Virtual Reality

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Back in 1999 I was just finishing my Masters degree at Victoria University of Wellington. I needed a subject for my research paper and I chose what was then a hot topic, Virtual Reality (VR). At the time, the computing resources that were available to most people were, by today’s standards pretty limited.

17 years ago we measured RAM in megabytes, and disk space in gigabytes. The Internet was not as pervasive as it is today, and most people, if they accessed the Internet at all, used dial up modems. Broadband was for most people, still in their future. As were smartphones and all the technology that we immerse ourselves in today.

Exploded view of a personal computer
Exploded view of a personal computer (Photo credit: Wikipedia)

As could be imagined, this limited the effectiveness of VR. If you were trying to set up a VR session between two geographically separated places, then the VR experience could be somewhat limited by the low resolution, the speed of updates of the views that the users experienced, and the lags caused by the (relatively) slow connections.

Nevertheless, research was taking place, and Head Mounted Displays (HMDs) and VR gloves were researched and developed. The HMDs provided the user with displays of the virtual world around him/her, and the gloves provided the tactile element to some extent.

English: zSight HMD by Sensics, Inc.
English: zSight HMD by Sensics, Inc. (Photo credit: Wikipedia)

These devices have their current descendants of course, though more is heard of the HMDs than the gloves. The HMDs range from the highly developed devices like the Oculus Rift right down to cheap devices like Google Cardboard which literally that, a head mounted device consisting of a cardboard body and a cellphone. The cellphone’s screen is divided into two and different images are provided to each eye for the 3-Dimensional effect.

It was evident, back in 1999 when I wrote my paper that VR was a technology looking for an application, and it still is. Some TVs have been made which incorporate 3D technology, but the production of these appears to have tailed off almost completely. Apparently the added ability to experience movies in 3D which involved wearing special headsets, wasn’t enough to offset the necessity to wear the headsets.

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People just used their imaginations when immersed in a program or movie and didn’t feel that they needed the extra dimension, and the headset added a barrier which prevented experience of shared movie watching that forms at least part of the entertainment value of watching movies with friends and families.

My paper was about diffusion of VR techniques into everyday life, and it mostly missed the point I think in retrospect (though the paper did help me get the degree!)  My paper used a Delphi Technique for the research. This technique involves posing a series of question on the research topic to a number of specialists in the field. Their answers are then summarised and passed back to the whole panel. Any subsequent comments are then also summarised.

English: Temple of Apollo in Delphi
English: Temple of Apollo in Delphi (Photo credit: Wikipedia)

Obviously as workers in the field my panel was positive about VR’s then prospects, as you would expect. They however did sounds some notes of caution, which proved to be well founded. I’m not going to do a critique of my paper and the panel’s findings, but I will touch on them.

Specifically, they mentioned that my questions were all about fully immersive VR, which is basically what I’ve been talking about above, the HMD thing. Augmented VR, where our view of the world in not (fully) obstructed by the technology, but the technology enhances our view of the world is used much more in practise, and was when I wrote my paper too.

Augmented reality - heads up display concept
Augmented reality – heads up display concept (Photo credit: Wikipedia)

Augmented VR is things like Head Up Displays (HUDs) and Google Glass where information is added to the user’s field of view, providing him/her with extra information about the world around him/her is much more common. HUDs are common in planes and the like where the operator cannot spare the time to go and look up important information so the information is projected into his field of view. Google Glass was similar but allowed the user to feed back or request information, but unfortunately this did not really catch on and was dropped.

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I mentioned in my questions to my panel that maybe the speed of the Internet was a barrier to the introduction of VR into everyday life. The panel were mostly sympathetic to this viewpoint, but in summary thought that fibre, which was on the horizon would significantly reduce this barrier to the everyday adoption of VR techniques. In fact people do not use the extra bandwidth for VR (except in a way that I will touch on in a minute), but for other things, like streaming TV shows and downloading music.

