Me on the net

What’s the answer?

The Maths is out There

Last year I posted an article which discussed some simple arithmetic and algebraic questions that people are posting on the Internet. I mentioned in that post that the questions are almost always not posted to be answered. They are posted to incite discussion. Since then, there has been an upsurge of such postings, and I am going to address this topic further and expand on it.

Most people have left school with the impression that there is only one way to solve an arithmetic or algebraic question, and there is only ever one correct answer.

This is true, in a way. The rules of maths are rigid. However, when we write a problem down on paper, we write down a representation of the maths, in symbols. In the simplest case, we write down the symbol for a number, eg the symbol ‘7’. However in Ancient Rome, a mathematician would have written the symbols ‘VII’ to represent the same number. Even when we say ‘seven’, the word only symbolises the number.

Of course, our minds cut out all this rubbish, and we, inaccurately, conflate the number and the symbol for the number. “This is the number seven,” we say, pointing to the symbol, but it isn’t really.

When we add mathematical operations into the mix, things get more complicated of course. We write “7 + 3”, and think “Seven plus three”, mentally come up with the sum, the number 10, and think everything is fine.

But what if we were from a culture that reads and writes from right to left? We might possibly think “Three plus seven”, and would come up with the sum, the number 10.

However the language that we would use is unlikely to be the same as the one that I am using here, and the symbols would be different. Nevertheless, in some eldritch way, the maths is identical.

This rather long preamble shows that mathematics, specifically arithmetic and algebra, is independent of the symbols on the paper, and, probably, independent of the way our brains think of maths.

The Need for an ‘Order of Operations’

From now on I’m going to assume that that we are not from a culture that reads and writes from right to left, but the following reasoning can be expressed in a similar way for those who do write that way.

Now, if I multiply two numbers I get a third number. (I’m not too concerned about what multiplication actually is.) The way that I write this down is simple. I write the two numbers with a multiplication symbol between them. I might then write a ‘=’ symbol next, and then the result.

5 x 4 = 20

A string of multiplications is easy:

5 x 4 x 2 = 40

Similarly with addition:

5 + 4 + 2 = 11

So far so good. Note that it makes no difference which order we perform the multiplications. If we decide to start with the ‘2’, rather than the ‘5’, we get the same answer at the end. ‘5 x 4′ gives us ’20’ and so does ‘4 x 5’.

The problems arise when we introduce division and subtraction into the mix. Firstly, you can’t reverse the order in which you perform a subtraction or division:

5 - 4 = 1, but 4 - 5 = -1
Worse, 5 - 4 - 2 = 1 - 2 = -1, but 5 - 4 - 2 = 5 - 2 = 3

Even worse things happen when you mix addition and subtraction with multiplication and division. It’s important to note that the order that we should perform operations on numbers is not an essential part of arithmetic and algebra, but is related to the way we portray numbers and operations. There are ways of writing mathematical expressions which do not need an order of operations (or brackets, see later), indicating that the issues are not something within mathematics itself.

There are two ways of resolving the issues with the common way of writing arithmetic and algebraic expressions. Firstly, an order of operations rule can be applied to writing such expressions. Then expressions such as

1 - 21 / 7 + 4 * 2 =  6

can be written and understood unequivocally. The order of operation rules that are most often used are usually referred by the mnemonic PEMDAS or BODMAS.

Secondly, brackets can be used to specify the order that operations are performed. The previous example could have been written as

(1 - (21/7)) + (4 * 2) = 6

You can always add brackets, even if they are not essential, as above.

So, if we agree to use PEMDAS, we can pass equations to and fro with a good chance of agreeing on the results, but there are some edge cases.

Is PEMDAS enough?

Some people write things like

2 / 3(5 -2)

I think that this is badly formed, and one should not write ‘…3(5…’, but people do it all the time. That said, there is an implied multiplication symbol between the ‘3’ and ‘(‘, so the same thing, with the implicit multiplication made explicit is

2 / 3 * (5 - 2)

Now there are two schools of thought on how this should be processed. The first group say that there is nothing special about the multiplication sign and the rules should be applied as usual. That is, from left to right as each symbol is reached.

2 /  3 * (5 - 2) = 2 / 3 * 3 = 2

The other group say that because the multiplication sign is implicit, the multiplication between the ‘3’ and the bracketed item should be processed as soon as the bracket is evaluated, before the usual left to right processing. In other words

2 / 3 * (5 - 2) = 2 / 3 * 3 = 2 / 9 = 2/9

The two schools of thought result in different answers, so which is correct? The answer is either. It depends on what the writer intended, and he/she could have used a set of brackets and made certain that the idea was communicated properly.

