What is Learning and Why is It Important

7/31/2019 What is Learning and Why is It Important

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What is learning and why is it important?

Some people tend to think of learning as gaining knowledge or so calledinformation. But this is not the correct way to define learning. And hence,this is the biggest reason why students dont find them selves interested inmathematics, science and other fields of education. Because they dontknow what exactly they are learning (or knowing in this case) and why is itimportant. I always think that there is a big difference between nyana andjankari. What I am implying here is gap between two words wisdom andknowledge. And what is this gap I am going to explain here.

Learning is basically acquiring knowledge and understanding itsimportance in practical life. For example, in case of mathematics learning isnot just memorizing big mathematical expressions but to understand whatbig arbitrary mathematical equations are saying to us. In case of science,learning means to understand the laws of science, their practical applicationsand beauty hidden inside the meaning of them. And above all, learningcomes from doubting your understanding and being curious to understand.Famous philosopher Rene Descartes once quoted Doubt is the origin of wisdom. But one should first know if he/she has actually und erstood someparticular concept. I am going to show some examples here to elaboratehow one should understand and learn. And what is the pleasure of findingthings out. So when I used the word wisdom, I meant not only knowledgebut also the thorough understanding of that knowledge and ability to applythat knowledge.

I would start with very fundamental example of mathematics, with whichmost of you would have come across. I would show you how mathematicscan be wonderful.

Let us consider, x = 0.99999 9Now multiply both sides with 10, we would get,

10x = 9.99999 Subtract x form both sides,

9x = 9.99999.. 0.99999..9x = 9x = 1 = 0.99999..


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Now, how is it possible? We just proved that 1 = 0.999, which cant betrue.The very fundamental mistake we did here is our wrong understanding of multiplication. Multiplication basically means additions of numerical. When

we multiply 9 with 8, we are actually adding number 9 with itself 8 times. Sohere, when multiply x with 10, we are actually adding x again and again withitself which is not possible. Because as x is tending to infinity, its addition isnot possible. In fact, all mathematical operations we know just simply docounting. Their methods and representation of counting can differ, but its all about measurement. And that is the reason why mathematics wasoriginated at first place.

Another similar example is proving 2 = 3. Lets see how we would do it.

Consider the expression, -6=-6Then we have, (9-15) = (4-10)Implies, (9-15+25/4) = (4-10+25/4)Implies square(3-5/2) = square (2-5/2)Implies (3-5/2) = (2-5/2)Implies 3 = 2

Now, this is ironic. The step where we went wrong was, when we saidthat if square a = square b , then it implies that a=b. This is not correct.

Because correct solution would be a = +/- b. So applying this law in ourabove example, the correct solution would be,

(3-5/2) = - (2-5/2)

One another to prove 2 = 3 is shown below,

Lets consider two equations,

3 a - 2 a = aand

a = b + c

Now, by using both equations, we have


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3 a - 2 a = 3 ( b + c ) - 2 ( b + c )

Implies 3 a - 2 a = 3 b + 3 c - 2 b - 2 c

Implies 3 a - 3 b - 3c = 2 a - 2 b - 2 c

Implies 3 ( a - b - c ) = 2 ( a - b - c )

Now from this, we can deduce,

3 = 2

Again it may seem strange. There is something went wrong in this deduction. Wedisobeyed a very fundamental law of mathematics. We canceled (a-b-c) fromboth sides. Now since we already assumed that

a = b+c

This implies that a-b-c = 0. Since we divided both sides by 0, this leads the mostphilosophical argument of mathematics: What would happen if you have nothingand you want to divide nothing into nothing? The language of argument mayseem arbitrary, but I will explain it.

When we talk about mathematical operation division, it was first created bysome ancient mathematicians to ease the trading. To provide a platform forbuyers and seller to distribute commodities equally. For example, if I have 100 kgof rice and I want to distribute it to 10 peoples equally. I would divide 100 by 10,which is equal to 10. So I would distribute 10 kg to each. Our ancientmathematicians Aryabhata , Bhramagupta, Mahavira etc had the understandingof this operation. Now the interesting question arises, what would happen if Ihave 100 kg rice and I want to distribute it equally among zero people. Simply, itdoes not make any sense. There is no way to distribute 100 kg among 0 people.

So we would say that the answer would be undefined. In computer language anynumber divided by 0 is supposed to be equal to infinity. Bhasakara was the firstmathematician who discovered this thing. Now, our fundamental argument in theexample above is, what would happen if I have 0 kg rice and I want to distribute itamong 0 people. Answer would be again undefined. One cannot divide 0 by zero.Thus here, we cannot divide (a-b-c) by (a-b-c).


