Monday, 17 June 2019

THE INVISIBLE FIELDS

We have a football field, a field of valleys and hills.  What exactly a field is ?  It can be thought as a area containing many, many points.  Each point may have a value like its height, its  temperature, its greenness etc.

Consider an LED lamp.  There is field of light around it.  But, this is 3-dimensional field unlike surface area.  The light is very bright close to the bulb and the light fads away with the distance.  This kind of fields always follow 'inverse square law'.  It says that the decrease in intensity (of light) is proportional to the square of the distance.  Our eyes can sense the light.  If you put any light sensitive-device in this field, it will be activated, example - light powered calculator.

Now consider a magnet, there is a magnetic field around it similar to the light field.  But it is not visible.  Only another magnet can sense it.  If you put iron pins in the field, it will be attracted. A  compass will be disturbed by the field.

Next, consider a mobile phone tower.  It radiates radio waves or there is a electromagnetic field around it.  All the mobile phone in the field are kept alive.  When we move away from the field, we get "out of reach" message.

'Remote' devices, Bluetooth devices, WiFi network, - all generate electromagnetic fields around them.  They connect other devices to them and keep them active.

Around any mass, plants, sun and stars,  there is a gravitational field.  The sun holds all the nine planets because of its gravity.  The earth keeps the moon in its hold because of its gravitational field.

Electric charges have electric field around them.  Moving and oscillating charges produce electromagnetic waves or field.  To day, we go ' wireless way' because of these fields.

Action at a distance, without contacting is possible only because of these fields.

Tomorrow, a virtual fence made using a field, may stop us from trespassing, encroaching and invading.
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Sunday, 16 June 2019

HOW THE COMPUTER COMPUTES

Let us recollect the binary system of numbers.

binary
0 - 0
1 - 1
2 - 10
3 - 11
4 - 100   and so on.
Hence all numbers can be represented in 1 s and 0 s.

Let us now come to four fundamental operations.
4 * 2= 8, that is adding 2, 4 times gives 8.  Hence multiplication is the repeated addition.
8/2 = 4, you can subtract 2, four times in 8.  Hence division is the repeated subtraction.
Now, we are left with only two operations '+' and '-" .
Even subtraction can be done through addition.  Let us see now.  To subtract 6  from 8, take the 10's compliment of 6.  Subtract 6 from 10 and get 4 which is 10's compliment .  Now add 8 and 4 to get 12.  Drop the carry 1 in 12 and get 2.  That is answer of 8-6 =2.
Taking compliment in binary system is easy.  0 is 1's compliment and 1  is 0's compliment.
Finally, we are left with only one mathematical operation "Addition".  Hence computing means just adding 1's and 0's.

How the computer adds?  Now we have  to understand the simple function of electronic circuit called Exclusive OR gate or EX-OR gate.  Ex-OR gate takes in two binary inputs and gives out one binary output.  If two inputs are similar (00 and 1,1) , it gives out '0'.  If the inputs are dissimilar (0,1) it output '1'.
0+1 = 1
1+0 =1
0+0 =0
1+1 =1'0'
Hence, what the EX-OR circuit does is the addition of binary digits (partly).  Along with Ex-OR gate, the computer uses other circuits and performs the addition of big binary numbers perfectly.
(We also know, high and low voltage represents 1 and 0 in digital electronics)
Today, computer diagnoses a diseases; recognizes a face; recommends a personal loan for a customer; advises what movie to watch and even drives a car.
Can you believe that the Addition of binary digits' is the main fundamental operation behind all the miracles performed by the computer?
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Friday, 14 June 2019

WHEN THE CAR'S AIR-BAG WILL DEFLATE ?

We assume that we know everything about the elementary concept "acceleration".  But there is more to know.

Definition:  Whenever a body undergoes change in speed or change in direction, it said to be "accelerating".

We know, if any body falls freely, its speed will increase by 9.8m/s^2 for every second due to earth's gravity and it is denoted by the symbol 'g'.  Also, we can say, if a body experiences 9.8 m/sˆ2 acceleration, it is acted upon by 'one g' force.

If you plop down on a chair, you will experience up to 10 g force for a brief time.

Even your sneeze will put you in a '2.5g' force.  In a thrill ride of roller coaster, we experience 'high g' for a very brief time.  There are 'human centrifuge' which creates 'high g' by spinning fast. pilots and astronauts are trained to experience 'high g' in these centrifuges.