English: Screenshot of NcFTP downloading a fil...
English: Screenshot of NcFTP downloading a file Category:Screenshots of Linux software (Photo credit: Wikipedia)

As I envisaged it, a typical VR setup would consist of someone in, say, London, with VR set interacting over the Internet with someone in, say, Tokyo who also has a VR set. They could shake each other’s hand, and view and discuss three dimensional objects in real time, regardless of whether the object was in London or Tokyo. Although I had not considered it at the time, a 3D printer could duplicate a 3D object in the other location, if required.

This has not happened. Teleconferences are stubbornly 2D, and there is no call for a third dimension. Some people, myself included, would not miss the 2D visual aspect at all, would quite happily drop back to voice only!

English: Washington, DC, August, 14, 2007 -- T...
English: Washington, DC, August, 14, 2007 — This FEMA video teleconference with the FEMA regional directors, state Emergency Operations Centers and Federal partners concerns Hurricane Flossie which is expected to pass just south of the island of Hawaii and Tropical Storm Dean which is building in the Atlantic and moving west toward the Caribbean Sea. FEMA’s National Response and Coordination Center (NRCC) is activated at Level 2. FEMA/Bill Koplitz (Photo credit: Wikipedia)

In one respect, though, VR has come and has taken over our lives without us realising. When we interact with our smartphones, texting, sending photos, emails and so on, in real time, we are immersing ourselves in a new sort of VR. When we are chatting about something and someone gets the cellphone out to google the Internet to check or look something up, we are delving into a new Virtual Reality that we could not have envisaged way back in 1999.

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So when I look back at my paper from that era, I could easily update it and make relevant to the current era, but only in the respect of that limited view of VR. That has not really eventuated, and most likely will have limited application (remote appendectomy anyone?), but it could be considered that facebook/twitter/google/gmail/dropbox and all the other tools that we use on our smartphones has opened up a different alternate Virtual Reality that crept up on us while we were not watching.

facebook engancha
facebook engancha (Photo credit: Wikipedia)

Imagine this….

Flying Swan
Drawn using Python and Matplotlib. This picture is serendipitous and not intended.

[Grr! While I finished my previous post, I didn’t publish it. Darn it.]

Since I’ve been playing around with computer generated images recently, my thoughts turned to how we see images. When you look at a computer or television screen these days, you are looking at a matrix of pixels. A pixel can be thought of as a very tiny point of light, or a location that can be switched on and off very rapidly.

Pixels are small. There’s 1920 across my screen at the current resolution, and while I can just about see the individual pixels if I look up close, they are small. To get the same resolution with an array of 5cm light bulbs, the screen would need to be 96 metres in size! You’d probably want to sit at about 150m from the screen to watch it.

A closeup of pixels.
A closeup of pixels. (Photo credit: Wikipedia)

The actual size of a pixel is a complicated matter, and depends on the resolution setting of your screen. However, the rating of a camera sensor is a different matter entirely. When I started looking into this, I thought that I understood it, but I discovered that I didn’t.

What complicates things as regards camera sensor resolutions is that typically a camera will store an image as a JPG/JPEG image file, though some will save the image as a RAW image file. The JPG format is “lossy” so some information is lost in the process (though typically not much). RAW image file are minimally processed from the sensor data so contain as much information about what the sensor sees as is possible. Naturally they are larger than JPG format images.

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When we look at a screen we don’t see an array of dots. We pretty much see a smooth image. If the resolution is low, we might consider the image to be grainy, or fuzzy, but we don’t actually “see” the individual pixels as such, unless we specifically look closely. This is because the brain does a lot of processing of an image before we “see” it.

I’ve used the scare quotes around the word “see”, because seeing is very much a mental process. The brain cells extend right out to the eye, with the nerves from the eye being connected directly into the brain.

Schematic diagram of the human eye in greek.
Schematic diagram of the human eye in greek. (Photo credit: Wikipedia)

The eye, much like a camera, consists of a hole to let in the light, a lens to focus it, and sensor at the back of the eye to capture the image. Apparently the measured resolution of the eye is 576 megapixels, but the eye has a number of tricks to improve its apparent resolution. Firstly, we have two eyes and the slightly different images are used to deduce detail that one eye alone will not resolve. Secondly, the eye moves slightly and this also enables it to deduce more detail than would be apparent otherwise.

