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.

Embed from Getty Images

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)

Computers and cells

English: "U.S. Army Photo", from M. ...
English: “U.S. Army Photo”, from M. Weik, “The ENIAC Story” A technician changes a tube. Caption reads “Replacing a bad tube meant checking among ENIAC’s 19,000 possibilities.” Center: Possibly John Holberton (Photo credit: Wikipedia)

(Oops! One day late this week!)

A computer has some similarities to living organisms. Both produce something from, well, not very much. A computer program has data input from various sources, and produces output to various sinks or targets. A living organism takes in nutrients from various sources, and produces branches, leaves, fur, bones, blood and other organs.

Of course there are differences. A computer is much, much simpler than a living being, even single celled organism. A computer in general only has a relatively small number of parts, but the “parts” in a living organism number in the billions. And of course, living organisms reproduce, but that may change in the foreseeable future.

English: The heterolobosean protozoa species A...
English: The heterolobosean protozoa species Acrasis rosea Olive & Stoian. Photographed at the Biology of Fungi Lab, UC Berkeley, California. (Photo credit: Wikipedia)

Some animals are sentient, but I’m not going to discuss that here. Maybe in another post.

A computer has hardware, software and operates on data. The data is either part of the software or read from buffers in the hardware. It stores its calculations in “memory”, which is special hardware with particularly fast access speeds.

English: 1GB SO-DIMM DDR2 memory module
English: 1GB SO-DIMM DDR2 memory module (Photo credit: Wikipedia)

The computer produces results by placing data into buffers in the hardware. This results in things happening in the real world, such as printing a letter or number on paper, or more frequently these days, on some sort of screen. It may also do many other things, such as control the flow of water by moving a valve or other control mechanism.

Computers communicate with other computers, by placing data in an output piece of hardware. The hardware is connected to a distant piece hardware of the same sort which puts the data into a buffer accessible to another computer. This computer may be a specialised computer that merely passes on the data. Such computers are called routers (or modems, or firewalls).

Railway network in Wrocław
Railway network in Wrocław (Photo credit: Wikipedia)

Computers, specialised only in their usage, are found in washing machines, cars, televisions, and we all these days have multi-functional computers in our pockets, our cellphones. It would be hard to find a piece of electronic equipments these days that doesn’t have some sort of computer embedded in it. Very few of these computers are completely isolated – they chatter to one another all the times by various mechanisms.

Internet (Photo credit: Wikipedia)

(Incidentally, I came across a bizarre example of connectivity of things the other day – a wifi teddy bear. Say you are sitting in the lounge and you want to send a message to your child who is in her bedroom. You pick up your tablet and send a message to a “cloud” web site. This sends a message to your child’s tablet which is in her bedroom with her. The teddy bear, which is connected to the child’s tablet by wifi, growls the message to the child. No doubt scaring her out of her wits.)

So in the current technological world everything is connected to everything else. Much like all the cells in a living being are connected to all the other cells in the organism, directly or indirectly. So how far can we take this analogy, where the organism is the network and the individual cells as the computers. (Caveat emptor – I am not a biology expert, so don’t take what I might say from here on as gospel).

Embed from Getty Images

A computer consists of hardware, software, and operates on data. A cell is sort of squishy, so “hardware” can only be a relative term, but a cell does have a relatively small number of organelles, such as mitochondria. The nucleus, which contains most of the genetic material, acts as the control centre of the cell, much as the CPU is the control centre of a computer.

The function of the nucleus is to maintain the integrity of these genes and to control the activities of the cell by regulating gene expression—the nucleus is, therefore, the control center of the cell.

In the cell, the genetic material is in some sense the software of the cell. It contains all the necessary information to create the cell itself or more interestingly the information needed to cause the cell to split into two identical daughter cells. This information is generally encoded in the DNA of the chromosomes.

