General – Page 15 – Me on the net

A Miscellany



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I’m going to try something different in this post. I won’t try to stick to a single theme, but will try to create a miscellany of short themes and see how it goes.

Firstly, a friend of mine is a keen photographer who keeps a blog and for five years he has posted one or more photos to his blog every day. It’s a fantastic achievement, and since I have trouble posting once a week, I can only imagine the persistence, application and diligence needed to post once every day.



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I’ve mentioned before that I have started blogs at various times in the past and have been unable to keep them going. This time around, for reasons that I can’t really fathom, I have managed to keep going for coming up to 150 posts now. If Brian succeeds in reaching 5 years of posting he will have posted over 1,870 times. Which is mind-boggling!!

One of the reasons that he has given for dropping his self-imposed regime of daily posting is that he feels that the quality of his posted pictures is possibly suffering from the requirement to post something every day and that the temptation to post a merely adequate (from his point of view) picture just to keep the chain going is strong.

English: Locomotive in KiwiRail livery (not a ... — English: Locomotive in KiwiRail livery (not a particularly good photo, but perhaps adequate until a better is found) (Photo credit: Wikipedia)

I must say that I have not seen any deterioration in his pictures, but I don’t look at them with his eyes. So I will continue to look forward to his posts, even though he will not be posting daily pictures once he reaches the 5 year target.

Of course, this has made me think about this blog and how long I intend to keep it going. I’ve posted nearly 150 times so far which represents a bit under three years. I’d like to reach at least 5 years too, which will be around 250 posts. That’s the current target, so let’s see if I can reach it.

English: 250 West Pratt Street in Baltimore (Photo credit: Wikipedia)

Next topic. If I was able to ask God a question, I would say “Quantum Physics. What were you thinking!” We like to think that the universe is logical and consistent. If it wasn’t then there would be no guarantee that the sun would not blink out 10 seconds from now. 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 0! OK we are fine this time.

I’m told, and I have an inkling about it from my reading and thinking, that Quantum Physics is logical and consistent. However the various popularizations of it appear counter intuitive and paradoxical. How can Schroedinger’s poor cat be both alive and dead? What exactly is a superposition of states? What (if anything) is the “collapse of the wave form”?

Omega-Point-Multiverse (Photo credit: Wikipedia)

General and Special Relativity were considered mysterious and paradoxical when Einstein first published his papers. At the time someone claimed that only three people in the world truly understood it, but it didn’t take long for it to be taught down to college and undergraduate levels. While strange and challenging, it was soon accepted as true by the majority of people who had come across it, although people still create web sites where they try to prove that Einstein was wrong.

Quantum Physics is also taught at undergraduate levels I believe but it remains (or so I get the impression) as a work in progress. The famous Copenhagen Interpretation was formulated around 90 years ago by Niels Bohr and Werner Heisenburg and there is still no accessible standard interpretation that is accepted by the majority.

Niels Bohr once said “Anyone not shocked by quantum mechanics has not yet understood it.” Richard Feynman said “Nobody understands quantum mechanics.” So, God, Quantum Physics. What were you thinking about?

Flags and things. There is a big debate in this country at the moment about whether or not to change the flag. People often refer to the Canadian flag as a case where a new flag was adopted after public discussion. It’s not a good case study though as the actual adoption of the winning flag involved a farcical mistake : “Through a six-week period of study with political manoeuvring, the committee took a vote on the two finalists: the Pearson Pennant (Beddoe’s design) and the current design. Believing the Liberal members would vote for the Prime Minister’s preference, the Conservatives voted for the single leaf design. The Liberals, though, all voted for the same, giving a unanimous, 14 to 0 vote for [it]”. (From Wikipedia).

The process for our new flag was decided on early. Firstly all submissions would be reviewed, and a “top 40” would be selected by a panel composed of, basically, a bunch of celebrities and other. No disrespect to them, but they were not flag experts, and if they were chosen to sort of represent the man/woman in the street that is what they achieved.

Of the top 40, four were “approved” by the ruling National cabinet. It’s not too clear how this was done, but only conspiracy theorists would contend that three out of the four contained the fern emblem that the Prime Minister favoured and that he somehow influenced the selection.

Stjórnarráðið in Reykjavik, the seat of the ex... — Stjórnarráðið in Reykjavik, the seat of the executive branch of Iceland’s government (Photo credit: Wikipedia)

Now we have the top four we are supposed to vote in a referendum to pick one to go up against the current flag in a second referendum. Interestingly a group has been formed to promote a fifth design (originally in the top 40) over the top four. We will see where if anywhere that this movement goes. I’d guess it will eventually fail.

One hundred words to go. Interest is high on the attempt of Jarryd Hayne, a former Australian rugby league player who has secured a spot in San Francisco 49ers NFL team. (That’s what is called “American Football” everywhere except the USA). Good luck to him, I say. I expect to see a surge of popularity for the sport in this part of the world.

He seemed to bring something new to the American game, but time will tell if opposition coaches find ways to nullify his effect or whether other players will adopt some of his style, which to my naive eye seems to be a more fluid running game. Or maybe he really is an exceptional player. Time will tell.

Well, I quite enjoyed jumping around through various topics but I don’t think that I will do it every time. I’ll just take it as it comes.

A show jumping course (Photo credit: Wikipedia)

Cycling through life

I’ve been thinking about cycles. A cycle is something that repeats, like the rotation of a wheel, or the rotation of the earth. A true cycle never has an end until something external affects it, and the same is true for the start of a cycle in that something external to the cycle has to happen to start the cycle off.

Conceptually, a perfect cycle would be something like a sine or cosine wave. It’s called a wave because if plotted (amplitude versus time) it resembles a wave in water, with its peaks and troughs. It’s fundamental constants are the distance between the waves and the amplitude of the maximum of each cycle.



