A Can of Worms

The Writer at Work
The Writer at Work

This is yet another post about the writing process. OK, it fascinates me, as I consider what happens in my brain/mind as I write something, but I risk the possibility of it not being interesting to anyone else. It’s around 1500 words long, which is a bit longer than my usual posts.

So, the conventional view of the writing process is that it is a linear process. The writer sits down at his or her desk, starts furiously writing, casting off page after page, until with a final flourish he types or writes “The End” and the deed is done.

The real process is much more dynamic than that, at least for me. The following is a brief description of what happened when I wrote a story that I have written about in previous posts. I haven’t included any elements of the story because I want to concentrate on the process.

The End
The End

In a previous post, I wrote about a story that, as I wrote it, became too long for the competition in which I wanted to enter it. When I had completed it, I modified it and shortened it. However I wasn’t happy with the result, so I abandoned it, and started again from scratch, cutting and pasting bits from the original now and then.

This worked fine and I submitted the story into the competition. However, I now had three versions of the same story, and one of them, the original short one, was significantly different from the other two. A core topic in the story had changed, and the motivation of the main character was consequently different. There were other things about that version that I didn’t like so I considered consigning it to the bit bucket. However (fortunately) I didn’t do that right away.

I was happy with the version that I submitted for the competition, but I felt that the longer version could be improved. With no limit on the length, I could be more descriptive, go into the characters a bit more and draw out their motivations and fill in their back stories. I could also pull in bits from the short version which did work, and also ideas from the competition version that weren’t in the longer version.

Merging three stories into one
Merging three stories into one

I hope that I’ve given some idea of how complex this was. I was effectively merging three versions into one, and some bits didn’t fit together too well. I was constantly revising the longer one so that the timeline and the events fitted together properly with the bits I was getting from the other two versions. Normally things don’t get as complex as this for me!

After I got a consistent story, I developed it further. I’d add a paragraph or two to bring out the motivation of some character or other, and as a result one or two of the minor characters blossomed into being more than minor characters.

Initially the main character and his wife were a bit aloof, but I decided to make them more sociable, more friendly. The wife mostly dropped out of the main story, but returns for a major cameo. Another major character developed to become almost the equal of the protagonist, and a minor character emerged from the shadows to become a more rounded character.

The Protagonist
The Protagonist, but not of my story! It’s actually the goddess, Nike.

By this stage my story was complete in the longer version, and, because I had effectively gutted and abandoned the original shortened version I deleted it, as mentioned above. So now I had two versions, the shorter competition version and the longer version.

Now, when I’ve written a story, and although it is in a sense complete, I don’t leave it there. I read it through, again and again, constantly revising and modifying it. I don’t usually change the story that much, but I go after spelling errors, grammatical errors, continuity errors, and so on. In every run through I change something. Maybe just the way that I said something. The position of a word in a sentence. Maybe a name, a location, a motivation. I could keep editing probably for ever. I never write “The End”.

My main point here is that, using modern technology, I have been able to, basically, rewrite the story twice and extend and revise the original story dramatically.

Juliet's Balcony
A balcony in Verona which has nothing to do with Romeo and Juliet, but still gets visited and photographed by tourists who think it has.

I wonder how ancient writers did it. I can’t imagine Shakespeare turning out multiple drafts of his plays. For one thing, he did it by hand. To create a new draft, he would have to write out the whole thing again with the changes. The decision to change the name of a character from “Fred” to “Mercutio” wouldn’t be taken lightly. For another thing, paper was, relatively speaking, expensive in those days. Printing was expensive.

Once he had written the play, it would be printed, but only a few copies would be produced. The printed copies were not intended for general reading, but were intended as “prompt books” for use in a theatre. This means, of course, that each printing might be different.

Old Books
Old books. I imagine that Shakespeare’s plays would have been printed in books like this.

I’ve not heard of Shakespeare making notes or outlines of his plays, but maybe he did. Maybe somewhere there is Shakespeare’s hand a scrap of paper that says something like “R sees J on blcny. J doesn’t see R. R calls J, J calls guards. R thrown out.” But we know that the final version doesn’t run that way!

I conclude that Shakespeare probably had the whole play mapped out in his mind, or at least great parts of it, including the words that he invented, the sentence construction, the characters and the plot. It’s an awesome feat if he did do it that way. The idea of juggling all those characters and scenes in his head, developing the story, and finally getting it down on paper in an almost final version is amazing.

