Miscellaneous – Page 17

Why Pi?

If you measure the ratio of the circumference to the diameter of any circular object you get the number Pi (π). Everyone who has done any maths or physics at all knows this. Some people who have gone on to do more maths knows that Pi is an irrational number, which is, looked at one way, merely the category into which Pi falls.

There are other irrational numbers, for example the square root of the number 2, which are almost as well known as Pi, and others, such as the number e or Euler’s number, which are less well known.

Illustration of the Exponential function (Photo credit: Wikipedia)

Anyone who has travelled further along the mathematical road will be aware that there is more to Pi than mere circles and that there are many fascinating things about this number to keep amateur and professional mathematicians interested for a long time.

Pi has been known for millennia, and this has given rise to many rules of thumb and approximation for the use of the number in all sorts of calculations. For instance, I once read that the ratio of the height to base length of the pyramids is pretty much a ratio of Pi. The reason why this is so leads to many theories and a great deal of discussion, some of which are thoughtful and measured and others very much more dubious.

Ancient and not so ancient civilisations have produced mathematicians who have directly or indirectly interacted with the number Pi. One example of this is the attempts over the centuries to “square the circle“. Briefly squaring the circle means creating a square with the same area as the circle by using the usual geometric construction methods and tools – compass and straight edge.

This has been proved to be impossible, as the above reference mentions. The attempts to “trisect the angle” and “double the cube” also failed and for very similar reasons. It has been proved that all three constructions are impossible.

English: Drawing of an square inscribed in a c... — English: Drawing of an square inscribed in a circle showing animated strightedge and compass Italiano: Disegno di un quadrato inscritto in una circonferenza, con animazione di riga e compasso (Photo credit: Wikipedia)

Well, actually they are not possible in a finite number of steps, but it is “possible” in a sense for these objectives to be achieved in an infinite number of steps. This is a pointer to irrational numbers being involved. Operations which involve rational numbers finish in a finite time or a finite number of steps. (OK, I’m not entirely sure about this one – any corrections will be welcomed).

OK, so that tells us something about Pi and irrational numbers, but my title says “Why Pi?”, and my question is not about the character of Pi as an irrational number, but as the basic number of circular geometry. If you google the phrase “Why Pi?”, you will get about a quarter of a million hits.

Animation of the act of unrolling a circle's c... — Animation of the act of unrolling a circle’s circumference, illustrating the ratio π. (Photo credit: Wikipedia)

Most of these (I’ve only looked at a few!) seem to be discussions of the mathematics of Pi, not the philosophy of Pi, which I think that the question implies. So I searched for articles on the Philosophy of Pi.

Hmm, not much there on the actual philosophy of Pi, but heaps on the philosophy of the film “Life of Pi“. What I’m interested in is not the fact that Pi is irrational or that somewhere in its length is encoded my birthday and the US Declaration of Independence (not to mention copies of the US Declaration of Independence with various spelling and grammatical mistakes).

What I’m interested in is why this particular irrational number is the ratio between the circumference and the diameter. Why 3.1415….? Why not 3.1416….?

Part the answer may lie in a relation called “Euler’s Identity“.

$e^{i \pi} + 1 = 0$

This relates two irrational numbers, ‘e’ and ‘π’ in an elegantly simple equation. As in the XKCD link, any mathematician who comes across this equation can’t help but be gob-smacked by it.

The mathematical symbols and operation in this equation make it the most concise expression of mathematics that we know of. It is considered an example of mathematical beauty.



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The interesting thing about Pi is that it was an experimental value in the first place. Ancient geometers were not interested much in theory, but they measured round things. They lived purely in the physical world and their maths was utilitarian. They were measuring the world.

However they discovered something that has deep mathematical significance, or to put it another way is intimately involved in some beautiful deep mathematics.

English: Bubble-Universe's-graphic-visualby pa... — English: Bubble-Universe’s-graphic-visualby paul b. toman (Photo credit: Wikipedia)

This argues for a deep and fundamental relationship between mathematics and physics. Mathematics describes physics and the physical universe has a certain shape, for want of a better word. If Pi had a different value, that would imply that the universe had a different shape.

In our universe one could consider that Euler’s Relation describes the shape of the universe at least in part. Possibly a major part of the shape of the universe is encoded in it. It doesn’t seem however to encode the quantum universe at least directly.

English: Acrylic paint on canvas. Theme quantu... — English: Acrylic paint on canvas. Theme quantum physics. Français : Peinture acrylique sur toile. Thématique physique quantique. (Photo credit: Wikipedia)

I haven’t been trained in Quantum Physics so I can only go on the little that I know about the subject and I don’t know if there is any similar relationship that determines the “shape” of Quantum Physics as Euler’s Relation does for at least some aspects of Newtonian physics.

Maybe the closest relationship that I can think of is the Heisenberg Uncertainty Principle. Roughly speaking, (sorry physicists!) it states that for certain pairs of physical variables there is a physical limit to the accuracy with which they can be known. More specifically the product of the standard deviations of the two variables is greater than Plank’s constant divided by two.

In other words, if we accurately know the position of something, we only have a vague notion of its momentum. If we accurately know its velocity we only have a vague idea of its position. This “vagueness” is quantified by the Uncertainty Principle. It shows exactly how fuzzy Quantum Physics.

The mathematical discipline of statistics underlay the Uncertainty Principle. In a sense the Principle defines Quantum Physics as a statistically based discipline and the “shape” of statistics determines or describes the science. At least, that is my guess and suggestion.



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To return to my original question, “why Pi?”. For that matter, “why statistics?”. My answer is a guess and a suggestion as above. The answer is that it is because that is the shape of the universe. The Universe has statistical elements and shape elements and possibly other elements and the maths describe the shapes and the shapes determine the maths.

This is rather circular I know, but one can conceive of Universes where the maths is different and so is the physics and of course the physics matches the maths and vice versa. We can only guess what a universe would be like where Pi is a different irrational number (or even, bizarrely a rational number) and where the fuzziness of the universe at small scales is less or more or physically related values are related in more complicated ways.



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The reason for “Why Pi” then comes down the anthropological answer, “Because we measure it that way”. Our Universe just happens to have that shape. If it had another shape we would either measure it differently, or we wouldn’t exist.