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The sine and cosine waves are derived from a circle – when a radius of the circle rotates at a constant rate, the sine and cosine can be measured off a diagram of the circle and the rotating radius. The point where the radius touches the circle is a certain distance above the horizontal diameter of the circle and is also a certain distance to the right of the vertical diameter of the circle. If the radius of the circle is one unit, then the sine is the height and the cosine is the distance to the right.

As the radius sweeps around the circle the sine of the angle it makes to the horizontal diameter goes from zero when the angle is zero and the radius lies along the horizontal diameter to one unit when it is at 90 degrees to the horizontal diameter. When the angle increases further, the sine decreases until it is again zero at 180 degrees, and as it sweeps into the third quadrant of the circle it goes negative, increasing to one unit again at 270 degrees (but downwards) and finally returning to zero at 360 degrees. 360 degrees is (simplistically) the same as zero degrees and so the cycle repeats.

The cosine starts at one unit at zero degrees, decreases to zero units at 90 degrees, decreases further to one unit downwards (conventionally called minus one) at 180, then increases to zero again at 270 degrees and finally to complete the cycle, it increases to one unit at 360 degrees.

When plotted against the angle, the sine and cosine produce typical wave shapes, but shifted by 90 degrees. If the radius rotates at a constant speed, the sine and cosine can be plotted against time, which produces a curve like the track of a point on a wheel as it is rolled at constant speed.

animation of rolling circle generating a cyclo... — animation of rolling circle generating a cycloid; black and white, anti-aliased (Photo credit: Wikipedia)

While these curves are pleasingly smooth and symmetrical, in the real world we can only get close to these ideals. A wheel will slip on the surface that it is turning on, friction on axles slows a freely spinning wheel, lengthening each “cycle” by small amounts, altering the curves so that they are minutely different at different times.

If an ellipse is drawn inside the circle such that it touches the circle at the points where circle touches the horizontal diameter, the radius will cut the ellipse at some point and it turns out that the curves plotted from the intersection point are still sine and cosine curves. However the heights or amplitudes of the curves are different.

An ellipse is approximately the shape of the orbit of a planet about a sun for reasons that I won’t go into here. It isn’t an exact ellipse, mainly because of the effects of other bodies, though it is accurate enough that things like the length of a planet’s year doesn’t vary significantly over many lifetimes. The most accurate atomic clocks can be used to measure the differences but they only need to be adjusted infrequently by very small to keep in line with astronomical time.

To account for these errors the astronomer Ptolemy devised an ingenious scheme. An ellipse can be looked on as result of imposing a smaller cycle of rotation on a larger one, a bit like having a jointed rod, with the larger part connected to the centre of a circle and the smaller part connected to the end of the larger part. If the smaller rod rotates at a constant speed at the end of the larger rod then the tip of the smaller rod draws out a more complex path. If the correct rotation rate is chosen, as is the correct starting angle between the two rods, then the tip of the smaller rod will draw out an ellipse.

Circles on an old astronomy drawing, by Ibn al... — Circles on an old astronomy drawing, by Ibn al-Shatir (Photo credit: Wikipedia)

Ptolemy suggested that the variations from an ellipse could be modelled by imposing other smaller cycles on the first two cycles, and indeed this does result in more accurate descriptions of the orbits.

Ptolemy got a bad press because he believed that these cycles were real manifestations of reality, and his system of epicycles on epicycles on epicycles was hugely complex, but his system can be extended to model any physical system to any degree of accuracy required. It can be proved mathematically that his process exactly matches any equation if the process is taken to infinity. It’s one method of fitting a curve to arbitrary data.

In particular Ptolemy was able to use his methods to calculate the distance of the planets, which was a singular success for his method. It is the sort of technique which is used today to calculate the orbits of newly discovered comets – when it is discovered the astronomer has only one point of location so he/she cannot predict the orbit. When the comet’s next position is measured, the astronomer can start to predict the orbit. A third observation can vastly improve the accuracy of the calculation of the orbit.

Subsequent observations allow the orbit to be refined even more until the astronomer can accurately predict the complete orbit of the comet and its periodicity using something like Gauss’ method as described in the link. In essence the procedure of observation, calculation and prediction/re-observation is the same as Ptolemy used, even though the underlying physics and philosophy is different. Ptolemy’s ideas may seem quaint to us, but in his time we knew much less about the universe, and, given the era in which he was working his ideas were not that outlandish. He did not even know that the planets revolved around the sun. He didn’t know about gravity as a universal force.

Early television and that mess of metal on the roof

In the beginning the consumer television set was a large box with a small blurry screen. To successfully receive one of the few channels being broadcast one needed an aerial to pick up the broadcasts. They came in two sorts. One was a huge “H” or “X” shape that was located on the roof and aligned with the signal from the broadcaster. The other was a small device consisting of a base made of plastic and two metal prongs, known as “rabbit’s ears“.

Of the two types you will only see the rabbit’s ears aerial still being used today. Since television has moved from the VHF (Very High Frequency) band to the UHF (Ultra High Frequency) band, television aerials have shrunk in size and the technology has now improved so that television aerials have become the compact roof top Yagi style aerials that are common today.

Nederlands: Schets Yagi antenne (Photo credit: Wikipedia)

Although it is obvious from the shape of the Yagi aerials that they receive a directed signal, I suspect that not many people know why they are the shape that they are. There is only one element that picks up the signal and that is one of the cross bars on the main shaft of the aerial. All others elements (including the mesh element at the back if there is one) serve to concentrate and direct the incoming signal towards the main element or dipole.

This means that the aerial can pick out weaker signals from general noise but it does mean that the aerial must be aligned fairly accurately with the transmitters signal.

There is a new type of aerial that has become common in recent years and that is the dish aerial. Dish aerials are generally used to pick up signals from stationary satellites and need to detect weak signals broadcast from space. The actual dipole is in the small plastic box in front of the dish. The dish is a passive reflector and just concentrates the small signal onto the dipole in the box, much like the Yagi aerial does for UHF frequencies. Satellite signals are of even higher frequency than the UHF ones.