Why is it such a big thing on the Internet?

People like to cause arguments! So they post ‘quizzes’ on the Internet which are ambiguous, and then sit back and watch the fireworks. Other people read the posts and provide answers which are informed or not informed as the case may be.

Then those who think that they know, mock those who they think are wrong. Neither side acknowledge the fact that it is a communications problem. There are those who try to point this out, but they are often ignored.

Those who know of BODMAS/PEMDAS are usually adamant that they are right because it’s maths and they were taught it, right? Those who don’t are ridiculed. The BODMAS/PEMDAS believers are certain that they are correct because, it’s maths, isn’t it, and maths is never wrong. They lose track of the fact that PEMDAS/BODMAS is just a convention , and other conventions, such ‘strict left to right’ or SADMEP/SAMDOB (the reverse of BODMAS/PEMDAS) could be used. Providing both parties agree on a convention, they can communicate mathematical (well, arithmetical or algebraic) ideas successfully to each other.

Those who have been taught about implied multiplication by juxtaposition dispute the answer with those who haven’t heard of it, but really, the answer to the poser is irrelevant. The reason for the posting is not to educate. It’s not to find the answer. It’s usually to stir discussion, and the rowdier the discussion is, the better from the poster’s point of view.

2 + 4 x 3 = ?

There are innumerable Facebook posts posing the above question (or similar). It usually results in more or less acrimonious discussions. There are two main camps: those who believe that the answer is fourteen (14), and those who believe that the answer is eighteen (16).

So, which camp is correct? Well, the answer is that the question is not complete. It doesn’t specify the way that the answer should be evaluated. If you do it one way, you get one answer, and if you do it another way, you get a different answer.

How can this be? The answer lies in how we break down the question in order to evaluate it. A mathematician or a computer programmer would perhaps ask how we intend to ‘parse’ the question.

When we learn arithmetic, we learn how to add and subtract, and how multiply and divide. For instance, we learn that:

7 + 6 = 13
4 x 8 = 32

Simple! A crucial point here is that it doesn’t appear to matter which way round the numbers appear.

6 + 7 = 13
4 x 8 = 32

If we want to add three numbers together or multiple three numbers, it doesn’t matter what order we perform the operation:

6 + 7 + 12 = 12 + 6 + 7 = 25
4 x 8 x 3 = 3 x 8 x 4 = 96

It also doesn’t matter if we work from left to right, or from right to left. If we start from the right we have the number 12, we add the number 7, giving the number 19, then finally we add the number 6, giving the final result. So far, so simple.

But if we had an arithmetic problem which involves subtraction or division, then things start to become complex. The order of symbols used and the direction in which the problem is processed does matter.

8 - 3 = 5          (Left to right)
8 - 3 = -5         (Right to left)
2 / 4 = 0.5        (Left to right)
2 / 4 = 2          (Right to left)

OK, a convention is called for. If I pose you an arithmetic question, I don’t want to have to tell you how I want it to be processed. So the convention, at least in languages which are written from left to right, is that arithmetic problems are also processed in the direction that the language is written. So from now on, I will assume that any arithmetic problem is processed from left to right.

I’d like to add that, though I’ve chosen the convention that the expression is processed from left to right, the issue can be resolved in other ways. For instance, I could suggest a convention that a bare number is always associated with the operator that precedes it. In other words:

8 - 3 = 8 + (-3) = 5 (LTR or RTL)

But this could cause other issues for more complex expressions.

If we mix addition and subtraction with multiplication and division, we get something like our original problem:

2 + 4 x 3 = ?

We can, some people may be surprised to learn, get more than one answer to this problem, depending on how we process the expression.

2 + 4 x 3 = 6 x 3 = 18 (proceeding strictly from left to right)
2 + 4 x 3 = 2 + 12 = 14 (using the BODMAS convention, see below)

Many people would argue that the first answer is correct. Why jump to the multiplication first in the second example? The answer is that it is simply a convention among mathematicians and computer scientists and programmers use. It’s the answer that you would get if you put those numbers and symbols into most calculators.

Some calculators (eg Microsoft’s Windows Calculator) can give either answer depending on what mode the calculator is set up to use. There’s a simple explanation in the linked article on why that is. Maybe too simple.

