Cycling through life

English: cycle that rotates on its axis Españo...

English: cycle that rotates on its axis Español: ciclo que gira sobre su propio eje (Photo credit: Wikipedia)

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.

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.

English: SINE and COSINE-Graph of the sine- an...

English: SINE and COSINE-Graph of the sine- and cosine-functions sin(x) and cos(x). One period from 0 to 2π is drawn. x- and y-axis have the same units. All labels are embedded in “Computer Modern” font. The x-scale is in appropriate units of pi. Deutsch: SINUS und COSINUS-Graph der Funktionen sin(x) und cos(x). Eine Periode von 0 bis 2π ist dargestellt. Die x-Achse ist in π-Anteilen skaliert entsprechend 0 bis 2π bzw. 0° bis 360° (Photo credit: Wikipedia)

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.

Graphing process of y = sin x (where x is the ...

Graphing process of y = sin x (where x is the angle in radians) using a unit circle. (Photo credit: Wikipedia)

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.

English: Section of ellipse showing eccentric ...

English: Section of ellipse showing eccentric and true anaomaly (Photo credit: Wikipedia)

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.

Illustration of Gauss-Newton applied to a curv...

Illustration of Gauss-Newton applied to a curve-fitting problem with noisy data. What is plotted is the best fit curve versus the data with the fitting parameters obtained via Gauss-Newton. (Photo credit: Wikipedia)

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.

Claudius Ptolemäus, Picture of 16th century bo...

Claudius Ptolemäus, Picture of 16th century book frontispiece (Photo credit: Wikipedia)

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Early television and that mess of metal on the roof

English: British Murphy black and white 405 li...

English: British Murphy black and white 405 line Television receiver 1951. (Photo credit: Wikipedia)

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

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.

English: Communal aerial This seems to be a co...

English: Communal aerial This seems to be a communal TV aerial for the farms hidden between Baugh Fell and the Howgills. (Photo credit: Wikipedia)

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.

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.

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.

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.

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!

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.

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.

English: How to connect telephone, radio, tele...

English: How to connect telephone, radio, television, internet via glass fibre Nederlands: Aansluiten van telefoon, radio, televisie, internet via glasvezel (Photo credit: Wikipedia)

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In the Zone

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

English: Two programmers

English: Two programmers (Photo credit: Wikipedia)

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.

This image was selected as a picture of the we...

This image was selected as a picture of the week on the Farsi Wikipedia for the 13th week, 2011. (Photo credit: Wikipedia)

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.

Wheel bugs mating

Wheel bugs mating (Photo credit: Wikipedia)

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.

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.

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)

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.

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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Weather, seasons and Christmas

English: Spring is on its way Snowdrops in Hat...

English: Spring is on its way Snowdrops in Hatfield churchyard are harbingers of spring although at the time there was still plenty of wintry weather around. (Photo credit: Wikipedia)

At this time of the year, we are looking forward to spring, even though spring is officially about a month and a half away, which puts us slap in the middle of winter. There are signs, though, that spring is around the corner. Plants which bloom early in the year are starting to show signs of life, and the buds on some trees are showing some green as they prepare to burst into green bunches of leaves.

Every burst of clear weather seems to produce both warmth during the days and frostiness during the night. It seems that each cycle is slightly warmer than the last but that might just be me wishing an end to winter! The wetter times don’t seem to be bringing the freezing cold wintry blasts, though there is the occasional shower of hail or sleet mixed in.

English: Snow pellet/Graupel Français : Grain ...

English: Snow pellet/Graupel Français : Grain de neige roulée (Photo credit: Wikipedia)

The main reason for the hope that winter is drawing to a close is the now noticeable lengthening of the days. The day length is up from 9 hours and 12 minutes or so at the solstice to 10 hours and 12 minutes or so today. The day is lengthening at a rate of more than 2 minutes per day at the moment.

I don’t mind the cold as such. It’s the constant shrugging on and off of clothes as one transitions between indoors and outdoors that bugs me, and the necessity of keeping the house warm, which in itself means going outdoors to fetch fuel, which of course involves donning extra clothing and all the annoyances which go with that.

English: A 1901 fashion plate of a Chesterfiel...

English: A 1901 fashion plate of a Chesterfield overcoat. (Photo credit: Wikipedia)

There is a sort of seasonal drag in the clothing department, incidentally. I’ve noticed that I tend to resist slinging on the extra clothing in autumn and early winter and I’m likewise reluctant to take it off as the weather and temperatures improve.

Of course, July and August are the warmer months in the Northern hemisphere and northerners will be experiencing shorter days and colder weather. As we track in to spring you Northerners will be heading towards autumn and eventually winter. We will be looking forward to spring and summer, which pretty much bracket Christmas for us.

Of course, since I originate from the Northern hemisphere myself I have had to become accustomed to having Christmas in summer and I personally think it’s great. With Christmas at the start of summer we can enjoy it without the hassle of keeping warm. It does make the traditional northern Christian festival meal seem a bit heavy though and who want to roast a turkey for hours in warm weather?

It does conflate two events however – the Christmas holiday period and the traditional summer holidays which seem to merge seamlessly into one another. One effect of this is that people seem to be unavailable from Christmas Eve through to the beginning of February, which was something that I had trouble adjusting to when I moved here.

English: A rather damp Sligachan old bridge on...