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In the early days of broadcasting and with the use of VHF frequencies, ghosting was a problem. Because early aerials (and “the rabbit’s ear” type of aerials) were not particularly directional they could receive signals which had bounced off various obstacles on their way from the transmitter to the receiver. The reflection from obstacles such as hills and large buildings meant that the receiver would collect signals which had travelled by different routes and hence had taken slightly different times to reach it.

The result of this was that the images on the screen either appeared to have shadows or duplicates. This phenomenon was called “ghosting” and in a bad case it might appear that in a broadcast soccer match that the match was being contested by two teams of twenty two players using two balls.



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This phenomenon is not often seen these days as UHF signals and satellite signals are much more directional and hence do not receive signals bounced from obstacles in their line of view which has a much narrower angle.

In the early days of television technology the electronic equipment in the receivers was in its infancy. The circuits leaked signals between their parts, and components were not as stable as they are today. Valves and other components had to “warm up” to operating temperature and often the oscillators and other circuits tended to “drift” away from the nominal operating frequencies.



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In real terms this meant that those watching the program would often find that the picture would appear to roll up or down the screen. Someone would have to leap up and twiddle the controls at the back of the television to try to stop the picture rolling. Very often the twiddler would adjust the control to stop the rolling, only to find that his or her very presence had affected the circuits and the screen would start to roll as soon as he or she moved away.

Other effects would cause other issues. Unstable circuits would cause the image to shake like a jelly, or tear completely in one or more places. It was a true art form to twiddle the available knobs (of which there were many) to produce a decent and more or less stable picture.



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Screens were small. Early sets had dimensions of perhaps 9 inches (23 cms). Today screens of 50 inches or more are common. Each screen had (in the UK at least) 405 lines all of which were scanned in one or more cycles. The early television tubes were not very accurate and each line could be clearly seen, and so sometimes could the “flyback” as the circuitry returned the beam to the top of the screen for the next scan.

The end effect was a small picture blurred by circuitry instabilities, often with artifacts like the “flyback” lines polluting the picture, and plagued by instabilities, but which showed pictures of news around the world, or educational programs or discussion panels, plays or game shows. And they even broadcast cartoons for the kids. Everyone wanted one, of course!



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Obviously things improved very quickly. Television electronics became much better, and the pictures much more stable especially when transistors were introduced. The screen increased in size, and colour television was introduced. Some would argue that the quality of the television content has dropped dramatically, but that doesn’t change the fact that most people have one or more televisions in their house and it has become the central focus of many lounges and living rooms. Many people have them in bedrooms, bathrooms and kitchens these days.



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It is ironic that broadcast television may well have peaked. More and more people use their television sets to show content that has not been broadcast, but which has been obtained over the Internet. It may be that this network distributed content may totally displace the broadcast television service and that people will no longer be tied to a broadcast schedule, picking up content that they want to watch from a myriad of Internet sources.

In the Zone

(Ugh! I forgot to post this last week. My apologies)

Programming, as I’ve probably said before is a strange occupation. You start with a blank sheet, steal bits and pieces from where ever you can find them and glue them together modify them, add some bits of original (to you) code and try to think of all the possible ways your program can go wrong.

Then you try and break your code (and usually succeed at first). Programming is still very much an art form. Of course things have changed a lot over the years, and we are able to use the work of others to help us in our endeavours, but my first paragraph is still true.

In the beginning there was “Hello World”. This is probably the simplest program that does something visible. It doesn’t take any information in and its output, the words “Hello” and “World” are not very useful in themselves. Actually, I’d say that there is an even simpler program that takes no input, produces no output, and in the process changes nothing. A “null” program if you like.

A programmer writing a new program may well jump in and start coding by grabbing some other code that he or she has access to, but that stolen code was developed, ultimately, from “Hello World” or the null program.

Picture of "hello world" in C by Use... — Picture of “hello world” in C by User:aarchiba. (Photo credit: Wikipedia)

A good programmer is one who steals code from elsewhere and modifies it to do what he or she wants. There is no stigma of plagiarism attached to this process, and it is in fact strongly encouraged that programmers share code. A spoof news item that I came across stated that all programming courses would be replaced with a course on how to find code on “Stack Overflow“. I’ve been unable to find the link again, but I believe that the item was on “The Onion“, a well known satirical website.

Of course, such a process may propagate errors or bugs across many programs, but it is such an effective strategy that it is used more often than not. If code exists to solve a problem then it would be silly to pass it by and write it ones self, maybe introducing bugs to the code. The advantage of “borrowing” code is that while errors and bugs may be in the borrowed code, many eyes will have looked at the code and there is nothing more that programmers like than pointing out bugs in the code of other programmers.

Stack Overflow allows anyone to post code and comment (up to a point), so code posted may not be top quality, but other programmers are quick to jump if they see bugs or inefficiencies in code. Contributors will also point out code which doesn’t follow standards or conventions in the programming language being used. This is considered useful, as the code, if modified, can be accessed and understood more easily, and may often be safer and free of more bugs than unconventional code.



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When a program is written it starts out as literally a few lines of code or even an empty file. Any programmer knows that a program grows swiftly and in ways that can’t be foreseen until it may be of enormous size. It won’t be all written in one sitting but is usually written in stages. I personally like to write my programs in very small chunks, building on what has gone before. I think that many programmers use this process, though there may be others who write a sizeable chunk of code before testing it.

Ah, testing! Testing is the less enthralling parts of writing programs. Any program must be tested, to ensure that it does all that is required and nothing else. Generally the program being written doesn’t do all that is required and does things that shouldn’t happen, and initially it is likely to crash or produce cryptic error messages under some conditions.