Information flows between DNA, RNA and protein...
Information flows between DNA, RNA and protein. DNA -> protein is another special transfer, but it is not found in nature. (Photo credit: Wikipedia)

The cell also contains, within the nucleus, an organelle called the nucleolus. This organelle (which is part of the nucleus organelle) seems from my reading to mostly relate to RNA, while the rest of the nucleus mostly relates to DNA, very roughly. RNA and DNA perform a complex dance called protein synthesis in organelles called ribosomes.

Cells produce chemicals, which can be consider analogous to computer outputs and receive chemicals from other cells, and so cells communicate, in a sense, with each other. Since all cells are equal genetically, it follows that a cell’s type, liver, skin, lung or brain neurone is determined by factors in its environment.

The model of an artificial neuron as the activ...
The model of an artificial neuron as the activation function of the linear combination of weighted inputs (Photo credit: Wikipedia)

This only loosely true as each cells is the daughter of another cell and inherits its type, but in the early days of an organism’s life, before organs are formed cells do differentiate. Just as when computers were new, they were all very similar, keyboard, monitor, and beige case.

As the computer-sphere evolved, special types of computer evolved, such as routers and modems, and firewalls. Not to mention phones. Computers became specialised. Similarly cells become differentiated, some going on to become liver cells for example, and others brain cells (neurones).

English: Front side of a Juniper SRX210 servic...
English: Front side of a Juniper SRX210 service gateway Deutsch: Vorderseite eines Juniper SRX210 Service Gateways (Photo credit: Wikipedia)

When an organism is young and a cell divides both cells are the same type, but when the organism is very young there is no differentiation. The DNA in the cell contains the necessary information to determine the cell type and tissues and organs are created in the more complex animals.

This process obviously can’t be random, otherwise cells of the various tissue types would be all mixed up. It seems to me, maybe naively, that while the “program” for creating cells is in the DNA, some factors in the environment convey such information as how old the organism is, and what type of cell needs to be created.

an example of a Program
an example of a Program (Photo credit: Wikipedia)

We know from investigations into fractals that a simple equation can result in the creation of an image that looks very much like a tree or grasses and that small changes to the equation can lead to different tree or grass shapes. It is tempting to think that a similar process takes place in organisms – a general rule is given which results in the right sort of cells being produced in the right places.

The problem with the fractal idea is that it only creates simple shapes. An arm with fingers, skin and so on is beyond the capabilities of a fractal process so far as I know. Fractals don’t stop. Again, so far as I know there’s no way to iteratively create a tree structures with leaves.

Embed from Getty Images

So the “software” of the cell, the “program” embedded in the DNA doesn’t appear to be analogous to a simple computer program that draws fractals. Of course that doesn’t mean that we can never describe a simple organism completely in fractal terms, and create analogous distinct individuals.

It seems that a long as the analogy is not pushed too far, computers in a distributed network are reasonably similar to living organisms. Please note I am note referring to the fractal type computer programs, but am talking about the way that computers themselves in a network are somewhat analogous to living organisms. Primitive ones!

Sample oscillator from hexagonal Game of Life.
Sample oscillator from hexagonal Game of Life. (Photo credit: Wikipedia)

Photographic Honesty

Category:Wikipedia requested photographs of ph...
Category:Wikipedia requested photographs of photography (Photo credit: Wikipedia)

I’m going to do something that I’ve never done before, something a little risky. I’m going to write a piece about an article on someone else’s website, a piece which resonated with me. Of course, I may have totally missed the point of the other person’s article. I hope not, and I can only apologise in advance for any misconceptions that I have about the article.

Please note that the pictures in this article are mere decorations and do not and not intended to relate to Tony Bridge and his art. Think of them as free association based on the words that I type.

English: Photography forbidden. A nightmare......
English: Photography forbidden. A nightmare… Français : Un cauchemar… Deutsch: Fotografieren verboten. Ein Albtraum… (Photo credit: Wikipedia)

The writer of the piece is Tony Bridge ( and the piece is entitled “On honesty in photography“.

