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Technolust



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I’m going to define technolust or technophilia as the almost uncontrollable urge to snap up the latest or most novel technical gadgets. I succumb to this disease frequently, although I do try to keep it under control. I do! Honestly!

I’ve been vaguely wondering about these selfie sticks, the ones where you stick your cell phone on the end of a pole and trigger it by using a bluetooth connection, so when I saw a bluetooth camera trigger in a local shop, I had to buy it. I had to buy it. I had no choice.



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Having got it home and played with it for a bit, I now have to find a use for the darn thing! I don’t particularly like selfies and you can only take so many of them, because essentially they are all the one picture with different backgrounds. You could essentially take one photograph against a “green screen” and chromakey in any background you desire.

My particular area of technolust is things related to or containing computer technology. It’s been with me all my life though I didn’t know it until I came across computer technology at home and at work. I had a Commodore 64 computer at home, and at work I worked on the old huge mainframes, mainly IBM ones. But it really blossomed when I came across mini computers, and the early PCs. I had one of the first portable PCs, like the one in the picture.

English: The IBM Portable PC 5155 model 68 (Photo credit: Wikipedia)

One mainframe computer I worked on had 256kB of memory and we agonised over how we should divide the address space up between three or four “domains”. Another had a staggering 2MB of memory.

Then at the other end of the scale one PC we had we also upgraded to 2MB of memory, which came on a plugin card which was around 30 – 40 cms long and 10 – 15 cms high. We had to leave the top of the case off to use it!

It’s not always physical things that trigger technolust or technophilia. Before all printers came with network connections they were connected (via a parallel cable usually) to a PC. It could then be shared to others over the network. HP produced a “JetDirect” device which connected the printer to the network either via a cable or a card inserted into the printer itself. I still remember the thrill that I got when I connected over the network to a JetDirect device (which is about the size of a small paperback book) using FTP as if it was a small computer in its own right, which in fact is what the device was.

I’ve got altogether too many computer-related devices in the house. Some I use all the time and others are gathering dust. If I was truly obsessive I could fill the house with devices and possibly go broke, but I haven’t gone to those extremes. So I have a “server” and a “workstation”, and my wife has a laptop. Strictly speaking I have a laptop, but I don’t boot it up very often. It is my wife’s old laptop which I fixed and rebuilt.

Some time ago we got an iPad, which I found amazing – something the size of a magazine, which was able to do much of what the other more conventional computers were able to, and which was run by the touch of a finger (or two!). I also got an Android phone and I fell in love with the thing, so I had to have an Android tablet. Had to. No question!



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I love my Android tablet! It’s a rare day when I don’t use it two or three times and often it is more than that. I investigated programming for it, though I don’t have a “killer app”, so most of my programming efforts are uncompleted. I mostly use it for reading ebooks, getting the latest news and to a lesser extent for email and other online web browsing.

I also use it for games. When I go to bed I take the tablet with me and complete a couple of Sudoku puzzles or similar before I go to sleep. Experts advise against this, but it works for me.

Many people these days appear to be afflicted with technophilia or technolust. When a new Apple device is released queues form at the Apple stores worldwide as people try to slake their desire for latest gadget. This is strange as their old devices, which used to be the latest devices at one time, are not rendered useless by the new devices, and transferring personal information to the new device can be challenging, in spite of attempts to make it easy.

Technolust also extends to software. Some people just have to have the latest apps, the latest operating system. The usual justification for such an upgrade is usually justified by the user as a desire for the new features in the new software or bug fixes in the new software. While I would not advocate never upgrading software, I find such justifications a little weak.

There is a danger that a software upgrade may “brick” a device, that is, it might stop the device from booting up and being used, which is why many people shy away from upgrades. While this is a real concern such happenings are rare and most upgrades go OK. Nevertheless, most users of technology have a horror story about how things have turned to custard during an upgrade.



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I’m what I would classify as a cautious early adopter. For instance, when the new software was released for my phone and tablet, and these devices informed me that the update was available, I waited for a few weeks and followed the news on the upgrade on the Internet. This is almost always a bad idea as long conversations between people who have had trouble (interspersed with odd rare comment “It went OK for me”) doesn’t encourage one to upgrade!