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How do I get from A to B?

We had reason to visit another suburb today. It wasn’t until I was sitting waiting for some traffic lights to change that I thought about how I was navigating from home to destination.

We just got into the car and drove there. I didn’t consider the route in advance, and it seemed that I just pointed the car and we got there. Obviously I knew the way, as we had been there or through there a number of times in the past. But I didn’t have the destination in mind from start to finish, at least not consciously. I’m not sure that I had it in the forefront of my mind at all.

I knew that it was in that direction though, and that did not leave a lot of route options. I did have a general feeling that I should go south, in this instance and that really only leaves two options, the back road, or the motorway. The back road is a lot prettier!

I made the choice to take the back road but it was not, as I said, at the forefront of my mind, as I was doing other things at the time, like finding my keys, my phone, my wallet and these things occupied the forefront, while the decision about which route to take was more background.

So the route was chosen more of less in the background, but not subconsciously. Much the same process happened on the way there, and at each junction or turning point, I didn’t have to consider at the front of my mind which direction I should drive. I just did it. Some part of my mind knew that to get to our destination I had to turn right, or go straight on or whatever.

This is good because the front of my mind was doing the driving, keeping the car on line, signalling, accelerating or braking, keeping us safe on the road. Except that it wasn’t right at the front mind, since I was also talking to my wife about various things. Christmas things from memory.

English: Two motorcycle trailing off the brake... — English: Two motorcycle trailing off the brakes through Tooele Turn at Miller Motorsports Park. Rider on the white bike is Warren Rose, Rider of the green bike is Dave Palazzolo (Photo credit: Wikipedia)

I’ve been driving for many years and I’m confident that if needed the driving part of my mind can instantly oust the things currently in my mind should the unexpected happen. Many year ago, when I used to smoke, I was driving with a friend and an emergency happened. When it was over I realised that I was no longer holding my cigarette. Meantime my friend was scrabbling between his legs where my cigarette had ended up when the driving part of my mind grabbed precedence and the cigarette holding part was temporarily ousted.

The route planning part of my mind would not suddenly get control like that, fortunately. That would be highly dangerous. I could if I had wanted have brought the route planning part of my mind to the front, but it wouldn’t say much except “turn left at the next junction”.

Turn Left, Turn Right (Photo credit: Wikipedia)

I have on occasion made a navigating mistake. I’m going to A and the route to B is the same in part. Suddenly I realise that I have missed a junction and will have to backtrack. It seems that the route finding part of my mind spends much of the time dozing and checks in only infrequently, sometimes missing the turning point or ritually following a more usual route.

It also seems that the information it keeps is like an instruction to take an action at each decision point rather than the whole route from home to destination as well as a general direction, less well specified. GPS guidance systems seem to work this way too in that they instruct you to take an action at each junction without setting out the whole route each time.



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The model of the mind that I’ve used above, of various parts of the mind at various levels of “forefrontness” or consciousness is nothing new. The need to make a part of the mind the one at the top of the conscious levels, suddenly as a result of a danger, or selectively by choice, as in route following reminds me of the way that computer programs

Computers have several methods for navigating through programs and reacting to things that happen when they are running. One big part is called “handling errors”. Dividing by zero is an error and if the computer reaches a point where it has to divide by zero something needs to be done. The program can report the error and gracefully stop, or it can take some action to fix the error and then carry on.

Computers handle error by means of “interrupts”. Whether the errors is software (eg divide by zero) or caused by hardware connected to it (eg input/output errors) the computer stops what it is doing and runs a bit of program that handle the errors by sending a message or fixing things up. The bits of program that were running are suspended and after the error is handled the bits that were running may be given back control.

The mind seems to work in a similar way. When an emergency arises the current part of the mind that is at the forefront gets suspended and the emergency is handled by another part of the mind. A pedestrian steps into the road and you react by standing on the brakes “before you know it” as the saying goes. As soon as the emergency is over, the conscious mind takes over again.

a short .gif of the Taiwanese animated pedestr... — a short .gif of the Taiwanese animated pedestrian road crossing sign (Photo credit: Wikipedia)

You do indeed react “before you know it”, one might say instinctively. But humans have not been driving cars for much more than one hundred years, so it appears that the reaction is not instinctive in itself, but is an instinctive reaction to a danger that has been learned. We seem to have this fast reaction to events which is instinctively based but can be applied to learned situations, which is much more flexible than hard-wired instincts would be.

So, pondering on how I get from A to B has led me to conjecture that there are parts of the mind which are forefront in our minds and other parts which are not directly in the forefront but which can be brought to the forefront in an instant, when an event happens. It is evident that these parts are only partially backgrounded as the mind as a whole has some aware of the location at the time, but they do act semi-autonomously, that is until the pedestrian steps out onto the roadway.



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Evidently there are parts of the mind that are less foregrounded and more backgrounded. When the part of the mind that is concerned with driving wants to signal or change gear, another part of the mind which controls the arms and legs wakes up and make the limbs move as needed.

I’ve spoken above as if all these different levels are discrete states, but I think it more likely that is a continuum from the foreground of the mind to the background or a least the series of levels of consciousness are close enough togerther to appear so. The mind is a complex and wonderful thing.



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[Comment: After finishing this post I went looking for other discussions of the same topic. I first found this Wikipedia article which has the issues mentioned in the article’s header. Interestingly the implication in the article is that there is a single level of consciousness at any one time. This I do not agree with. Another article I found was a little better, I feel, but only because it acknowledges that several levels may be active at the same time, but divides them into three levels with well defined scopes. I feel that it is a lot more complex than that, with all sorts of sections of the mind at all sorts of levels being active at the same time. Neither article deals with the issue of one section of the mind apparently seizing the highest level when an external event triggers it.]

Updates and Upgrades



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I have currently got computer issues so this week’s posting has not been written.😱 I’m writing this as a placeholder until I can catch up. The subject will be, as above, “upgrades”.

One of the joys of using a computer is applying the updates that come out for the operating system and applications. With a multitude of computing devices that a person has these days, this can be time consuming.



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On desktop computers running the Windows operating system, this can be made pretty much invisible, but on phones and tablets, and on other operating systems this can be a chore.