The convention that mathematicians and computer scientists use is not a law of arithmetic or mathematics, as some people believe. So, why is a convention necessary? The real answer is so that you can pass a random piece of mathematics to someone else and they will understand how to process it unambiguously, if there is a commonly used convention for processing such expressions.

In particular, in algebra and computer science, using the common BODMAS conventions actually reduces the complexity of the strings of symbols necessary to express a mathematical idea. Einstein’s famous equation would be more complex without the convention – there would need to be a multiplication symbol between the ‘m’ and the ‘c’, if the equation was to be understood strictly left to right.

E = mc² is more explicitly E = m*(c²)

The convention that I’m using here is that if two non-operator symbols are adjacent to one another, there is an implied multiplication operator between them. e.g.

2ab is equivalent to 2 x a x b
2a + b is equivalent to 2 x a + b

This convention is, strictly speaking, not part of BODMAS.

Notice the brackets around the exponentiation. Brackets are the ‘B’ of BODMAS, and are always evaluated first. The ‘O’ stands for ‘orders’ or powers, so an expression with multiplication and powers is interpreted as follows:

3 * 2⁴ = 3 * 16 = 48

It is not interpreted as follows:

3 * 2⁴ = 6⁴ = 1,296 (Wrong!)

The D and M of BODMAS stand for division and multiplication. If there are both multiplications and divisions in an expression, division is not always done first. The multiplications and divisions are processed, by convention, from left to right, and the same holds for addition and subtraction, but multiplications/divisions are done before additions/subtractions. I’ve seen explanations of BODMAS that say that divisions should precede multiplications and subtractions should be carried out before additions, but this is not so, and gives wrong answers. Or rather answers that don’t really comply with the BODMAS convention, as understood by most people.

Fine, that’s all sorted. Except that it isn’t. There are cases where the simple BODMAS, left to right, convention is insufficient. One such case is the case of exponentiation on exponentiation:

2 ^ 3 ^ 4 interpreted as 2 ^ (3 ^ 4) = 2 ^ 81 = 2.417x10^24
2 ^ 3 ^ 4 interpreted as (2 ^ 3) ^ 4 = 8 ^ 4 = 4096
Note: The '^' is used here for the exponentiation process, because it is difficult to apply superscripting twice. It also makes things a little clearer.

This case is usually interpreted by the first method, above. Such cases aside, the BODMAS convention clearly describes how to evaluate any arithmetic or mathematical expression. If you are not sure of the correct methods to use to create a complex expression, you should use brackets to clarify matters, whichever convention is used. If you are trying to evaluate a dubious one, you are out of luck, unless you can contact the author of the expression!

So, given that mathematicians and computer scientists (and many others) use the BODMAS conventions, what does that say about the expression ‘2 + 3 x 4’? Is the correct answer fourteen (14)?

The problem is posed ambiguously on purpose. The original setter was not really requesting an answer. He/she was inciting debate. Therefore the ‘solution’ doesn’t really matter. For what it is worth, I understand and use BODMAS, so I favour the answer of 14, but if the poser of the conundrum really wanted a unique answer, then they would have included brackets. Either:

2 + (4 x 3) = 14 or (2 + 4) x 3 = 18

Unfortunately the debate often quickly becomes acrimonious, with one side or the other hurling insults. But that’s the Internet for you.

What Happens When Your Body Encounters a Virus?

Image by Zeathiel. Downloaded from Freeimages

When your body encounters a virus, any virus, the virus enters your body and starts to multiply. It multiplies fast. It does this by taking over the genetic systems of the cells, and so the cells can’t maintain themselves and die. When this happens the cells burst open and release many copies of the virus from each cell into your body. Each copy of the virus finds another cell to invade. This applies to all viral infections, not just Covid-19.

Let’s say that each cell releases 100 copies of the virus, a number which is far smaller than the real number. The real number is much higher. So in the first step one virus becomes 100 viruses. Each copy infects another cell, and each produces 100 viruses. So, at the second step, 10,000 virus copies are released. At the third step, 1,000,000 copies are released. At the fourth step, 100,000,000 copies of the virus are released. By the time that the replication has gone through 10 steps, an astronomical number of copies of the virus are floating around your system. After 20 steps… Remember that replication factor is enormously more than 100, too. This is termed exponential growth.

Of course, the virus doesn’t have things all its own way. Your body has an immune system. It detects the virus and starts to fight it. If the virus has not yet managed to reduce your lungs to a bag of slime, or dismantled your nervous system, or whatever, your immune system starts to fight the virus. It starts killing infected cells thus preventing them from creating copies of the virus.

