sciencecapsules

             In normal dictionary, the words are arranged according to alphabetical order.  But we can arrange the words according the frequency of occurrence.  That is, most used words will appear first, less used words follows.  Then each word will have a rank and frequency.  If we multiply rank and frequency, we get a number.  That number will be the same (more or less) for all the words and it is a constant.  That is zipf's law. [ In the above paragraph, five  'the' are present out of 70 words. hence frequency percentage is 5*100/70=7.1% ]      Frequency percentage * rank = constant.      The most used words in English is 'The'.  It occurs 7 times in 100 words.  Or the percentage of frequency is 7 % .  A list is given below. Rank R     word       frequency            constant                              percentage F           F * R = C    1.            the                6.8%            1 * 6.8 =6.8 %    2.             of                3.1

          6.25 , here 6 is the first digit.      72.5, 7 is the first digit      12.65  1 is the first digit.      We think, all the digits (1 to 9) have equal probabilities to appear as first digit.  That is, they has to appear 1 out of 9 times - 11% probability.      But a man, named Benford researched heavily and gave a law.  "The 'one' appears as a first digit 30% of the time".  The small numbers 1,2,3 appears more as first digit than large numbers like 7,8,9.     Benford law holds good in baseball statistics, area of rivers, population sizes, street address, city populations, super market prices etc.     Let us consider door numbers in a street which has 30 houses. 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19.20,21,22,23,24,25,26,27,28,29, 30. 1 appears 11 times as first digit out of 30.  So around 30% times.     Let us say, a price starts at 1 dollar and goes up 10% every time. 1.00.1.10, 1.21,1.33,1.46,1.61,1.77,1.95,2.14,2.36,2.59..... S

         There is a popular book by name 'who moved my cheese'.  It is just little booklet.  The central point in the book is: 'The block of cheese will be moved now and then, the cat should be always ready to go that extra mile'.  Meaning: the world will change continuously, the people must adopt and update themselves continuously.     Let us take the example of music industry.  Long, long ago, music means live concert only.  Then it was recorded and played on a disc using vibrating needle.  Next music was recorded on a plastic tape using magnetism.  It was compact than a disc.  Earphones came.  It helped us to listen music without disturbing others.  Next music was recorded on a CD using pits and pumps which were etched by laser.  Pits and bumps represents zeros and ones using which music is coded.  Now,music is digitized.      Next silicon chips (electronic memory) stored music.  Now, 'apps' streams desired music to your smart phone.  The 'app'

             We know, vibrations produce sound.  When a bell is stroked; it vibrates; creates air pressure waves; reaches our ear; vibrates air drum; and we perceive the sound.  Every object vibrates with its own frequency (no. of vibrations per second).  Our ear is designed to hear the frequency range 20-20000 cycles per second.  If the sound frequency is above 20000 cycles, it is called ultrasound.  Some animal can hear ultrasound but we can not.  People have found many uses for the ultrasound.  First, how to produce such a high frequency sound.      Here the quartz crystal comes to our help.  It is 'silicon oxide'.  Positive and negative charges are evenly distributed in it.  So it is electrically neutral.  But if we press that crystal, the charges are displaced; positive charges move to one side; negative charges move to another side; electrical field is created; a voltage develops.  If we connect the two sides of quartz externally, current (electrons) will flow.  Hen

              Today, everybody can afford a fountain pen.  but long back, only the rich can buy a fountain pen.  Then, people used what is called a 'dip pen' or a quill.  A bird's feather was taken.  It was sharpened at one end.  People dipped it in a ink  bottle and wrote with it.  You know, frequent dipping was required.      Fountain pen was invented.  It has a surprising science behind it.  First, it has so many parts.  reservoir, nib, feed or collector, cap, clip, barrel miniature piston mechanism or ink cartridge and even a breathing hole.      Take an ink bottle.  Open its wide mouth.  Try to write with it.  We know, the ink will uncontrollably flow out.  We will only create a nasty mess and will not write a word.      We are aiming for the controlled leak in the pen.  Hence the design of the pen is very important.      Now cover the ink  bottle with its cap and make a thin hole with a pin.  Turn the bottle upside down.  Ink will not fall through the hole be