That said, the eye is not made of plastic metal and glass. It is essentially a ball of jelly, mostly opaque but with a transparent window in it. The size of the window or pupil is controlled by small muscles which contract or expand the size of the pupil depending on the light level (and other factors, such as excitement).

English: A close up of the human eye. Notice t...
English: A close up of the human eye. Notice the reflection of the photographer. (Photo credit: Wikipedia)

The light is focused on to an area at the back of the eye, which is obviously not flat, but curved. Most the focusing is done by the cornea, the outermost layer of the eye, but the lens is fine tuned by muscles which stretch and relax the lens as necessary. This doesn’t on the face of it seem as accurate as a mechanical focusing system.

In addition to these factors, human eyes are prone to various issues where the eye cannot focus properly, such as myopia (short sightedness) or hyperopia (long sightedness) and similar issues. In addition the jelly that forms the bulk of the eye is not completely transparent, with “floaters” obstructing vision. Cataracts may cloud the front of the cornea, blurring vision.

English: Artist's impression of appearance of ...
English: Artist’s impression of appearance of ocular floaters. (Photo credit: Wikipedia)

When all this is considered, it’s amazing that our vision works as well as it does. One of the reasons that it does so well is, as I mentioned above, the amazing processing that our brains. Interestingly, what it works with is the rods and cones at the back of the eye, which may or may not be excited by light falling on them. This in not exactly digital data, since the associated nerve cells may react when the state of the receptor changes, but it is close.

It is unclear how images are stored in the brain as memories. One thing is for sure, and that is that it is not possible to dissect the brain and locate the image anywhere in the brain. Instead an image is stored, as it is in a computer, as a pattern. I suspect that the location of the pattern may be variable, just as a file in a computer may move as files are moved about.

Expanded version, with explanations.
Expanded version, with explanations. (Photo credit: Wikipedia)

The mind processes images after the raw data is captured by the eye and any gaps (caused by, for example, blood vessels in the eye blocking the light). This is why, most of the time, we don’t notice floaters, as the mind edits them out. The mind also uses the little movements of the eye to refine information that the mind uses to present the image to our “mind’s eye“. The two eyes, and the difference between the images on the backs of them also helps to build up the image.

It seems likely to me that memories that come in the form of images are not raw images, but are memories of the image that appears in the mind’s eye. If it were otherwise the image would lacking the edits that are applied to the raw images. If I think of an image that I remember, I find that it is embedded in a narrative.

Narrative frieze.
Narrative frieze. (Photo credit: Wikipedia)

That is, it doesn’t just appear, but appears in a context. For instance, if I recall an image of a particular horse race, I remember it as a radio or television commentary on the race. Obviously, I don’t know if others remember images in a similar way, but I suspect that images stored in the brain are not stored in isolation, like computer files, but as part of a narrative. That narrative may or may not relate to the occasion when the image was acquired. Indeed the narrative may be a total fiction and probably exists so that the mental image may be easily retrieved.

One bubble memory track and loop
One bubble memory track and loop (Photo credit: Wikipedia)


The Banach Tarski Theorem

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There’s a mathematical theorem (the Banach Tarski theorem) which states that

Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball.

This is, to say the least, counter intuitive! It suggests that you can dissect a beach ball, put the parts back together and get two beach balls for the price of one.

This brings up the question of what mathematics really is, and how it is related to what we loosely call reality? Scientists use mathematics to describe the world, and indeed some aspects of reality, such as relativity or quantum mechanics, can only be accurately described in mathematics.

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So we know that there is a relationship of some sort between mathematics and reality as our maths is the best tool that we have found to talk about scientific things in an accurate way. Just how close this relationship is has been discussed by philosophers and scientists for millennia. The Greek philosophers, Aristotle, Plato, Socrates and others, reputedly thought that “all phenomena in the universe can be reduced to whole numbers and their ratios“.