Well, I wrote that before actually wondering if there was anything on the Internet about how Shakespeare wrote his plays. The answer is fascinating, at least to me! It seems that Shakespeare and his fellow playwrights of the era cooperated extensively with each other, adding bits to each other’s plays. So Shakespeare’s plays were, in part, written by others! Interestingly, that’s very similar to the way that TV shows are written today, I understand.

An author at work
An author at work

We have the luxury, these days to dash off a story (or a play or whatever) and not worry too much about the details. We can fix those on the second go through! Electrons are as cheap as chips. I could have edited the bit about Shakespeare above, but I wanted to demonstrate how I was thinking, since this is post is about my thought processes when I write things.

So, I’d say the my writing style is like opening a can of worms. Who knows in what direction they are going to wriggle? Who knows where they are going to take us? I have a strong feeling that when I write a story, I’m only nominally in charge. The characters seem to have a life of their own, and they have their own needs and desires. They interact in way that I would not have predicted when I started writing their story and often the story changes as I write it. I’m often interested in how it is going to turn out.

That’s how I write. But others do it differently. Some, even in this electronic era write things out by hand. Others use mechanical typewriters and a few swear by old, really old, versions of software.

Mechanical typewriter
Mechanical typewriter

Things are different from Shakespeare’s day in many ways. It is more usual to write novels, rather than plays, and books are cheap and widely available. Writers do not, as a general rule, cooperate, as in Shakespeare’s day. A book will perused by an editor and checked by a proof reader many times before it is printed, and may be revised many times.

Even for those who write things by hand have the advantage of paper being cheap and readily available. They, and those who use mechanical typewriters, can easily rewrite a page and slot it into the manuscript fairly easily.

If you read the advice out there on how to write, you would sometimes think that the bare essentials are a well developed plot and well defined characters. I’ve read advice to that effect many times, but there are people who advocate the “just start writing” approach, and that is, as you can see above, my preference. I would not like to be straitjacketed by a rigid plot and static characters.

Inspiration?
Inspiration?

But some people prefer that approach and good luck to them! And there are those in the middle. Those who might have plot in mind or a set of characters, but aren’t about to spend time in developing the plot or the characters in detail. That’s maybe most writers.

Whatever approach you prefer, it is a good idea to research how to write. How to structure a story, how to develop characters and so on. It’s silly to think that all you need to do is pick up a pen and write, and you will produce a best seller. Even the best writers didn’t do that. They wrote at home and at school as kids, and they will have read voraciously, in all sorts of genres, and they may have actually formally studied literature. They will have practised extensively. And that’s what I am doing, and continue to do. Studying and practising. It’s one of the reasons for this blog!

Editing the first draft
Editing the first draft. That’s not me. I would be doing it directly on the computer!

Let’s be Rational – Realer Numbers

Symbol often used to denote the set of integers
Symbol often used to denote the set of integers (Photo credit: Wikipedia)

Leopold Kronecker said “God made the integers, all else is the work of man”. (“Die ganzen Zahlen hat der liebe Gott gemacht, alles andere ist Menschenwerk”). However man was supposedly made by God, so the distinction is logically irrelevant.

I don’t know whether or not he was serious about the integers, but there is something about them that seems to be fundamental, while rational numbers (fractions) and real numbers (measurement numbers) seem to be derivative.

English: Note: The irrational and rational num...
English: Note: The irrational and rational numbers make the set of real numbers. (Photo credit: Wikipedia)

That may be due to the way that we are taught maths in school. First we are taught to count, then we are taught to subtract, then we are taught to multiply. All this uses integers only, and in most of it we use only the positive integers, the natural numbers.

Then we are taught division, and so we break out of the world of integers and into the much wider world of the rational numbers. We have our attention drawn to one of the important aspects  of rational numbers, and that is our ability to express them as decimal fractional numbers, so 3/4 becomes 0.75, and 11/9 becomes 1.2222…

Parts of a micrometer caliper, labeled in Engl...
Parts of a micrometer caliper, labeled in English. Someone can replace this with a prettier version anytime. (Photo credit: Wikipedia)

The jump from there to the real numbers is obvious, but I don’t recall this jump being emphasised. It barely (from my memories of decades ago) was hardly mentioned. We were introduced to such numbers as the square root of 2 or pi and ever the exponential number e, but I don’t recall any particular mention that these were irrational numbers and with the rational numbers comprised the real numbers.

