\documentstyle{book}
\title{Poetry for the Mathematician}
\author{By Kevin Iga}
\date{Sept. 1989}
\maketitle
\chapter{Introduction}
\chapter{Information}

What is information?  It's not anything physical; yet knowing some
might win a battle, get you an A on a test, cure cancer, or allow you to
understand this book.

Yet, the report from the battlefield, the facts in the textbook, and the
prescription to cure a disease are completely useless to someone who doesn't
understand it.  Imagine an Arab who doesn't understand English trying to
read this book.  He sees nothing but gibberish.  It is not information, but
random markings on a page.  Alternately, consider the situation with you
trying to read a book in a language you do not understand, be it Yoruba or
Basque, Tibetan or Mayan.  You might be intrigued by the writing if it is
different from ours, but it has virtually no information to you.

Does this sentence have meaning to, say, a pencil?  It might.
We would probably doubt it, though.  To a bookworm that sentence might
mean ink-flavored spice on the paper.  Is that information?

People spend their lives studying information.  To do so would be pointless;
after all, this is a book about poetry.  Instead, we make a makeshift
definition.  It is very qualitative and is more of a philosopher's definition
than a mathematician's.
\footnote{The mathematician's definition is more of a unit of measurement,
using probability and entropy.  It measures how many questions of a certain
kind are required to determine the desired fact.  This definition does not
concern us here.}

Let information be defined so that:
\begin{enumerate}
\item Information may exist in a conscious mind.

\item Once in a conscious mind, it will never leave until the mind is
damaged.

\item Information may be coded into other physical media.

\item Some information may be transmitted from one conscious mind to another.

\item Some information may be coded into and from physical media, if the
transmitter/receiver knows a feasible code.
\end{enumerate}

We can categorize information according to what it describes:
\begin{description}
\item[Factual information] coding of external conditions, such as ``2+2=4'',
``I am human'', or ``This book is boring.''

\item[Emotional information] coding of internal conditions (in the mind),

\item[Metainformation] information inherent to the coding itself
\item[Other information] We cannot rule out this possibility.

--page break--
Written language

	In the previous section we mentioned coding into physical
media.  The system is, in our experience, generally arbitrary.  In
written language, the medium is paper, stone, papyrus, microfilm, silicon, or
whatever will receive stable imprints based on geometric forms known
by the literate to be a code.  (Okay, maybe silicon is pushing it).
	The fact that it is a code is part of metainformation:
information inherent in the coding itself.  Think of a language you
don't know.  Choose one (since chances are you don't know all of
them): Catalan, Frisian, Mongolian, Swahili, Umbrian, Fijian.  Imagine
seeing a page written in this language.  Would you know it was written
in that language?
	Let's say it was written in cursive.  Let's say the cursive
script was written by some illegible handwriting and reflected in a
mirror, and by some printing error, was scattered across the page.
Would you know it was something in ANY language?
	The metainformation requires some knowledge of the language.
The more you know of the coding system, the more information you pick
up.  First, the metainformation (saying you recognize the letters),
then the factual, emotional, meta, and anything else all (apparently)
at once.
	Throughout the rest of the book, I will assume we are talking
about English since it is probably the most familiar to the majority
of the readers.  But whatever is applicable to English should be
applicable to Mandarin or Cherokee, as well.

Spoken language

	The medium here is air (and sometimes electric wiring), and
again, is a code that requires knowledge to recognize it.  There is
often a correspondence between a spoken and a written language.  This
is not always the case, but it is a good generalization.
	Comment: Written English and spoken English are two different
languages.  In one, information is coded in geometric figures on a
spatial medium; in the other, it is coded in air vibrations in a
temporal medium.
	Comment: There is a very good correspondence between written
and spoken English in that a being can listen to one being dictated
and transcribe it; or read one aloud, easily.  It is generally
word-for-word, and the factual information is generally kept the same
(except when the metainformation allows for ambiguities like to, two,
too; or wind (winnd) and wind (wahynd).)
	Comment: Mapping emotional information between the two is
often difficult.  In written English, it is usually done in context,
through the aid of punctuation.

--page break--
The word in isolation

	Each word carries information.  In isolation, it carries very
little, if any, factual information.  Its metainformation is changed
little.  And its emotional information is partly there.

