Of Toadstools and Other Things.

When I was a small child, I would go to the fair with my grandmother and I hated it, the noise, the grubbiness, the smell of sweat and the stickiness of candy floss all upset me; my grandmother on the other hand was in her element, she would display clear delight as her penny rushed down a wooden channel, then slowed and wobbled hesitantly as it ran towards her frequently missed winning number. Better still, she could place a ping pong ball in the open beak of a huge yellow fibreglass duckling that waggled from side to side until the ball was ejected from its bottom to run into one of a variety of differently numbered compartments. With five balls to place, the lucky, or perhaps ‘unlucky’ high scorer might win a hideous brown vase as brittle as brown crystalline sugar.

Like his mother before him, my father enjoyed similar entertainments, his favourite was the circus. My parents took me to one when I was about six years old and it was an horrifying experience. Why were men in outsized outfits with gaudily painted faces driving a junk car around an arena until the doors blew off with a bang? By the response of the crowd it was obvious that it was me – the one with the ‘can we go home now’, sense of humour failure, that was out of place. Maybe the 1950s was a time when we laughed at different things – apart from me that is – I was laughing at different different things.

Today, more complex games are available than my grandmother could ever have imagined, let alone find at the fair; the mindless nature of these new forms of entertainment invade our homes every day via the internet to be absorbed by our children’s brains, the greatest wasters of irretrievable time so far devised (the games not our children, although sometimes….?). Certainly modern electronic games eat into more spare time than was ever available to my grandmother and father combined, both of them having no other choice but to live in the real world. I have watched my children as they get sucked into imaginary meaningless worlds each with a slightly different slant on predictable stories told with uninspiring graphics – the flickering opiates of a darkened room. O.K. I’m from a different galaxy, but I’ll struggle on, deriving pleasure from the natural wonders that my adopted planet has so far managed to hang onto, and as I do, I will do my best not to get suckered by the incredullous cheap tricks that have infected the minds of generations of my gullible family.

I met a man today who wanted to know what I though I was doing – and that’s not unusual – I meet people everyday who ask the very same question, and I’m often obliged to explain why I am lying front down in the dirt. On this occasion I was photographing toadstools and I told him exactly that; then I notice that he had a dog with him, and I said, ‘That’s a nice dog’, because it was. ‘What’s his name?’

‘It’s Improbable’, said the man.

And my response was that this was an unusual name for a dog.

‘People often say so’, he replied, ‘but I don’t think that this is the case. It is simply an improbable name for a dog, whereas Unusual might be an unusual name for another dog’.

So, it seemed that he was a wise guy, but I was completely drawn in by the way he thought, and so I asked him why he had called his dog Improbable’.

‘Because he’s very big for a small dog’, he said, ‘and so for me he’s a bit like the Universe – improbable. But, I should add, by no means impossible.

I realised that I should then have said, ‘A well behaved dog then?’, but by the time I’d thought of that the moment had passed. So having lost my best opportunity, I didn’t know quite what to say, but I did know that if I asked the obvious question, Impossible would be an impossible name for yet another dog. All that I wanted to do at this stage was the usual thing, and that was to pretend I hadn’t noticed anybody standing close by, but it was too late for that, and so instead I said (rather stupidly in hindsight), and as much for something to say as in reply.

‘Are you perhaps interested in the improbability of the Universe?’

‘No I am not’, replied the man. ‘I’m not interested in the Universe or anything of that sort. I don’t have a telescope or any of the required knowledge that would allow me to be remotely knowing about such a thing – I simply wouldn’t know where to start. Infact, I’m not interested in science, mathematics or anything along those lines… I think it is safe to say that I’m not an inquisitive person’.

I couldn’t help myself. ‘Are you interested in anything at all’. I asked.

‘I am’, he said.

There was a pause and I thought the conversation might mercifully be over, but this wasn’t the case.

He continued, ‘Mostly I’m interested in novelty, mystery and the misfortunes of others’.