Most updates are for applications and not for the operating system itself, but often a user may have no idea of the difference. A tech-savvy person asks what operating system a user is using, expecting to hear “8.1” or “7” or even “Vista” or “XP” he/she is surprised to be told “Internet Explorer” or even “GMail”.

An application upgrade is usually benign and the user will not notice any difference as the changes will be behind the scenes, but now and then a user visible change is made and the user often thinks that his machine is broken.

Geeks often have a quiet snigger at this but it is a bit unfair. The user is using the computer as a tool, and tools as a rule do not change. A spanner doesn’t suddenly overnight change from Imperial sizes to Metric sizes and the computer user is not unreasonable in expecting his/her computer to not suddenly change.



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Some updates however are far from benign, causing data loss or serious computer issues. Those not of the “Windows World” frequently blame Microsoft for such issues, but when there are billions of users out there, using different hardware configurations, it is not surprising that things occasionally break. Nastily!

When I talk about the “Windows World”, I am talking about the users of the Microsoft Windows operating system, by far the largest group of computer users. Until recently the other major groups of users were the “Mac World” and the “Linux World”, but more recently these have been joined by the “Apple World” and the “Android World”.



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Since Macs are made by Apple, arguable the “Mac World” and the “Apple World” are the same, but by the “Apple World” I mean those users of iPads, iPhones and even the iPod. The “Mac World” refers to users of desktop and laptop Macintosh computers.

The application updates are arguably more visible on handheld devices and owners of such devices may be notified two or more times a week that such and such an app needs updating or has been automatically updated. It’s not too much of an issue, but naive users may not be performing the necessary couple of clicks to update the apps.



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Of course, by taking this course they may be missing out on security and stability fixes or fixes for serious bugs, to them the risk of fiddling with their devices may seem higher, and I can understand that.

Computer users, especially naive users, develop a pattern of working, a “workflow” if you like that suits them and works around any bugs or issues in their apps. No wonder they get furious when their workflow is disrupted! In one case, (reputedly) a computer user who had her machine updated was outraged that her icon had “gone”, when in fact it had moved to a different line.



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It’s easy to laugh at such happenings, but really, one should try to see here point of view. The icon did something when she clicked. It had moved and even if it looked the same in its new position, she could not be sure that it would do the same thing.

If a more sophisticated user were to notice that an icon had moved, they would probably assume that it would work the same, and in 99.99…. per cent of the time they would be correct. But the naive user did not know the odds and of course, she was correct in that there was a non-zero possibility that the icon would behave differently.



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There is a subtle difference between an update and an upgrade, I believe. I don’t know if it is an official definition, but when updates are mentioned I feel that such changes should be minor and with little visible impact. Updates may be changes made to applications and to the operating system itself, but the key feature is that they do change functionality or user workflow fundamentally, and would predominately be bug fixes or small enhancements.

Upgrades on the other hand, would be more fundamental changes and may result in majorly changed functionality and workflows, like the changes between Windows 7 and Windows 8. The change between Windows 8 and Windows 8.1 would probably be an update rather than an upgrade, but this one is marginal.

Tux, the Linux penguin (Photo credit: Wikipedia)

I’m in the “Linux World” and my desktop runs Ubuntu. I’ve recently upgraded to version 14.10 (also known as Utopic Unicorn) and I had a number of issues, none of which was a show stopper, but some of which were annoying. I’ve previously upgraded successfully with few issues, but maybe I accumulated too much junk.

I definitely don’t think that the issue is with Utopic Unicorn as the forums don’t have posts which relate to my issues, which they would if it were a general issue, so it is something related to my own setup, most likely.

Official Ubuntu circle with wordmark. Replace File:Former Ubuntu logo.svg. Español: logo de Ubuntu + marca denominativa Français : Logo officiel d’Ubuntu. Remplace File:Former Ubuntu logo.svg. (Photo credit: Wikipedia)

So I’ve reinstalled, which has taken some time. There is one niggly issue that should be fixed shortly, but I was without access to some essentials, like Facebook and GMail on my desktop machine, for a day or two. Fortunately I was able to access these absolute essentials on my tablet (Android) and phone (also Android).

During this time I had to fix my daughter in law’s Windows laptop and upgrade the iPad to the newest version of IOS. Now my Android phone wants to upgrade to Android version 5.0 (also known as “Lollipop”). I think that I will wait for version 5.0.1 or 5.1!



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Fractals

Now and then I fire up one of those programs that displays a fractal on the screen. These programs use mathematical programs to display patterns on the screen. Basically the program picks the coordinates of a pixel on the screen and feeds the resulting numbers to the program. Out pop two more numbers. These are fed back to the program and the process is repeated.

There are three possible outcomes from this process.

Firstly, the situation could be reached where the numbers being input to the program also pop out of the program. Once this situation is reached it is said that the program has converged.

Secondly, the numbers coming out of the program can increase rapidly and without bounds. the program can be said to be diverging.

Thirdly, the results of the calculation could meander around without ever diverging or converging.

English: The Markov chain for the drunkard’s walk (a type of random walk) on the real line starting at 0 with a range of two in both directions. (Photo credit: Wikipedia)

A point where the program converges can then be coloured white. Where it diverges, the point or pixel can be coloured black. A point where the program seems to neither converge nor diverge can then be coloured grey. A pattern will then appear in the three colours which is defined by the equation used.

Anyone who has seen fractals and fractal programs will realise that a three colour fractal is pretty boring as compared to other published fractal images. Indeed the process that I have described is pretty basic. A better image could be drawn by colouring points differently depending on how fast the program converges to a limit. This obviously requires a definition of what constitutes convergence to a limit.

Convergence is a tricky concept which I’m not going to go into, but to compute it to say in a computer program you have to take into account the errors and rounding introduced by the way that a computer works. In particular the computer has a largest number which it can physically hold, and a smallest number. Various mathematical techniques can be used to extend this, but the extra processing required means that the program slows down.

I’m not going to explain how this difficulty is circumvented, since I don’t know! However the fact is that the computer generated fractals are fascinating. Most will allow you to continually zoom in on a small area, revealing fantastic “landscapes” which demonstrate similar features at all the descending levels. Similar, but not the same.

fractal landscape (Photo credit: Wikipedia)

The above far from rigorous description describes one type of fractal of which there are various sorts. Others are described on the Wikipedia page on the subject.

