Imagine this….

Flying Swan

Drawn using Python and Matplotlib. This picture is serendipitous and not intended.

[Grr! While I finished my previous post, I didn’t publish it. Darn it.]

Since I’ve been playing around with computer generated images recently, my thoughts turned to how we see images. When you look at a computer or television screen these days, you are looking at a matrix of pixels. A pixel can be thought of as a very tiny point of light, or a location that can be switched on and off very rapidly.

Pixels are small. There’s 1920 across my screen at the current resolution, and while I can just about see the individual pixels if I look up close, they are small. To get the same resolution with an array of 5cm light bulbs, the screen would need to be 96 metres in size! You’d probably want to sit at about 150m from the screen to watch it.

A closeup of pixels.

A closeup of pixels. (Photo credit: Wikipedia)

The actual size of a pixel is a complicated matter, and depends on the resolution setting of your screen. However, the rating of a camera sensor is a different matter entirely. When I started looking into this, I thought that I understood it, but I discovered that I didn’t.

What complicates things as regards camera sensor resolutions is that typically a camera will store an image as a JPG/JPEG image file, though some will save the image as a RAW image file. The JPG format is “lossy” so some information is lost in the process (though typically not much). RAW image file are minimally processed from the sensor data so contain as much information about what the sensor sees as is possible. Naturally they are larger than JPG format images.

When we look at a screen we don’t see an array of dots. We pretty much see a smooth image. If the resolution is low, we might consider the image to be grainy, or fuzzy, but we don’t actually “see” the individual pixels as such, unless we specifically look closely. This is because the brain does a lot of processing of an image before we “see” it.

I’ve used the scare quotes around the word “see”, because seeing is very much a mental process. The brain cells extend right out to the eye, with the nerves from the eye being connected directly into the brain.

Schematic diagram of the human eye in greek.

Schematic diagram of the human eye in greek. (Photo credit: Wikipedia)

The eye, much like a camera, consists of a hole to let in the light, a lens to focus it, and sensor at the back of the eye to capture the image. Apparently the measured resolution of the eye is 576 megapixels, but the eye has a number of tricks to improve its apparent resolution. Firstly, we have two eyes and the slightly different images are used to deduce detail that one eye alone will not resolve. Secondly, the eye moves slightly and this also enables it to deduce more detail than would be apparent otherwise.

That said, the eye is not made of plastic metal and glass. It is essentially a ball of jelly, mostly opaque but with a transparent window in it. The size of the window or pupil is controlled by small muscles which contract or expand the size of the pupil depending on the light level (and other factors, such as excitement).

English: A close up of the human eye. Notice t...

English: A close up of the human eye. Notice the reflection of the photographer. (Photo credit: Wikipedia)

The light is focused on to an area at the back of the eye, which is obviously not flat, but curved. Most the focusing is done by the cornea, the outermost layer of the eye, but the lens is fine tuned by muscles which stretch and relax the lens as necessary. This doesn’t on the face of it seem as accurate as a mechanical focusing system.

In addition to these factors, human eyes are prone to various issues where the eye cannot focus properly, such as myopia (short sightedness) or hyperopia (long sightedness) and similar issues. In addition the jelly that forms the bulk of the eye is not completely transparent, with “floaters” obstructing vision. Cataracts may cloud the front of the cornea, blurring vision.

English: Artist's impression of appearance of ...

English: Artist’s impression of appearance of ocular floaters. (Photo credit: Wikipedia)

When all this is considered, it’s amazing that our vision works as well as it does. One of the reasons that it does so well is, as I mentioned above, the amazing processing that our brains. Interestingly, what it works with is the rods and cones at the back of the eye, which may or may not be excited by light falling on them. This in not exactly digital data, since the associated nerve cells may react when the state of the receptor changes, but it is close.

It is unclear how images are stored in the brain as memories. One thing is for sure, and that is that it is not possible to dissect the brain and locate the image anywhere in the brain. Instead an image is stored, as it is in a computer, as a pattern. I suspect that the location of the pattern may be variable, just as a file in a computer may move as files are moved about.

Expanded version, with explanations.

Expanded version, with explanations. (Photo credit: Wikipedia)

The mind processes images after the raw data is captured by the eye and any gaps (caused by, for example, blood vessels in the eye blocking the light). This is why, most of the time, we don’t notice floaters, as the mind edits them out. The mind also uses the little movements of the eye to refine information that the mind uses to present the image to our “mind’s eye“. The two eyes, and the difference between the images on the backs of them also helps to build up the image.

It seems likely to me that memories that come in the form of images are not raw images, but are memories of the image that appears in the mind’s eye. If it were otherwise the image would lacking the edits that are applied to the raw images. If I think of an image that I remember, I find that it is embedded in a narrative.

Narrative frieze.