The Banach Tarski theorem seems to go against all sense. It seems to be an example of getting something for nothing, and appears to contravene the restrictions of the first law of thermodynamics. The volume (and hence the amount of matter) appears to have doubled, and hence the amount of energy contain as matter in the balls appears to have doubled. It does not appear that the matter in the resulting balls is more attenuated than that in the original ball.

The Banach–Tarski paradox: A ball can be decom...
The Banach–Tarski paradox: A ball can be decomposed and reassembled into two balls the same size as the original. (Photo credit: Wikipedia)

Since the result appears to be counter intuitive, the question is raised as to whether or not it is merely a mathematical curiosity or whether it has any basis in reality, It asks something fundamental about the relationship between maths and reality.

It’s not the first time that such questions have been asked. When the existence of the irrational numbers was demonstrated, Greek mathematicians were horrified, and the discoverer of the proof (Hippasus) was either killed or exiled, depending on the source quoted. This was because the early mathematicians believed that everything could be reduced to integers and rational numbers, and their world did not have room for irrational numbers in it. In their minds numbers directly related to reality and reality was rational mathematically and in actuality.

English: Dedekind cut defining √2. Created usi...
English: Dedekind cut defining √2. Created using Inkscape. (Photo credit: Wikipedia)

These days we are used to irrational numbers and we see where they fit into the scheme of things. We know that there are many more irrational numbers than rational numbers and that the ‘real’ numbers (the rational and irrational numbers together) can be described by points on a line.

Interestingly we don’t, when do an experiment, use real numbers, because to specify a real number we would have write down an infinite sequence of digits. Instead we approximate the values we read from our meters and gauges with an appropriate rational number. We measure 1.2A for example, where the value 1.2 which equals 12/10 stands in for the real number that corresponds to the actual current flowing.

English: A vintage ampere meter. Français : Un...
English: A vintage ampere meter. Français : Un Ampèremètre à l’ancienne. (Photo credit: Wikipedia)

We then plug this value into our equations, and out pops an answer. Or we plot the values on a graph read off the approximate answer. The equations may have constants which we can only express as rational numbers (that is, we approximate them) so our experimental physics can only ever be approximate.

It’s a wonder that we can get useful results at all, what with the approximation of experimental results, the approximated constants in our equations and the approximated results we get. If we plot our results the graph line will have a certain thickness, of a pencil line or a set of pixels. The best we can do is estimate error bounds on our experimental results, and the constants in our equations, and hence the error bounds in our results. We will probably statistically estimate the confidence that the results show what we believe they show through this miasma of approximations.

Image of simulated dead pixels. Made with Macr...
Image of simulated dead pixels. Made with Macromedia Fireworks. (Photo credit: Wikipedia)

It’s surprising in some ways what we know about the world. We may measure the diameter of a circle somewhat inaccurately, we multiply it by an approximation to the irrational number pi, and we know that the answer we get will be close to the measured circumference of the circle.

It seems that our world resembles the theoretical world only approximately. The theoretical world has perfect circles, with well-defined diameters and circumference, exactly related by an irrational number. The real world has shapes that are more or less circular, with more or less accurately measured diameters and circumferences, related more or less accurately by an rational number approximating the irrational number, pi.

Pi Animation Example
Pi Animation Example (Photo credit: Wikipedia)

We seem to be very much like the residents of Plato’s Cave and we can only see a shadow of reality, and indeed we can only measure the shadows on the walls of the cave. In spite of this, we apparently can reason pretty well what the real world is like.

Our mathematical ruminations seem to be reflected in reality, even if at the time they seem bizarre. The number pi has been known for so long that it no longer seems strange to us. Real numbers have also been known for millennia and don’t appear to us to be strange, though people don’t seem to realise that when they measure a real number they can only state it as a rational number, like 1.234.