Another interesting fractal is created on the number line. Take a fixed part of the number line, say from 0 to 1, and divide it into three parts. Rub out the middle one third. This leaves two smaller lines, from 0 to 1/3 and from 2/3 to 1. Divide these lines into three parts and perform the same process. Soon, all that is left is practically nothing. This residue is known as the Cantor set, after the mathematician Georg Cantor.

English: A Cantor set Deutsch: Eine Cantor-Menge Svenska: Cantordamm i sju iterationer, en fraktal (Photo credit: Wikipedia)

This particular fractal can be generalised to two, three, or even higher dimensions. The two dimensional version is called the Sierpinski curve and the three dimensional version is called the Menger sponge.

One of the fractal curves that I was interested in was the Feigenbaum function. This fractal shows a “period doubling cascade” as shown in the first diagram in the above link. If you see some versions of this diagram the doubling points (from which the constant is determined) often look sharply defined.

I was surprised the doubling points were not in fact sharply defined. You can see what I mean if you look closely at the first doubling point in the Wolfram Mathworld link above. Nevertheless, the doubling constant is a real constant.

English: Bifurcation diagram Česky: Bifurkační... — English: Bifurcation diagram Česky: Bifurkační diagram Polski: Zbieżność bifurkacji (Photo credit: Wikipedia)

Another sort of fractal produces tree and other diagrams that look, well, natural. A few simple rules, a few iterations and the computer draws a realistic looking skeleton tree. A few tweaks to the program and a different sort of tree is drawn. The trees are so realistic looking that it seems reasonable to conclude that there is some similarity between the underlying biological process and the underlying mathematical process. That is the biological tree is the result of an iterative process, like the mathematical trees.

Русский: Ещё одно фрактальное дерево. Фракталь... — Русский: Ещё одно фрактальное дерево. Фрактальное дерево. (Photo credit: Wikipedia)

I’ve mentioned natural objects, trees, which show fractal characteristics. Many other natural objects show such characteristics, the typical example which is usually given is that of the coastline of a country. On a large scale the coastline of a country is usually pretty convoluted, but if one zooms in the art of the coastline that one zooms in on stays pretty much as convoluted as the large scale view.

This process can be repeated right down to the point where one can see the waves. If you can imagine the waves to be frozen, then one can take the process even further, but at some point the individual water molecules become visible and the process (apparently) reaches an end.

If you want a three dimensional example, clouds, at least clouds of the same type, probably fit the bill. Basically what makes the clouds fractal is the fact that one cannot easily tell the size of a cloud if one is simple given a photograph of a cloud. It could be a huge cloud seen from a distance or a smaller cloud seen close up. Of course if one gets too close to a cloud it becomes hazy, indistinct, so one can use those clues to guess the size of a cloud.



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Fractals were popularised by the mathematician Benoit Mandlebrot, who wrote about and studied the so-called Mandlebrot set, wrote about it in his book, “The Fractal Geometry of Nature”. I’ve read this fascinating book.

While I was searching for links to the Mandlebrot Set I came across the diagram which shows the correspondence of the period doubling cascade mentioned above and the Mandlebrot set. This correspondence, which I did not know about before, demonstrates the interlinked nature of fractals, and how simple mathematics can often have hidden depths. Almost always has hidden depths.

I forgot!



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Well, I almost forgot to write my weekly post. My excuse is that Monday is a public holiday and this upset my schedule. Of course this is only an excuse.

It did start me thinking about forgetting things. We have probably all forgotten appointments at one time or another, though with cell phones being ubiquitous and possessing calendars, we probably should never do so in the future. Yeah, right!

A page of a calendar. (Photo credit: Wikipedia)

The reasons why we forget appointments can be myriad, but I’d suggest that at least some of the appointments that we miss are ones that we would prefer to miss, such dentist appointments. I’d guess that we would be much more likely to remember lunch appointments or some other types of appointments that we would enjoy.

Some people seem to forget things that I am unlikely to forget, such as plane flights. It always amazes me that people can turn up for flights at the last minute. I’m usually in the airport, waiting, well before the official check-in time starts.



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It is probably a consequence of our busy lives that we need calendars and other “aide memoires” like shopping lists. One can imagine that in earlier times to-do lists were shorter and the number things that one needed to carry on a normal life was a lot smaller and our memories were able to cope. But then again, that may be an illusion. Was life really simpler in the past?

If you miss an appointment that affects not only you, but the people with whom you have the appointment. The dentist will be looking at an empty chair, and while he may enjoy the break, it will cost him money. That’s why some service providers like dentists may charge you a fee if you forget an appointment. Some places get the receptionist to send you a text the day before as a reminder.

Although I’ve suggested above that maybe in simpler times the need for a calendar was less, the need was not non-existent. Farmers, for example, need to know the best time to plant seeds to ensure a good crop.

The Babylonian calendar for example was based on both lunar and solar cycles which would enable the priests to suggest the correct time for planting crops. This calendar has its origins around 2000 BCE according to Wikipedia.

The Mayan calendar is even older, with roots in the 5th century BCE. The Mayan calendar came to popular attention in 2012, when it was conjectured that the Mayan calendar would end on 21 December 2012, and that this would signal a global catastrophe.

Of course nothing significant happened and the Wikipedia article on the topic explains that the Mayan calendar did not end on that date. Surely very few people seriously thought that it would. Even the ancient Mayans did not predict a calamity at that time, so far as scholars are aware.

Forgetting important dates is a recipe for matrimonial disharmony. There seems to be a gender bias here as most males do not worry too much if you miss a birthday, but it seems more important to females. Whether or not this is real gender difference or merely a societal one, I’m not prepared to guess. Whatever the cause, it is best to remember one’s spouse’s birthday. I personally find it very difficult to remember dates other than the usual wedding anniversary, spouse’s birthday and my children’s birthdays.

There is another sort of forgetting though, one that creeps up on one as time passes. Some of that can be attributed to loss of facilities due to age, but memories do seem to fade regardless of ageing. Even in your twenties your recall of events ten years earlier can be faulty, though for some reason some things can be said to stick in your mind.

It’s difficult to work out what we have forgotten and what we have simply had no reason to remember. Something may, for some reason or other, trigger a memory, and we say “Oh, I had forgotten that!” when obviously, we hadn’t.