Narrative frieze. (Photo credit: Wikipedia)

That is, it doesn’t just appear, but appears in a context. For instance, if I recall an image of a particular horse race, I remember it as a radio or television commentary on the race. Obviously, I don’t know if others remember images in a similar way, but I suspect that images stored in the brain are not stored in isolation, like computer files, but as part of a narrative. That narrative may or may not relate to the occasion when the image was acquired. Indeed the narrative may be a total fiction and probably exists so that the mental image may be easily retrieved.

One bubble memory track and loop

One bubble memory track and loop (Photo credit: Wikipedia)


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The Banach Tarski Theorem

There’s a mathematical theorem (the Banach Tarski theorem) which states that

Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball.

This is, to say the least, counter intuitive! It suggests that you can dissect a beach ball, put the parts back together and get two beach balls for the price of one.

This brings up the question of what mathematics really is, and how it is related to what we loosely call reality? Scientists use mathematics to describe the world, and indeed some aspects of reality, such as relativity or quantum mechanics, can only be accurately described in mathematics.

So we know that there is a relationship of some sort between mathematics and reality as our maths is the best tool that we have found to talk about scientific things in an accurate way. Just how close this relationship is has been discussed by philosophers and scientists for millennia. The Greek philosophers, Aristotle, Plato, Socrates and others, reputedly thought that “all phenomena in the universe can be reduced to whole numbers and their ratios“.

The Banach Tarski theorem seems to go against all sense. It seems to be an example of getting something for nothing, and appears to contravene the restrictions of the first law of thermodynamics. The volume (and hence the amount of matter) appears to have doubled, and hence the amount of energy contain as matter in the balls appears to have doubled. It does not appear that the matter in the resulting balls is more attenuated than that in the original ball.

The Banach–Tarski paradox: A ball can be decom...

The Banach–Tarski paradox: A ball can be decomposed and reassembled into two balls the same size as the original. (Photo credit: Wikipedia)

Since the result appears to be counter intuitive, the question is raised as to whether or not it is merely a mathematical curiosity or whether it has any basis in reality, It asks something fundamental about the relationship between maths and reality.

It’s not the first time that such questions have been asked. When the existence of the irrational numbers was demonstrated, Greek mathematicians were horrified, and the discoverer of the proof (Hippasus) was either killed or exiled, depending on the source quoted. This was because the early mathematicians believed that everything could be reduced to integers and rational numbers, and their world did not have room for irrational numbers in it. In their minds numbers directly related to reality and reality was rational mathematically and in actuality.

English: Dedekind cut defining √2. Created usi...

English: Dedekind cut defining √2. Created using Inkscape. (Photo credit: Wikipedia)

These days we are used to irrational numbers and we see where they fit into the scheme of things. We know that there are many more irrational numbers than rational numbers and that the ‘real’ numbers (the rational and irrational numbers together) can be described by points on a line.

Interestingly we don’t, when do an experiment, use real numbers, because to specify a real number we would have write down an infinite sequence of digits. Instead we approximate the values we read from our meters and gauges with an appropriate rational number. We measure 1.2A for example, where the value 1.2 which equals 12/10 stands in for the real number that corresponds to the actual current flowing.

English: A vintage ampere meter. Français : Un...

English: A vintage ampere meter. Français : Un Ampèremètre à l’ancienne. (Photo credit: Wikipedia)

We then plug this value into our equations, and out pops an answer. Or we plot the values on a graph read off the approximate answer. The equations may have constants which we can only express as rational numbers (that is, we approximate them) so our experimental physics can only ever be approximate.

It’s a wonder that we can get useful results at all, what with the approximation of experimental results, the approximated constants in our equations and the approximated results we get. If we plot our results the graph line will have a certain thickness, of a pencil line or a set of pixels. The best we can do is estimate error bounds on our experimental results, and the constants in our equations, and hence the error bounds in our results. We will probably statistically estimate the confidence that the results show what we believe they show through this miasma of approximations.

Image of simulated dead pixels. Made with Macr...

Image of simulated dead pixels. Made with Macromedia Fireworks. (Photo credit: Wikipedia)

It’s surprising in some ways what we know about the world. We may measure the diameter of a circle somewhat inaccurately, we multiply it by an approximation to the irrational number pi, and we know that the answer we get will be close to the measured circumference of the circle.

It seems that our world resembles the theoretical world only approximately. The theoretical world has perfect circles, with well-defined diameters and circumference, exactly related by an irrational number. The real world has shapes that are more or less circular, with more or less accurately measured diameters and circumferences, related more or less accurately by an rational number approximating the irrational number, pi.

Pi Animation Example

Pi Animation Example (Photo credit: Wikipedia)

We seem to be very much like the residents of Plato’s Cave and we can only see a shadow of reality, and indeed we can only measure the shadows on the walls of the cave. In spite of this, we apparently can reason pretty well what the real world is like.