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Moving on, I would like to share some of the wonderful magic of mathematicswhich are really interesting and logical. One of the very beautiful series of mathematics is Grandis series after Italian philosopher, mathematician GuidoGrandi. The series is,

1-1+1-1+1- 1+1

One way to treat this series is (by treat, I mean to find the summation of series),

(1-1)+(1-1)+(1- 1)+.. = 0+0+0. = 0

However I can also be treated as,

1-(1+1)-(1+1)- (1+1). = 1-0-0- 0. = 1

Both seem to be quite accurate. One very interesting method is howeverdescribed below,

Suppose, x = 1-1+1- 1+1.

Implies , 1-x = 1-(1-1+1- 1..) =1-1+1- 1+1.

Implies, 1-x = x

Implies, 1 = 2x

Implies, x =

In other words, 1+1-1+1- 1......... =

Another similar interesting mathematical series is

1-2+3- 4

Now this is paradoxical series because its sum can be proved to be equal to ,which is not an integer. Mathematics says that sum of integers should always beequal to an integer, but here it can be proved that this series sum is equal to .How? We will see,

If we try to see what this is doing,


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1=1

1-2= -1

1-2+3 = +2

1-2+3-4 = -2

1-2+3-4+5 = +3

1-2+3-4+5-6 = -3

Hence, interesting it seems like this sequence would cover up each arithmeticinteger as it would go adding more and more its elements.

Now, to find the sum of this series, let us assume

x = 1-2+3- 4.

Thus, 4x = (1-2+3- 4) + (1-2+3-4) + (1-2+3- 4) + (1-2+3-4)

4x = (1-2+3- 4) + 1+(-2+3-4)+1+(-2+3- 4)-1+(+3-4+5-6 .)

4x = 1+(1-2-2+3)+ (-2+3+3-4)+ (3-4-4+5) + (-4+5+5- 6)+..

4x = 1+0+0+0.

4x = 1

x =

Hence Proved..

And now, comes the greatest story ever told; most magical sequencemathematician came across, and to be precise Italian mathematician Fibonaccicame across. Its the most profound work of mathematics and reflects the

nature of universe. It is called Fibonacci sequence named after its inventor. It isdefined as follows,

First take first two whole numbers 0 and 1. Now start making by adding twoconsequent numbers and we get,

0,1, 1,2,3,5,8,13,21,34,55,89.. and so on.


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The original problem that Fibonacci was trying to solve was about how fastrabbits could breed. Suppose one male and one female rabbits are put in afield. Rabbits are able to mate at the age of one month so that at the end of itssecond month a female can produce another pair of rabbits. Suppose that our

rabbits never die and that the female always produces one new pair (onemale, one female) every month from the second month on. The puzzle thatFibonacci posed was. How many pairs will there be in one year? At the endof the first month, they mate, but there is still one only 1 pair. At the end of the second month the female produces a new pair, so now there are 2 pairs of rabbits in the field. When third month ends, the original female produces asecond pair, making 3 pairs in all in the field. At the end of the fourth month,the original female has produced yet another new pair, the female born twomonths ago produces her first pair also, making 5 pairs. And this series goes

on.

Now, from this series if we start dividing two successive numbers such that wedivide each number by the number before it, we will see the following results,

1/1 = 1;

2/1 = 2;

3/2 = 1.5;

5/3 = 1.666;

8/5 = 1.6;

13/8 = 1.625;

21/13 = 1.6153;

As we go on further, we would realize that this ratio is converging to 1.6181which is known as golden ratio, golden number and sometimes Godsnumber. We say two quantities are in golden ratio if the ratio of sum of twosmaller quantities to the largest quantity is equal to the ratio of largestquantity to smallest quantity. Its easy to imagine in a triangle. The sides of atriangle follows golden ratio if the ratio of sum of two smallest sides to thelargest side is equal to the ratio of largest side to smallest side.


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Enough with the mathematics, now I would like to discuss the mostinteresting topic known to us; research and discoveries on which lead to allscientific revolution and the modern world we see today. I am talking aboutthe big picture: Our Universe. It was the curiosity of scientists to understandthe universe and meaning of its existence which lead to all scientific changes.They want to know about it, so one by one they made different theories,

different laws. And due to practical application of these discoveries, we seethe world today surrounded by tv, refrigerators, cell phones, cars etc.

Thus it becomes very important to understand the world around us. Andhow modern physicists think the universe operates. And hence, important tounderstand how these laws, these theories came into the picture tomodernize everything.