‘Oh’, I said, because I couldn’t think of anything to say to that. So I changed the subject.

‘My name is Stephen’, was all I could think of at short notice.

‘Mine’, said the man, ‘is Arthur… Arthur Cottingley’.

‘That’s an unusual name’, I said, and he didn’t say, ‘What – Arthur?’, because he wasn’t that predictable. Instead he said, ‘I am sure you already know it, because you must have heard it before’.

I decided to ignore his presumption about what I must have heard before and changed the subject for a second time.

‘The light isn’t quite right for this shot’. I said, ‘I’ll have to come back and try again tomorrow morning’.

And it was then that he asked a rather strange question.

‘And will you be doing your picture from the position you are in now, or will you do it from the other side?’

‘This is the shot’, I said, ‘it has to be exactly from here’.

‘Exactly?’ he asked in confirmation.

I checked the shot and said yes, but when I looked up Arthur Cottingley was nowhere to be seen, and I must admit to being quite relieved.

As the sun began to set, I packed up my gear and walked out of the wood.

The next day I went back and took the picture below; and thought no more about Arthur Cottingley until the result had been imported into my computer, and then I began to wonder if I’d ever met Arthur Cottingley at all.

When you take a picture, you don’t always save the Planet, but once in a while, you get an image that your grandmother might find entertaining – improbable as that might sound.

RIMG0373.FAIRY.FIX FINAL2_C_edited-1

UP, UP AND AWAY. From Ebola to Exponential and Beyond.

Perhaps the most reliable way to ‘save the planet’ is to take a picture that has been constructed by using mathematics and arithmetic; these exist in a variety of forms, but most commonly they are represented as charts or graphs that can provide at a glance, information on any subject for which there is reliable data, and graphs in particular are good at showing numerical change against a baseline of time.

I’m one of those unfortunates who have trouble adding up a column of figures – seldom do I get the same total twice – even with a calculator! That’s discouraging, but it’s not a valid excuse to give up.  And mathematics doesn’t come any easier, but let’s face it, we owe it to the planet to try, because mathematics is the key to measuring everything important that is going on around us.

A politician or national spokesman who says, ‘I’m just hopeless with maths’ or ‘math’ (depending on where they are standing) and then laughs it off, should be looking elsewhere for work. There is understandable concern when the people who represent us do not usually have backgrounds in mathematics or science – political science doesn’t count, because that’s an oxymoron. Anyway, the ‘I don’t get mathematics’ excuse is unacceptable from any elected official and we should urge them to ‘try harder’.

When I heard a health spokesman say recently that the Ebola virus epidemic in West Africa was growing exponentially month by month there was obvious cause for concern. The spokesmen then gave the number of infections that occured during the previous month followed by the predicted figure for the month to follow, and the figures were exactly the same. This implied that he either didn’t understand exponential, or the increase wasn’t exponential at all. The statement was confusing: was the  rate of infection steady and controllable? Or was it expanding  exponentially, suggesting that  heading for the hills was the best possible option?

Understanding exponential growth shouldn’t be a problem. Most small children can draw it, even if they can’t describe the outcome.

Little Timmy can't say the word, but he can certainly draw it - a simple example of exponential growth.
Little Timmy can’t say the word, but he can draw a simple example. Here, a single person infects two others and if the disease is passed on in the same manner, the infection quickly gets out of control. This kind of growth applies to many things including human population growth.

In everyday life, most people don’t think much beyond arithmetic progressions, where the increase between numbers is constant.  But exponential growth is nothing like that. Once you start down the road to exponential, by doubling up, it isn’t long before the figures are mind blowingly large, and if they relate to a dangerous disease that goes unchecked, no health service on the planet will be able to deal with it.