Firstly I urge you to visit Tony Bridge’s site and view the many amazing and attention grabbing photographs that Tony has assembled on his site. I am in awe of his skill, his technique, and particularly of his professional photographer’s eye. (Please remember that none of these images are his. I would not presume…)

English: A photographer between waves and mussels
English: A photographer between waves and mussels (Photo credit: Wikipedia)

I’m no photographer. I take photographs, I try to ensure that the photographs are interesting, I try to “compose” them a little, I try to pay attention to the lighting of the subject versus the background and things like that, but these days I rarely stray from the automatic settings on my camera, which is a cheap FujiFilm one.

As for post-production, the removal of perceived mistakes in composition and specks of dust, changing hues and saturation and so on, well, I rarely do more than remove red-eye and shift the contrast. Tony’s article talks about a possible perceived over emphasis on the post-production of some modern photography. It is the main topic of Tony’s article.

Photoshop-work (Photo credit: Kjell Eson)

With tools like Photoshop anything in or about a picture can be manipulated, from simple removal of flaws to major changes to the image. Indeed there are numerous  photo manipulation “fails” to be found on the Internet, ranging from failed enhancements of “beauty” shots, to badly photoshopped propaganda photographs from the likes of North Korea.

Follow Me, Ladies
Follow Me, Ladies (Photo credit: Dοn)

Is this new? I think not. Apparently Henry VIII of England was deceived by a painted likeness of Anne of Cleves, complaining that “She is nothing so fair as she hath been reported.” To be sure this is not post production alteration of the image, but it is similar in kind. Henry could, probably justifiably, have called for more honesty in image production.

Painting of Anne of Cleves, fourth wife of the...
Painting of Anne of Cleves, fourth wife of the English King Henry VIII, by Hans Holbein the Younger (Photo credit: Wikipedia)

Of course there were movements in portraiture and other painting for more honesty in portrayal. Oliver Cromwell, is alleged to have required that his portrait be painted “warts and all”. However most painting tended to emphasise some aspects of the subject over others, the epitome being the painting of “The Monarch of the Glen” by Landseer, an over idealised painting of a stag. Nevertheless, a great painting.

sir Edwin Landseer, The Monarch of the Glen (1...
sir Edwin Landseer, The Monarch of the Glen (1851) in the Museum of Scotland. (Photo credit: Wikipedia)

Some painters realised the way that images were being enhanced and moved in another direction away from realism, leading to such schools of painting as impressionism, cubism, surrealism,  pop art, to name only a few. Again the paintings were, are amazing. I draw a parallel between non-realistic art with highly post-processed photography.

Photography, springing up in the early 20th century in the shadow of painting, at first had few tools to do other than report what the lens had seen. Photographers were still learning about the new medium, but soon techniques started to arise, such as vignetting (softening the corners of an image) to alter the image.

Untitled (Photo credit: Smithsonian Institution)

But the tools soon arrived. The standard model of camera has the image plane perpendicular to the lens axis with the lens axis at or near to the centre of the image plane. Later cameras allowed the lens to be shifted and twisted to allow various effects, such as better images of tall buildings and so on. No doubt the photographers of the time might argue for a more honest approach, though I’m pushing the analogy to breaking point.

In the darkroom similar effects could be performed by manipulating the chemical baths and the enlarger used for the printing process. Many of the image manipulation processes are over 100 years old according to Wikipedia. It was probably the advert of colour films and processing that severely reduced the amateur use of darkroom processes in photography, because of the extra complexity of processes. That’s a pity, as nothing beats the feeling you get when an image appears from nothing on a white piece of paper.

Student developing a map image. Photograph tak...
Student developing a map image. Photograph taken during the making of a BBC documentary. IMAGELIBRARY/166 Persistent URL:… (Photo credit: Wikipedia)

The digital revolution has put the power back in the hands of the amateur again. Anyone with a phone can take a photograph, process it through Instagram and the result has been …. a cascade of rubbish!

Against this unprecedented tide of rubbish, real photographers, amateur and professional struggle to promote their art. So is real photography the poorly lit, over exposed, blurry, shaky, hand-held phone stuff, or the highly processed, sharp as a tack, rigidly tripod mounted, Canon/Nikon/Hasselblad shot stuff, or the story board, lightly processed, possibly hand held stuff?