IPod touch with software upgrade and web clips (Photo credit: Wikipedia)

Those who grow up with technology tend to use that technology without giving it much thought. Televisions are part of the environment. Cell phones are part of the environment. Maybe soon 3-D printers will be part of the environment. Smart phones and tablets, while desirable, are not quite so novel to the kids of today. They will no doubt direct their technolusts to other technologies.



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Beauty – and the beast

Modern society has something of a fixation with beauty. This has led to such bizarre things as “boob jobs” or cosmetic breast enhancements. Other women inject toxins like “Botox” into various parts of their anatomy to firm them up.

Whole magazine shelves are devoted to “beauty” magazines, and in recent times, they have been augmented by rows of magazines devoted to exercise. TV “infomercials” extol the virtues of this or that exercise machine for men or women, designed to perform miracles on a person’s shape for as little as 10 minutes exercise per day.



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Somewhere there may be someone who is happy with their weight and body shape, but I doubt it. I know that I am not completely happy with mine, but I don’t obsess over it. Some people turn around it and strive in the opposite direction from the mean and try to become, say the heaviest man in the world.

None of this artificiality is beauty. If one measures a beautiful woman for example, one will probably find that the statistics of her measurements are well removed from the average. Miss Beautiful Woman 2015 is way down the bell curve in many ways.

Angeline Jolie, considered to be a beautiful woman, says:

I don’t see myself as beautiful, because I can see a lot of flaws. People have really odd opinions. They tell me I’m skinny, as if that’s supposed to make me happy.

If Jolie is not 100% happy with her looks, how can other women, with less of the physical advantages of Jolie be expected to feel happy with their lot? Of course most women are realistic enough to know that not all women can look like Jolie (or would even want to for that matter), but that doesn’t stop them wishing. Similar holds for men. Not everyone can look like me or George Clooney.

It is evident however, that there is not one standard of beauty (for men or women). Beauty pageants promote one standard of beauty, but films and TV promote another. Beauty is very much in the eye of the beholder. Though it is not usually considered to be a usual measure of beauty, body building is also all about having the best body.

There’s a double standard here, of course. People aspire to be beautiful, and to be highly regarded as such, but if someone goes out of his (or her) way to look at beautiful people, on the Internet, in magazines, all around them, it is rightly considered that there is something wrong with them.



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So on the one hand you have people who want to be beautiful, and that is pointless if they are not seen to be beautiful and on the other hand you have people who are obsessed with beauty, which is unhealthy. Of course most people as is usual fall somewhere in the middle ground – they want to be prettier, but they wouldn’t go to the lengths of cosmetic surgery or Botox.

So you have people who go to the gym twice, eat a week and a half of “healthy” food and then relapse back to their usual ways. They then feel some degree of remorse, have some degree of acceptance, and maybe resolve to try again some time in the future. (It’s these people who the gyms make their money out of, not the enthusiasts who turn up week in week out!)

Some expressions of the search for beauty verge on the bizarre. In particular the “child beauty pageants” are disturbing and border on the weird. Very young children are dressed up and made up like adults with revealing costumes and perform suggestive actions and dances on stage. Costumes sometimes include fake breasts on children well under teenage.

I personally find these shows distasteful. It teaches mostly female children pretty much all the wrong things about sexuality. The parents of the children justify these shows by claiming that it gives the child confidence and often that the child is the one that is driven by the urge to compete.

All this happens in a world where parents are told to constantly be on their guard on behalf of their children. The message is that there is a sexual predator behind every bush. While the advice to be on guard for the children is good advice, is it true that there are a vast number of pedophiles out there?

It seems unlikely that there are more than there were in previous generations. It may be that there is more opportunity for such people as people these days know far less about their neighbours than previously and people do move about much more than they used to. Maybe this has allowed such people to. if not flourish, to become more of an issue.

Even so, I think that the pendulum has swung a little too far in the wrong direction. Sure we should keep our children safe, but it seems that parents are being targeted for innocent photographs of their children. It would be a rare parent who has not taken photographs of their children in the bath, and to think that taking such photographs is a sign of a perversion is perverse.