When a car crashes, it suddenly decelerates (negative acceleration).  The airbag in front of all the seats will be inflated only if the acceleration exceeds '60g'.  Prince Diana's car crash produced  '70-100g' force.  A word of caution.  If you experience a force of 4g-6g for a long time, you will be "blacked out".  Our body has many organs with different densities and masses.  Hence each will get its own g - force.

Feather or boulder; earth always gives 'one g' force to everything.  It is because gravitational force proportionally increases with the mass [g = force/mass ].

In pole-vault jump, the person falls on the cushion, to reduce g- force. In a car, the engine is mounted on front and luggage is kept on the back to reduce the effect of g-force in an impact.

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Wednesday, 12 June 2019

HOW TO ROUGHLY CHECK YOUR INCOME TAX STATEMENT

DIGIT SUM:     We should know first, what is digit sum?
8+1+2+4+5 = 20  Again add 2+0 = 2.  Hence 2 is the digit sum of 81245.  By repeatedly adding digits; till we reach a single digit, we get digit - sum.

Note :  In a number, we can ignore 'nines' and the digits which add up to nine.  They will not have any effect on the calculation of digit-sum.

For example; in 7295, 7,2 and 9 can be ignored, and the digit-sum is just 5.
In usual method  7+2+9+5 =23=2+3=5, Also we get 5.

To verify multiplication
7195*4321 = 31089595
Find the digit-sum of each of the above numbers
4 * 1 = 4
Hence verified.  So the rule is; 'The digit-sum of the multiplicand when multiplied with the digit-sum of the multiplier should equal to the digit-sum of the product'.

TO VERIFY DIVISION
5046/42 = 120; REMINDER 6 , WE KNOW 5046 = 120*42 +6
DIVIDEND = DIVISOR * QUOTIENT + REMINDER
Now we will use digit-sums and verify.
6 = 3* 6+ 6
AGAIN DIGIT- SUM
6 = 6  checked.

3475+9892 + 7461 = 20828   using digit sum
1    +  1      +  9      = 2
2 = 2
it is Ok.

Similarly, we can verify squaring, square root, cube, cube rooting.
" When the sum-digits does not match, we can say the answer is 100 % wrong."

But when the sum_digits matches, the answer is mostly correct and NOT 100%  CORRECT.  We have to employ a few more techniques to confirm the answers.

1. 7212 *3982, these two numbers can be taken as 7000 and 4000.  Hence the answer should be around 28000000.
2. The answer should have eight digits.
3. The last digit of the answers must be 4 (2*2 =4)
Intuitively, we can employ techniques like this and check the answers.

The rough and fast checking is useful for students giving competitive exams; the executives verifying 'typo' in a balance sheet; etc.,
This method belongs to vedic mathematics
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Monday, 10 June 2019

THE FIVE AVATARS OF MATTER

We usually talk about the three phases of matter, solid, liquid and gas.  But there are two more phases with which we are not very much familiar.

Let us take water for example.  Water is made up of H2o molecules.  The hydrogen atoms are slightly positive.  The oxygen atom is more negative.  There is attraction between negative oxygen of one molecule and positive hydrogen of another molecule. It is called hydrogen bonding.  Hence there is adhesive force between molecules.  That is why they cling together as drops, as fluid or as ice.

When we supply heat energy to the water, its temperature increases.  And the molecules moves randomly and vigorously due to thermal energy.

When we cool down the water, the motions slow down.  The molecules stick together more closely and become ice, that is solid.  Hence matters move into solid phase, if the temperature is lowered.

If the temperature is increased, the molecules of ice, set into vibrations or random motions in spite of bonding.  And the matter reaches liquid phase of the molecules. If they get more energy, they move vigorously, rapidly and come apart.  Next they enter into gas or vapor phase.

Suppose, the temperature is increased to very high level, the negative electrons are stripped out of the atoms.  The atoms becomes positive ions.  We get a cloud of positive and negative charges(ions).  This is the fourth state of matter called plasma.  The sun has very high temperature.  Hence its atmosphere is mostly plasma.  Modern CFL lamps contains plasma.  And the plasma TV has many tiny CFL on the screen.

At absolute zero (-273 degree), all atoms and molecules come to a stop because of zero thermal energy.  We are not able to achieve absolute zero. But we have reached very, very close to absolute zero.  When the Rubediyam atoms are cooled and brought very near the absolute zero, they just become one atom or one molecule or one unit.  This state is called Bose-Einstein condensate (BEC).  This is the fifth phase of matter.  Hence all the matters reach 'oneness' or become single entity at the real zero temperature.