	Consider the word

		COLD

	Look it over.  Stare at it.  What factual information does it
carry?  It seems to say that something is cold.  Exactly what is
uncertain.  In isolation an adjective tends to say that something has
the property.  Don't expect this to hold outside of isolation, though.
	What kind of emotional information did you experience?  You
might have felt a little chilly because of it.  You might have
remembered when you were cold, or when you heard of some cold
conditions.  The word COLD triggers subconscious passages in the brain.
	How about metainformation?  It's written in English, is
written with four letters, with Roman lettering style, and is written
in all caps.
	If translated to spoken English, it is monosyllabic, in
consonant, vowel, consonant, consonant pattern, contains a guttural
plosive followed by a back open long vowel, followed by a blend of a
liquid consonant and a voiced dental sound.
	The only thing it lacks is a syntactical place, that is, a
function in a context.

The word in context

	Look at the following sentences:

1)	The bear was cold.
2)	She gave him the cold shoulder.
3)	For health purposes, the refrigerator must be kept cold.
4)	Everyone nowdays has a cold.
5)	Cold packs are available at the first aid station.

	Here, cold has more factual information.  Note that this may
not be unique.  Here cold acquires more emotional information.  In
this way, the whole is greater than the sum of the parts, or 1+1 > 2.

Definition: The factual information contributed by a word is called
the DENOTATION of the word.

Definition: The emotional information contributed by a word is called
the CONNOTATION of the word.

	The metainformation is a bit too complicated for now; we will
put that on hold.
	In sentences 1 and 2, cold is grammatically used the same.
But in sentence 2, we associate "cold shoulder" as a single unit; it
is for all purposes as if we had invented a new word.  Their
denotations are different.  Their connotations, though similar, are
not quite the same.
	In sentences 1 and 3, cold has the same denotation, that is,
low in temperature, or, the average kinetic energy of the molecules is
lower than what might otherwise be expected.  But in sentence 1, not
enough information is given to give a firm sense of connotation.  If
you sympathized with the bear, you might feel one way.  If you
sympathized with a tourist it was chasing, you might feel another way.
If you were a zoologist, you might feel distant, thinking only about
the effects of cryogenics on a living object.  It is a neutral
connotation, without sufficient information.  In sentence 3, you might
feel a positive connotation, meaning you feel a tendency to desire or
want the situation.  Just because of "For health purposes" and the
verb "must."
	Do the same with the other examples.  Remember that your brain
does all this junk automatically.  To do it rationally takes some work
because we don't really understand ourselves.  We understand that we
see a ball doesn't tell us about our optic nerve system.  Which brings
me to the psychological interlude.
--page break--
Psychological interlude

	In language, we are often involved in transmitting
information.  When we transmit information, we want the other being to
receive the information in a certain way.  To understand how the other
being is going to receive the information is a matter of psychology.
	Does it ever occur to you that we talk and understand each
other despite the fact that we were never explicitly told the code we
were using?  I mean, did you ever wonder if there were some other
rational interpretation of the English language in which every
statement carries information, but that information is different, like
good meaning bad, or something?  What would happen if one child grew
up thinking one way, and someone else interpreted it differently?
Yes, it's bizarre, it's scary, but the point is we understand in ways
we ourselves cannot understand.
	Think about the sentence: Life is wonderful.  Do you
understand it?  Why?  Why do you think it says what you think it says?
The advantage to written English is that you can break it up into
words.  (The disadvantage is that you think that's always okay).
Break it up: Life.  What does life mean?  Can you define it?  How do
you know what it means?  Is.  What does "is" mean?  What does
"wonderful" mean?  Yet, we get some information out of the whole
sentence in an inexplicable way.
	Think about the sentence: Mary had a little lamb.  You imagine
a little girl owning a pet white lamb.  Why?  In this case, it's
probably because of associations with some nursery rhyme book you saw
a while back that had pictures in it.  How do you know it's not saying
that the Virgin Mary gave birth to a little child who would be the
Lamb of God?  How do you know it's not saying Mary went to a
restaurant and ordered a little lamb for dinner?
	How about: Time flies quickly.  Do you think this is a
statement about the comparative rapidness of the passage of time?  Or
is it a command to measure the speed of small insects so you can get
your biology lab in before the bell rings?
	Often we base our understanding on previous knowledge.  But
obviously there must have been a time when we had very little previous
knowledge (Shirley McLaine notwithstanding).  How did we understand
things then?
	By now it should be clear that the means in which we
understand things is not quite understood.  It's one of the major
problems of linguistics, and one of the hardest problem of Artificial
Intelligence.
	Certain codes add factual and emotional information to our
brains.  In most cases we don't know how.  We only know that some
patterns on paper tend to create other patterns in the final
information.  In most cases, we tend to analyze ourselves, asking
ourselves what new information we got when we read something.
	This is not foolproof.  When we want to analyze poetry, we
want to say what the author wanted to say, as well as what the common
reader would find.  If it affects us in a different way than it is
supposed to, we get the "wrong" answer.  Of course, if enough people
get misled, it might be a valid question to ask why.
	For now, let's keep this all on hold and remember that we
can't rationalize everything.  Because when we analyze poetry, we are,
in part, analyzing the human mind.
--page break--
Music in isolation (instrumental music)