There is an ancient Persian story that explains the process well. An inventor who pleased his king with a wonderful invention was asked to name his reward; but he at once disappointed the ruler with the seemingly meagreness of his choice. The inventor asked for grains of wheat to be placed upon a chess board in the following manner: one grain on the first square, two grains on the second, four on the third, eight on the fourth, 16 on the fifth and so on, until all of the 64 squares were covered. The numbers start small and most of us don’t think much beyond the 8th square where the total hits 128 grains, which isn’t an outrageous figure. Quite a surprise then to discover that to reach the 64th square requires 18,446,744,073,709,551,615 grains of wheat – more wheat than was available in the whole kingdom. The tale is spun as  an example of intelligence winning the day, or alternatively, it is a story of cunning and greed –  the inventor either becomes ruler of the kingdom, or he loses his head.

In today’s world we might relate this story to pyramid selling where an investment doubles up every move it makes down the line and before long the numbers become vast, but by then, many individuals have dropped out of the scheme and never pay their contributions, while those who stay in begin to run out of suckers to sell to.

Telling a story is a great way to explain numerical change, but an artful graphs is a more visual approach. The two graphs below are free of annotation which allows the image to pass for art if you prefer it – perhaps as a late Matisse paper collage.

This could be a late period Matisse paper collage, but we might also consider it as representing two curves on a graph running along a base line of time. curves
Consider the above as two curves on a graph with a base line (or x axis) representing the passage of time, and a vertical (or y axis) representing the numbers or the density of an animal population increasing linearly as the line progresses upwards. This colourful ‘picture’,  interpreted correctly, contains enough information to save the planet .

The upper curve begins between yellow and red but continues for the most part  between yellow and green – it starts shallow, then rises exponentially before levelling off. This forms a ‘logistic curve’ first used by Pierre Verhurst  in the mid 1800s to show natural population growth where numbers are held to an upper limit by predation and availability of resources.

The lower curve that runs at first between red and yellow and then red and green takes time to rise, but when it does the line steepens rapidly – this is exponential growth that hasn’t levelled off. The world human population presently follows this ‘run away’ curve, but without infinite resources it cannot continue to grow in this manner. In a finitely resourced world the predictable result is a sudden levelling of the curve and a plummet downwards that mirrors the up. To alleviate suffering, it makes sense to control the drop – this really is a case of the higher you go the harder the fall.  Birth rates are presently falling across the developed world, but for economic reasons the numbers are usually bolstered by immigration (O.K. there will then be fewer people somewhere else, but that doesn’t regulate the population in places where people are genuinely trying to control their numbers).

The logistic curve along with the wave curve (see the predator prey relationship graphs below) apply to almost any species other than our own and they have longterm benefits for both the species and the environment – and make better models for longterm regulation than does uncontrolled exponential growth. All the information we need for responsible behaviour is contained within a couple of simple graphs, indicating that self regulation of human population is a better option than the inevitable collapse that continued exponential growth has in store .

Unfortunately, governments do not run economies with a view to longterm sustainably – they invariably opt for growth above all else, and are reluctant to make changes, preferring instead to pass the parcel onto the next generation – a ticking time bomb which they’ve chosen to ignore. Economies are run as if resources are infinite and without cost beyond extraction, refining and transportation. However, at a certain point, the Earth will no longer be able to sustain this, and if the present generation continues to charge up the steep end of exponential… future generations will be forced to pay the price, and will know that we had all the information available to make the right decisions, but instead carried on, business as usual.

 

HERE WE ALL ARE, UP ON THE STEEPEST PART OF THE CURVE.

Human population growth started off slowly.It is obvious that population wasn't a problem prior to 1800, but an agricultural revolution, an Industrail Revolution and the development of modern medicine has aided population growth and  when the graph is climbing as it is today, there is a genuine need for us to engage with the reality.
Human population growth started off slowly. Population growth clearly wasn’t a problem prior to 1800, but an Agricultural Revolution, an Industrial Revolution and the recent development of modern medicine have all helped to allow our numbers to grow exponentially and there is now a genuine need for us to engage with reality.