To parents, their children are beautiful, clothed or unclothed and while it not impossible that parents could be sex offenders in that way, it is probably very rare. I’d suggest too, that it should be relatively quick and easy to determine whether or not parents are sex offenders. Here is another article about the case of a family in England, in which the authorities explain some of their thinking in such matters.

In one case of beauty and the beast, the beauty and the beast are the same. I refer to the situation where a young lady dresses in a beautiful if revealing dress and proceeds to get very very drunk. There is nothing beautiful in a young lady throwing up into a bush or stumbling into the gutter, not to mention the danger that she is putting herself in by getting into such a state.

Obviously the fact that a drunken woman might be vulnerable does not in any way justify someone taking advantage of her while she is in that state. Nothing does.



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Lemmings

English: Traffic Jam in Delhi Français : Un em... — English: Traffic Jam in Delhi Français : Un embouteillage à Delhi (Photo credit: Wikipedia)

In Australia there have been traffic jams up to 28 kilometres long. In New Zealand the end of the holiday period is likely to create “traffic hell“. Meanwhile, those of us who have stayed at home, have found the roads to be eerily empty.

Why do people rush away at Christmas in the Southern Hemisphere? Of course, it is our summer, and getting away from home for a few days is always attractive, but it is evident that if thousands of people try to travel the same roads at the same time there will be congestion.



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I call those who join the exodus and arrival progressions lemmings. This is of course unfair to both the furry creatures and to the humans. Lemmings don’t really commit mass suicide, and the humans, in many cases, don’t have a lot of choice of travel time.

In the Garfield cartoon, Garfield meets a mouse who is half lemming. Garfield asks the mouse what a lemming is. The mouse replies “A gerbil with suicidal tendencies”. (This cartoon may be online, but I’ve been unable to find it. The Garfield strip for my birthday is quite funny, though.)



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In our bigger cities, there will always be traffic problems, because of the sheer number of people that need access to the CBDs and who have to come, in the main from dormitory suburbs. If the roads were sufficient to carry all the traffic it is likely that there would be little room for the CBD itself.

The land of the automobile, the USA, has probably reached the best compromise between the needs of the car and the needs of those who live and work in the centres of cities. Special roads carry cars from the outskirts to the centres of the cities where special buildings have been built to house the cars during the day while the owners are working and shopping. Other special roads take traffic past the city centres and on to other cities. Other countries have copied or extended this model.

Nighttime view of Downtown Los Angeles and the... — Nighttime view of Downtown Los Angeles and the Hollywood Freeway, USA. (Photo credit: Wikipedia)

Humans often don’t have much choice of when they travel, given that they have to work and working days around holidays are pretty much fixed. Some places even shut down on certain days to avoid having to staff offices when few people will be around.

In the Southern Hemisphere Christmas falls in summer, so the natural desire is to go away from home at this time of the year, on a holiday or, as they say in the USA, on a vacation. So it is unfair, really, to call them lemmings. They don’t have a lot of choice.

The lemmings are unfairly tagged with the appellation of suicidal maniacs. The story goes that periodically the lemmings migrate usually as the result of population pressures. Geographical features have changed over the millennia and consequently the lemmings fall over cliffs (which didn’t feature in the ancestral environment) or drown in rivers and fjords which have widened since their ancestors swam them.

These theories were used to “explain” why numbers of lemmings are found dead at some times and dead lemmings are rare at other times. The Wikipedia article on the animals has some interesting theories on issue, such as the spontaneous generation of the animals in mid air resulting in their demise on hitting the ground.

While we may laugh at these theories, we must remember that in 1530s science was nowhere nearly as sophisticated as today. In 500 years time, it may be that our scientific knowledge may look just as silly.



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I believe that people don’t have to all travel at the same time. Sure the dates are constrained and working requirements also constrain the dates that people can travel, but usually there is some leeway. People could travel a day earlier or a day later. Most employers are more than happy to accommodate such slight variations. If it is impossible for an employee to vary travel dates then a change of travel times would do the trick.

Frequently the call is for the roads to be widened or, as the euphemism has it, improved. This solution may well work in a country like the USA which has a large population which is concentrated in cities with little population in between, but is problematic in smaller countries. In New Zealand, not only are the main centres much smaller, but the population is a lot more dispersed than in the USA.