In everyday life, we are not able to see BEC except LASER.  But the day is not far away, when we will make BEC at our will.

PHILOSOPHY
We understand, one can become many and many can become one.  Heat is the vehicle of transformations between the phases of matter.
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Friday, 7 June 2019

HEART SURGERY AND THE ART OF PAPER FOLDING

The Japanese art of paper folding is called origami.  It has moved from entertainment to science.  It is math in action.  One can make a bird, a frog, a sailboat or complicated and intricate objects.

In 1970, Japanese astrophysicist Korya Miura invented his Miura map fold method.  Very large maps are folded and unfolded using his technique.  Here one shape is repeated over and over, with no gaps.  Normally crease pattern is a 'tiling of parallelograms'.  It opens and close very easily.

The crease pattern on the paper is the blue print of the origami object.  A crease creates a valley or a mountain in the paper.  Origami follows certain math laws.

1. Colorobility
One can colour any crease pattern with just two colours without ever having the same colour meeting".

2. Directions of fold:
The directions of the folds at any vertex (corner) - the number of mountain folds, the number of valley folds -always differs by two.

3. No penetration:
No matter how many times you try to stack folds and sheets, a sheet can never penetrate a fold.

4. Total angle:
Every angle around the vertices comes out to 180 degrees.

REAL USES

Dr. Miura map folding method is used to deploy large solar panel into outer space.  Think of each parallelogram as a solar cell, all of which are then connected by hinges.  The array can then fold up into small package to be put on a space satellite before being launched on a rocket.  Once in space it could be opened by a simple expansion rod without the help of human hands.

Sometimes, coronary artery (an artery feeding the heart muscle) is narrowed by a build up of fatty deposits.  It can reduce blood flow causing chest pain.  A stent is a tiny wire mesh tube.  It is collapsed (folded) one and it is moved into the area of the blockage.  It unfolds, expands and holds the artery open.  Here origami techniques are tried and used.

Fordable umbrella,  folded carton box, fordable staircase, fordable lens demonstrate origami principle.

Origami is explored in Bio-Engineering to send the toxic medicine safely into the body.
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Monday, 3 June 2019

THE STRANGE BEHAVIOUR OF THE WATER

We all know water is made up of H2O molecule.  The molecule is 'V' shaped; oxygen at the vertex and two hydrogen at the edges.  The oxygen has more electrons (16).  Hence the molecules is more negative on oxygen side and slightly positive on hydrogen side.  We say, this molecule acts like electric dipole.  Hence there is attraction between oxygen of one molecule and hydrogen of another molecule.  We call this attraction as "hydrogen bonding".  Because of the hydrogen bonding, the molecules cling together as droplets, drops , liquid,  ice, ice crystals.

Top surface of the water in a container is called free-surface.  Above the free-surface -No forces.  But below the free surface, there are attractive forces due to hydrogen bonding.  Hence top surface is pulled inwards and looks curved.  All the water surfaces are always under tension.  If you jump into a big well containing water, you will feel pain in the chest due to surface tension(here the surface acts like a steel sheet).  You can throw a stone before jumping to break surface tension.

Since there is a downward force on the surface, there will be upward force due to reaction.  The upward forces raises water in the plants; blood in the body; oil in a wick of a lamp.

It takes large amount of heat to break hydrogen bonding between molecules.  Hence water requires large amount of heat to raise its temperature.  Remember water's boiling point is very high(100 degree c).  All other substances requires much less heat than water.  Because of this property, water is cold in the well in summer and hot in the winter.  Sea breeze and land breeze also occurs due to this property.

Again due to hydrogen bonding water expands while freezing (contrary to other substances).  Hence ice is less denser  and it  floats above water.

At 0 degree c, the three forms of water; ice; liquid and vapour co-exist.

If we put a spoon full of salt, into water, it dissolves.  How?  We know, salt is just sodium chloride.  The negative side of water molecules (oxygen) surround positive sodium ion of salt and pulls it apart.  Similarly positive side of water molecules (hydrogen) surround negative chlorine ion and rips it apart.  Hence salt dissolves.  Most substances dissolve in water.

Body fluids are mainly made up of water.  The hydrogen bonding gives us many life-sustaining properties.

Appreciate the nature's ingenuity.
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