        You can, if you own a new Tesla car.  Bond lifts up the car side ways even up to 90 degrees and drives it on just tow wheels.  He again brings the car back to normal position without toppling.  It may be a screen gimmick.  But today, It can be real.      First, we should understand stability.  Consider 'Thanjavur doll'.  It is heavy and hemispherical at the bottom.  If you push the doll to one side, it will not fall down but will return and oscillate back into its original position.  Why?      Center of gravity (CG) of a body is a point in the body at which all the weight of the body acts.  Or, at CG, one can balance the body with a tip.      Draw a vertical line from the CG. If the line falls with in the base of the body, it will have good stability.  That is, when a body is pushed to one side and the line from CG falls with in its base, the body will return to its original position.  If the vertical line crosses the base, the body will topple.      To ac

           On earth, we pour the coffee in a cup and drink it without any effort.  "Drinking coffee' works smoothly because of earth's gravity, but in space, in the absence of gravity, the liquid misbehave or stay put.      Say, a astronaut wants to drink coffee. Let us also assume that there is some coffee in a cup. (even pouring liquid in a cup is impossible in zero gravity).  The man takes the cup and brings it close to the mouth.  Suppose he gives some shakes to the cup, a little coffee may go into his mouth.  The remaining coffee may go all over his face and the body.      In zero gravity, every thing stays still or moves in  random directions.  If forces are given on them, the things behave unpredictably.  Hence, even 'sipping a coffee' is a task in the space station.  It is solved by designing a coffee cup based on the principle of 'capillary action'.      What is capillary action?  Take a glass tube of narrow width, say 0.5 mm and put in

           On land we measure distance in kilometers and miles.  For a ship sailing in ocean for months and for a jet plane flying from one continent to another, these measurements will not be suitable because earth is spherical and curved.  That is where the 'nautical mile' comes in.  Let us understand the concept.      The earth roughly takes 365 days to go round the sun once.  Hence mathematicians divided a circle into 360 equal parts and defined the total angle of circle as 360 degrees.      To improve accuracy,  one degree is sub-divided into 60 minutes and a minute is further segmented into 60 seconds.  The same technique is followed in the clocks since the clock handles move in circles.      We have drawn imaginary vertical and horizontal lines on the earth called latitude and longitude.  They are based on angle measured in degrees.  They are used by GPS to pinpoint a location on the surface of the earth.      Nautical mile is the distance suspended by one mi

         Men communicated through sign language long back.  It is still used by physically challenged people.  Men invented language.  It paved way for the oral and written communication.      When distance increases, how to communicate?  Written message on palm leaf, cloth,paper  were sent on horses, trains and ships.  Today, we call it snail mail.  But it is still vogue.      Telephone , telex, telegram were invented.  Messages were sent through wires with electricity. Voice was converted into electrical signal and sent through telephone cables.  In telegram, two sounds represented each alphabet in English.  The letters are converted into sounds and sounds into electrical pulses.  Then the pulses travel from one post office to another.  The postmaster had to undergo special course to decipher the message in those days.      Radio was born.  That is, Radio waves receiver set.  Speech and songs were converted into electricity than into Radio waves(electromagnetic waves) and tra

        A man has bought six slices of pizza.  He ate first one.  He enjoyed the taste.  It satisfied his energy.  He took second one.  It gave 'marginally' less enjoyment and fulfillment.  After eating third, his satisfaction further decreased.  After fourth one, he felt a little satisfaction.  When eating fifth slice, he felt nothing.  He reached the saturation point.  Sixth slice made him uncomfortable and nauseating- a negative effect.      Pizza slices can be named as unit of consumption in Economics.  The satisfaction is named 'utility' or marginal utility.  Let us make a table and allot  points  for satisfaction or utility. Pizza slices                      satisfaction            total utility        or                                or Units of consumption      marginal utility       1                                     20                           20       2                                     15                           35       3