It recognises infected cells by proteins on the surface of the cell. These proteins are different for different viruses, and the immune system ‘remembers’ the signature of an infected cell, and eventually, if you are lucky, the immune system succeeds in killing off all virus infected cells and the infection is over.

(Please note that specialists in this field would probably find the above hysterically funny, but I don’t think that it is too far off the mark.)

So that’s what happens when a person encounters a virus for the first time. The outwards signs of the battle between the virus and the immune system are what we consider to be the disease. That is, raised temperature, headache, spots, cough, sneezing, and so on. Maybe more life-threatening symptoms. The virus does not directly cause any symptoms itself.

When a person who has already encountered the virus encounters it again, the immune system already knows about the virus and kicks in immediately. It doesn’t have to work out, firstly, that there is a virus and secondly, how to fight it. Your temperature might peak and you might have a headache, but any symptoms will likely be much reduced this time around, and virus will be killed off much faster.

But while your body is fighting the virus, there is a short time interval when the virus is in your body and you may be mildly infectious. Since your body is already fighting the infection, the infectious period will be short, and you won’t be ‘shedding’ as much virus to infect others.

The vaccine, any vaccine, is designed to fool the immune system and provide it with the necessary information to fight the virus without actually inflicting the virus on the body. It does this either by supplying the body with the dead virus or with a very much weakened virus, or with the information necessary to detect virus infected cells.

To do this, it needs to trigger some parts of the immune system into action, but doesn’t need to do more than that, so any side effects will be minor. A sore arm, for example.

A side effect indicates that your body is configuring your immune system to handle the virus. If you had previously encountered the virus in the wild, you would, at that time, possibly have had a severe infection. Side effects of the vaccines are rare, but if there is one, it signifies that your body is doing its job, and preparing a defence against the virus.

Of course, it is theoretically possible that you might have a reaction to some component of the vaccine. It’s theoretically possible that you will be killed by a piece of falling space junk such as a falling space toilet, of course. Or you could win the lotto. All these things would be of the same order of possibility. They are theoretically possible but very unlikely.

Worrying about the contents of the vaccine seems to be silly. If you end up in hospital after an accident, or you are hospitalised for something like pneumonia, or something worse, you would be pumped full of all sorts of things. Full blood. Blood plasma. Antibiotics. Many other things that the doctors and nurses would put into your body to save your life. They might even shoot X-rays through you, or irradiate you to kill cancer cells. It is ludicrous to worry about the contents of a simple vaccine, most ingredients of which are present only in microscopic amounts.

If you tell people that there is the possibility of a side effect on taking a medicine, then a number of people will experience that side effect, even when they are not given the medicine, but are instead given a placebo. A chalk pill or an injection of plain saline. If they are worried or concerned, the likelihood of the side effect will be higher. This is called the nocebo affect, and been blamed for up to two thirds of the ‘adverse reactions’ to the Covid-19 vaccine.

When someone who hasn’t been in contact with virus catches it, it takes a relatively long time for the body to learn how to fight the virus, which means that the body is shedding virus during the period that the body is learning how to fight the virus, and while the body is destroying the virus.

On the other hand, if the person has already had the virus or has been vaccinated against it, the body doesn’t have to learn how to fight the virus. That means that the shedding period is much shorter and the level of the virus in the body is lower, so that the total amount of virus that is shed is very much lower.

In summary, a vaccinated person sheds less of the virus for a shorter period and doesn’t usually get sick. There is less chance, therefore that they will infect someone else.

People often ask if you can catch the Covid-19 virus twice. Of course you can. The protection that the vaccine gives you wanes over time, which is why we need booster shots. This is also true for other viruses, like the flu virus. If you have had the flu, then you are protected for a while by your immune system, but the immunity fades over time. That, and variants of the virus, are why we have to have a flu booster shot every year.

If you don’t come in contact with the virus, then vaccination has no effect. If you do encounter it, it doesn’t stop the virus from entering your body. No vaccine does. It just allows your body to deal with the virus quickly and efficiently. Sometimes, in spite of you catching the virus before or being vaccinated, your body doesn’t properly remember that you have had it or been vaccinated, because the protection has waned.

In which case you will get the infection again, but it is likely that your body will at least partially remember the previous infection, so if you catch the virus twice the second time will likely be less severe.

Can you infect others if you are vaccinated? Yes, you can, if your body is fighting off the infection at the time, but the chances of you doing so are very much reduced. The virus will be in your body for only a short period, and you will not have time to shed much of the virus in that time.