Our mathematical ruminations seem to be reflected in reality, even if at the time they seem bizarre. The number pi has been known for so long that it no longer seems strange to us. Real numbers have also been known for millennia and don’t appear to us to be strange, though people don’t seem to realise that when they measure a real number they can only state it as a rational number, like 1.234.

English: The School of Athens (detail). Fresco...

English: The School of Athens (detail). Fresco, Stanza della Segnatura, Palazzi Pontifici, Vatican. (Photo credit: Wikipedia)

For the Greeks, the irrational numbers which actually comprise almost all of the real numbers, were bizarre. For us, they don’t seem strange. It may be that in some way, as yet unknown, the Banach Tarski theorem will not seem strange, and may seem obvious.

It may be that we will use it, but approximately, much as we use the real numbers in our calculations and theories, but only approximately. I doubt that we will be duplicating beach balls, or dissecting a pea and reconstituting it the same size as the sun, but I’m pretty sure that we will be using it for something.

I see maths as descriptive. It describes the ideal world, it describes the shape of it. I don’t think that the world IS mathematics in the Pythagorean sense, but numbers are an aspect of the real world, and as such can’t help but describe the real world exactly, while we can only measure it approximately. But that’s a very circular description.

English: Illustrates the relationship of a cir...

English: Illustrates the relationship of a circle’s diameter to its circumference. (Photo credit: Wikipedia)





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Turtles and More


Turtle graphics. This to me resembles a Kina or Sea Urchin

My wife recently became interested in the Spirograph (™) system. Since her birthday was coming up, so did I, for obvious reasons. If you have never come across Spirograph (™) I can highly recommend it, as it enables the production of glorious swirls and spirals, using a system of toothed wheels and other shapes. When you use multicoloured pen, the results can be amazing.

Of course, I had to translate this interest into the computer sphere, and I immediately recalled “Turtle Graphics” which I have used before. It is possible to create graphics very similar to the Spirograph (™) designs very simply with Turtle Graphics.


This resembles the sort of things generated by Spirograph (TM)

Turtle Graphics have a long history, stretching back at least to the educational programming language Logo. Although variations of the original Logo language exist, they are fairly rare, but the concept of Turtle Graphics, where a cursor (sometimes shown as the image of a cartoon turtle) draws a line on a page, still exists. The turtle can be directed to move in a particular way, based on instructions by the programmer.

For instance the turtle can be instructed to move forward a certain distance, turn right through 90°, and repeat this process three times. The result is a small square. Or the turtle could be instructed to move forward and turn only 60°, repeating this 5 times to draw a hexagon. Using simple instructions like this allow the drawing of practically anything.

Square and Hexagonal spirals

Square and hexagonal spirals drawn by Turtle Graphics

I use an implementation of Turtle Graphics in the turtle module of the Python programming language but it is probably available for other programming languages. Python is probably an easy language to learn from scratch than Logo, and in addition Python can be used for many other things than Turtle Graphics. Python is available for Windows, OS/X, and Linux/Unix, and for several other older or less well known platforms.

Where things become interesting is when the looping abilities of Python are used to enhance a program. If the programmer gets the turtle to draw a square, then makes the turtle turn a little and repeats the process, the result is a circular pattern. Starting with a more interesting shape can produce some interesting patterns.

Rotated Square - Turtle graphics

Rotated Square – Turtle graphics

After a while, though, the patterns begin to seem very similar to one another. One way to add a bit of variation is to use the ability to make the turtle move to a specific position, drawing a line on the way. As an example, consider a stick hinged to another stick, much like a nunchaku. If one stick rotates as a constant speed and the second stick rotates at some multiple of that, then the end of the second stick traces out a complex curve.

Flower shape

Flower shape – turtle graphics

In Python this can be expressed like this:

x = int(a * math.sin(math.radians(c * i)) + b * math.sin(math.radians(d * i)))
y = int(a * math.cos(math.radians(c * i)) + b * math.cos(math.radians(d * i)))

where c and d are the rates of rotation of the two sticks and and b are the lengths of the stick. i is a counter that causes the two sticks to rotate. If the turtle is moved to the position x, y, a line is drawn from the previous position, and a curve is drawn.

The fun part is varying the various parameters, a, b, c, d, to see what effect that has. The type of curve that is created here is an epicycloid. For larger values of c and d the curves resemble the familiar shapes generated by Spirograph (™).



The equations above use the same constants in each equation. If the constant are different, some very interesting shapes appear, but I’m not going to go into that here. Suffice it to say, I got distracted from writing this post by playing around with those constants!

The above equations do tend to produce curves with radial symmetry, but there is another method that can be used to produce other curves, this time with rotational symmetry. For instance, a curve can be generated by moving to new point depending on the latest move. This process is then iterative.

