heal, and they also caught
more throat infections.

One theory is that
CMV plays a key role
in immune ageing.

And good vagal tone
improves emotional and
social well-being.

In conclusion, a haiku from me:

I hope these will lead
if not to better haiku,
to a better you.

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Haiku Detector Achieves its Purpose (and will now proceed to have an existential crisis)


I originally wrote Haiku Detector because my friend Gry saw Times Haiku and wondered whether there were any haiku in her Ph. D. thesis. The other day I heard back about the haiku she found. It turns out that even the title of the thesis is a haiku:

Developments for
studies of the extremes of
nuclear matter

Here’s another one, which could be about anything. The last line is a bit of an anticlimax.

As of today, the
origin of this strength is
not well understood.

When I read this one, I wondered if miniball was a mini-golf style version of another ball game:

At HIE-ISOLDE
the MINIBALL would be used
for the same purpose.

The impurities
of 48,50Ti
are easily seen.

After seeing these, I sent her the as-yet-unreleased new version of Haiku Detector, which can detect haiku made up of several sentences. Having mostly had my name on papers authored by the entire CMS collaboration, I expected her to find a lot of haiku in the author list. But ISOLDE is much smaller, and also this is her thesis that she wrote, not some paper whose author list she got tacked onto. So she got some from references:

Kitatani, S.
Goko, H. Toyokawa,
K. Yamada, T.

C 47,
537
(1993).

and some things with section numbers tacked on:

2.1.1
Open shell nuclei and
collective models

This matrix is the
starting point for the Oslo
method. 45

That last one has so many possibilities. I like to think of it as being about an electronic band called The Oslo Method which released a 45rpm record about The Matrix. Unfortunately, nobody can be told what the haiku is. You have to see it for yourself. And indeed, you can see the other haiku she found on the #MyHaikuThesis tag on Twitter.

I noticed something interesting while writing this post — some of the ‘haiku’ Gry found include gamma (γ) symbols:

The γ-ray strength functions
display no strong enhancement
for low γ energies.

5.2.3
Particle energy-γ-ray
energy matrix

Haiku Detector on her Mac has treated them as having zero syllables, as if they are not pronounced, and I think I recall characters like that not being pronounced in the Princeton Companion to Mathematics. But I just checked on my Mac running Mac OS X Yosemite, and the speech synthesis (which Haiku Detector relies on for syllable counting) pronounces γ as ‘Greek small letter gamma’, so Haiku Detector does not find those erroneous haiku. I think that this might be a new feature in Yosemite.

But here’s where it gets weird: you’d think that it’s just reading ‘Greek small letter gamma’ because that’s the unicode name of the character. I tried with a few emoji and other special characters, and that hypothesis is upheld. But the unicode character named ‘chicken’ (🐔) is pronounced ‘chicken head’. Spooky. Another strange thing is that there is no unicode ‘duck’ character.

If you’ve been paying attention, you probably know why I happened to come across those oddities. I’ll have to investigate them later, though; right now I’m in Edinburgh for NSScotland, and it’s about time I looked at some tourism information.

So, Haiku Detector; what now? Maybe look for supersymmetric haiku?

Update: It seems that in Mac OS X 10.8, γ is not pronounced, and 🐔 is pronounced ‘chicken emoji’. Other emoji also have ’emoji’ in their pronunciations, while still others are not pronounced. I wonder if pronunciations were added (and later edited to remove the ’emoji’) for certain emoji, and now the default pronunciation has changed from nothing to the unicode name. So ‘🐔’ ended up with the explicit pronunciation ‘chicken head’ while others which were not previously pronounced use their unicode names. So this should be a haiku in Yosemite, though for some reason Haiku Detector does not detect it:

🐒🐔
🐔🐒🐒
🍄🍄🐍

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Unintentional Haiku Spoken in a Courtroom 241 Years Ago


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:

Read the rest of this entry »

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Unintentional Haiku in Time Cube


I’m not sure if I’ll keep up the daily poems for NaPoWriMo for the rest of the month, because I remembered that the deadline for a short story contest I plan to enter is also at the end of the month, so I’ll need time to write something for that. But today’s What If reminded me of the hilariously incoherent ‘Time Cube‘ website, and I wondered if there were any unintentional haiku in it. I ran Haiku Detector on it, and I found these ones on the first page:

I have so much to
teach you, but you ignore me
you evil asses.

Humans ignore their
4 corner stages of life
metamorphosis.

All 4/24
hour days occur within
1 Earth rotation.

I have created
simultaneous 4 day
rotation of Earth.

Your God claimed to have
created a single day
rotation of Earth.

Singularity
educated humans are
not intelligent.

I like the first one best. I hadn’t read this far before, but it turns out the second page has some weird statements supporting racial segregation on it, so if you’re likely to be bothered by ridiculous-sounding racist statements by a crackpot, read no further.