I have tried to explain what happens when you are infected by a virus, such as Covid-19. It is always a good idea to be vaccinated. If you decide not to get vaccinated because of the very small chance of having a usually mild side effect, that is like being in a crashing plane and refusing a parachute because ‘you know, those parachute things have been known to get tangled and people have been killed by tangled parachutes’.

Asking for Donations

I’m useless at self-promotion, so up until now, I’ve avoided asking for donations for my work. It’s partly because of the ‘imposter syndrome’, and it’s partly because the tools that were available were once difficult to use or expensive.

It’s the ‘imposter syndrome’ which really cripples me and causes me to hesitate to ask for money. Questions arise like ‘Am I being cheeky, asking for donations?’ or ‘Is my writing good enough to be asking for donations?’ or ‘Can I really call myself an author?’.

I’m less worried by the technical complexities that go with asking for donations. Technical stuff has been my whole life, and I don’t usually have problems with that sort of thing, but sometimes a prerequisite of the technical stuff is a paid subscription to something, and that is a problem for me.

There also has to be a driver. Why do I want to ask people for money? The reason is that I want my writing to improve. I want it to be worth reading, and that involves asking people for advice. People, friends and relations could be asked to help, I suppose, but to really get the lowdown on my writing I would need to employ a professional editor.

So that is why I am asking for donations. If I can get enough, I can ask someone to look over my work, and give their professional opinion. I should be able to improve my writing, both by editing my past work, and by taking account of the editorial comments when writing new stuff.

Please consider donating via Paypal (you don’t have to have Paypal to do it), so that I can improve my past and future writing. Thank you.

A Self-Limiting Problem

Some wag, way back when dinosaurs ruled the earth, once commented that homosexuality is a self-limiting problem. I assume that he (or for that matter, maybe, she) meant that homosexuals don’t breed, so they can’t produce more little homosexuals. Of course there’s many things wrong with this comment, not the least of which is that homosexuality is somehow a ‘problem’.

The writer of the comment assumes that homosexuality has a genetic component. That is, homosexuals are born not made, which is almost certainly true. But the writer was totally wrong when he/she suggested that homosexuals do not breed. They can, they do, and they have always done so, by one means or another.

I don’t know whether the babies of homosexuals are more likely be homosexual or not, but if I were to hazard a guess, I’d say that the kids of homosexuals would be slightly more likely to be homosexual than the kids of heterosexuals. This would be because the kids of homosexuals would be less likely to suppress any homosexual tendencies in themselves than the kids of heterosexuals. Just a guess.

The mothers of homosexuals are mainly heterosexual women, so homosexuals are not going to die out unless the human race changes and homosexuals are not born. This is good, because they are often colourful and interesting characters. I know that’s a stereotype, but it’s not far off the mark.

The thoughts above came to me when I was thinking about something completely different. Anti-vaxxers. They are far from my favourite people. They are the aggressive fundamentalists of this era, the sort that get up in your face and cover you in spittle as they shout their arguments at you from very short range. That’s also a stereotype, and it is also not far off the mark.

When we get vaccinated, we protect ourselves and others from diseases like Covid-19. We all wear masks because that probably reduces transmission of the disease. The vaccines will protect us and will reduce the effects of the virus if we come in contact with it, but they are not perfect. A few people will get the virus even though they have been vaccinated, but only a small number out of an already small number will need hospitalisation. Very few will die.

But those who have not been vaccinated will, if infected, probably need medical help. Many of them will end up in hospital. Some will die.

So, will anti-vaxxers die out? Will they die or recant before they can have children? That seems unlikely, as many of them already have children and scream “You’re not putting that junk into my child’s arm!”

Also, being an anti-vaxxer is probably not hereditary. Of course, their children will be indoctrinated by their parents with their parents’ anti-vaxxer views, and in that way the parents’ views would be ‘inherited’ by the children. Later the children could encounter a disease that kills them because they are not protected against it. They would not pass along the anti-vaxxer mind set to their potential children and the anti-vaxxer mind set would die out, but only in that family.

Unfortunately, the anti-vaxxer mind set can spread sideways much faster than it can die out. An anti-vaxxer can ‘infect’ many others with their mind set in a very short time.

Since it looks like anti-vaxxers are not a self-limiting problem, we will have to live with them. We’ll need to get vaccinated, and we will need to pay our taxes to provide the medical services that they and their kids will likely need. It’s the price we pay for living in a free society. It would be a lot easier if we could compel them to get vaccinated, but that is not something that anyone in their right mind would want to do.