When these factors are considered, it may not make sense to continue to continue to build wider highways in smaller countries. A six lane highway that may be heavily used four times a year doesn’t make economic sense. A four lane highway that is heavily used much of the time does make sense.

English: View of Moscow's MKAD / highway ring ... — English: View of Moscow’s MKAD / highway ring Deutsch: Blick auf den Moskauer Autobahnring MKAD (Photo credit: Wikipedia)

I frequently hear people call for “improvement” of roads that I regularly travel with few hold ups and issues. This is because I travel at times which are called “off peak”. People travel to work at the same times every day, and consequently you can travel easily in the opposite direction to the majority and wonder if they could not slightly change their schedules to avoid the hold ups, and indeed some people do do so.

Some people travel in to work very early (and leave early too, of course). Some people “work from home”. This latter can be a euphemism for goofing off of course, but most people who work from home treat this option seriously and with the state that the art of technology has reached, people can usefully contribute from home.

There is an example of the pitfalls of merely “improving” roads near where I live. When I came to this city I recall sitting in traffic on a four lane (two each way) highway into the centre of the city. Subsequently a motorway was built into the city and the four lane highway is relatively lightly used. (The road I refer to is on the left of this picture).

Obviously in this case the motorway was not considered at the time that the four lane highway was built, but it does demonstrate that often the most obvious solution can often be less than efficient over the longer term.

Growing up, down and sideways, and George Clooney.

Often a plant seed will end up in a place that is not particularly suitable for it. In particular it may end up in a gravel path or similar where there is little real soil. Or it may end up in sand which drains quickly and may, if near the sea, contain high amounts of salt.

In such an environment it may grow stunted or may be deformed. For instance Bonsai trees are kept in a small container and kept relative short of nutrients so that stay small and become gnarled and twisted. They may even have their roots trimmed.

One can imagine a society of concerned individuals fighting against the sustained torture of the trees treated in such a manner, but strangely, I’ve never heard of one. Maybe it is because trees can’t scream?

All members of a species have the same genetic make up, the same genotype. All individuals grow in much the same way, to produce similar adult individuals. This is termed the phenotype.

There may be sexual dimorphism, where the female of the species differs from the male of the species, but in most ways, all members of one sex are pretty similar to one another. I am not too dissimilar from George Clooney. My wife is much like Angelina Jolie.

Of course individuals are not identical. I’m slightly taller than George, for instance. This difference can be genetic, or it may be environmental. My genes may be the cause of the difference, or maybe the environment when we were growing up has slightly affected our growth. Our good looks are almost certainly genetic.

Sometimes a plant grows in a particular way in one environment will look completely different in another environment. Also a young specimen of a plant may look different from a mature specimen of the same species. Lanceword (Pseudopanax crassifolius) has a juvenile form so different from the mature form that it was initially thought to be two different species.

The environmental effect on the phenotype or expressed shape can be seen in genetically identical twins. One would expect their phenotypes to be identical at all ages, however, while “identical twins” look very very similar there are detectable differences.

English: Comparison of typical zygote developm... — English: Comparison of typical zygote development in monozygotic identical and dizygotic twins. (Photo credit: Wikipedia)

For instance if one twin had suffered a serious illness at a critical stage of growth, then their adult sizes may be significantly different. If one twin had a rich diet and the other twin a restricted diet that also might affect their sizes and expectations of longevity. Scientists can tell a lot about the processes of growth and development by studying genetically identical twins.

A more subtle variation in the phenotype can be seen when populations are considered rather than individuals. A population of moths that lives on darker surfaces may tend to be darker in colour than the same species that lives on lighter surfaces. Since this effect happens slowly, over many generations, it appears to be a genetic change or shift. However this change to the genotype is at a lower level than the species as the lighter moths and the darker ones can interbreed.

Some plants look completely different if grown in different environments. The weed that grows in gravel may look completely different from the weed that grows a metre away in a more favourable environment. It’s as if a switch has been thrown which turns on a totally different way of “building” the plant, as it may well be something like that.