Read the rest of this entry »

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Unintentional Haiku… of Mars


Kurukkan suggested using Haiku Detector to find the unintentional haiku in Edgar Rice Burroughs’ ‘A Princess of Mars’. This it seemed like a fine idea to me. I haven’t read it yet, but I’ve heard of it, and there was even another movie based on it (‘John Carter’) released recently. There are quite a few haiku which have a nice twist in the last line; one even has a rhyme. I’ve trimmed out some that really don’t work, but since they’re not much effort to read anyway, I’ve left in some that still sound picturesque even if they don’t break nicely into the lines. If you’re not into Mars fiction, there are some haiku about a real Mars mission, and an opportunity for you to send your own haiku to Mars, at the end.

On regaining the
plaza I had my third glimpse
of the captive girl.

“Some day you shall know,
John Carter, if we live; but
I may not tell you.

And now the signal
has been given to resume
the march, you must go.”

“I am glad you came,”
she said; “Dejah Thoris sleeps
and I am lonely.

I have twice wronged you
in my thoughts and again I
ask your forgiveness.

Sola and I walked,
making Dejah Thoris ride,
much against her will.

I have escaped from
worse plights than this,” and I tried
to smile as I lied. Read the rest of this entry »

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Unintentional Haiku in the works of Lewis Carroll


The other day I decided to run Haiku Detector over the works of Lewis Carroll, as found on Project Gutenberg. This is what I found. It’s a bit of a mixed bag in terms of how well they work as haiku, to the extent that I can still measure that after reading so many (I will have to try out linguistic tagging and work out some heuristic based on parts of speech beginning and ending lines), but simply as bite-sized samples they give a nice sense of the work. I can’t tell whether they’re made more or less whimsical by being stripped of their context.

From Alice’s Adventures in Wonderland:

‘But it’s no use now,’
thought poor Alice, ‘to pretend
to be two people!

But if I’m not the
same, the next question is, Who
in the world am I?

They all sat down at
once, in a large ring, with the
Mouse in the middle.

But I’d better take
him his fan and gloves—that is,
if I can find them.’

‘I haven’t the least
idea what you’re talking
about,’ said Alice.

Read the rest of this entry »

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Unintentional Haiku in the Princeton Companion to Mathematics


I’ve had a copy of the Princeton Companion to Mathematics for a while, and intended to start a series called ‘forms and formulae’, where I’d write about some of the articles using poetic forms from the Princeton Encyclopaedia of Poetry and Poetics (addendum: I have since started a series called Forms and Formulae doing just that.) However, both books are huge and difficult to read on the bus, and the articles are long, so so far all I’ve managed to do in that vein is write a poem about platonic solids in a duel, and procrastinate my way out of writing about the entries whose names were alphabetically closest to Emmental. So I was excited to discover this morning that there is a pdf of the Princeton Companion to Mathematics available for free, apparently legally. Finally I can carry it around with me on my iPad and write poems about it whereever I want. But I don’t even need to do that, now; thanks to Haiku Detector, I can easily find the poems that are already in it. And boy are there some nice ones. Some were missed because Haiku Detector doesn’t know how to pronounce Greek letters and a lot of other mathematical notation, and the book sometimes hyphenates at the ends of lines so it looks like they’re good places for line breaks when they’re not. But these are the best ones I found. First off, some which don’t even sound like they’re about mathematics:

Watch your hand as it
reaches out gracefully to
pick up an object.

The difference between
the two definitions of
a secret is huge.

These ideas will
occupy us for the rest
of the article.

This opens you up
to new influences and
opportunities.

In our case, there are
two natural properties
that one should ask for.

Suppose that households
are able to observe one
another’s outputs.

Everything is now
a martingale and there can
be no arbitrage.

The magician can
at once identify which
digit has been changed.

This definition
has the advantage of great
flexibility.

Let us briefly sketch
the argument, since it is
an instructive one.

Moreover, it was
a thought that took many years
to be clarified.

The blocks are the sets
of seed varieties used
on the seven farms.

If you didn’t know where it came from, this could be about anything, but it also sums up the appeal of mathematics:

But then again, who
can deny the power of
a glimpse at the truth?

And a more transparent statement about the nature of mathematics:

“All roads lead to Rome,”
and the mathematical
world is “connected.”

But I really love it when you can’t tell it’s about mathematics until the last line:

The answer turns out
to be that we should weaken
our hypotheses.

It is important
to have a broad awareness
of mathematics.

We will focus on
the most important special
case: vector bundles.

Sometimes relations
are defined with reference to
two sets A and B.

This remains as an
outstanding open problem
of mathematics.

Church’s thesis is
therefore often known as the
Church–Turing thesis.

How, though, can we be
sure that this process really
does converge to x?

It turns out that both
choices are possible: one
automorphism

We shall now describe
the most important of these
extra assumptions.

