Continuity and Discontinuity

The human form of life is always spending in analyzing the beauty of nature and its emulation. We may try everything and come to solutions of few problems but there is a difference between us and god which makes him almighty. The name is no misnomer for him; he always has an extra edge over us. The perfection of god can be realized by experiencing many phenomena. People have different perception levels and their level of understanding varies according to age, intelligence and education. So according to my observation the biggest drawback of humans lies in failing to make continuous things. According to me, we emulate to fool ourselves by modelling continuous things with contiguous behaviour.

Let me add proof to my words.

Digital imaging has been fascinating me for the last 2-3 years but I've not done much about it, though I know few things which are worth sharing. When you see an image which is digital, the first thing which should strike to your mind is why this is called digital. It makes sense when you try to enquire a little. Digital displays are made up from small dots called pixels. The digital image is built up from these dots. The smaller and closer the dots are together, the better the quality of the image. The story of pixels may be a little incomprehensible but if I can apprehend it then everybody can savour it.
I'll explain with the number line. When I was a kid, I thought there are numbers from 1 to as much you can think and also zero. When I studied in higher classes I realized that there are certain numbers which when added are capable of reducing the original value of a number, they are negative numbers. Negative numbers did trouble me a lot with their opposite behaviour and as a matter of fact I was never a good mathematics student. To add to my woes, I was informed that between any two numbers there are infinite numbers possible.
The above fact may distract you away from this post but please keep reading as if you have come so far then the rest of my post is also not so arid, banal and boring.
The number line story teaches us something, there are infinite numbers between any two numbers. Please bear this fact in your mind while reading rest of the post, it'll surely help. I know everybody must be aware of the visible spectrum of light. Light has seven visible components. However, Red, Green and Blue consists all the primary colours and their appropriate composition can give light all the different variations of colours that we can appreciate. This is capitalized in digital imaging.

Take an example with a pinch of salt.

A random point in space can be described with the help of three parameters, rather three coordinates. To be exact, it's horizontal and vertical distance, and the lateral shift with respect to your position. I know this is a bit difficult for non-science background readers to digest but this would be clear if you give it a little thought.

A red spot can be described as an area of complete red region. Red region means the colour of the region is red. Several distinct points in space can be joined to form a curvilinear figure. Two points if joined makes a straight line and hence forth. A straight line has many points, in fact, infinite points but only two points are sufficient to describe a straight line. This fact is not true for other figures. An area is also comprised of many points. The details of several points may give us an idea about the area; it may not be exact but could suggest something.
A red spot needs a description which is very simple. A large number of points with the same colour namely red makes the spot red. Similarly, for a green and blue spot we have infinite number of points with the same colour. However, a spot can be of various colours and if every point has the same colour, it makes the spot of that particular colour. Imagination can create wonders. Instead of every point of same colour if we have some points of red and others of other colours we will have a mixed colour spot rather an image. Every point is also known as pixel in scientific jargon. A pixel can depict any colour depending upon the ratio of red, blue and green components in it. In more common terms, the RGB value (Red-Green-Blue value) of a pixel decides the colour of the pixel. For example, if percentage of red, green and blue is equal then we get white light or a white spot. The colour of our skin can also be viewed by an appropriate composition of colours in various pixels. The resolution or rather the clarity of an image can be increased by increasing the number of dots known as pixels.

The above transition in the number of pixels gradually illustrates the effect of number of pixels in an image. In the first square, only one pixel is used which produces a blue spot. The second has four different types of colour regions due to four pixels. The number of pixels eventually increases to give sufficient approximation to the actual image when the number of pixels rises to 10000. One thing which should be kept in mind is the final image is not the exact continuous image but the best contiguous example in the above set of images. If we double the pixel numbers or reduce the individual size of pixels then the clarity or resolution will increase but our eyes treat the final image as the best one because of limit to the sensory perception.
Let us take a smooth transition from static images to moving images or videos. Digital videos are just yet another example of the contiguous behaviour. Our eyes can differentiate between 10 images in one second and if we try to observe more than ten, our eyes cannot function properly. In digital videos around 24 frames or images are smoothly exposed to our eyes and all are linked to each other such that we cannot differentiate between them and thus once again the contiguous model fools us and we term the phenomenon as moving pictures.

PS:What is your New Year resolution?
PS:This post also deals with resolution, albeit related to resolution of images.
PS:I know this post is not exhaustive but please let me know if you know anything more about this topic.
PS:Happy New year and do take a resolution.