English: Hasselblad 503 CW with Zeiss F-Distag...
English: Hasselblad 503 CW with Zeiss F-Distagon 3,5/30 and digital back Ixpress V96C (16 megapixel sensor). Français : Appareil moyen format Hasselblad 503 CW avec optique Zeiss Distagon 3,5/30 et dos numérique Ixpress V96C (Résolution 16 MP). Nederlands: Middenformaatcamera Hasselblad 503 CW met Zeiss F-Distagon 3,5/30 en digitale achterwand Ixpress V96C (16 megapixel). (Photo credit: Wikipedia)

In my opinion, it is an invalid question. Consider the famous “Monsoon Girl” photograph by Brian Brake. This is an awesome photograph and I don’t see why it should denigrated because it was a set up. Is it honest? It is honest to the story it told. It expresses perfectly the promise that the monsoon brings of growing things and plenty in the future. However it wasn’t a real photograph of a real girl in real monsoon rain.

Monsoon Girl
Monsoon Girl (Photo credit: colonos)

Similarly with the awesome images that can be created by Photoshop and other tools. One of my favourite site for images is the NASA site. Wonderful images! However many of them are “false colour” images, of the sun and other objects. It’s not Photoshop, (so far as I know) but it is highly manipulated images. Are they “honest”? In one sense they are in another they are not. Are they amazing photographs? Yes, of course.

English: Landsat 7 false colour image of the N...
English: Landsat 7 false colour image of the Nile Delta (Photo credit: Wikipedia)

If I had a photo good enough to be used in a magazine or book or whatever, would I do whatever I could to make it as defect free as possible? Yes, I would and I would not consider that dishonest.

Tony Bridge questions whether or not we need the latest cameras, a longer lens, the next highest resolution or the next update of photo manipulation software. Of course we don’t. But if they help us get our message across, then they are useful. They are pretty nice toys, too! A long lens is great. An extremely long lens may enable things to be photographed that can’t otherwise be photographed, but only the photographer’s eye can make the picture shine.

Schematic of a catadioptric (mirror-lens) tele...
Schematic of a catadioptric (mirror-lens) telephoto camera lens (Photo credit: Wikipedia)

I recall that I posted an image on Facebook of a stick insect shedding its skin. This event occurred practically right in front of my nose, just outside my front door. I really couldn’t have missed it. Brian Harmer, a photographer and blogger friend of mine congratulated me on my photo, and when I said that I couldn’t have missed it, he wisely said “Most of the genius in any image is what you point it at when you shoot. Your eye saw the image. the (camera) merely recorded it”.

Stick insect shedding skin
Stick insect shedding skin


My picture was no work of art, but I take his point. What makes a good photo or photo essay is the photographer’s eye and the photographer’s heart, and I believe that is something like what Tony Bridge means by “honesty”. Technique and tools can aid the photographer but they can’t make a mediocre picture into a great one. 

One last comment. Does the use of less post-processing in digital photography. and a reliance on more honest photography mean that digital photography is maturing? Again, I will sit on the fence. Yes, it shows maturity if it erases the distinction between prior photography (analog photography?) and digital photography. When a photograph is just a photograph, and digital or analog post processing is not relevant, then digital photography has matured.

A 1.5 bit Multiplying Digital to Analog Converter
A 1.5 bit Multiplying Digital to Analog Converter (Photo credit: Wikipedia)

But I hope that is not totally true, as with maturity comes the danger of stagnation. I don’t believe that as technical a pastime or profession as photography can ever mature in that sense, fortunately. The technology will keep changing, opening new avenues for photographers, both amateur and professional, as its sisterly arts of painting and sculpture demonstrate.

Employees of Southern Bell & Telegraph Company...
Employees of Southern Bell & Telegraph Company at work: Miami, Florida (Photo credit: State Library and Archives of Florida)

Thank you Tony Bridge for providing your thought provoking article, which has been the inspiration of this post.

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