Photo by Andrzej Pobiedziński from FreeImages

With any luck the rise and fall of the anti-vaxxers will parallel the rise and fall of smoking. At first no one smoked. Then everyone did. It became apparent that people were dying as a result, and while the smokers and the tobacco industry pushed back, the numbers slowly started to fall though it will be a long time until smoking tobacco all but disappears.

Probably the most effective measure that was taken to reduce the number of smokers was the banning of smoking in public places, like pubs and restaurants. It used to be automatic to light up after sitting down. When you had to go outside to light up, it became a chore and this make it easier to give up.

I think that one way to reduce the number of anti-vaxxers would be to ban unvaccinated people from public places, like cinemas and clubs, but that is hard. If everyone carried an inoculation ‘passport’, it might work. Almost everyone carries a driver license, and that works, but there are valid reasons to be wary of requiring everyone to carry an inoculation passport.

Maybe the anti-vaxxers will come to their senses eventually, when they see their unvaccinated family members dying off. Maybe. But by then they will have passed the virus on to others. Innocent people who would get the vaccination if they could, but can’t for some medical reason.

Every unvaccinated person is a Typhoid Mary. It is worth reading that Wikipedia article to get an idea of the mayhem that an uncooperative unvaccinated person can cause. If you are not vaccinated, and you infect someone and they die, then it would make sense that you could be charged with manslaughter. The problem would be proof.

Photo by Marcus Österberg from FreeImages

New Stories and More

I’ve been bad! I’ve not been keeping my website and my Facebook Author page up to date, but I have been writing some short stories. I’ve created a new page to contain the links to these new stories, and I hope that you will drop by and have a look at them.

I’m always interested in reflecting on my creative processes, and one thing that I have discovered is that I am much more interested in writing the stories than I am in publicising them. I suspect that I’m not alone in this!

It is likely, I feel, that there are people out there who are more interested in telling people about their stories than in writing them, and I understand that, but I find it hard.

When you self-publish, your free options for publicising your books and stories are limited. You can make them available on Amazon, or on Kobo or similar sites, or you can make them available through Smashwords or some other aggregating site.

Putting them up there, on the Internet, doesn’t guarantee that people will find (and buy) your books. You also need to tell people about them, so one of the first things that you need to do is to set up a Facebook Author page like I did.

People will still not find your stories, but there is something that you can do, to direct people to your stories, and that is to buy adverts. You can do it on Facebook and you can also buy Google ads.

That means spending money. Well, if you are prepared to spend money, good on you. I don’t want to spend money, so I am resigned to selling one or two books a decade. Unless I’m extremely lucky, (and my books are good enough, which I’m unsure of), I won’t have a best seller on any list!

One more thing that I could do, is give people the option of paying me money to read my books right here on my website. I might do that in future.

Please note, I’ve decided to share my stories here as PDFs. If you would prefer a different format, for example, an ePub file, just let me know through my feedback form.

Some of my stories have been published on Amazon (as eBooks and paperbacks) and Kobobooks and Smashwords (as eBooks). Here are the links to my Author Pages on those sites.

The Creative Process

Photo by Wojtek Piekutoszczak from FreeImages

I’m constantly fascinated by the creative process, at least in so far as it applies to my writing.

I constantly read articles about how to write stories or even novels. The secret, apparently is to plan everything out, usually based on some scheme or template. You have to develop your characters, maybe give them a backstory, a history. Then there must be a problem, an issue, or a difficulty, otherwise there is no story of course.

Only when all this structure is in place can the poor author actually write the story. Avoiding adverbs of course. This works for some people, and there are programs out there to help you if you write in this manner.

There is another way. Draw up a piece of paper or open a word-processing document and write. This is the way that I do it. Oh, I do get an idea in my head, and it does bounce around for a while, attracting characters, plot points, problems and so on, well before I touch a keyboard.

Take the piece that I am writing at the moment. (No, not this post, Johnson!) I’ve already written two stories about a group of people, and I wanted to close out a trilogy. I don’t know why. It just seemed right.

So, there’s a group of characters. They’ve jelled as a group, and are comfortable with each other. I’m comfortable with them, but I can’t just write about their normal lives. No dramatic tension.

So, I just write. I assemble them (it’s the beginning of term), and I have an idea. They’re college age, so boyfriends and girlfriends! They have classmates, and they don’t like one of them, and that character becomes their antagonist. The story is starting to take off.