Several themes balance
in Hilbert’s career as a
mathematician.

Indeed, the study
of such designs predates their
use in statistics.

This turns out to be
a general fact, valid
for all manifolds.

However, it is
a well-understood kind of
singularity.

In particular,
we can define the notion
of winding numbers.

This is exactly
the task undertaken in
proof complexity.

Questions mathematicians ask themselves:

How much better would
you do if you could compound
this interest monthly?

Why are spherical
harmonics natural, and
why are they useful?

What consequence should
this have for the dimension
of the Cantor set?

Can we reduce this
computational problem
to a smaller one?

How about checking
small numbers a, in order,
until one is found?

For what values of
the edge-probability
p is this likely?

Is every even
number greater than 4 the
sum of two odd primes?

Can one make sense of
the notion of a random
continuous path?

Perhaps this is the answer:

In mathematical
research now, there’s a very
clear path of that kind.

This one sounds like some kind of ‘how many roads must a man walk down’ question:

How many walks of
length 2n are there that start
and end at 0?

And while this isn’t actually a haiku, I can imagine it being sung in response to that song, with ‘the number of such walks’ to the tune of ‘the answer my friend’:

The number of such
walks is clearly the same as
W (k − 1).

Mathematicians don’t always answer questions in ways that other people find useful:

If instead we were
to ask each person “How big
is your family?”

In particular,
the average family size
becomes infinite

It follows that at
some intermediate r
the answer changes.

Things only a mathematician would feel the need to state explicitly:

This is a sum of
exponentials — hence the phrase
“exponential sums.”

What makes them boring
is that they do not surprise
us in any way.

Proof is left as an exercise for the reader; it probably takes several pages, but:

If you do know it,
then the problem becomes a
simple exercise.

Once this relative
primality is noticed,
the proof is easy.

All we have to do
is use one more term in the
Taylor expansion.

Doing things this way
seems ungainly to us, but
it worked very well.

It is not hard to
see that the two approaches
are equivalent.

(Of course, one needs to
check that those two expressions
really are equal!)

But this subtlety
is not too important in
most applications.

Some interesting statements:

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

That is exactly
what a sphere is: two disks (or
cups) glued together!

Thus, recursion is
a bit like iteration
but thought of “backwards.”

Nevertheless, it
turns out that there are games that
are not determined.

(It can be shown that
there is exactly one map
with this property.)

The remainders get
smaller each time but cannot
go below zero.

There are other ways
to establish that numbers
are transcendental.

(The term “Cartesian
plane” for R2 is therefore
anachronistic.)

As usual, we
identify R2 with
the complex plane C.

Note that a block of
size 1 simply consists of
an eigenvector.

The upshot is that
we should always use a prime
number as our base.

Among the other
important number fields are
the cyclotomic fields.

Thus we obtain a
number that is less than the
quantity we seek.

So we might define
the “points” of a ring R to
be its prime ideals.

(For both halves, the pinched
equator is playing the
part of the point s.)

Thus, we have deduced
that length-minimizing curves
are geodesics.

For example, the
geodesics on the sphere
are the great circles.

The generators
correspond to loops around each
of the two circles.

The image of this
map will be a closed loop C
(which may cross itself).

We consider what
happens to C if we add
a small ball to it.

It is not hard to
show that the orbits form a
partition of X.

There are many ways
of combining groups that I
have not mentioned here.

I have thrown classes
of groups at you thick and fast
in this last section.

To apply Newton’s
method, one iterates this
rational function.

A quick overview
of physics will be useful
for the discussion.

can get away with
not understanding quantum
mechanics at all.

The quantum version
of Hamilton’s principle
is due to Feynman.

These encapsulate
the idea of a proof
by contradiction.

(A graph is simple
if it has neither loops nor
multiple edges.)

It is really an
algorithm that inputs
n and outputs an.

(An involution
is a permutation that
equals its inverse.)

If the tree has 2
vertices, then its code is
the empty sequence.

But the number of
possible orders of A,
B, and C is 6.

Number theory is
one of the oldest branches
of mathematics.

The percolation
and Ising models appear
to be quite different.

First, Albert shouts out
a large integer n and
an integer u.

This one is interesting if you imagine it’s about lines of poetry:

Another affine
concept is that of two lines
being parallel.

A mathematical protest slogan:

equality if
and only if x and y
are proportional.

A title of the mathematician’s equivalent of a song about unrequited love:

5.1.5
Why Is It so Difficult
to Prove Lower Bounds?

A series of short films:

10 Differences in
Economic Life among
Similar People

And something said in a soothing tone after a litany during a maths/mass:

Now let us return
to polynomials with
n variables.

The probability of finding a good haiku in the end matter is low, but I think this one’s pretty neat, even if it only has the right syllable counts if you say the ‘and’ in 906 but not 753:

law of large numbers,
753,
906

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