Equally, memories may be replaced by false memories. For instance, for years I believed that I had a memory of an event at a particular place involving my sister’s pushchair. When I visited the place many years later, it was apparent that the event could not have happened as I remember it. The slope of the path, the flower beds were all wrong.

It seems to me that memories can be true, or totally false, and that a memory of events may be completely lost, and this would make the study of memory very difficult and that relying on memory for veracity is impossible.

There are people who claim to have memories of a previous life. I don’t believe such claims, as I don’t believe that there is such a thing as reincarnation. If there were such a thing, one wonders why those who remember their previous lives were always important and powerful people in past lives.

But memory loss definitely gets worse as one gets older. Some unfortunate people suffer so badly from memory loss that they cannot recognise their own families and get lost in places with which they were once familiar. As people live for longer this phenomenon is becoming a big problem.

Of course there is research into both ageing and memory, so this situation will hopefully improve, but at the moment, it doesn’t seem attractive to live to 100+ and lose all one’s faculties.



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Memory is one of the things that makes you you. You can remember many things from your past, and while you can’t completely remember being the person that you were, you can remember some of it. Maybe you can remember what you were feeling at the time, maybe not.

But you believe that the person that you remember was you, in spite of the forgotten things, the things that you remember wrongly, because there is a continuous thread of memory between the person that you remember and you in the here and now.

Yet in another sense, that person was not you. His memories only encompass the time up until his now. Your memories of the time from then on are of events that have changed you and your memory of events before that person’s now have also changed, or been lost. How could you be the same person?



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One Hundred and One

The last post that I made was my 100th post on this blog. I’ve tried to keep blogs before now, but I’ve always failed at some point. There are blogs started by me at various places on the Internet, but this is the only one to have got past a few dozen posts.

I’m not sure of the reason why I’ve been able to keep this blog going and I’ve failed before. I don’t think that it is the fact that this is a WordPress blog, as I’ve not found significant differences between the various type of blog. They all do pretty much the same thing.

English: WordPress Logo (Photo credit: Wikipedia)

Of course, there are myriads of themes out there, but it is impossible to hide the underlying structure completely – you create a blog post, you post it and people are able to look at it.



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There are no doubt those who have specific needs and need specific features, for example if they are selling something and need to accept payments, who find that a specific blogging platform is required to fill their needs, but most people will find, I think, that the blogging platform that they use is mostly irrelevant.

I have committed myself to creating blog post of around 1,000 words once per week and so far I’ve been able to achieve this. I plan to have a post ready to go on Monday evening. Below I’m going to describe how I write a post. It’s a creative process, with a small ‘c’. It’s not Creative with a large ‘C’, a work of Art, as I don’t aspire to such exalted levels. It’s just my small blog.

When I sit down to write a post, I usually, but not always, have a topic in mind. If I am lucky I will have been thinking about it during the week and I have some idea on what I am going to include in the post. However, I don’t plan it out as such. I just some ideas, some pretty well developed in mind.

Sometimes though, I sit down at the computer with maybe only a topic or not even that. I type the title and I’m away! So far I’ve not had any real difficulty in reaching the 1,000 words, and sometimes I have to leave things out.

It is usually reckoned that a work of this sort has a distinct beginning and end. I certainly open with a sentence on what I about to write about and then go on to write about it, but I don’t try to tag on a definitive conclusion, especially if I am running on, and the word count gets significantly higher than 1,000 words.

So anyway, I start writing. As I write I might plan ahead a little, but more often than not I put down my current thought which might take a sentence or three and I correct and formulate my sentences as I go. I look back a little too, and may revise a sentence or phrase in the current paragraph if it strikes me as being too ugly.

I don’t however have the whole thing in my mind, though I may remember and revisit thoughts that I have written earlier if something strikes me. I do think ahead a little, or maybe a paragraph or two, but in general, I compose as I write as I go.

Sometimes I pause, as I just did, to think my way ahead. This is an indication to me that I’ve said all that comes to mind on the point that I was making and that I should start another point.



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I am not formal about references and in fact mostly use Wikipedia for any references, but I try to link to the work of others and sometimes to major references. If a reader has an interest in any of the topics that I touch on, Wikipedia, for all its faults, can be a good place to start.

The result, I suspect, is almost certainly more of a ramble through the topic in question than a serious analysis of it. Caveat Emptor! Of course, anything that I write is my opinion only.

When I have finished writing the post, I save it, and then start “decorating” it. By this I mean that I insert images every paragraph or so, to break up the post into more readable chunks. A single mass of text is off-putting I find. That’s also why I kept the paragraphs short too.

I choose the picture purely on their look. I don’t check the websites that the image come from, so people should not assume that I in any way agree or disagree with the authors of the websites that I borrow images from.

This is probably not a big deal, as I usually use Zemanta to provide the images and they provide links mainly from Wikipedia. Also using a source like Zemanta means that there should be no copyright issues with the images that I include.

When I have finished writing the post and I have inserted my images, I categorise the post using my usual categories and include tags. Doing this is supposed to help people looking for posts on particular topics and tagging in particular should enable my posts to come up in searches. Apparently tagging posts helps search engines.



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The way that I write posts mean that there is a danger that I might meander through a topic rather than do a tight analysis of it. That’s OK by me. However I don’t know if the readers of my posts consider them to be rambling or whether I unconsciously put in there a structure that I am unaware of when I write a post.

Essentially, though, I write for myself, to get my ideas out there, to amuse myself and to test myself. When I write, I am, in my own mind, in a way, writing to myself, as if I the reader were a different person to I the writer. I know the occasional real person stumbles on my writing, and if they get something out of it, I am glad. If they don’t get something out of it, well, that’s fine, but I guess that they won’t be back!

Electric Cars

There is a perception that electric cars are greener than petrol-driven cars. While I would not like to give the impression that I am against electric cars, as I am actually in favour of them, long term, in the short term I see some issues with them.

Firstly, consider the auto mobile. There are 250 million of them in the United States alone. That require a huge infrastructure which we don’t often consider. Firstly the crude oil is extracted from the ground using huge drills. While the technology is fairly basic, a lot of planning goes into a well before the hole is drilled, and then the drilling rig, and the workers are brought in and eventually crude oil flows.