Why do I not remember being taught about the real numbers? Maybe it was taught but I don’t remember. Maybe it isn’t taught because most people would not get it. There are large numbers of rational accountants, but not many real mathematicians. (Pun intended).

Square root of two as the hypotenuse of a righ...
Square root of two as the hypotenuse of a right isosceles triangle of side 1. SVG redraw of original work. (Photo credit: Wikipedia)

In any case I don’t believe that it was taught as a big thing, and a big thing it is, mathematically and philosophically. It the divide between the discrete, the things which can be counted, and the continuous, things which can’t be counted but are measured.

The way the divide is usually presented is that the rational numbers (the fractions and the integers) plus the irrational numbers make up the real numbers. Another way to put it, as in the Wikipedia article on real numbers, is that “real numbers can be thought of as points on an infinitely long line called the number line or real line”.

Collatz map fractal in a neighbourhood of the ...
Collatz map fractal in a neighbourhood of the real line (Photo credit: Wikipedia)

Another way to think of it is to consider numbers as labels. When we count we label discrete things with the integers, which also do for the rational numbers. However, to label the points on a line, which is continuous, we need something more, hence the real numbers.

Real numbers contain the transcendental numbers, such as pi and e. These numbers are not algebraic numbers, which are solutions of algebraic equations, so are defined by exclusion from the real numbers. Within the transcendental numbers pi and e and a quite large numbers of other numbers have been shown to be transcendental by construction or argument. I sometimes wonder if there are real numbers which are transcendental, but not algebraic or constructible.

A rather sexy image of Pi from the german wiki...
A rather sexy image of Pi from the german wikipedia. (Photo credit: Wikipedia)

The sort of thing that I am talking about is mentioned in the article on definable real numbers. It seems that the answer is probably, yes, there are real numbers that  are not constructible or computable.

Of course, we could list all the constructible real numbers, mapped to the real numbers between 0 and 1. Then we could construct a number which has a different first digit to the first number, a different second digit to the second number and so on, in a similar manner to Cantor’s diagonal proof,  and we would end up with a number that is constructed from the constructible real numbers but which is different to all of them.

English: Georg Cantor
English: Georg Cantor (Photo credit: Wikipedia)

I’m not sure that the argument holds water but there seems to be a paradox here – the number is not the same as any constructible number, but we just constructed it! This reminds of the “proof” that there are no boring numbers.

So, are numbers, real or rational, just labels that we apply to things and things that we, or mankind as Kronecker says, have invented? Are all the proofs of theorems just inventions of our minds? Well, they are that, but they are much more. They are descriptions of the world as we see it.

Apollonius' theorem
Apollonius’ theorem (Photo credit: Wikipedia)

Whether or not we invented them, numbers are very good descriptions of the things that we see. The integers describe things which are identifiably separate from other things. Of course, some things are not always obviously separate from other things, but once we have decided that they are separate things we can count them. Is that a separate peak on the mountain, or is it merely a spur, for example.

Other things can be measured. Weights, distances, times, even the intensity of earthquakes can be measured. For that we of course use rational numbers, while conceding that the measurement is an approximation to a real number.

Tape ruler
Tape ruler (Photo credit: Wikipedia)

A theorem represents something that we have found out about numbers. That there is no biggest prime number, for example. Or that the ratio of the circumference to the diameter is pi, and is the same for all circles.

We certainly didn’t invent these facts – no one decided that there should be no limit to the primes, or that the ratio of the circumference to the diameter of a circle is pi. We discovered these facts. We also discovered the Mandlebrot Set and fractals, the billionth digit of pi, the bifurcation diagram, and many other mathematical esoteric facts.

Mandlebrot Fractal made with Paint.NET
Mandlebrot Fractal made with Paint.NET (Photo credit: Wikipedia)

It’s like when we say that the sky is blue. To a scientist, the colour of sunlight refracted and filtered by the atmosphere, peaks at the blue wavelength. The scientist uses maths to describe and define the blueness of the sky, and the description doesn’t make the sky any the less blue.

The mathematician uses his tools to analyse the shape of the world. He tries to extract as much of the physical from his description, but when he uses pi it doesn’t make the world any the less round as a result. Mathematics is a description of the world and how it works at the most fundamental level.

English: Adobe photoshop artwork illustrating ...
English: Adobe photoshop artwork illustrating a complex number in mathematics. (Photo credit: Wikipedia)

[I’m aware that I have posted stuff on much the same topic as last time. I will endeavour to address something different next week].