	Now that I've established that we don't understand everything
about words, I'm going to introduce something we know even less about.
When we listen to instrumental music, we receive emotional information
and very little factual information.  If we know something about music
theory, we might be able to sort out some metainformation.
	The elements of a musical sound is:
	1) pitch: how high or low the note is (middle C, F#, etc.)
	2) duration: how long it lasts
	3) volume: how loud or soft it is (may vary with time)
	4) timbre: the complexity of the tone (violin vs. oboe...)

	We will consider only one voice at a time, to simplify matters
immensely.  It turns out in poetry any subordinate voices are too
minute to detect, much less analyze.
	In classical music, pitch centers on a particular pitch called
the tonic.  No matter where one is in a piece, the ear feels a
tendency toward a particular pitch.  I can't explain why.  It's just
scientific fact.  In most music, the particular pitch is constant
throughout a piece.  Sometimes a secondary pitch becomes a tonic.  But
even in those cases, there is a nagging tendency back to the original
tonic.
	In classical music, pitches are generally adjacent, flowing
from one note to the other using notes in between.  This makes a song
easier to sing, and is what our ear expects.  When a jump occurs, this
is unexpected and draws attention toward the interval.  It accents the
participating notes in a strong way.
	In classical music, cadences give the music form.  A cadence
is anything that gives the listener the sense of pause, as if a
partial or full completion.  Often, a cadence is a note that is longer
in duration, but that is not always the case.  A strong cadence is
generally one that is gradually approached, more descending than
ascending in pitch.  In the "Star-Spangled Banner," we pause after
"can you see."  It is a note longer in duration, and because of it, we
feel a pause.  We also hear a pause after "dawn's early light."
Comparing the two, the second gives a greater sense of continuation,
since it is not the tonic.  After "we hailed" comes another cadence,
but after "last gleaming" we hear a very strong cadence.  Here is the
first descending cadence, and that fact strengthens it.  It lands on a
pitch one octave below the tonic (an octave difference in pitch
generally gives a strong sense of relation between the pitches), so an
almost-complete sense of ending is achieved.
	In classical music we need to concern ourselves with harmony
between notes.  But we will be analyzing pitches that are in a much
more limited range, where harmony is difficult to achieve.
	In classical music a certain rhythm tends to accent certain
emotions.  The rhythm, or the general variation of volume over time,
often has an approximate periodicity.  After a while, it repeats.  But
it often has slight variations.  Think about "As the Saints Go
Marching On."  It follows a fast, regular, strong rhythm, associated
with festive marching.  In "Pomp and Circumstance," the rhythm is slow
but very regular.  It gives the sense of solemnity.  The first
movement of Beethoven V has a strong rhythm that's almost regular.
	The timbre of the music gives endless possibilities, and it is
impossible to discuss all of its manifestations, especially in speech
which is our main objective in later sections.  Yet it is so
important, we will treat separate vocal sounds separately and not
discuss timbre at this point.