If the genome of the organisation is a “program” to “build” the plant, it is perfectly feasible that a lack of resources at an early stage in the plant’s life might well kick in a different path in the developmental process from the path that it would take if resources were abundant.

if (abundant_resources == true)

then build_good_version

else build_poor_version

This is a simple branching process in a computer program, but the process is almost certainly a lot more complex in real life. However the principle is sound, I believe.

A simple iterative process can be used to generate complex shapes that look a lot like real plants. Minor changes to the process can cause significant changes to the end results. Tall thin shapes can morph into shorter bushier ones with a few changes to fixed numbers (constants) in the iterative process.

The phenotype of a plant of a particular species will be similar in all individuals. If an individual has leaves, stem, flowers of a particular sort then the phenotype of an individual in a different (eg poorer) environment, will most likely have similar parts, though some differences will be obvious.

Maybe the stem into of being long and flexible, it may be a lot shorter and stiffer. Maybe the leaves will be a lot thicker and fleshier in the poor environment plant and may therefore be able to retain water which will be scarcer in the poor environment. Perhaps the flower will be more robust in the harsher environment.

One would expect such variations of phenotype, the poor and the rich, to be implicit in the genome if the wider environment is patchy, with areas of rich soil mixed up with areas where the soil is poor. Otherwise, the ability of the genome to be expressed in multiple ways would likely be bred out of the population, as nature always goes for the simpler rather than the more complex.

The flexibility of the genome is something that the organism benefits from its whole life. For example there are some fish which live in groups of one male and several females. If the single male is killed by another fish, an octopus or a human being, one of the females will change sex and become male, taking the place of the missing male fish.

I’ll not speculate on how that happens in detail, but it seems that it must be implicit in the genome. The trigger is the absence of the male fish, but how the “genetic program” detects this, I don’t know, but once is does it transforms the largest female into a male, presumably by triggering changes in the genetic organs. That’s bound to be a complex process.

The central idea in this post is that the genome is much like a computer program and that the environmental influences are like the parameters to such a program. This is probably an over simplification in many ways, but by considering it as a program can explain why the same genome can produce such different individuals.

A computer program can be controlled by inputs while it is running, and similarly the environment can shape an organism while it is growing and after it has reached maturity. The idea of organism as computer controlled machine is not new, but I like to bring it out and have another look at it now and again.



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The Solstice Again

Today is the summer solstice in the Southern Hemisphere, the time when the sun is furthest south in the sky and hence at its highest. From here on in, the days get shorter as we slide back towards winter.

In the Northern Hemisphere, it is of course the winter solstice, and those living there can expect the days to lengthen, as they move towards summer. Today is the Northern Hemisphere’s shortest day.

Seasonal lag means that we can look forward to the warmest months of the year after the solstice, and those unfortunate enough to live in the Northern Hemisphere can look forward to a couple of their coldest months before things start to warm up.

I read somewhere that winter months are the months when people tend to put on weight and this was attributed to the fact that in winter, in the coldest weather people tend to exercise less and eat more. The reduced exercise is attributed to the tendency to stay home in the warm, by the fireside to avoid the often hostile weather.

And the eating more is because, well, what else is there to do but eat, when you are trapped by the weather. Our ancestors used to use up all the reserves that they had laid up for just this occasion, the hams and preserves, dried fruit and root vegetables and so on.

When the summer solstice happens, the weather is warmer and better, so people can get out an exercise, and, for our ancestors at least, agriculture kept them on the move, and the aim was to replenish the stores for the winter months, hence an emphasis on growing rather than eating. Besides, most crops would not be ready for harvesting.



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The winter solstice is one candidate for the start of the year. It marks a definite point in the cycle of the year. It’s after the solstice (a few months after the solstice) that things start growing again. The summer solstice is probably not a good choice as things are humming along then, ploughing and planting, growing and nurturing so it doesn’t really fit as the start of the year.

The spring or vernal equinox falls in March, around the 21st in the Northern Hemisphere. This is also a candidate for the start of the year, but to my mind, it is too late. Winter is tailing off at that time, things are starting to grow and because of the seasonal lag, it’s the start of spring. The year, are I see it, is already under way.