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Testing is supposed to reduce the number of such unwanted happenings, and the programmer may do some rudimentary testing and may handle at least some errors. However the programmer will realise that users who are unfamiliar with how the program is written may well do something that he has not expected.

So clever people have developed ways of automatically testing programs. To do this they have had to write the programs that are used to test programs. And of course those testing programs may have bugs. You can see where that leads to!

Zebra (programming language) (Photo credit: Wikipedia)

When a programmer knows a programming language really well, he is able to literally think in that language. The word “literally” has been devalued in recent time, but I am using it in the true sense of the word. This is hard for some people to understand as they think of language as something like French or Tagalog, and they can’t understand how one can think in a programming language, which is qualitatively different from a spoken language.

An interesting thing happens when a true programmer is programming something. His thought processes become so involved in the process of programming and in thinking in the programming language that he loses track of the outside world. That’s why programmers are whimsically thought to subsist on fizzy energy drinks and dialled in pizza. It is because those things are easily acquired and the programmer can keep programming.



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A programmer “in the zone” is so embedded in the world of the program that he or she may often be reluctant to leave that world and respond to irritations like bodily needs and colleagues. I doubt that there is a real programmer who has not surfaced from a deep dive into the depths of a programming problem and realised that all his colleagues have left and it is late at night or very early in the morning. That’s the reason programmers stay after all other people have left – they know that they can slay the current bug with just a few more changes and a few more runs of the program.

The zone has similarities to the state of meditation. While meditation is passive though, programming is an active state. In both cases the person basically disconnects from the world, so far as he or she can, and the concentration is directed internally. Now that I think about it, any deep thought, be it meditation, programming, or philosophising, even playing a sport at a very high level, needs such concentration that much of the world is disregarded and the exponent enters the zone.



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Time and time again



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Well, this will be my third post in a row about time. I think I’ll discuss something else next week!

As I’ve said before, the path of a particle as it travels through space in the usual way can be represented as a line in a four-dimensional space-time system. There will be one and one line only that represents the history of the particle from the time it is created until the moment that it is annihilated. If we decide to plot only this particle’s location over time there will be no others lines in this space.

Diagram showing phase space plot of particle u... — Diagram showing phase space plot of particle undergoing betatron motion (Photo credit: Wikipedia)

The path will twist and turn as the particle is affected by fields and other particles. It may take a sudden turn when our particle collides with another particle. This interaction can be visualised by adding the data about the other particle to the same space-time graphs. However, since the particle is constantly jostled by other particles the diagram would quickly become crowded so to keep it simple let’s drop out the lines of all the other particles.

So we are back to the original single line we started out with. If we assume that it can’t time travel, there will be no loops and gaps in the line. In other words, for every time between its creation and destruction there will be one and only one set of three space coordinates. Of course the line will have curves and kinks as the particle interacts with other particles and fields.

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)

Suppose we allow choice into our system. Suppose we have two choices A and B. At the point that the choice is made (at a macro level), there are two possibilities for the space-time position of the particle. From that point on the particles history could be represented by an A line and a B line, which at first glance appears to contravene the single point rule. However by making a choice we are saying that either A will occur, OR B will occur, but not both, so we really have only one line.

A choice is not the same as travelling in time though, so let’s plot A AND B, and we will get a multiply branching tree of lines as the time line splits on every point where a choice is made.

The question arises as to which of these lines is the “real” life line of the particle. This we don’t know in advance because we don’t know what the choice will be, which leaves us in the uncomfortable situation of having something unpredictable happening and physics deals in things that can be predicted.

When a choice is made by someone, it is highly likely that one option is much more likely than the other. Maybe the probability is 0.8 to 0.2 (80:20 in percentage terms). Another way of looking at it is to say that, all other things being equal, if the choice were to come up 100 times, A would be chosen 80 times and B would be chosen 20 times. Of course in a 100 tests, it could be that the actual figures might be 79 and 21.

It would be highly unlikely that A would be chosen once and B chosen 99 times in 100 trials of course, but it remains possible. (We have to remember that the circumstances of the choice must be identical, that is, all other things being equal)

We could incorporate this into our system by adding a “probability” axis (running from 0 to 1, or equivalently to 0 to 100). A point on this axis would represent the probability of the choice that was made and the whole sheet represents the life of the particle.



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It appears that two points on the line are axis, the ones at 0.8 and 0.2 are “special”. In the stated situation those at two probabilities of the outcomes A and B. The probability of any other outcome say Z are zero and effectively outcome Z does not exist.

All things being equal there appears to be no physical reason why someone would choose one option over another. It may be that, all things being equal, that one option gets chosen more often than the other, but the sum of all the probabilities is one – in other words it is absolutely certain that one of the options is chosen. I find this totally mysterious. A choice is an event where the outcome is not dictated by the prior history of the event and is decided by the person making the choice.

English: Figure 1. Demonstration of the decisi... — English: Figure 1. Demonstration of the decision space (Photo credit: Wikipedia)

However the person’s mind is making the decision, and the person’s mind is equivalent to the state of his/her brain and the state of his/her brain is determined by physics, chemistry and biology. I see no “wriggle room” to allow for a person to make a choice.

Can we solve this dilemma by introspection? Descartes looked within himself and concluded that “I think therefore I am“. I don’t know if Descartes intended or realised it, but the implication is that thinking, which happens in the mind/brain, occurs before consciousness. In other words, consciousness is an epiphenomenon of the mind, just as the mind is an epiphenomenon of the brain.



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Why then do we think that we make choices and decide things? Well, by introspection I can look at any decision that I have made and I can always point at reasons why I made the choice. Well, of course this may be simple rationalisation. We look at the decision that we made we look at the reasons that might explain why we chose that course and we pick and choose the ones that we like.

While that may be the reasons that we give, and some of them may be true, I do believe that we have reasons for what we do, but those reasons are physical – the configuration of our brains, as a result of past events and happenings, results in a foregone conclusion – we perform an action which looks to the outside world like a decision.