Gravity Wave - turtle graphics

Gravity Wave turtle graphics

For instance, the next position could be determined by turning through an angle and move forward a little more than the last time. Something like this snippet of code would do that:

for i in range(1, 200):

a = a + 1
c = c + 10

This brings up a point of interest. If you run code like this, ensure that you don’t stop it too soon. This code causes the turtle to spin and draw in a small area for a while, and then fly off. However it quickly starts to spin again in a relatively small area before once more shooting off again. Evidently it repeats this process as it continues to move off in a particular direction.

Turtle graphics - a complex curve from a simple equation

Turtle graphics – a complex curve from a simple equation

Another use of turtle graphics is to draw graphs of functions, much like we learnt to do in school with pencil and squared paper. One such function is the cycloid function:

x = r(t – sine(t))

y = r(1 – cosine))

This function describes the motion of a wheel rolling along a level surface and can easily be translated into Python. More generally it is the equation of a radius of a circle rolling along a straight line. If a different point is picked, such a point on a radius inside the circle or a point outside the circle on the radius extended, a family of curves can be generated.

Cycloid curve - turtle graphics

Cycloid curve – turtle graphics

Finally, a really technical example. An equation like the following is called a dynamic equation. Each new ‘x’ is generated from the equation using the previous ‘x’. If this process is repeated many times, then depending on the value of ‘r’, the new value of ‘x’ may become ever closer to the previous value of ‘x’.

x(n+1) = rx(n)(1 – x(n))

If the value of ‘r’ is bigger than a certain value and less than another value, then ‘x’ flip-flops between two values. If the value of ‘r’ is bigger than the other value, and smaller than yet another value then ‘x’ rotates between 4 values. This doubling happens again and again in a “period doubling cascade“.

Turtle graphics - electron orbitals

Turtle graphics – electron orbitals

I’ve written a turtle program to demonstrate this. First a value for ‘r’ is chosen, then the equation is repeated applied 1,000 times, and the next 100 results are plotted, x against r. In the end result, the period doubling can easily be seen, although after a few doubling, the results become messy (which may be related to the accuracy and validity of my equations, and the various conversion between float and integer types).

Period doubling

The “fig tree” curve calculated in Python and plotted by Turtle Graphics.

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The modern theory of natural selection derives...

The modern theory of natural selection derives from the work of Charles Darwin in the nineteenth century. (Photo credit: Wikipedia)

If we accept Darwin’s theory of evolution, which I do, then we accept that we are the way we are as a result of a very period of gradual changes brought about by the pressures that our species has experienced through emergence and during process of its existence.

But let’s take a step back. All organisms have so called genetic material, stuff within them which encodes the way they are and the way that their offspring will be. The genetic material is copied as a part of the process of living, of growing and of repairing the organism if it sustains damage.

If that were all there was to the process, then organisms would be static, with no changes and no evolution. In fact the process is not perfect and both minor and major changes to the genetic material happen all the time, by all sorts of means.

Obviously, if too many changes or major changes occur in the genetic material, then the organism may not grow properly and may not repair itself properly when damaged. Also if the genetic material is passed to the organism’s descendants, they may they may not be viable or they may be disadvantaged and be unable to thrive and reproduce.

Baby turtle, species unknown.

Baby turtle, species unknown. (Photo credit: Wikipedia)

To counter this, our bodies have mechanisms to repair our genetic material, our DNA. If our bodies did not have this ability, it is unlikely that we would last long, as our body cells could experience millions of cases of damage to our genetic material per cell per day. That’s an awful lot of damage!

As described in the Wikipedia reference above, the errors in our genetic material could result in cell death or unregulated growth resulting in tumours. The DNA repair mechanism in our cells  do a good job, but they are only effective if the DNA strands are broken or incomplete. If a change is minor, and is properly reflected on both strands of our double helices, then the repair system will not notice the change.

English: Close up of The Double Helix

English: Close up of The Double Helix (Photo credit: Wikipedia)

This allows small changes to slip through, and provided they don’t cause life threatening problems, they may get passed to our descendants. The same applies to organisms other than ourselves of course.

Some major changes do slip through and organisms may end up with extra chromosomes or with damaged chromosomes. Sometimes these issues may not cause too many problems for the organism, while in other cases the descendant organism may not survive long enough to breed.

English: Illustration of the chromosomal organ...

English: Illustration of the chromosomal organisation of haploid and diploid organisms. (Photo credit: Wikipedia)

The minor errors mentioned above may affect the descendant organism to some extent, making it more or less successful than its parent organisms. The theory of evolution suggests that if the change in the genetic material makes it more successful than its siblings who don’t have the small errors, then, over generations, organisms carrying the new DNA changes will eventually replace those who don’t carry the change.

