SCIENCE CAPSULES

  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 ...

      Consider this equation              p(n+1)=p(n)*r*(1-p(n))     This equation is taken from population modeling.  Here p represents population and r the rate of growth.  We need not go into the origin of the equation.  Here, the important point;  p(n) is calculated from the equation and the p(n) is fed back into the equation to get the next p(n).  The output to the input feed back calculation is repeated many times(iterated).  In computer language, the equation can also be written as                  p = p*r*(1-p)   Let initial p be 0.25 and let r be fixed at 1.5.  Let us calculate p repeatedly in a spreadsheet and draw a graph between p and number of iterations.  The screen shot is shown below.  The p initially increases and then stabilizes at 0.333.      Now let us change only r to 2.5.  As...

                                                          N = n*e^(r*t)    The equation yields the natural growth or decay of any quantity.  Here, the initial amount of quantity   n becomes N after time lapse of  t at the rate of growth r .  When we apply the equation for decay, the r becomes negative. we know Euler's constant e =2.71...        The applet given below draws the curve for the equation, you can play with the rate r  and see it's effect on the curve. The initial quantity n = 1.  The curve gives the quantity N (y) as the time t (x) progresses.  The curve rapidly grows or decays and then it becomes slow.  But the curve tends to go to infinity.  To view the curve properly adjust the graph sheet in the applet.          ...

      Everybody knows Pythagoras theorem. The figure 1 states it clearly. If sides are equal to unity, what will happen to hypotenuse c^2=1^2+1^2 = 1+1 = 2 c = root of 2  = 1.414... (figure 2) Hypotenuse turns into root of 2 , a never ending irrational number. Suppose hypotenuse is 1, what will be the Pythagoras relationship? According to trigonometry, adjacent side is 1*cos x and opposite side is 1*sin x.  Applying Pythagoras theorem we get,  (1*cos x)^2+(1*sin x.)^2 = 1^2 (cosx)^2+(sinx)^2=1 So this is the trigonometric equivalent of Pythagoras equation.(figure 3) We can extend the Pythagoras principle to higher dimensions.  For example, we can calculate the diagonal inside the 3 D cube as shown in the figure 4. We can link number of triangles and apply the Pythagoras theorem as shown in the figure 5 .   Pythagoras equation is satisfied by some whole numbers or integers as given below. x^2+y^2 = z^2 3 ^2+ 4 ...

   Newton law says, every object in the universe attract every other object by gravitational force.  Scientist Cavendish proved that two lead balls attract each other using torsion balance experiment.  He also measured the universal gravitational constant G using that experiment.  The gravitational force is the weakest one but a long range force.       Gravitational force is responsible for the formation of galaxies, stars and planets.  It keeps planets revolving around the sun and satellites around the planets.      On launching, a rocket must reach the speed of 11.2 km/sec.  Then only it can pierce out of earth's gravitational field(escape velocity).  Even if the speed is slightly less, it will fall back to the earth due to gravity.      Once out of the gravitational field, everything start to float.  Astronaut can sleep in any position since there is no gravity and consequent...

  ELECTRONS AT WORK  Electron was discovered by J.J. Thomson  more than 100 years ago.  It is said to carry negative charge and negligible mass.  It is present in all the elements      When electron flows in a conductor, it is electric current.  We know, nothing serves like electricity.       Around the moving electrons magnetic field is formed and it gives rise to electromagnet.   When the electron oscillates electromagnetic waves like radio waves are radiated.  It is used for communication purpose.     While the electrons are moving in a conductor, they collide with the atoms and produce heat.  Many heating devices are made using this principle.  In atoms, when electron jumps from higher orbit to lower orbit, it loses energy in the form of light waves, X-rays etc,.   When the electrons moves in the magnetic field  at an angle, it experiences a force called Lore...

  Take a piece of salt harvested from ocean.  It  basically has cubical shape.  It is made up of sodium chloride molecules(NaCl).  The sodium and chlorine atoms are joined by ionic bond.  They are alternately arranged in rows, into planes and take the shape of cube.  We know sodium and chlorine are atoms that are made up of protons, neutrons and electrons.  Now they say, protons and neutrons are built from the particles called quarks.        Hence all non-life matters are made from fundamental particles like electron, proton etc,.  The particles constitute themselves into atoms.  Atoms are binded together to form molecules.  Molecules arranged themselves into some shapes or go shapeless like liquid and gas.        Life starts from non-life.  The atoms of some elements particularly carbon and hydrogen form complicated molecules.  The different set of molecules make plant ...