For instance, if we are filling in a form and we are required to check a box, we “choose” the box depending completely on what has gone before. If the boxes are “Male” or “Female” we know what sex we are so naturally we would choose the correct box. No real decision is made. If we are annoyed at the form or we are in a joking mood we might tick the wrong box. It depends on our state of mind before making the decision what we do, and it depends only on that.

English: checkbox, check box, tickbox, tick bo... — English: checkbox, check box, tickbox, tick box Italiano: checkbox, check box, tickbox, tick box (Photo credit: Wikipedia)

Time Travelling

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Time stories have been around for years, and yet we have seen no time travellers. If there are time travellers, then they are hiding from us. That would be pretty hard, since society and language are changing all the time, and they would most likely look out of place.

If they came from the past, their mannerisms, clothing and use of language would likely give them away. Imagine someone from the time of Sir Francis Drake appearing in the current era. He would quickly be spotted.



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For someone travelling from the past, the issue is that he or she would not know what to expect as the present is the future of times past, so they would not be able to prepare themselves for the future, as they would consider it.

If a citizen of the future where to travel to the current time, he or she could presumably prepare his/herself for what would be the past to him/her. The time traveller could learn about our era and equip him/herself with clothes, money and other things from our era and would be able to learn the idioms of the language of the current time, as well as the ethics and morals of the era.

There are web sites on the Internet which claim to have proof of time travel (I’m not going to link to one – a Google search will bring up many of them). In most cases the evidence is far from compelling, relying on blurry photographs and dubious eye witness accounts.

I’ve recently been scanning my old photographic slides and in one of them, from the early 1980s or late 1970s, the person in the picture appears to be holding an iPad! What in fact she is holding is a place mat, with a cream coloured border and relatively dark picture on it. This demonstrates how easily “evidence” of time travel can be found if you look hard, and if you strongly believe that time travel is possible.

Every person, every object, even every elementary particle has position which can be measured (leaving aside the issue of Heisenberg’s Uncertainty Principle and Quantum Physics for now) at any moment in time. The four dimensions, three of space and one of time uniquely identify an event in the life of the person, object or particle.

These four coordinates represent a single point in a four dimensional space. Since we find four dimensions hard to visualise, this space/time is usually represent by a depiction of a three dimensional space of two space and one time coordinate axes. The path of a person, object or particle through life consists of a single unbroken line in the four dimensional space.

Note that in time dimension, if time travel is not possible, for every value of the time coordinate there will only be one point of the person’s life line. In other words, while the person could visit and revisit the same three dimension spot in space many time, they will only pass through a particular time once and once only. A person’s now is unique.

Time travel means that a person could pass through the same moment in time multiple times, and the possibility arises of loops in time. It seems obvious that the same event could not appear on the time traveller’s life line. In other words the loops in a life line would not cross.

To get from one event in space/time to an earlier event in space/time, the person could either travel through the intervening times or just jump from the first event to the second. In other words time travel if it is possible would be represented by a line going backwards in time or it could be discontinuous, with a break the in the person’s time line.

From the point of view of an observer, a discontinuous time line for the time traveller would be seen as a sudden appearances from nowhere and a later sudden disappearance. If the time line is contiguous, the observer would again see a sudden appearance of the time traveller, and then two instances of the time traveller both apparently travelling into the future at one second per second.



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One will be the time traveller doing just that, and the other will be the observer’s view of the time traveller as he travels backwards in time. Eventually the observer will see one of the instances (people!) merge with another instance of the time traveller and disappear. Since we don’t normally observe such sudden appearances and disappearances it’s very tempting to say that time travel does not happen.

To see what I mean, take a piece of paper and draw a line from top to bottom with a look in it. Now horizontal lines across the page represent time as seen by the observer. If you move a ruler down the page, at first there is a single line, the time line of time traveller. But at the point that the time travellers has travelled back to, suddenly there are (apparently) three lines travelling down the page. At the point that the time traveller travels from, two of the lines merge and disappear.

English: Meter stamp catalog image, three stac... — English: Meter stamp catalog image, three stacked horizontal lines (Photo credit: Wikipedia)

If time travel is discontinuous the observer would first see one instance of the traveller, and then another instance would pop into existence. The two would coexist for a time, and then one instance (the original one) would disappear, with the second continuing to exist.

As I said, it’s tempting to say that this proves that time travel is not possible. Certainly, a macro level we don’t see people appearing and disappearing so it is definitely very unlikely, though reasons for this not to be noticed can be constructed.

At an atomic level though, we do see spontaneous generation of particles, into a particle and its anti-particle. If the anti-particle the meet another particle and they annihilate one another, this could be construed to be a single particle with the anti-particle being the particle travelling back in time.

This is bad news for time travellers. To travel back in time by this method, the time traveller would have to be zapped into a burst of energy and an anti-traveller who would then travel back in time to the earlier time when a burst of anti-energy would be required to zap the anti-traveller into another instance of the time traveller. These occurrences would be likely to destroy the integrity of the time traveller’s body. That is it would destroy it.

Dwelling in the past

Some accounts have the wizard Merlin living his life from future to past, in the opposite direction to the rest of us. This meant that to him, what would a final farewell to us would be a joyous first meeting for him, and a first meeting would a sad goodbye. He remembered the future, but the past was a complete mystery to him.

The trolls in Terry Pratchett’s Diskworld had similar ideas. They considered that they travelled through time from past to future, as is normally understood, but they also considered that we were facing backwards in time as we travelled through it. This was conjectured by the trolls, to explain the fact that we can see where we are going when we travel in whatever direction we choose but we cannot see where we are going in time. Similarly we can’t see where we have been when walking from one place to another, but we can see where we have been in time.