Things often start off slowly before exponential growth kicks in. With the human population nothing much changed for a very long time. There was even a period around70,000 years ago (long before the time line represented in the above graph), when the human population dropped so low we almost disappeared altogether.

It may well have been cooking meat and the development of  agriculture that started things moving, but there have been other set backs: the black death was a devastating pandemic and can be seen as a dip in the population graph around 1400. Prior to the plague weather conditions around the mid-1300s  were unfavourable, and throughout Europe crops repeatedly failed. It was a perfect storm of a disaster and millions died – but the loss of a third of Europe’s population did change the economy. Suddenly, there was a shortage of workers and for the first time in recorded history a more reasonable wage could be asked by those who survived the devastation. Poverty was still widespread, but many people were liberated from serfdom, and took the first steps along a path that generations later would drive the Agricultural Revolution, the Industrial Revolution and eventually the modern Western economic system we have today.

In the broadest sense exponential growth isn’t a disaster, it is often the way things increase in the natural world, but there are always boundaries. A fertilised ova wouldn’t develop at a rapid enough rate if cell growth wasn’t initially exponential, but once a certain functional level has been reached, cells are programmed to be replaced when and where they are needed – if they keep on dividing without control, we call it cancer.

Almost everything that relates to our rapidly increasing human population is unsustainable.  The graph below demonstrates a normal predator prey relationship where foxes are eating hares; it could equally be wolves preying on deer, or any number of other predator prey interactions.

Along a base line of time the green curve of prey animals increase, producing more food for predators which set the pattern for controlling the prey as the prey numbers decline, so do the predators. The winner is plants. Without the predators the world becomes less diverse as the plants are eaten. This of course is an oversimplification as there is a web of life, but the principal holds.
Along a base line of time, the green curve shows prey animals beginning to increase in number, thus producing more food for their predators, the foxes – shown in black. Foxes then increase in number, eat more hares and cause their prey to decline. Fox numbers begin to fall in response to the diminishing food supply and hare numbers pick up again – the process continues in a cyclical manner.

Other species also benefit as predator and prey numbers ebb and flow. Plants for example will escape total obliteration by hares and rabbits as predators reduce herbivore numbers. Without natural predation environments become less diverse as certain species are eaten beyond their capacity to regenerate. However, the predator prey graph is an oversimplification, and although the general principle holds true, the system is really a three dimensional web of life that demonstrates far greater complexity. We refer to a natural balance of nature, but the reality is closer to a series of peaks and troughs. If our human population followed closer to the logistic curve, modern technology would allow us to regulate against a roller coaster of loss and gain in a manner that can’t so easily be applied to the steep end of exponential growth.

Related closely to our population numbers is the extraction and burning of fossil fuels.

This graph shows the level of oil extraction (fossil fuel) and as would be expected it follows the same line of exponential growth for the human population. Coal extraction starts a fraction earlier on the time line, but follows the same exponential growth line.
This graph shows the level of oil (a fossil fuel) extraction.  As expected it follows the same line of exponential growth shown on the human population graph. Coal extraction starts a fraction earlier on the time line, but clearly follows a similar exponential growth curve.

It is impossible for us to remove and burn fossil fuels indefinitely, because such resources are finite and as time passes, these diminish and become increasingly difficult to extract. And another consideration is the effect that burning fossil fuels has on our atmosphere should we decide to try it.

The increasing emission of carbon into the atmosphere when fossil fuels are burned is clearly changing the Earth’s atmosphere.

Not surprisingly Carbon dioxide emissions due to the burning of fossil fuels also follows an exponential line.
The time line starts here at 1600 – before this time, man’s burning of fossil fuels was negligible, but when the Industrial Revolution kicked in Carbon dioxide emissions began to pick up and were soon growing exponentially. Once again the sudden ‘up’ part of the curve runs close to the curve for human population growth.