English: The School of Athens (detail). Fresco...
English: The School of Athens (detail). Fresco, Stanza della Segnatura, Palazzi Pontifici, Vatican. (Photo credit: Wikipedia)

For the Greeks, the irrational numbers which actually comprise almost all of the real numbers, were bizarre. For us, they don’t seem strange. It may be that in some way, as yet unknown, the Banach Tarski theorem will not seem strange, and may seem obvious.

It may be that we will use it, but approximately, much as we use the real numbers in our calculations and theories, but only approximately. I doubt that we will be duplicating beach balls, or dissecting a pea and reconstituting it the same size as the sun, but I’m pretty sure that we will be using it for something.

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I see maths as descriptive. It describes the ideal world, it describes the shape of it. I don’t think that the world IS mathematics in the Pythagorean sense, but numbers are an aspect of the real world, and as such can’t help but describe the real world exactly, while we can only measure it approximately. But that’s a very circular description.

English: Illustrates the relationship of a cir...
English: Illustrates the relationship of a circle’s diameter to its circumference. (Photo credit: Wikipedia)





Turtles and More

Turtle graphics. This to me resembles a Kina or Sea Urchin

My wife recently became interested in the Spirograph (™) system. Since her birthday was coming up, so did I, for obvious reasons. If you have never come across Spirograph (™) I can highly recommend it, as it enables the production of glorious swirls and spirals, using a system of toothed wheels and other shapes. When you use multicoloured pen, the results can be amazing.

Of course, I had to translate this interest into the computer sphere, and I immediately recalled “Turtle Graphics” which I have used before. It is possible to create graphics very similar to the Spirograph (™) designs very simply with Turtle Graphics.

This resembles the sort of things generated by Spirograph (TM)

Turtle Graphics have a long history, stretching back at least to the educational programming language Logo. Although variations of the original Logo language exist, they are fairly rare, but the concept of Turtle Graphics, where a cursor (sometimes shown as the image of a cartoon turtle) draws a line on a page, still exists. The turtle can be directed to move in a particular way, based on instructions by the programmer.

For instance the turtle can be instructed to move forward a certain distance, turn right through 90°, and repeat this process three times. The result is a small square. Or the turtle could be instructed to move forward and turn only 60°, repeating this 5 times to draw a hexagon. Using simple instructions like this allow the drawing of practically anything.

Square and Hexagonal spirals
Square and hexagonal spirals drawn by Turtle Graphics

I use an implementation of Turtle Graphics in the turtle module of the Python programming language but it is probably available for other programming languages. Python is probably an easy language to learn from scratch than Logo, and in addition Python can be used for many other things than Turtle Graphics. Python is available for Windows, OS/X, and Linux/Unix, and for several other older or less well known platforms.

Where things become interesting is when the looping abilities of Python are used to enhance a program. If the programmer gets the turtle to draw a square, then makes the turtle turn a little and repeats the process, the result is a circular pattern. Starting with a more interesting shape can produce some interesting patterns.

Rotated Square - Turtle graphics
Rotated Square – Turtle graphics

After a while, though, the patterns begin to seem very similar to one another. One way to add a bit of variation is to use the ability to make the turtle move to a specific position, drawing a line on the way. As an example, consider a stick hinged to another stick, much like a nunchaku. If one stick rotates as a constant speed and the second stick rotates at some multiple of that, then the end of the second stick traces out a complex curve.

Flower shape
Flower shape – turtle graphics

In Python this can be expressed like this:

x = int(a * math.sin(math.radians(c * i)) + b * math.sin(math.radians(d * i)))
y = int(a * math.cos(math.radians(c * i)) + b * math.cos(math.radians(d * i)))

where c and d are the rates of rotation of the two sticks and and b are the lengths of the stick. i is a counter that causes the two sticks to rotate. If the turtle is moved to the position x, y, a line is drawn from the previous position, and a curve is drawn.

The fun part is varying the various parameters, a, b, c, d, to see what effect that has. The type of curve that is created here is an epicycloid. For larger values of c and d the curves resemble the familiar shapes generated by Spirograph (™).


The equations above use the same constants in each equation. If the constant are different, some very interesting shapes appear, but I’m not going to go into that here. Suffice it to say, I got distracted from writing this post by playing around with those constants!