Music inherent in speech

	In English we tend to vary pitch in speech.  When we reach a
question mark, don't we pause while rising in pitch?  On the other
hand, a period descends in pitch to a rest.  The question mark
suggests continuance, ascending to an unstable cadence.  The period
suggests rest, returning to an implied cadence.
	The pitches found in English are limited.  It includes three
found in general speech, one found rarely (in exclamations!) and some
subtle variations inherent to poetry.  Commonly, a sentence will start
out in pitch 2 (1 being the lowest) and will fluctuate with pitch 3,
and will sometimes dip quickly into pitch 1.  At the end, it will
descend from pitch 3 to pitch 2 then pitch 1 for declarative
statements and will ascend from 1 to 2 to 3 for questions.  This is
not always the musical effect desired.  Sometimes we want to accent a
syllable by making it jump from pitch 1 to pitch 3, or even pitch 4!
It depends on what is desired.
	Rhythm in speech is sometimes regular, sometimes irregular.
When regularity is intended, we call the regular rhythm the METER.  To
simplify our work we will assume English has two volume levels, called
stressed and unstressed.  This is not quite the case, but it is a good
approximation in local instances (In parenthesis, for instance, the
pitch is generally lower, but it varies in the same way, as if
stressed ans unstressed were re-defined in the parenthesis).  Accent
generally consists of a stressed volume, a high pitch, and a long
duration.  It need not consist of all three, but the more it has, the
stronger the feeling of meter.  Look at the following word:

	Window
vol.:   2  1

	It can be split into two syllables, "win" and "dow."
Convention places the stress on the first syllable.  (We will use the
notation above, 1 meaning unstressed, 2 meaning stressed.  It is often
also used with breves and accent marks.)  We can use this
fact to distribute stress on other words, making some words more
important than others, or at least stand out more:

	But soft, what light from yonder window breaks!
vol.:   1   2     1    2     1    2  1   2  1   2
pitch:  2   3     2    3     2    3  2   3  2   4
durat.: 1   3     1    2     1    1  1   2  1   3

sum:    4   8     4    7     4    6  4   7  4   10
strong:     ^          ^                 ^      ^^

	In the above chart, I have marked volume level, pitch level,
duration level, and the sum of all three levels.  I also noted which
ones are particularly high.  The author makes these levels stronger in
order to tell the reader that these words are more important.  And,
indeed, these words determine the main concept inherent in the
sentence: "soft, light window breaks!"  The other words not only
modify or qualify the meaning, but give a certain grace to the
sentence.
	Notice that the volume follows a regular rhythm: 1 2 1 2 ...
This meter is called IAMB. (pronounced as in the last two syllables
in, "I think, therefore I am.")  This line can be written as a
repetition of a (1 2) component.  This component is called a FOOT.
Notice also that there are five (1 2) feet in the line.  In poetry
analysis language, we say:
Iambic (repeats a (1 2) foot)
Pentameter (five feet in the line).
	It turns out that Iambic pentameter is the most like English
speech, so it is the easiest meter to use.

	On the shores of Gichi Gummi
vol:    2  1   2      1  2 1   2  1
pitch:  3  2   3      2  3 2   3  2
durat.: 2  2   2      2  2 2   2  2

sum:    7  5   7      5  7 5   7  5

	This is an example of a very regular line.  It never varies in
duration, and the pitch and volume both vary with the same periodicity
in phase.  The feet here are (2 1), which is what analysts call a
TROCHEE (pronounced as the last two syllables in "Metro K").  We say
it is:
Trochaic (repeats a (2 1) foot)
Tetrameter (four feet per line).

These are some feet you might find.  Pronounce the words in their meters.
Iamb (1 2)
Trochee (2 1)
Spondee (2 2)
Anapestic (1 1 2)
Dactylic (2 1 1)

There are more, but this should be enough for now.

monometer: one foot
dimeter: two feet
trimeter: three feet
tetrameter: four feet
pentameter: five feet
hexameter: six feet
heptameter: seven feet
octameter: eight feet

Again, you probably won't need any more, but if you do, pick a Greek
or Latin number prefix and try it out.

	Duration is modified with punctuation, usually commas,
semicolons, colons, periods, question marks, and exclamation marks.
But in a complex or compound sentence when no punctuation separates
the two clauses, the duration is slightly longer (though not as long
as it would be with the comma).  Duration tends to be shorter on
small, common words like a, an, the, and, or; but even this is not a
rule.  If the poet discusses THE rule, as opposed to any old rule, or
a bunch of things AND a something else in addition, he may wish to
emphasize it, either as I have with capitalization, or through
placement in meter, or sometimes with no written clue at all.  To
analyze duration you just have to say it out loud and see its effect
on you.  Remember that poetry is, in part, an analysis of the human mind.
	The combined effect, as I said, can transfer metainformation
about what words are more important.  But this information is not the
only important aspect of the music in words.  We are often moved by
music, and music affects the human psyche in ways we are just
beginning to understand.  Though this area is gray, we still have the
power to listen to them and let our subconscious decide for us.
--page break--