This could lead to problems for an organism. If we consider a stable population with few pressures, that has plenty of resources, there is little that would cause any permanent changes to the population, and small genetic traits could appear and disappear over time and not have any measurable effect.

Boreray sheep - on Boreray - -...

Boreray sheep – on Boreray – – 1439988 (Photo credit: Wikipedia)

If the environment then changes, such that one trait provides a large benefit to those individuals who have this trait, then over time there will be a tendency for the trait to be found in more individuals and the number of individuals without it would fall.

If the environment changes back again, then those with the trait may be disadvantaged and those without the trait could then come to dominate the population. However if enough time had passed and all the individuals without the trait in their genetic material had died out, then the population would be stuck with the trait.

Français : Trait du Nord - Salon de l'Agricult...

Français : Trait du Nord – Salon de l’Agriculture 2010 (Photo credit: Wikipedia)

It would be extremely unlikely but not impossible for the change in the genetic material to be reversed by chance as this would require another minor error to exactly reverse the original error. In effect, evolution as reflected in the genetic material never (or astronomically rarely) reverses.

If a group of organisms gets isolated from the rest of its species, some of the genes that are present in the population at large will not be present. In addition, some of the genes in the isolated population will also die out, either by chance, or because the trait that they confer is not beneficial in the isolated environment.

This can cause problems for the population if the environment changes dramatically to the detriment of the organisms. While the population at large may have genes which would enable the population to survive the changes, but those genes may have died out in the isolated environment, and the population may fail.

Of course, a mutation may arise which would enable organisms to survive in the new conditions, but environmental changes would almost certainly be faster than the rate of evolution through mutation.

exemples de mutations possibles sur l'ADN

exemples de mutations possibles sur l’ADN (Photo credit: Wikipedia)

Some species have different behaviours and appearance while still remaining the same species. Some of Darwin’s finches are an example. At least two varieties of one of the species feed on the Opuntia cactus, but they have different ways of feeding on them. One variety has a long beak and can punch holes in the cacti, while the other variety, with a short beak, break open the cacti to feed.

The birds can and do interbreed, so they are indeed the same species. This is similar, I presume, to the variation in skin colour in humans or the various blood types in humans. Such species have the same genes, but have slightly different versions (alleles) of it. This is called genetic polymorphism.

English: Trumpeter Finches (Bucanetes githagin...

English: Trumpeter Finches (Bucanetes githagineus), Valley of the kings, Egypt. Español: Camachuelos trompeteros (Bucanetes githagineus), Valle de los reyes, Egipto. (Photo credit: Wikipedia)

A species, like the finches, has to adapt. If its environment changes and it is unable to respond, then it will die out as innumerable species have done and are still doing. However, a species needs time to respond to environmental changes. For instance, polar bears may die out because the sea is is not freezing over as it usually does, and as a result there are no seals for the bears to hunt.

Whether or not you attribute the warming to mankind’s actions or not, the lack of freezing is a fact, and the bears are so far unable to adapt to the new conditions, and are often becoming a nuisance to arctic communities.

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How to change the world

English: Riot police in Washington, D.C. takin...

English: Riot police in Washington, D.C. taking a lunch break at the Old Post Office during International Monetary Fund protests. Français : Des membres de la police anti-émeute font une pause-déjeuner à Washington durant des manifestations contre le Fonds monétaire international. (Photo credit: Wikipedia)

Why do people think that petitions and protests can change the world? Well, they can but only if many, many other factors also fall in line. I’m thinking here of the protests about Post Offices or Bank Branches that are shut down when the demand for the services falls away.

If demand is falling, then the branches will not be financial profitable, and the bank or Post Office will be very unlikely to keep them open. Banks and the Post Office and not charitable institutions and have to make a profit for their shareholders, and they would not be able to do that if the branches are unprofitable.

English: ANZ Bank branch in Temora, New South ...

English: ANZ Bank branch in Temora, New South Wales (Photo credit: Wikipedia)

In the same way cash strapped public services (such as the Police) are also being forced to close public offices. While the Police closures mentioned in the linked article cite the danger to the volunteers who man the offices, and the closures are supposed to be temporary, many people believe that the real reason is costs. In fact the Police management claim that using modern technology police of the street can be more mobile and do not need to use the offices so frequently.

Whatever the true reasons, protest and petitions are unlikely to have any effect. If changes are for operational or financial reasons, then unless the reasons change, the changes are very unlikely to be reversed. Any opposition is going to be ineffective.

English: Graph of profits made by BAIR company...