Burning fossil fuels has a special place in the grand scheme of things, because it increases the levels of Carbon dioxide in the atmosphere and that in turn increases global temperatures. Continuing to do so at an ever increasing rate not only changes the atmosphere, it also changes the weather and at a certain point these changes may be irreversible.

Some times politicians and spokesmen do know how to use the figures in their favour. Global temperatures are evidently rising, but what if they were to show you only the section on the red box?
Some politicians and spokesmen do appear to know how to use graphs when they work in their favour. Global temperatures are clearly rising, but what if you were shown only the section of graph in the red box?

If you looked only at a graph showing the period between 1950 to 1970 you’d consider global temperatures to be fairly stable.  There has also been a similar levelling of temperatures in recent years; these are the favoured areas for climate change sceptics to cherry pick their examples and tell us, ‘there’s nothing to worry about’, but unfortunately, there can be no denying the general temperature trend is upwards – the planet is warming, which supports the idea that it is necessary to always view the whole picture.

The Ebola infection figures discussed earlier do indeed appear to be growing exponentially (at the time of writing). The curve ran fairly level through May and June, which would have been the ideal time for the developed world to have moved in and defeated the disease before it took off. To have ignored this opportunity seems careless if not arrogant. The question is, if I can manage the calculation on the back of a cigarette packet (see below), why can’t those in power do the same. It would be generous to put the terrible suffering in West Africa down purely to ignorance, but sometimes it is suffering economies rather than suffering people that elicit the most rapid responses.

Below: an ‘on the back of a cigarette packet’ calculation derived from figures freely available from news reports. This was quite tricky – not the mathematics… it’s just that I don’t smoke.

A back of a piggy packet graph for Ebola infection. Hopefully the infection will now begin to come under control - an exponential doubling month by moth is almost too horrible to contemplate.
A back of a ciggy packet graph for Ebola infection shows more than 13,500 cases at the time of writing ( I drew this graph during October. Since then the figures have rapidly picked up and I’ve had to extend the graph upwards). Hopefully the infection will now begin to come under control – an exponential doubling month by moth as can be clearly seen between the beginning of October and the beginning of November is too horrible to contemplate. Potentially, there is a long way to go before the disease peaks and crashes naturally if it is allowed to spread unhindered.

 

So far there have been around 5,000 deaths due to Ebola and there will be many more in the coming months, but hopefully, now that medical help is arriving in the affected West African countries (better late than never), the infection will begin to come under control.

Whenever we hear a spokesman say that ‘growth is exponential’ it is good to be clear about what he or she means. Certainly this is important when it refers to human population growth; or the increasing use of fossil fuels; and the rapid spread of a contagious disease. In each case we need to ask the right questions, then be certain that our answers make sense, and last but not least, act as quickly as possible – and so far we have been unforgivably slack on the last one.

The ciggy packet slip aside, all of the simple ‘mathematical’ pictures shown above have been colourful, and without exception are easy to interpret – this isn’t intended purely for the benefit of small children – it is also to grab the attention of the mathematically challenged politicians making important decisions; they really do need to, ‘get the picture, act in good time’, and in so doing, ‘save the planet’.

In mid October 2014 Tony Abbott predicted that coal would be the world’s principal energy source for decades to come. It was he said, ‘Good for humanity’. I wonder if I’m living in a parallel universe – Tony Abbott must be better informed than I am… he’s the prime minister of Australia.

At the time of posting there was some hopeful news. A decrease in the number of reported cases of Ebola in Liberia. WHO’s spokesman Bruce Aylward said the response to the virus was now gaining the upper hand, but warned the crisis wasn’t over. The Head of the U.N. Mission says that ‘presently he doesn’t have the  resources to defeat the disease’. How nuts is  that?

For a perceptive and amusing view of man’s destruction of the Planet,  take a look at this cartoon:

http://laughingsquid.com/man-animated-short-showing-our-destructive-relationship-with-earth/