The above equations do tend to produce curves with radial symmetry, but there is another method that can be used to produce other curves, this time with rotational symmetry. For instance, a curve can be generated by moving to new point depending on the latest move. This process is then iterative.

Gravity Wave - turtle graphics
Gravity Wave turtle graphics

For instance, the next position could be determined by turning through an angle and move forward a little more than the last time. Something like this snippet of code would do that:

for i in range(1, 200):

a = a + 1
c = c + 10

This brings up a point of interest. If you run code like this, ensure that you don’t stop it too soon. This code causes the turtle to spin and draw in a small area for a while, and then fly off. However it quickly starts to spin again in a relatively small area before once more shooting off again. Evidently it repeats this process as it continues to move off in a particular direction.

Turtle graphics - a complex curve from a simple equation
Turtle graphics – a complex curve from a simple equation

Another use of turtle graphics is to draw graphs of functions, much like we learnt to do in school with pencil and squared paper. One such function is the cycloid function:

x = r(t – sine(t))

y = r(1 – cosine))

This function describes the motion of a wheel rolling along a level surface and can easily be translated into Python. More generally it is the equation of a radius of a circle rolling along a straight line. If a different point is picked, such a point on a radius inside the circle or a point outside the circle on the radius extended, a family of curves can be generated.

Cycloid curve - turtle graphics
Cycloid curve – turtle graphics

Finally, a really technical example. An equation like the following is called a dynamic equation. Each new ‘x’ is generated from the equation using the previous ‘x’. If this process is repeated many times, then depending on the value of ‘r’, the new value of ‘x’ may become ever closer to the previous value of ‘x’.

x(n+1) = rx(n)(1 – x(n))

If the value of ‘r’ is bigger than a certain value and less than another value, then ‘x’ flip-flops between two values. If the value of ‘r’ is bigger than the other value, and smaller than yet another value then ‘x’ rotates between 4 values. This doubling happens again and again in a “period doubling cascade“.

Turtle graphics - electron orbitals
Turtle graphics – electron orbitals

I’ve written a turtle program to demonstrate this. First a value for ‘r’ is chosen, then the equation is repeated applied 1,000 times, and the next 100 results are plotted, x against r. In the end result, the period doubling can easily be seen, although after a few doubling, the results become messy (which may be related to the accuracy and validity of my equations, and the various conversion between float and integer types).

Period doubling
The “fig tree” curve calculated in Python and plotted by Turtle Graphics.


The modern theory of natural selection derives...
The modern theory of natural selection derives from the work of Charles Darwin in the nineteenth century. (Photo credit: Wikipedia)

If we accept Darwin’s theory of evolution, which I do, then we accept that we are the way we are as a result of a very period of gradual changes brought about by the pressures that our species has experienced through emergence and during process of its existence.

But let’s take a step back. All organisms have so called genetic material, stuff within them which encodes the way they are and the way that their offspring will be. The genetic material is copied as a part of the process of living, of growing and of repairing the organism if it sustains damage.

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If that were all there was to the process, then organisms would be static, with no changes and no evolution. In fact the process is not perfect and both minor and major changes to the genetic material happen all the time, by all sorts of means.

Obviously, if too many changes or major changes occur in the genetic material, then the organism may not grow properly and may not repair itself properly when damaged. Also if the genetic material is passed to the organism’s descendants, they may they may not be viable or they may be disadvantaged and be unable to thrive and reproduce.

Baby turtle, species unknown.
Baby turtle, species unknown. (Photo credit: Wikipedia)

To counter this, our bodies have mechanisms to repair our genetic material, our DNA. If our bodies did not have this ability, it is unlikely that we would last long, as our body cells could experience millions of cases of damage to our genetic material per cell per day. That’s an awful lot of damage!

As described in the Wikipedia reference above, the errors in our genetic material could result in cell death or unregulated growth resulting in tumours. The DNA repair mechanism in our cells  do a good job, but they are only effective if the DNA strands are broken or incomplete. If a change is minor, and is properly reflected on both strands of our double helices, then the repair system will not notice the change.