English: Graph of profits made by BAIR company from 1892 to 1903. The values are taken from page 131 of “The World Abir Made: The Margina-Lopori Basin, 1885-1903” by Robert Harms from Issue 12 of the Journal of African Economic History of 1983. The first two years are averages of a value given for a two year period. The black line represents a general trend described by Harms for years with no data. (Photo credit: Wikipedia)

Sometimes a protest or petition can be effective, but that requires that a lot of things go the the way of the protesters. In this country the Mixed Member Proportional election system was selected in 1996 to be the method of electing Parliament.

There were two main factors that enabled the selection of MMP as the election system. Firstly, there was a feeling that a change needed to occur, as many people thought that with the then existing system a vote for a losing candidate was a wasted vote, and that minor parties were unable to make an impression on Parliament – frequently a minor party would get 10 to 15% of the vote, but would get maybe only one or two seats out of 100.

English: Election signs for the major parties ...

English: Election signs for the major parties plus a sign supporting the MMP side in the referendum in the constituency of Ottawa South. Ontario premier Dalton McGuinty is the Liberal candidate there. (Photo credit: Wikipedia)

In the two previous elections, one party, Labour, had secured more than 50% of the vote, but had lost out to National, because they had won more seats. Naturally the Labour voters were incensed by this seeming injustice.

The second big factor was a small and vociferous group of people who felt that it was necessary to change and the system and who were able to use their political connections to influence media and political commentators to promote their favoured system, MMP. It also helped that they had no effective opposition, as the opposition was politically naive and unorganised.

Crowds outside the National Assembly, with sig...

Crowds outside the National Assembly, with signs calling for the resignation of Prime Minister Said Musa. (Photo credit: Wikipedia)

Dubious tactics were alleged (and probably were used, on both sides), and well before it came to a vote in a referendum on the subject, it was almost a foregone conclusion. Actually the result was closer than many people predicted, though in retrospect that was probably just due to political inertia, and many people voted for the status quo of the time, rather than the new and untested alternative.

There were no real financial or operational reasons for not changing the voting system. If, say, it made it a lot more expensive to run an election, then the voting system would not have been changed, and if it made it a lot more complicated to vote (as did one of the competing systems, STV), then it would not have been changed.

Similarly, if the proponents of the new system had been disorganised, disunited, or politically naive, then they would not have stood a chance. They would have failed at the first hurdle, which was getting a Royal Commission to look into the options set up.

As an example of how it can go wrong, fairly recently a referendum was held to decide if we were going to keep our existing flag or get a new one. There was no groundswell of dissatisfaction with the existing flag, except for the niggle that it kept getting mistaken for the Australia flag and vice versa.

English: Flag of New Zealand. Taken outside th...

English: Flag of New Zealand. Taken outside the Beehive, Wellington Deutsch: Flagge Neuseelands. Aufgenommen vor dem Beehive, Wellington. (Photo credit: Wikipedia)

There was no politically inspired organisation to push for a new flag and there was no obvious contender for a new flag. Therefore, there was no momentum going into the referendum for a change in the flag. So the referendum came down to firstly choosing between some mediocre choices for a replacement and then a fight off between the existing flag and the alternative.

An interesting point is that the “winning” alternative was not the one that got the most votes at the first count. As the selection was done on the STV system, as flags were removed from the list and the votes were reassigned, the second highest polling flag in the first round gained enough votes to overtake the highest polling flag.

This demonstrates a deficiency of the STV system, though its supporters would claim that it was an advantage! In any case the alternative flag lost out to the existing flag by a fairly wide margin.

As an example of how to change the world, this debate and referendum was a dud. There was just not enough political nous on the side of those who would change the flag for it to become a reality. In addition, while the change was sponsored by the Prime Minister, it was not adopted by his party in a comprehensive way. It gave the impression that it was a pet project of the Prime Minister, and was not fully endorsed by his party.

So that is brief and by no means exhaustive look at how to change the world. It starts with a small number of dedicated and driven people and builds from there. It doesn’t matter if the ideas are actually good or bad, because if you can get the ball rolling, people will fight to sign up for the cause.

English: Thetford Post Office Centrally locate...

English: Thetford Post Office Centrally located dedicated Post Office at the top of King street. (Photo credit: Wikipedia)

If you can’t build the support, well, then your aims and ideals will go nowhere. That’s why little protests about Post Offices and Bank Branches will never win. They can’t build the momentum.

Enormous snowball made in South Park in a snow...

Enormous snowball made in South Park in a snow-covered Oxford (Photo credit: Wikipedia)

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Most people know that bees make cells which are hexagonal to store their honey. As it says in the article, this is the most economical structure in terms of the amount of wax that is needed to construct it, as the linked article describes.

Some people go into raptures about how clever the bees are and assume that they have some instinct which guides them in constructing these almost perfect hexagons. In fact the cells start out round and the bees warm them to make the wax mobile and liquid tension does the rest.