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Interestingly our fiscal year ends on 31st March. This is the date used by individuals to account for tax obligations. In many countries using the Gregorian calendar, the fiscal year ends on 31st December and almost aligns with the (winter) solstice based year. Other countries which use other calendars have fiscal years which relate to the local calendar.

As I have said the summer solstice in the Southern Hemisphere falls on 21st December (in most years). It is an astronomical point in time, not a whole day and can happen on 20th December. In the decade from 2010 to 2020 it falls on the 20th on three occasions.



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The summer solstice, Christmas Day, and the official 1st January New Year Day all fall within just over a week of each other. There is good reason to suspect historical links between these days, and there is much debate on the actual historical relationship between these events.

It is often said that early Christians adopted the winter solstice in the Northern Hemisphere, to squeeze out or replace a pagan celebration at that time. This may or may not be the case (or it may be partially true), but what is evident is that many cultures outside of the Tropics of Cancer and Capricorn celebrate a festival at around the time of the solstice.

Between the two Tropics the sun is overhead twice in a year while the sun reaches a southerly point at the time of the southern solstice (winter in the north and summer in the south) and a northerly point at the time of the northern solstice, the hottest time occurs when the sun is overhead. This divides the year into unequal parts in these latitudes.

The climate of these regions is dependant on local conditions, such as whether or not the region is close to an ocean or is in the middle of a continent, and many tropical areas have wet and dry seasons, typically of unequal extents. One example know to many people outside the tropics is the monsoon season when a regions rainfall may predominantly happen.



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On the Arctic and Antarctic circle, at the solstices the sun just grazes the horizon at the summer solstice and the day lasts 24 hours. At the winter solstices the sun just barely reaches the horizon and the night lasts 24 hours. Closer to the poles the number of sunless days or days with the sum always above the horizon increase. At the poles the sun is below the horizon for three months and above it for three months. (I hope this is correct. I did research this a little, but I am not 100% sure).

Interestingly, I learnt recently that the sunset will continue to become later for the next few weeks. The reason for this according to the linked article is because we have tied our clocks to 24 hours exactly and the day is not exactly 24 hours long. Not only is it not exactly 24 hours, but its length varies during the year. In Wellington the sunset goes out to around 3 minutes to 9 and doesn’t dip below that time until 7th January 2015.

English: Sunrise at Winter Solstice (December ... — English: Sunrise at Winter Solstice (December 21, 2006 at 8 a.m.) as viewed through the doorway half way up Maiden Tower (Photo credit: Wikipedia)

(December data here, January data here).

While looking up these numbers I noticed that the day length in Auckland is nearly half an hour shorter up there. Also sunset is about a quarter of an hour later in Wellington meaning that when the summer weather finally arrives we will have an extra 14 minutes to enjoy the balmy evenings. That’s yet another reason to prefer Wellington over Auckland! We have more time to celebrate the solstice.

[Darn! I completed this on Monday but forgot to publish it. Better late than never, I guess!]

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.]

Dis-Continuum

Where ever one looks, things mostly seem to be in lumps or clumps of matter. We live on a lump of matter, one of a number of lumps of matter orbiting an even bigger lump of matter. We look into the sky when the bigger lump of matter is conveniently on the other side of our lump of matter and we see evidence of other lumps of matter similar to the lump of matter that our lump of matter orbits.

We see stars, in short, which poetically speaking float in a void empty of matter. We can see that these stars are not evenly distributed and that they gather together in clumps which we call galaxies. Actually stars seem to clump together in smaller clumps such as the Local Cluster of a dozen or so stars, and most galaxies have arms or other features that show structure at all levels.

The galaxies, which we can see between the much closer stars of our own galaxy, also appear to be clustered together in clumps, and the clumps seem to be clumped together. Of course, the ultimate clump is the Universe itself, but at all levels the Universe appears to have structure, to be organised, to be formed of lumps and clumps, variously shaped into loops, whorls, sheets, arms, rings, bubbles, and so on.

OK, but in the other direction, towards the smaller rather than the larger, our planet has various systems, weather, orogenic, natural, social and evolutionary. All sorts of systems at all levels, from global scope to the scope of the smallest element.