English: Close up of The Double Helix
English: Close up of The Double Helix (Photo credit: Wikipedia)

This allows small changes to slip through, and provided they don’t cause life threatening problems, they may get passed to our descendants. The same applies to organisms other than ourselves of course.

Some major changes do slip through and organisms may end up with extra chromosomes or with damaged chromosomes. Sometimes these issues may not cause too many problems for the organism, while in other cases the descendant organism may not survive long enough to breed.

English: Illustration of the chromosomal organ...
English: Illustration of the chromosomal organisation of haploid and diploid organisms. (Photo credit: Wikipedia)

The minor errors mentioned above may affect the descendant organism to some extent, making it more or less successful than its parent organisms. The theory of evolution suggests that if the change in the genetic material makes it more successful than its siblings who don’t have the small errors, then, over generations, organisms carrying the new DNA changes will eventually replace those who don’t carry the change.

This could lead to problems for an organism. If we consider a stable population with few pressures, that has plenty of resources, there is little that would cause any permanent changes to the population, and small genetic traits could appear and disappear over time and not have any measurable effect.

Boreray sheep - on Boreray - -...
Boreray sheep – on Boreray – – 1439988 (Photo credit: Wikipedia)

If the environment then changes, such that one trait provides a large benefit to those individuals who have this trait, then over time there will be a tendency for the trait to be found in more individuals and the number of individuals without it would fall.

If the environment changes back again, then those with the trait may be disadvantaged and those without the trait could then come to dominate the population. However if enough time had passed and all the individuals without the trait in their genetic material had died out, then the population would be stuck with the trait.

Français : Trait du Nord - Salon de l'Agricult...
Français : Trait du Nord – Salon de l’Agriculture 2010 (Photo credit: Wikipedia)

It would be extremely unlikely but not impossible for the change in the genetic material to be reversed by chance as this would require another minor error to exactly reverse the original error. In effect, evolution as reflected in the genetic material never (or astronomically rarely) reverses.

If a group of organisms gets isolated from the rest of its species, some of the genes that are present in the population at large will not be present. In addition, some of the genes in the isolated population will also die out, either by chance, or because the trait that they confer is not beneficial in the isolated environment.

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This can cause problems for the population if the environment changes dramatically to the detriment of the organisms. While the population at large may have genes which would enable the population to survive the changes, but those genes may have died out in the isolated environment, and the population may fail.

Of course, a mutation may arise which would enable organisms to survive in the new conditions, but environmental changes would almost certainly be faster than the rate of evolution through mutation.

exemples de mutations possibles sur l'ADN
exemples de mutations possibles sur l’ADN (Photo credit: Wikipedia)

Some species have different behaviours and appearance while still remaining the same species. Some of Darwin’s finches are an example. At least two varieties of one of the species feed on the Opuntia cactus, but they have different ways of feeding on them. One variety has a long beak and can punch holes in the cacti, while the other variety, with a short beak, break open the cacti to feed.

The birds can and do interbreed, so they are indeed the same species. This is similar, I presume, to the variation in skin colour in humans or the various blood types in humans. Such species have the same genes, but have slightly different versions (alleles) of it. This is called genetic polymorphism.

English: Trumpeter Finches (Bucanetes githagin...
English: Trumpeter Finches (Bucanetes githagineus), Valley of the kings, Egypt. Español: Camachuelos trompeteros (Bucanetes githagineus), Valle de los reyes, Egipto. (Photo credit: Wikipedia)

A species, like the finches, has to adapt. If its environment changes and it is unable to respond, then it will die out as innumerable species have done and are still doing. However, a species needs time to respond to environmental changes. For instance, polar bears may die out because the sea is is not freezing over as it usually does, and as a result there are no seals for the bears to hunt.

Whether or not you attribute the warming to mankind’s actions or not, the lack of freezing is a fact, and the bears are so far unable to adapt to the new conditions, and are often becoming a nuisance to arctic communities.