The same process occurs in bubbles in a bath. If the bubbles are all roughly the same size, they also form a hexagonal array. This sort of diminishes the mystery of the beehive and the seeming ability of the bees to do geometry, but it seems obvious in retrospect. Bees don’t know geometry but they do know (in some sense) the properties of beeswax.

The above is a prime example of trivia. As defined at trivia is merely inconsequential information. However, it can be more than that, as while the information is (in most situations) totally useless, many people find it interesting and a few find it fascinating.

A Trivial Pursuit playing piece, with all six ...

A Trivial Pursuit playing piece, with all six wedges filled in. (Photo credit: Wikipedia)

For a very few people trivia can become lucrative and even a full-time occupation. The prevalence of quiz shows where people are rewarded according to their ability to recall inconsequential facts shows that the human race as a whole appears to have the ability to remember obscure facts which apparently have little to do with their needs as they navigate through their daily lives.

All humans remember items of trivia. Granny might be able to recall what her sister told her on her wedding day, or exactly what Grandpa said when he returned from the war, but these are probably of no relevance to her Grandchildren. Memory is fluid however, and Great Aunt Mary might have totally different memories of the occasion.


Cathy (Photo credit: Wikipedia)

It may be that being able to remember trivia is one of the things that separates us from the rest of the apes. It would presumably be an evolutionary advantage to store great amounts of apparently irrelevant information because one never knows when apparently irrelevant information suddenly becomes relevant.

For instance, staring at the stars and noting their apparently irrelevant patterns suddenly becomes relevant when you notice that about the same time that that particular pattern rises in the sky that the whole river valley becomes flooded and it is time to temporarily move to the hills.

Some people have minds that soak up inconsequential facts and others do not have that ability to the same extent. I know that my mind does so, and this has gained me invitations to join quiz teams and so on, and I’ve even managed to get onto a TV quiz show, though I didn’t do too well on it.

I’m constantly amazed at what trivia my mind has stored in it. When watching a quiz show on TV I quite often know the answer to obscure questions, and I’ve no idea how I picked it up. Sometimes it is something that I could perhaps only have heard once, in passing, and it for some reason stuck in my head.

Memory lane

Memory lane (Photo credit: Wikipedia)

Memory is fickle though. Many times I have been asked a question or a question has come up on a TV show and I am sure that I know the answer but I’ve been unable to recall it. When the answer is given there is a sense of “Of course!”.

As I mentioned above, memory can be totally false as well. Often an answer to a trivia question will pop into my head, and I’m certain that it is right, only for it to turn out to be wrong. I’m left with a sense of disappointment that my memory is incorrect.

Some people, call them Quiz Masters, are able to store and remember trivial facts much better than the rest of us. These people star in quiz shows, win prizes and travel the world on the strength of their abilities. It’s not necessarily a sinecure, as they constantly have to top up their knowledge by reading, well, trivia.

On occasions a Quiz Master will mention that they have “just revised” a particular topic. Or that one of their peers has just recently told them something that just happened to occur in a question. A true Quiz Master apparently has to work pretty hard to keep on top of the facts that may occur in a quiz, to the extent of studying facts about something that they have no real interest in.

English: Coronation Stone of the Saxon Kings o...

English: Coronation Stone of the Saxon Kings of England, Kingston Upon Thames, showing the name of Athelstan. (Photo credit: Wikipedia)

I mentioned above that I have no idea why the human race has this ability to store all this useless information. It’s evident that animals remember things, as you would not be able to train your dog if it didn’t remember things. However, it seems to me that other animals do not have this immense capacity to remember seemingly irrelevant information.

Maybe this is part of what leads to out ascendance on this planet. With our vast stores of information about things around us, we can use this information to survive where other animals can’t. Maybe it is this vast store of information, the ability to recall it all, and the ability to use or brains to process and use this information that allowed us to become ascendant.


Information-integration (Photo credit: Wikipedia)

Maybe the Quiz Masters are the intellectual descendants of the proto-humans who worked out that when those stars rose in that place in the sky that the animals that were their prey would be migrating around that time, and it was a good time to visit the migration trails.

Whatever the reason that we have the ability to remember information that appears at the moment of remembering to be totally irrelevant, we can nevertheless enjoy that moment when the Quiz Master on the TV gets the trivia question wrong and we can triumphantly claim “I knew that!”, in spite of the fact that we didn’t know the answers to the preceding twenty or thirty questions.

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The previous post that I made was the 200th since I started writing this blog. I started in January 2013 and intended, at the time to make it about cooking and my successes and failures in that respect. However the cooking has pretty much disappeared (at least for now) and I’ve been writing about things like science, politics and philosophy. It’s strange how things turn out!

200 posts mean 200,000 words, more or less. However some of the early ones are shorter and so I’ve probably not quite reached the 200,000 word point yet. I aim to keep going at least until I hit 250 posts which implies a word count of 250,000 or so.