All the while I am thinking about them when I’m not writing. What if they do this? What if they do that? I guess in a sense that I’m writing the story even when I’m not actually writing the story. I’m considering what they will get up to while I’m wandering the aisles of the supermarket.

Gradually I get an inkling of the main thrust of the story. Obviously, I have my team, I have their antagonist, and maybe their antagonist has a team too. The differences between the two groups escalate, and need to be resolved.

In addition, key scenes occur to me. They may not yet be linked into the story, and not all of them will be in the story in the end, but if I decide that they do belong in the story, the narrative must lead naturally to them.

As regards my current story, I do not have a resolution to the conflict, and only a vague idea of a conclusion, yet, but they will come, inevitably, as I continue to write the story.

The planning approach. It’s not for me, but it may work for you. I’ve tried it and I got nowhere. It may help some people to get their thoughts in order, to steadily work through the plot from introduction to conclusion, but that changes it, for me, from being enjoyable to being, well, tedious. Work, in the negative sense.

But… I can’t emphasise this enough, planning everything out works well for some people. So try it.

But even if you think that you would do best with a well honed plan, I believe that you should try to write a story without a plan. It may be that the method that works for you lies somewhere between the two extremes, and only by experimenting will you work out the way that suits you best.

Rule one of writing is that there are no rules.

My Lastest Stories

I just realised that I’ve not posted any of my stories for a while. In fact I’ve not posted much at all! I’ve still been writing stories, but most of the time I’ve been polishing ones that I’ve already written.

The stories that I am posting below are ones which I’ve not posted before, but when I’ve figured out how to update files on this site I will update some of the older ones. I’ve not substantially changed them though. I’ve just changed a few sentences, corrected some grammar and spelling mistakes. That sort of thing. I hate seeing mistakes in my stories!

Under the Bridge

The troll didn’t have a name, and the humans teased him. He lived quietly under a bridge, and appreciated the smoothness of a stone, the strength of a rock, and the trickling of the stream. But he saves the humans and meets an intriguing fellow stream dweller.

Under the Bridge Download

A Cat’s Tale

There was something about the cat, the Boffin decided, that was not quite right. The Mage agreed, so they kept an eye on her. She led them to an encounter with a prickly Cat Queen, and the Mage and the Boffin uncovered a plot.

A Cat’s Tale Download

The Master and the Student

The Master lives high on the mountain known as the Behemoth. He sees climbers come to try to conquer the mountain and often, they die. The Master knows everything, except those things that he deliberately chooses not to know. He is waiting for his Student to appear from the world below.

The Master and the Student Download

The Girl

It’s a time of war, and a time of disruption. The girl robs dead bodies for food because her mother is dead and her father is missing. She is barely surviving, but then one of the dead bodies turns out to be not as dead as she thought.

The Girl Download

A Sailor on the Endless Sea of Stars

Azathoth searches for something, but he doesn’t know what. He travels the infinite universes, searching for life and the meaning for his existence. He meets a girl and lives a full human life, but there is more to him than that.

A Sailor on the Endless Sea of Stars Download

Please note, I’ve decided to share my stories here as PDFs. If you would prefer a different format, for example, an ePub file, just let me know through my feedback form.

The featured image of a cat is from FreeImages and is by Lesli Lundgren.

Updating my stories

I’ve been reviewing and updating my earlier stories, and I’ve removed a few spelling and grammar errors, and tidied up the language a bit here and there. I’ve not radically changed them, but I thought that I’d package them as a PDF and make the new package available on my website. So, if you want to have all my early stories in a convenient package, please download it from here.

If you want my stories in a different format, a MOBI file for a Kindle, for example, let me know via my feedback page, and I will see what I can do.

Some of my stories have been published on Amazon (as eBooks and paperbacks) and Kobobooks and Smashwords (as eBooks). Here are the links to my Author Pages on those sites.

LibreOffice – Style Considerations

hieroglyphs — Photo by Krzysztof (Kriss) Szkurlatowski from FreeImages

Every modern word processing program comes with a feature, usually called ‘styles’, which allows you to control the look of your final document. Microsoft Word does. LibreOffice and OpenOffice do. I’d be surprised if there was a major program word processing program that doesn’t.

A style is a collection attributes, such as font, font size, indentation, alignment, colour, and many other attributes that describe an element in a document. The element can be a page, a character or set of characters, a paragraph, an image, and many other things. A style can be applied either by default, or by selecting an element and clicking on a list of available styles.