It flows, ultimately to refineries where, apart from fuel oil, many other oil based products are extracted. The fuel is then trucked around the country or to other countries and ultimately to petrol supply stations (or gas stations as they are referred to in North America). Special equipment, the bowsers, are used to load the fuel into the cars.

The cars also require lubricating oil, which can be purchased in the petrol supply stations. More often the lubrication oil is supplied at special workshops set up to cater for the auto mobile users. These have special equipment to attend to and repair internal combustion engine. Replacement parts are manufactured and distributed to these workshops.

In contrast the fledgling electric car industry is small. There are few recharging stations, and the repair stations for electric cars are currently few and far between. Technicians who can work safely on electric cars are rare.

For electric cars to compete directly with petrol engined cars the infrastructure for electrical cars needs to match the current infrastructure for the petrol cars and that will require significant investments from someone. New electrical charging stations will need to be created or petrol supply stations will have to give up some space to electrical charging stations.

While charging stations are being created, there are less than 10,000 world-wide and a few thousand in the US. In the US there are approximately 3 charging points per station, so there are relatively few places to charge electric cars.

Charging an electric car at an outlet takes a minimum of 10 minutes and to do it this fast requires special equipment, for which special expertise is required. To provide this expertise requires special training, comparable to the expertise required to deal with petrol bowsers. Cross-training of petrol bowser experts in electrical outlets is of course possible, but the expertise is sufficiently different that a whole new pool of experts will need to be built up.

Bowser at Ariah Park, New South Wales, Australia. (Photo credit: Wikipedia)

When an electrical car requires repair for any reason, it will need to be taken to a mechanic who knows how to deal with one. It’s likely that some repair locations will switch to electric rather than petrol, since the equipment is so different, though these days the petrol repair locations already use sophistic electronics in the diagnosis and repair of petrol engined cars.

So, in summary, electric car facilities will have to replace petrol car facilities as electrical cars become more common. This will not happen quickly and easily as the industry supporting petrol cars will no doubt resist. The electric car industry will have an expensive fight on its hands as all new equipment will have to be provided and a fledgling industry wont have a lot of financial backing.

What is needed is for the costs of the petrol car industry to climb significantly, and that will cause other significant societal problems. Then it will make sense to invest in the electrical car industry.

Another issue as regards electric cars is related to the charging of them. It takes significantly longer to charge an electric car as opposed to filling up a car’s tank with petrol. In a fast charging station, with special equipment in the charging “bowser” and special connections in the car, it could take anything from 10 minutes upwards.

Cars can be charged at home, and from standard electrical connections, but this would normally have to happen overnight when there is less other usage of electricity in the home. However, if you charge a car from a standard electrical connection, it will take a long time, up to eight hours or more. So those who charge their cars at home can expect not to use the car in the evening, and a flat battery is more of an issue than a flat battery in a petrol car.

The cables both in the house and in the supply connections needs to be robust because of the inevitable heating from the continual high current, and if you be chance draw too much current, either the car charging or the house will be temporarily cut off. If you were to have medical equipment in the house then this could be life threatening.

A CH-46E Sea Knight helicopter's downwash kick... — A CH-46E Sea Knight helicopter’s downwash kicks up a dust cloud resulting in brownout (Photo credit: Wikipedia)

Of course there are mechanisms that can be ensured to reduce the impact of these problems, but that means that the wiring infrastructure in the house needs to be upgraded. It’s not a big problem until you multiply it by the number of houses that would need to be upgraded.

A bigger issue is that the electricity infrastructure is built for, really, quite light usage. If everyone in the street were to get an electric car, then the local infrastructure would come under stress. There are already “brown-outs” and “black-outs” of the infrastructure in the US at times of heavy demand. Add onto that the charging of numerous electric cars and one wonders if the infrastructure could be upgraded in a reasonable time or whether blackouts and flat batteries would become common.

This problem goes all the way back to generation, which currently depends mostly on fossil fuels in many parts of the world. It’s not much good if reducing fossil fuel usage at the consumer end results in increased fossil fuel usage at the generation end.

So while electric cars and fossil free generation should eventuate, at the moment there are high barriers to widespread adoption of electric cars and reduction of dependence on fossil fuels.



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The Law of the Land and of Nature

(This should be posted early as I will not be in a position to write a post next weekend. If I don’t make it, it may be late!)

Laws. When we think of laws we think of speeding fines, fines for drunken driving and so on, but there are a myriad of other laws that we don’t often think about. Ones about wills and probate. Laws to protect the young, the elderly, and other vulnerable people. Laws to deter people from stealing and cheating. Laws for almost everything.

Laws are odd, when you think about it. They prevent or deter people from doing things. They basically act against personal freedom. They set limits and they are restrictive. But they are usually created on public demand or at least with public acquiescence, if not approval.

A whole section, a powerful section, of our societies has grown up to maintain and enforce our laws. The police are tasked with ensuring that laws are followed and are given the power to arrest those who appear to be breaking them, although they do not decide whether or not those persons have in fact broken the laws.

The judiciary are the people who decide whether or not the laws have been broken, based on the evidence provided. Sometimes the judges or magistrates act alone, and at other times they use the judgement of a randomly selected group of citizens formed into a jury.

If the person is found guilty there are several types of punishments, fines, bans, even imprisonment and in the past, execution. A whole group of people is needed to oversee the sentence.

From the time when the person is charged with a crime until and often after the verdict he or she will rely on the services of a specialist in laws, a lawyer or attorney. These people dedicate their lives to helping prove the innocence or guilt of persons charged with a crime.

Another huge section of society is responsible for making and amending laws. One of the functions of Government is to do this, but how do they decide how to add, change, or remove laws? I find that an interesting question. It seems to me that the representatives bring their own biasses and beliefs to the party.

They would be bringing a need hopefully communicated to them by the people who they represent, either for a change in the law or a new law or for the removal of a redundant law.

There’s a huge part of human endeavours devoted to making and administrating laws. Why do we spend such a large effort in stopping people doing things that they basically want to do?

Well, in most cases laws are there to prevent people doing things that cause harm to others, either intentionally (eg stealing) or inadvertently (eg drunken driving). Some laws are intended to prevent people harming themselves (eg drug laws).