Marker post, Tattenham Corner -

Marker post, Tattenham Corner – – 923637 (Photo credit: Wikipedia)

I, and most other bloggers I guess, blog about things that interest me. I don’t do it as a job, and I don’t seek out to address any particular set of people or demographic. I just hope that what I write is at least mildly interesting to those who stumble across it. I have around 100 “followers”, people who have subscribed to this blog, but I can’t tell how many of those skip over the emails that tell them that I have posted a new article.

Posting articles must fulfil some need that I have, but I don’t really know what it is. This is the first time that I’ve done something like this and not failed to keep it going. My random ramblings don’t spring out of a need to “reach out” to those out there. I don’t have a burning desire to see that my message is promulgated to all that will listen. I don’t even have a message.

Nevertheless, blogs are a way of putting out there the things that interest me, like science, religion, and, basically, philosophy. It’s not a way of sorting out my thoughts and rubbing the rough edges off of my ideas. I don’t even think that my ideas are unique! When I do what little research I do while writing these articles, I often stumble across some article that addresses the same issues that I am writing about, probably in a more organised and coherent way.

I cite Wikipedia quite often, not because I think that it is the best reference collection on the Internet, but because I can almost always find an article on there on whatever topic I am searching for. Wikipedia is often criticised for being potentially inaccurate, and to some extent that is true as it is maintained by enthusiastic amateurs, after all. It does represent a good starting point for research and is generally not that bad.

Wikipedia events haunt you forever. It's true....

Wikipedia events haunt you forever. It’s true. I heard it on the internet. (Photo credit: Wikipedia)

When I started blogging I didn’t have any time schedule in mind, and I hadn’t settled on the target article size of 1000 words. As I recall the first few posts were sporadic and short. Some of the really early ones have been removed. It wasn’t until I settled on an article size of 1000 words and a publishing schedule of once a week that the blog took off (so far as I was concerned anyway) and I have been able to maintain the schedule over the last three years or so.

I originally intended to publish on a Saturday. This has slipped to Monday and I write these articles mainly on a Sunday. I’ve maintained this schedule for three years or so, and the nearest that I came to breaking the chain was when my sister was visiting and I didn’t have the time to write the articles. After she left I worked out how many weeks that I had missed and wrote and published the missing articles over a couple of weeks. It was one of the hardest things that I’ve done.

I’ve taken inspiration from other bloggers. A friend of mine has a blog that he, until fairly recently updated with his photographs on a daily basis for many years. Well done, Brian!

Deadlines and milestones are, for me, the key to keeping up with this blog. Making a contract with myself to publish weekly affects no one else, unless someone out there is really waiting on the latest instalment of the blog, which I doubt.

English: Deadline Falls on the North Umpqua River

English: Deadline Falls on the North Umpqua River (Photo credit: Wikipedia)

Douglas Adams said about deadlines : “I love deadlines. I love the whooshing noise they make as they go by.” However, when I’ve blogged before I’ve found that missing a deadline has been fatal to my attempts to keep a blog going. Sure, I’ve missed a few but caught up again, and my self-imposed deadline has slipped a couple of times, so there must be other factors.

I think that I probably passed a watershed where I might have stopped if I missed a deadline and that watershed may have been at the 50 or so mark, where I would have been reaching about a year of posts. Anyway the longevity of the blog certainly aids in continuing when things get sticky.

Things do get sticky. Sometimes I sit down to write, on a Sunday usually, and nothing comes to mind. I’ve never experienced a total “writer’s block”, though. I get through it by basically waffling about something until a theme comes to mind. That is not the case this time though!

Milestones are what we strive for. I want to keep going at least until the 250 post mark, but earlier on in the blog the milestones were far more modest. When I reached 50 posts that was a significant milestone, as where 100, 150, and now, 200.

Madagascar milestone

Madagascar milestone (Photo credit: Wikipedia)

Milestones show us how far we have come, and if we have a destination in mind, how far we have to go. The thing about milestones is that they shouldn’t be too far apart, and indeed a mile could probably be very loosely described as a reasonable distance that can be covered in a reasonable amount of time, and is roughly one thousand paces as measured by Roman legions on the march.

If milestones (general ones, not the specific distance related ones) are too far apart, then we often break that distance down into smaller parts. For instance, if we have a boring job to do, say weeding a garden we may break it into chunks – this bit to that shrub, then that bit to the peonies, then the bit to the small tree, and so on.

Maple Walnut Fudge chunks. From 'Truffles, Can...

Maple Walnut Fudge chunks. From ‘Truffles, Candies & Confections” by Carole Bloom. (Photo credit: Wikipedia)

All the smaller, quicker to accomplish tasks give targets that are short to complete but which still add up to the larger goal in the end. It’s funny how we fool ourselves in this and other ways.

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