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In other personal worlds, below the level our interactions with our families, we have all the systems that make up our own bodies. The system that circulates our blood, the system that processes our food, the system that maintains our multiple systems in a state homeostasis.

That is, not a steady state, but a state where all the individual systems self-adjust so that the larger system does not descend into a state of chaos, leading to a disruption of the larger whole. Death.

By and large most systems in our environment are made up of molecules, which are in turn made up of atoms. Atoms are a convenient stopping point on the scale from very large to very small. They are pretty “well defined”, in that they are a very strong concept.

Atoms are rarely found solo. They are sociable critters. They form relationships with other atoms, but some atoms are more sociable than others, forming multiple bonds with other atoms. Some are more promiscuous than others, changing partners frequently.



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These relationships are called molecules, and range from simple to complex, containing from two or three atoms, to millions of atoms. The really large molecules can be broken down to smaller sub-molecules which are linked repeatedly to make up the complex molecules.

To rise higher up the scale for a moment, these molecules, large and small are organised into cells, which are essentially factories for making identical or nearly identical copies of themselves. The differences are necessary to make cells into muscles or organs and other functional features, and cells that make bones and sinews and other structural parts of a body.

A section of DNA; the sequence of the plate-li... — A section of DNA; the sequence of the plate-like units (nucleotides) in the center carries information. (Photo credit: Wikipedia)

As I said, atoms are a convenient stopping point. Every atom of an element is identical at least in its base state. It may lose or gain electrons in a “relationship” or molecule, but basically it is the same as any other element of the same sort.

Each atom consists of a nucleus and surrounding electrons, a model which some people liken to a solar system. There are similarities, but there are also differences (which I won’t go into in this post). The nucleus consists a mix of protons and neutrons. While the number neutrons may vary, they don’t significantly affect the chemical properties of the atom, which makes all atoms of an element effectively the same.

An early, outdated representation of an atom, ... — An early, outdated representation of an atom, with nucleus and electrons described as well-localized particles on well-localized orbits. (Photo credit: Wikipedia)

Each component of an atom is made up of smaller particles called “elementary” particles, although they may not be fundamentally elementary. At this level we reach the blurry level of quantum physics where a particle has an imprecise definition and an imprecise location in macroscopic terms.

Having travelled from the largest to the smallest, I’m now going to talk mathematics. I’ll link back to physics at the end.

We are all familiar with counting. One, two, three and so on. These concepts are the atoms of the mathematical world. They can be built up into complex structures, much like atoms can be built into molecules, organelles, cells, tissues and organs. (The analogy is far from perfect. I can think of several ways that it breaks down).

Below the “atomic” level of the integers is the “elementary” level of the rational numbers, what most people would recognise as fractions. Interestingly between any two rational numbers, you can find other rational numbers. These are very roughly equivalent to the elementary particles. Very roughly.

One might think that these would exhaust the list of types of numbers, but below (in a sense) the rational numbers is the level of the real numbers. While many of the real numbers are also rational numbers, the majority of the real numbers ate not rational numbers.

The level of the real numbers is also known as the level of the continuum. A continuum implies a line has no gaps, as in a line drawn with a pencil. If the line is made up of dots, no matter how small, it doesn’t represent a continuum.

A line made up of atoms is not a continuum, nor is a line of elementary particles. While scientists have found ever more fundamental particles, the line has apparently ended with quarks. Quantum physics seems to indicate that nature, at the lowest level, is discrete, or, to loop back to the start of this post, lumpy. There doesn’t seem to be a level of the continuum in nature.

That leaves us with two options. Either there is no level of the continuum in nature and nature is fundamentally lumpy, or the apparent indication of quantum physics that nature is lumpy is wrong.

Pineapple Lumps (240g size) (Photo credit: Wikipedia)

It’s hard to believe that a lumpy universe would permit the concept of the continuum. If the nature of things is discrete, it’s hard to see how one could consider a smooth continuous thing. It’s like considering chess, which fundamentally defines a discontinuous world, where a playing piece is in a particular square and a square contains a playing piece or not.

It’s a weak argument, but the fact that we can conceive the concept of a continuum hints that the universe may be fundamentally continuous, in spite of quantum physics’ indications that it is not continuous.



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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.