Interestingly I heard about an experiment where a bunch of students were engaged to play a game, but the game had no rules. After a while the students started to make rules, even rules about how to make rules. So far as I know they didn’t make rules about enforcing rules or have penalties for breaking the rules! I’ve subsequently tried to find references on the Internet to this game, but I’ve been unable to find any, but it does seem as if human like rules or laws.

There is another sort of law – one which cannot be broken, the so-called law (or laws) of nature. Mankind has been obsessed with these laws for a long time, longer even than they have known that there were laws.

It’s not difficult to spot that day follows night follows day. That is, I guess, a law in itself. The underlying causes for it are not apparent. All sorts of theories were tried, including Sun Gods and flaming chariots and things like that. It was realised fairly early on that the movement of the sun across the followed some fairly simple rules.

For example the sun is higher in the sky in summer, and lower in winter, and the day is longer in summer than in winter and its height depends on how far north or south one is. One of the better explanations involved celestial sphere rotating about the earth. By this time it was becoming clear that the earth was round.

As the power of the scientific method became apparent, the likes of Newton and his contemporaries really applied its power. The idea that everything was explainable in terms of a set of known laws became really prominent. I think that what was missed was that all descriptions, even back to the Sun Gods and similar, were just that, descriptions.

Some trajectories of a particle in a box accor... — Some trajectories of a particle in a box according to Newton’s laws of classical mechanics (A), and according to the Schrödinger equation of quantum mechanics (B-F). In (B-F), the horizontal axis is position, and the vertical axis is the real part (blue) or imaginary part (red) of the wavefunction. The states (B,C,D) are energy eigenstates, but (E,F) are not. (Photo credit: Wikipedia)

Newton’s laws of gravitational attraction were descriptions of how masses appeared to move under gravitational forces. Every massive object was described as being gravitationally attracted to any other massive object and Newton provided equations to model this interaction.

When one asks what a “massive object” is, one finds oneself in a spot. A massive object is one which has mass and which is attracted to other massive objects. It is evident that this is a circular definition. OK, given the concepts of massive objects and attraction, why should they have particular a particular mathematical relationship, rather than any other?

Newton’s law of gravitational attraction have been hugely successful, notably being used to calculate the orbital period of Halley’s Comet. But in the early 1900s Einstein showed that Newton’s laws of motion and gravitation are not absolutely accurate if the massive objects. Einstein’s formulations of the laws is more accurate under these extreme conditions.

The question comes to mind – is Einstein’s formulation the ultimate explanation? Firstly I’d argue that it is a description and not an explanation at all. As such, some different description may be needed under even more extreme conditions or maybe to merge the scientific description of moving objects at high speeds and the description of quantum level events.

There may be no ultimate explanation or mathematical laws accessible to humans. A photon behaves as it does because that is the way that a photon behaves, if it is correct to label a particular physical phenomenon as a photon.

(This is the post for next Sunday/Monday, since I won’t be able to do a post then. The post after that should be back on schedule.)

For the little gods’ sake…

(Spoiler alert: This post contains commentary on “Small gods” by Terry Pratchett and as such gives away vital plot details.)

Cover of "Small Gods (Discworld)" — Cover of Small Gods (Discworld)

I often use the phrase “For the little gods’ sake…” as an expression of frustration. I got the expression from the Diskworld novel “Small gods” by Terry Pratchett. The premise of the story is that everything has a god or goddess, and there is even a Goddess of Things That Get Stuck in Drawers, Anoia. These deities are constantly jostling for prominence and for followers, because followers equate with influence and without influence a god will fade away into a sort of background of powerless whispering.

Anoia is lucky in this respect as much of her influence comes from the annoyance that people feel when they open a drawer and it gets stuck. She doesn’t have to rely on believers. In the stories minor deities who do not have enough followers are served by priests of more major deities on an agency basis.

Although Anoia’s cause if peripherally helped by the events in the book, the book’s main theme is another small god, who is in desperate straits as he has only one follower and is accidentally incarnated as a tortoise. He regains his deity by persuading an eagle to drop him on the head of the villain of the story, thereby killing both himself and the baddie.

Pratchett is obviously drawing on the story of Aeschylus’ death as a result of a tortoise being dropped on his head. The interesting thing is the theology that Pratchett weaves around the incident where everything has a god or goddess and there is a hierarchy of gods who continually jostle for position.

A huge pantheon seems, well, wasteful. One single Deity seems more logical, as gods are supposed to be all-powerful, all-seeing, etc. One way out of this dilemma is to see each member of the pantheon as being mere aspects or manifestations of the one Deity. Many religions seem to make this compromise.

English: The Maya rain deity (Photo credit: Wikipedia)

A god is supposedly a non-physical being, and supernatural. A deity is supposed to be able to subvert the laws of nature and cause unexplainable things to happen. Most if not all deities are thought of by believers as anthropomorphic manifestations – in other words, like people.

However, a non-physical being presumably cannot have physical attributes, like people, so it seems to me to be wrong to believe that a deity is in any way like a person. One consequence of ascribing attributes to deities is to make them fallible as people are fallible. One only has to look at descriptions of the supposed behaviours of the Greek, Roman or Norse mythologies to see the consequences of your deities having human characteristics.

Gods are powerful beings and in most cultures power equates to ambition and ambition leads to conflict. Goddesses, if the religion has them, are generally idealisation of the status of women in the society, the mothers, the sisters, the daughters, the wives and generally the peace makers and the artists.

The pantheon of many religions are an unruly bunch with cheating, back-stabbing, sex, killing and many other unsavoury pursuits, but these are stories made up by us humans about the deities. These behaviours are mirrors of our own best and worst characteristics, but on a heroic scale.

Obviously the stories come from the minds of the adherents to the religion, but where do they get the stories, how do these legends arise? They arise as a result of humans attributing human characteristics to their deities, and then wondering what they would do with these characteristics. The legend makers will see the goings on of the rich and famous and will see their deities behaving the same ways but writ larger than life. Others then pass these stories on as facts.

Deities are supernatural entities and have the ability to transcend the laws of nature. While many examples exist of unlikely, improbable and apparently impossible things happening, in the majority of cases it appears that there are physical explanations of these events. For a deity to perform a genuine miracle, then, the miracle should be without possible explanations.