Scientists have no difficulties with direction in time. In an equation with a time variable in it, one can trace the changes to other variables from the nominal zero point to see what would occur in the future, merely by incrementing the time variable. A scientist can predict the trajectory of a thrown item (a parabola) merely by substituting later times into the time variable in the equation.

y =ax² + bx + c

The scientist should compare these results to experiment and find, that this more or less works. Lets say though, that the scientist is an astrophysicist investigating an asteroid or other object on a parabolic trajectory around a larger object, like a moon or planet. (A parabolic trajectory is the trajectory which divides objects in hyperbolic trajectories which are not bound by the larger body’s gravity, from those in elliptical trajectories where the object is bound by the larger body’s gravity).

The astrophysicist would be able to track the trajectory of the body backwards in time, simply by substituting negative values for time into his equations. He would be able to see where it had been. However this process of substituting negative time values into the equations only works so far. At some point the body will feel the influence of other objects and the retrograde trajectory will deviate from the values predicted by the parabolic equation.



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Of course, if the trajectory is projected forwards far enough similar considerations arise. Eventually some other body will divert the body away from the parabolic trajectory. However in the region in which the parabola applies, the behaviour is symmetrical with respect to time. From a film of the event one could not tell whether or not the film was being run forwards or backwards.

Of course, if a film is run backwards for any length of time, it becomes obvious that something is wrong. Things fall upwards, and broken crockery comes back together again. People walk backwards.



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On a closer look, people can intentionally walk backwards and it is possible that a spring or other mechanism could be used to shoot things upwards, but it is a lot harder to imagine a way of reversing the breakage of the crockery. It implies that some process involved in the breaking of crockery is not reversible at a macro level.

It is likely that the process in question is at the molecular level or slightly above. To rejoin two broken surfaces spontaneously would presumably require that the molecules be in the correct positions and that a little burst of energy (equivalent to the little burst of energy that comprises the sound that the crockery makes in breaking and any heat release) be supplied at an instant in time. The weak bonds between the parts of crockery would need to be created, and that is really difficult.



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There’s therefore a discrepancy between the scientist’s view of the world, through his equation which time-symmetrical, and the man in the street’s view of the world, which is asymmetrical with respect to time. In fiction this asymmetry is used to good effect, when the protagonist may “wind back time”, to write a wrong or divert history to an alternate course.

When we consider space we usually imagine a three dimensional space. Events happen at locations in this space and three coordinates are enough to locate an event in space. Every possible point in space has its set of unique coordinates. It is common to add an extra dimension for time, making the space four dimension and consequently difficult to imagine successfully.

All events in space and time have a location and time and are represented by a point in the four dimensional space. The path of a particle is a line within this space, and any point on the line represents the position of the particle at a particular time. Positions on the line are either before or after this point, so it constitutes a “now” point for the particle. There is no actual motion over the line, since in the 4-D space all points represent the past and the future of the particle. They are already there.

The Klein bottle immersed in three-dimensional... — The Klein bottle immersed in three-dimensional space. (Photo credit: Wikipedia)

To move to an earlier time, all we need to do is move to an earlier spot on the line. We would need to either travel back along the line at a speed of so many seconds per seconds where the first “seconds” is seconds measured in the space and the second “seconds” is some other time scale or we could jump out of the space-time completely and return to the requisite point earlier in time. We’d need to do the latter in some other space-time that embeds the original space-time, adding a number of extra dimensions to the mix.

Both options require the addition of extra dimensions, which while possible complicates the situation unacceptably to my mind. The process of adding extra dimensions could be repeated and go on forever, so we end up with infinite dimensions. I believe that it is correct to employ Occam’s razor at this point and declare that it appears unlikely that we could either roll back time or jump to an earlier point in time because of the implication that we would needs infinite dimensions as a result.

Cold

At the time that I write this the temperature at this desk is 12.7 degrees Centigrade. Of course it will warm up soon, but overnight the temperature drops dramatically at this time of year. I hate the cold. As the saying goes it makes your bones ache.

The climate here is “cool to warm temperate”. This means that places in the south see low temperatures which drop to zero degrees Centigrade or a few degrees below, with occasional falls to lower temperatures in some places. Snow rarely lasts long except of course in the mountains and hills.

A powder snow avalanche (Photo credit: Wikipedia)

In the north, places like Auckland rarely drop to zero, remaining a few degrees above zero in most winters. Auckland and further north rarely experience snow, and a flurry of sleet in Auckland would usually gets a mention on the television news.

While snow rarely lasts long at low altitudes, it tends to come in quantity when it does, closing hill roads and even sometimes brings southern cities to a halt. Dumps at higher altitudes can of course cause severe issues to farmers. The farmers’ worst nightmare is a dry summer and autumn resulting in low yields from pastures followed by an early heavy fall of snow.

Of course the skiers rejoice when there is a snow dump and they head for the many ski fields in their hundreds sometimes causing traffic jams on the access roads! Snow for skiing can be undependable so most major ski fields have snow generating machinery as a backup.

When the snow melts the rivers rise of course. New Zealand rivers can be chillingly cold as a result. Many parts of the country have what is know as braided rivers, which appear to be mostly boulder filled for much of the time. Sometimes during a dry spell it may be possible to cross the river from bank to bank without getting one’s feet wet, while a surprising amount of water travels below the surfaces between the boulders.

When there is a thaw or after heavy rain such rivers rapidly fill and the water rises to the surface, creating a broad and sometimes heavy flow filling the river bed from bank to bank. The flow can be impressive, carrying large trees and other debris from the higher altitudes down to the lower altitudes.

Consequently there are long bridges on these braided rivers that seem to mostly traverse an expanse of rocks and boulders with maybe a relatively small looking river, possibly split into several channels.

Sometimes the boulder banks are populated by Russell lupins, which can block and change the nature of these braided rivers. While picturesque, the lupins are an introduced species and can damage the river’s ecosystem.

