"BITS" OF INFORMATION

If a dog bites man, it is not a news. If a man bites dog, it is a news. Anything surprise is the news and an information. If an event certainly is not going to occur then its probability of happening is 0 and it is not an information. If an event is certainly going to happen then its probability is 1 and it is also not an information.

An event which is having probability between 0 and 1 carries some information. For example: In tossing of a coin getting a head or tail is having a 50% chance or 0.5 probability. Out come of the toss is an information. In the case of rolling of dice, each outcome has 1/6 chance or 0.167 probability. Certainly the outcome of a dice is the surprise and an information.

Shannon gave a formula to calculate information content in an event based on probability.

I want to calculate the information content of coin toss and I also want to represent it in bits-binary digit format. Here probability p = 0.5 and to represent in binary, the logarithm's base must be 2.

From figure 2 we get, information content is 1 bit. That is , outcome tail can be indicated by a bit 0 and head by a bit 1.

An institution follows the following grading system.
O - outstanding
A- first class
B - second class
C- third class
F- fail

How much information is there in the grades O,A,B,C,F.
Each appearance of the grade has 1/5 chance or 0.2 probability.
From figure 2, information content in the grades is 2.3 bits. That is , slightly over 2 bits is required to encode the grades.

O- 0
A-1
B-10
C-11
F-100

Suppose we have a string like this,
"AAAACCBBBADBBAA"
Info. content in the string can be calculated using slightly modified Shannon's formula and we also get maximum number of bits required to encode it efficiently.

Initially the computer system was based on 8 bits code then we moved to 16 bits, 32 bits, and even 64 bits. More bits means more info, more pixels, more colours and more clarity.

Shannon's formula is basic to today's digital communication. It has led to efficient error-detecting and error-correcting codes. It is used in CD's, DVD's, data compression and extracting meaning from DNA sequences.

Science update: Stephen Hawking appears as hologram in Hong Kong and discusses present situation of the world.

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LISSAJOUS FIGURES

Definition: "When a particle is subjected to two sine wave motion or two oscillatory motion at right angles, the particle describes lissajous figures". We know sine wave motion and circular motion is basically same. Hence we draw two circles A and B perpendicular to each other. The circle B rotates twice faster than circle A. That is, frequency of circle B is two times than that of A. A particle at the intersection of two circles is subjected to two sine wave motion A and B at 90 degree simultaneously. The particle will describe figures depending on the frequency and phase of A and B . In our case, the ratio of frequency is 1:2 and the two waves are in phase. To draw lissajous figures : A moving point in both the circles are chosen. Here we should remember; during the time taken by the circle A to complete one rotation, circle B completes two. Hence the points are marked on the circles according to their speed. Then straight lines

THE PARABOLA

A jet of water shooting from a hose pipe will follow a parabolic path. What is the so special about parabola. Y= x^2 Draw a graph for the above equation. It will result in a parabola. This parabola is also called unit parabola. Any equation involving square will yield a parabola. Example: Y = 2x^2 +3x+3 (also called quadratic equation) X= 2 and -2, both satisfies the equation 4 = X^2. Parabolic equations always have two solutions. Any motion taking place freely under gravity follows parabolic path. Examples: An object dropped from a moving train, A bomb dropped from flying plane, A ball kicked upwards. If a beam of light rays fall on the parabolic shaped mirror, they will be reflected and brought to focus on a point. This fact is made use of in Dish Antenna, Telescope mirrors, etc. Inverted parabola shape is used in the construction of buildings and bridges. Because the shape is able to bear more weight. A plane

CASINO'S GAME

Let us find out how the casino survives with mathematics. Say, your friend invite you for a game of dice. You must bet (wager) 2 dollars. If you roll 'six' you will get back 8 dollars. The game will go on for 30 rounds. All sounds good. The probability of rolling 'six' is 1/6. Since the game will be played for 30 times, the 'expected win' is 30*1/6 = 5. That is, you are expected to win 5 rounds out of 30. Hence your gain will be 5 * 8 =40 dollars. ok. This also implies that you will loose 25 rounds. Hence your loss will be 25*2 =50 dollars. Your net gain will be gain-less = 40-50 = -10 dollars. For 30 rounds, the loss is -10 dollars, Hence, for one round =-10/30 = -1/3 dollars. There will be a loss of -1/3 or 0.33 dollars per round. It is not a fair game. Let us make a simple formula to calculate 'Pay out per round\. The probability for a win = p The pay-out in case of win = V No. of rounds = n The expect

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