Sounds complex? It isn’t really. When you want to create a heading for example, you can type some text, select it, change the font type to make it bold, change the font to make it stand out, and increase the size. Or you could simply type the text and then apply one of the builtin Heading styles with a single click and everything is done for you.

I’m mostly concerned here with paragraph styles. That is, styles which apply to whole paragraphs, and not just single characters or words. In MS Word, LO Writer and other word processing programs, if you start typing a paragraph it will be formatted according to a default style. In MS Word I believe it is called “Normal”. In LibreOffice it is “Default Paragraph Style”. The current paragraph style is usually shown somewhere in the editing screen.

(In my text below I will refer to things in LO Writer terms, because that is what I use. But the concepts should apply to MS Word and probably other word processing programs too, even if the details are different.)

It is my strong belief that everything that affects the look and feel of a document should be achieved with styles, because it makes it so much easier to change things.

For instance, suppose you decided to make one of your paragraphs stand out. You could select the paragraph text and make it bold using the style toolbar at the top of your editor screen. That would work.

But several hours later and many pages later, you decide to also indent it. You have to search back through the document for it. Again you could use the on-screen tools to indent the paragraph. Again, that would work.

You return to end of your document, and create another paragraph, which you bold and indent. So far, so easy. But then, you decide that the bold paragraphs would look better in a different font size. Now you have two places to go to change the font and each time you create a bold paragraph, you need to bold it, indent it, and change the font to be consistent.

By the time that you have six or more bold paragraphs, and you want to change something else about them, you will find yourself flicking about in your document. And what if you miss one of the bold paragraphs? Your formatting is no longer consistent!

It would be a lot easier if you had created a “Bold Paragraph Style” (based on the “Default Paragraph Style” for example) the first time that you decided that you needed a bold paragraph. Then you could change all the occurrences of the bold paragraphs without needing to visit all of the occurrences individually. Just change the style!

Creating a new style is not hard. You don’t have to supply all the attributes. You base your new style on an existing one, and just change the things that you want to be different.

I would avoid changing the builtin styles. This is because every style except the “Default Paragraph Style” is based on another style, and all builtin styles are descendants of the “Default Paragraph Style”. In other words the style system is hierarchical, and if you change the “Default Paragraph Style”, any styles which inherits from it, directly or indirectly, may change.

I would not use “Default Paragraph Style” for ordinary text paragraphs, as it is the ancestor of all builtin style. Instead I would choose “Text Body” or one of the styles that inherit from it, and then the consequences are limited.

Since styles are arranged hierarchically, a style such as “Heading 1” for example inherits from the style “Heading”, which in turn inherits from the “Default Paragraph Style”. So some of the settings of “Header 1” come from “Heading” and some from way back in “Default Paragraph Style”.

This is all pretty straightforward and logical, but difficult to explain. The main lesson is that if you use styles, be really cautious about changing the builtin styles, as changing one style may affect any styles which inherit from it.

This is not a good reason to avoid styles as they can make life so much easier for you!

But what if you want all your documents to have the same formatting. The chapters of a book should ideally all look the same, so that when you combine them, it all looks neat and tidy.

You don’t have to modify the styles in each document that you create! That would be tedious and error prone. Instead you can take a document that is in the format that you require, and save it as a template. I’m not going to detail the process here, because there are a couple of ways of doing it in LibreOffice Writer, and that is almost certainly true in MS Word and other word processing programs too.

You can edit the template to remove all the text, if you wish, but the template will have all the necessary styles in it, and writing a new chapter will be easy, with just a click now and then to apply the styles!

One final point is that once you have created a template and are using it to create documents, then everything is not set in concrete. You can change the styles in the template and revisit and save your documents to update the styles in them. This may be tedious, but it is simple! You can even apply a template retrospectively to your old documents, but that is beyond the scope of this article.

In conclusion, I strongly believe that anyone who uses a word processing program that provides a style-like feature and a template-like feature should use the features in almost situations. OK, you write a letter and may think that you would not need to style that, but then you come to write another similar letter. If you had spent a few minutes styling your first letter, you could use it as a template for any subsequent letters. “Dear Mum…”

Don’t be scared of styles. They aren’t really that complex. Styles will not cause you to lose any work or break your word processing program. If things get too messy you can always cut and paste your text into a brand new empty document. I ended up with a mess because I like to experiment with things and only read the documentation after I’ve tried something (and usually screwed it up). But my documents are going to look perfect by the time that I’ve finished.