The water in the rivers is cold and can be bone-achingly cold as the water is mainly melted snow from the Southern Alps and other mountain ranges. Consequently swimming in such rivers can be challenging. I have swum in a river in the United Kingdom, wearing a wetsuit, with chunk of ice floating down the river, and that was an experience that I will not forget. The rivers here are likely to be at least as cold.

Ice is a strange substance. Well, perhaps that should be water is a strange substance. As water is cooled its volume reduces, like other substances. When it reaches four degrees Centigrade however it reaches a maximum density and then starts to expand again, which is counter intuitive. The reason for this behaviour is related to the way that water molecules link weakly to one another, as a result of the polar nature of the water molecule.

So water at 3 degrees Centigrade is lighter than water at 4 degrees Centigrade and so tends to move to the surface of the water. At 0 degrees Centigrade the water turns to ice, which floats on top of the liquid. This allows all sorts of things and protects fish and other aquatic organisms from the elements and from freezing solid, up to a point. It also allows us to skate on the surface of frozen bodies of water since the slight pressure of the blades causes the ice to temporarily melt.

When a human body gets cold, the body has various defences. As warm blooded animals we need to maintain our body temperature and if we don’t we die. So, when we get cold, blood flows to the centres of our bodies to maintain our core temperature, which means that our hands and feet become significantly colder than the rest of our bodies.

If the cold reaches into our core bodies, things start to shut down and hypothermia sets in. Brain function is hit hard and we start to behave irrationally and we would be in danger of dying. Fortunately as humans we have invented things like fire, houses, and clothing to keep us warm when the weather is cold. I personally have problems with maintaining heat as I do not like to wear gloves and I don’t like any form of headgear!

Another thing that I find in cold weather is that my breath passes over my moustache and beard so in colder weather the moisture in my breath condenses on my moustache and beard making them wet, and if it is cold enough the condensed moisture will freeze. My moustache and beard develop icicles.

On cold days everyone likes to sit beside the fire. An open fire, though, is horrendously inefficient! Even a free-standing stove, which radiates heat into the room, sends much of the heat directly up the chimney or flue. Even the radiant heat quickly rises to warm the air in the ceiling of the room. To add insult to injury, the air that keeps the fire burning is drawn from other places in the house, and has to be replaced by cold, cold air drawn into the house making these other places even colder.

I’ll conclude by noting that the days are becoming longer and while we are still in the depths of winter, spring is around the corner. Indeed, some early blooming plants are already showing signs of life, although they won’t amount to much until later in the year. The day length here will increase by one minute and 11 seconds tomorrow, and this rate of increase will grow rapidly until the equinox (around 21 September) by which time we should be much more cosy. However due to seasonal lag, we may still have the coldest times for this year ahead of us.

Rising San Bernard River causes flooding in Fort Bend County neighborhood

Teamwork and sport

First soccer team of Bagé, called Sport Club B... — First soccer team of Bagé, called Sport Club Bagé, in 1906. (Photo credit: Wikipedia)

A team is an interesting thing – a group of people all with the same aim, working together to some sort of objective. Individually each person knows his role in the team and relies on others in the team to achieve the desired objective. There is a great deal of trust in such a group relationship, as one under performing member can result in the team as a whole reaching their goal.

This interdependence of the team members can lead to strong bonds outside of the group project – the members of a successful team are frequently close friends outside of the team environment. This can make it difficult for a new team member to fit in initially.

There may be personality clashes within a team, leading perhaps to physical interactions between team players. The scuffles and fights may well “clear the air”, and allow the team to function better in the team environment with most of the interpersonal tensions resolved or reduced. A divided team will never perform as well as a united team.

A team will have its support staff – in a sports context it will have the manager, the coach, the medical staff, the team drivers and so on. They are so important that they could be considered to be a part of the team, even though they don’t actually play the games themselves in the most part.

This inclusiveness can of course be expanded out as far as the supporters of the team, but this is not usually done. In amateur sport there is more reason to include the supporters as they are usually mothers or fathers of team player and often fill the roles of coaches and managers and provide transport to match for the players.



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Supporters of a professional sports team do have a large role to fulfil though, that of providing the revenue for the team, the support staff, the stadium, and other ongoing expenses.

They also provide support on the game day, but I wonder how much that has an effect. Obviously the crowd will make a noise when the teams first come out onto the field, but when the game is being played it is likely that the players will be concentrating on the game and the crowd noise will just be a background noise.



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Nevertheless, the crowd does have an effect. When the teams come on to the field the players have the leisure to hear them and respond to them and when the team is pressing for a score, the sound level from the supporters is going to increase and be noticeable to the players. However the intensity of play of the attacking team is liable to be higher at those times anyway.

There have been times when matches have been played to empty stadiums, either for safety reasons or if it is expected that friction between the fans would cause violence. Sometimes I, seem to remember, teams can be penalised for some off field offence committed by the fans, the management or the players.

It would be interesting to get the teams view of what it is like to play to an empty stadium, but I don’t know if the players have been seriously asked to report what it is like. It’s unlikely to have no effect!

In sport at the grass roots level players are unlikely to specialise over much. They all may take turns at being goalie for example and every kid wants to score goals or touchdowns. Coaches at this level often enforce substitutions and switches so that every kid gets a go and enjoys himself/herself. That’s what sport is about at that level.



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But even at a quite low level player start to specialise, fulfilling a specialist role in the team as defender, or attacker, or bowler or batsman. One player will also be called on to be captain, and read the run of the game and set the strategy. Sometimes the strategic role will not be on the field as in American Football where the coach may make the strategic calls. In this case the captain’s role is much reduced.

Sports, especially the contact sports, can be considered to be ritualised warfare or at least ritualised conflict. It can possibly reduce tensions between different nations or rival groups, but is rarely specifically undertaken to do so, and indeed supporters sometimes come to blows during tense matches. Sportsmen who through personality or skill have an impact on the course of the game are treated like heroes.