English: A rather damp Sligachan old bridge on Skye. This ‘summer’ holiday photo shows some light rain on Skye with Glamaig just visible through the mist! (Photo credit: Wikipedia)

Tradesmen tend to be unavailable from the start of the Christmas period well into the New Year and some smaller shops also close for an extra week or two. Obviously this has its advantages for the shop keepers, but I still feel disappointed when my favourite barber is closed until mid-January!

We have a Public Holiday for the Queen’s Birthday in June (June 1 this year) and the next Public Holiday is on October 26, which means that there is almost 5 months of the year without a Public Holiday during the darkest part of the year. One advantage of having Christmas in mid-winter is that it gives one something to look forward to as the days close in.

English: The Royal Gibraltar Regiment at the p...

English: The Royal Gibraltar Regiment at the parade for the Queen’s Birthday, Grand Casemates Square, Gibraltar (Photo credit: Wikipedia)

Winter is cold, obviously, but that in itself is bearable (up to a point). But there’s a phenomenon called the “chill factor” which makes windy winter days seem much colder. My weather app on my phone tells me that the temperature outside is 6.9 degrees centigrade, but the it “feels like: 4 degrees centigrade. It recommends 3 – 4 layers of clothing and a windproof layer. Brrrrr! Fortunately it doesn’t seem too wet out so walking the dog should not be too arduous.

In this season of the year we tend to get low pressure system after low pressure system forming in the Tasman Sea which bring cold fronts across the country with associated fronts bringing storms and rains. Sometimes they come down from the tropics and hit us from the north, usually bringing warmer but wetter weather from the north. We tend to get better more settled weather when a high pressure system comes to us, spun off from  a high pressure system over Australia.

The Tasman Sea caused some violent and spectac...

The Tasman Sea caused some violent and spectacular bursts of water at the Pancake Rocks, Punakaiki. (Photo credit: Wikipedia)

(I took a break and walked the dog. While we out we were hit by what you could euphemistically call a “wintry shower”. In other words, wind, hail and rain!)

Many people from the Northern hemisphere tend to find Christmas in summer unsettling, but I quite like it. I’m not a barbecue person, but the occasional meal taken outside is very pleasant, and it is becoming more usual over here to have a barbecue on Christmas Day. Another advantage is that when one is Christmas shopping one doesn’t have to dodge the weather as one dashes between shops and fights one’s way through the crowds of late shoppers, all after that elusive and critical last gift.

Barbecue barbecook

Barbecue barbecook (Photo credit: Wikipedia)

However, although I think that mulled wine is an abomination, there is something pleasant about sipping your favourite alcoholic tipple in front of a roaring fire. Maybe while doing something traditional, like listening to a CD of carols carefully enunciated by Korean choirs who have no word of the English language and who have little to no idea about the traditions involved.

One thing about having winter at this time of the year, it means that I can tease relatives who live in the Northern hemisphere as we climb up towards warmer weather while they slide down to autumn and winter. However I have to acknowledge that they can get their revenge in six months later as the cycle of the seasons continues to repeat. I’ll be looking out the thermal undies when they start talking about snowdrops and crocuses.




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Time and time again

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 w...

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.

English: Tree of choice for creative commons l...

English: Tree of choice for creative commons licenses. (Photo credit: Wikipedia)

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.

Brooklyn Museum - The Life Line - Winslow Homer

Brooklyn Museum – The Life Line – Winslow Homer (Photo credit: Wikipedia)

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.

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.

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.

Magnetic Resonance Imaging - Human brain side ...

Magnetic Resonance Imaging – Human brain side view. emphasizing corpus callosum. (Photo credit: Wikipedia)

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)



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Time Travelling

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.

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.

Bruntons Traveller

Bruntons Traveller (Photo credit: Wikipedia)

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.

English: Front of black iPad 2.

English: Front of black iPad 2. (Photo credit: Wikipedia)

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.

Figure showing light crossing the x1 axis and ...

Figure showing light crossing the x1 axis and corresponding representation in optical phase space (Photo credit: Wikipedia)

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.

Spiral loop

Spiral loop (Photo credit: Wikipedia)

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.

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.

Intended for inclusion in Wikisource article f...

Intended for inclusion in Wikisource article for Flatland (Photo credit: Wikipedia)

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.

Burst Apart

Burst Apart (Photo credit: Wikipedia)


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Dwelling in the past

Merlin, from the Nuremberg Chronicle (1493).

Merlin, from the Nuremberg Chronicle (1493). (Photo credit: Wikipedia)

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.

Troll becoming a mountain ill jnl

Troll becoming a mountain ill jnl (Photo credit: Wikipedia)

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.

discworld town lancre terry pratchett

discworld town lancre terry pratchett (Photo credit: Wikipedia)

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).

English: Parabola showing relation between the...

English: Parabola showing relation between the focus, directrix, and a point on the curve. (Photo credit: Wikipedia)

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.

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.

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.

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.

English: Coordinates as distances from coordin...

English: Coordinates as distances from coordinate planes in 3 space. (Photo credit: Wikipedia)

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.

English: The Church at Ockham William of Occam...

English: The Church at Ockham William of Occam, died 1285 is commemorated in the church in a stained glass window. He gave his name to ‘Occam’s Razor’, whereby in any investigation: follow the obvious path first – it’s likely to be correct. (Photo credit: Wikipedia)


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