The Roman Catholic faith has a church body which is concerned with verification of miracles called the “Congregation for the Causes of Saints.” They take miracles very seriously. Most modern miracles it seems are cures of illnesses, and documentary evidence of the state of health of the beneficiary of a miracle, both before and after the event are required.

I am uncomfortable with the concept of miracles as it is hard to see how a non-physical cause can cause a physical event. I’m not even sure that “a non-physical cause” makes sense. All causes are physical, aren’t they? An effect without a physical cause would not then make sense.

All physical effects seem to have a physical cause, even if the statement is softened to an assertion that the state of the Universe now is caused by the state of the Universe before and the tendencies or laws of nature.

The concept of a miracle changes this to something like “the state of the Universe now is caused by the state of the Universe before and the tendencies or laws of nature, or something else, outside of the framework of the physical Universe and the laws of nature”.

This pretty much means that anything can happen, but we don’t see this in practise. The Universe follows the laws of nature, be they classical or be they quantum physical.

If a deity cannot have physical attributes, because a deity is not a physical entity, then what attribute can a deity have? Certainly a deity would not have a gender as that is a property of physical biological entities, such a animals and plants. I’ve said above that I don’t think that there can logically be more than one deity, but singularity or plurality seem to be physical properties (but numbers may not be).

If we work back from the definition above, a deity is “something else, outside the framework if the physical Universe that allows things to happen that are not the result of the laws of nature operating on the Universe”. I think that’s a round about way of saying that we don’t know what a deity would be like if there is such a thing.

English: Basic physical properties of soil Čes... — English: Basic physical properties of soil Česky: Základní fyzikální vlastnosti zeminy (Photo credit: Wikipedia)

Politics, the art of the Possible

The title quotation is from Otto von Bismark and previously attributed to R A Butler. It also features in the hit musical Evita, where the generals play a sedate games of musical chairs. At one stage Juan Perón is left without a chair, but one of the junior generals gives up his seat when Perón stares him down.

There are many forms of politics, and in my opinion, political systems work best when they are simple. Some systems which are simple in concept (such as democracy) are often implemented in a complicated fashion which arguably fails the test of providing the results implied or entailed in the objectives of the system.

The Houses of Parliament are situated within t... — The Houses of Parliament are situated within the Palace of Westminster, in London. (Photo credit: Wikipedia)

All systems provide some of the objectives that they are set up to provide and in that cases they pass the much weaker “Bismark test” of providing what it is possible for them to provide.

Politics is all about interactions between individuals and the system. The smallest possible political system is three people, I’d say, where there are a number of ways that they can interact. Each individual may act alone in interactions between the three or two may pair up in interactions with the third, or they may interact in a cooperative way. My mathematical tendencies see another options – they may choose to not interact at all, but in real situations that’s unlikely.

Women standing in line to vote in Bangladesh. (Photo credit: Wikipedia)

In political systems one or more people may become or make themselves leaders. In a group of three or even a pairing one person may always take the lead in things or leadership may be exercised by different individuals depending on the situation.

Most leaders will like leading, and may take steps to maintain their leadership, to the point of discouraging or even disposing of rivals for the task. Of course, there are generally some trapping of leadership, prestige, often respect, money, property, sometimes fancy dress and so on, but many leaders are likely to believe that at least in part, that they are the best people to lead.

The much maligned Niccolò di Bernardo dei Machiavelli is usually invoked when someone wants to describe an unscrupulous politician, but Machievelli’s book, the Prince, is a set of pragmatic options for retaining power. Machievelli argues that public and private morality are different, and as such a leader may do things which he might personally consider immoral to maintain his position.

In Machievelli’s day, it may be been accepted that torture and assassination were appropriate behaviour for a leader. Is the situation that different today, though? While physical torture and actual assassination no longer have a place in politics, political leaders may well use such tools in non-physical ways to rid themselves of unwanted opponents and would be future leaders.

In democracies political parties tend to align themselves along a left-right spectrum as if politics has suddenly become one dimensional. This leads to a polarisation of political groups into left or right. So we see right wing adherents attacking left wing opponents in a modern day version of political assassination, while intra-group interactions may be characterised as “back stabbing”. Has politics really changed from Machievelli’s day?

Our voting system is called Mixed Member Proportional representation. It’s a superficially simple system, where people have an electoral vote and a party vote. Since the party vote determine the mix of MPs in Parliament, it is more important than the electorate vote in most cases.

We had one of the exceptions in our electorate. The local MP represents a small party and because the party is a small one, its party vote was tiny, both in the electorate and the party.

One effect of the proportional part of the system is that the various parties construct lists of candidates who don’t have to stand in an electorate. This essentially means that parties can put people on their lists who could run in an electorate, either because they are not popular, or because the party wants to run another person in a seat.

Obviously this “simple” system is not that simple in practise. As an example we had the bizarre case where an electorate candidate was urging voters to vote for another candidate! This was to insure that a third candidate did not win. The electorate candidate was also high on the party list, so enters Parliament anyway. (He would not have done so had the party vote fallen dramatically).

I hope that shows how a supposedly simple voting system can lead to complexities. As always parties and candidates (and voters for that matter) act pragmatically in their own best interests. Senior politicians of all shades tend to migrate to the safest options, and the newcomers are given the more risky options. A politician (and the public) can judge his standing in the party by where he ends up.

Politics being “the art of the possible”, minor parties try to work the system. If they are left leaning they will usually try to engineer an alliance with the major left wing party, preferably before the election, but often after the event. The opposite applies to the minor right wing parties.

Minor parties may indicate which policies of their they are willing to forgo for this “marriage of convenience”. Even if they can’t get the major parties to agree before the election they can try to convince the public that the major party will agree after the election.

A minor party may strongly deny that they will ally with a major party before the election while forming an alliance with them after the election. This generally doesn’t harm the long prospects of party it seems!

Politics is indeed the “art of the possible”. Political expediency is the rule of thumb. To succeed in politics one must be prepared to compromise. A politician has to decide, when dealing with other parties and the public what his line in the sand comprises, which policies are essential to him, and which policies can be sacrificed or deferred. It surprises me that people do not appear to understand this issue, as it is exactly what happens when people deal with other people in non-political life.