Sport sometimes makes the players very rich. At the top levels of basketball and in English soccer, for example, players may make millions of dollars or pounds during a relatively short career. Other may only earn relatively little. In order to try to prevent this becoming out of hand some sports use a “salary cap” to restrict excessive salaries and allow relatively poor clubs to compete on a more level basis with the richer clubs.

Fairness is considered to be obligatory in sport, at all levels. If a player is considered to have behaved unfairly he or she will be punished according to the laws of the sport. He or she may be ejected from the field of play or even the game. His or her team may have points deducted or the other team may be given a temporary advantage. The overall intent is to allow the team who are best on merit to win the match.

It is a fact of life that, especially in contact sports, that players get injured. This may be in accidental incidents on the field of play, such as a collision between two players or they may occur as a result of stress as the player exerts himself or herself in playing the game.

New players may temporarily or permanently replace injured players, and old players may “retire” from the game. The team will be constantly changing and the skill of the captain and the other players in supporting players leaving or joining the team can go along way to ensuring that the team relationships are harmonious and the team melds into an efficient unit.



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“Yet feet that wandering have gone, turn at last to home afar”

The title is part of the poem spoken by Bilbo Baggins at the end of “The Hobbit” by J.R.R Tolkein, as he sees his home from afar on his return. However he did not finally settle there, moving to Rivendel before the events of “The Lord of the Rings”. Eventually he and others, including Frodo and Gandalf sailed off to the West and out of the knowledge of the people of Middle Earth.

This poem came to mind as we returned to New Zealand from England, having visited relatives in England, Wales and Ireland. We had a great time and it was sad to leave, but when we touched down in Auckland I have never previously felt so deeply that we had arrived home. And we still had the leg to Wellington to complete!



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The leg from Auckland to Wellington was brilliant! The air was so clear, although with some cloud, so the mountains poked their snowy heads through the white blanket. Even the lower peaks of some of the hills showed snow cover, as New Zealand had just emerged from a cold snap.

As we closed on Wellington I could see Kapiti Island from the window. Unfortunately my cell phone had run out of power so I could not take any pictures. To add insult to injury we turned left and passed south of Kapiti Island before passing to the west of Titahi Bay Porirua Harbour.

Just before Porirua city the clouds closed in, hiding the city itself and the northern suburbs of Wellington. The cloud cleared a little further south but not in time for me to spot our roof from the air!

As we passed over Wellington Harbour I got a good view of the lower Hutt Valley, including Petone and its wharf, close to where I used to work. Then it was all stations go for landing.

My own experiences led me to consider travels in general. As you do. We were excited to leave, since were going to see our relatives and have interesting times. Bilbo Baggins set out excitedly and with trepidation. In his case he knew very little about what was going to happen to him, and had he known, his cautious streak may well have impeded his going.

As with Bilbo’s travels, our travels had their excitements and their tedious aspects. As with Bilbo, the first sight of home came as an immense relief and the experiences of our travels became things to tell other about, to share with them. We however met no dragons though we saw many representations of them in Wales.

English: Side view of Smaug at the Juarez stre... — English: Side view of Smaug at the Juarez street portion of the parade. (Photo credit: Wikipedia)

This seems to me to be a common pattern. Even to blasé businessman travellers there must be some slight anticipation of events of the day or days ahead. When returning home, even the businessman would probably be looking forward to sleeping in his own bed. Even a simple commute to work embodies this pattern of anticipation, experiencing and relief on return to home.

Frodo reports that Bilbo warned of the dangers of going on a journey.

“He used often to say there was only one Road; that it was like a great river: its springs were at every doorstep, and every path was its tributary. ‘It’s a dangerous business, Frodo, going out of your door,’ he used to say. ‘You step onto the Road, and if you don’t keep your feet, there is no knowing where you might be swept off to.'”.

While neither Bilbo (in “The Hobbit”) or Frodo (in “The Lord of the Rings”) left home completely willingly, Bilbo being chivvied into it by Gandalf, and Frodo out of duty, many people completely willingly step into the “great river” that starts at every doorstep. There appears to be a conflict between the desire to remain comfortable at home and to experience new things.



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We were extremely tired by our journey which took a mere month or so. I can’t imagine how people such as Christopher Columbus and Marco Polo spent so long travelling. Marco Polo was away for 24 years!

Interestingly many travellers returned with truly amazing tales, of tribes of people with no heads, their faces in their torsos. Of people who consisted of large feet with eyes and mouths, presumably divided into left-footed and right-footed tribes. Where are these strange tribes today?

Today of course we can travel round the earth in a day, and to places in between in a few days or so. It is apparent to us that those fanciful peoples could never have existed, so where did they spring from?

Well, a traveller would know that his tall tales would be next to unverifiable. He may well have been travelling for months and would know that it was unlikely that anyone would go and check his reports. It may be that his communications with local inhabitants was limited and that he misunderstood the locals and then reported what he thought they had told him as his own experiences.



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Maybe the traveller would be trying to source funds to go back again, maybe to bring back one of these mysterious people. I can report that all the people that I met and saw were built to the standard pattern!

One thing that Columbus and Polo would not have had to cope with is jet lag. This condition is a consequence of moving to fast between time zones. At the rate that Polo was travelling that would be the least of his problems. I’ve not read his history but I can guess that he did not so much as travel slowly as move his home steadily to the east and then to the west as the commercial opportunities arose. While Columbus travelled faster, his rate of travel through the time zones probably caused him few problems.



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So, glad as I am to get home, I find jet lag debilitating. I’m fine when I get up, and fine during the day, but for some reason, when 7pm or 8pm rolls around my eyes start to droop. They say that jet lag lasts for a few days, so I should be over it in a day or so.



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(This blog has returned to normal. I hope someone out there enjoys my maunderings.)

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