As far as we know we believe that the universe works on certain laws. It

follows the characteristics of some laws for the functionality of nature. Wedont know how these laws are created by nature. We have just observednature and made standard laws on that basis. These laws are called laws of nature or forces of nature. Force is a property by virtue of which certainobjects or particles attract each other or repel each other in certain standardfashion. But these laws alone do not describe everything which is happeningor has happened in universe. These laws provide the best possible outcomes.They give the probabilistic measurements which are very accurate. Butcomplete theory of universe also includes lots of randomness happening in

universe. Thus history of universe is codetermined by these laws and longsequence of random outcomes in addition.

The nature of universe or its functionality can be compared to a gamesay game of chess. Suppose god made this universe and put certain lawswhich it has to follow like a game of chess where each piece has to follow


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certain rules always. Whatever may be the condition, they have to alwaysfollow the rule given to them. Now, if someone from other planet comes toearth and start observing the game of chess, he might realize some of therules by observations. As time goes by, one may realize that bishop

maintains its color. He also may conclude that queen moves horizontally andvertically but later one may realize that queen can also move diagonally. Thisis the same way how scientists work. They try to observe more and moreand conclude laws. Then by observing more, modifying their laws or rules.We humans have large opportunities to observe as we are gifted by ourperception of seeing, touching, hearing, speaking and taste. And above all,we have the ability to think. We are gifted with intellect which we callintelligence. Now going back to chess example, what might have happened isthat, God made universe as a chess game and he is not allowing us to see it

directly, but instead we can see it from an edge. We try keep looking againand again and when we observe something strange we start to analyze it andimprove our old law. But all we have to do is keep looking and asking. Rulesof physics tend to become simpler and beautiful as scientists discover newthings. They might seem to be more complicated but they are actually takingelegant and beautiful shape. And by beautiful I mean that they can beexpressed in very small and simple mathematical expression. Einstein usedto ask himself that If I were God, how would I like to make universe. Andthen he used to say that God must create universe very simple and elegant

though its consequences may appear to be complicated. So he stronglybelieved that universe must obey a single one inch mathematical law. Hetried 30 yrs to find out this law but could not find it. Now scientists havecome up with a very profound unification theory called string theory whichmight be able to give explanation of everything happening in nature.

Some scientists also believe that finding the laws of nature is likepeeling onion skin. They peel skin of onion to look deeper and deeper whichmeans they go deeper and deeper to find out ultimate truth. Every time a

skin is removed, a new law appears which appears to be more accurate.

These laws are the unification of the reason behind the lots of differentphenomena occurring in nature. Thus one law may be sufficient to explainlots of natural phenomena. These attraction or repulsion is measured


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quantitatively using mathematics. Thats when mathematics plays a vitalrole. Its the tool to measure characteristics of natural laws.

Scientists so far have discovered four natural laws who are supposed to

govern whole universe; from stars to planets to us. They are Gravitaionalforce, Electromagnetic force, Strong nuclear force and weak nuclear force.Gravitaional force is responsible for the formations of large spherical starsand planets. Electromagnetic force is responsible for most of the phenomenahappening on the earth and for all the major scientific inventions likeelectricity, tv, refrigerator, computer etc. Strong nuclear force is responsiblefor holding together inter-nuclei particles. And weak nuclear force isresponsible for the radioactive decay.

The first law of physics was Newtons law of gravitation which wasformulated by Newton in 17 th century. This law says that two objects whoposses mass are attracted to each other by some force called Gravitationalforce. The force between two massive objects is directly proportional to themultiplication of their masses and inversely proportional to the square of distance between. It means if I have two balls of certain matter and I amtrying to calculate the amount or extent by which they attract each other,then that value will be given by the expression:


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This means, if I double the mass of one ball, then the force between themwould also double; and if I twice the distance between them, then the forcebetween them would decrease to times the earlier value. This law can be

seen everywhere in nature. Remember the story of apple falling on tree,when Newton becomes curious and asks himself why this apple felldownward. This force is no ticeable in large masses and thats why peoplesdont attract to each other like earth attracts apple. This is the reason whywe stay on ground. So at each moment we are attracted by everyone aroundus, but we dont observe it because gravitational force is quantatively verylow. All stars, sun and moon attract us, but the force comes out to be verylow because our mass is very low and our distance from sun and stars is veryhigh. Similarly we are attracted by earths gravitation pull and in this case

since the distance between us and earth is very low, this force workssignificantly and we fell attracted toward earth. At the very same time, if weare sitting in a classroom with lots of classmates around us; we all attracteach other and we are attracted by gravitational force of tables, walls, pen,pencil etc. But we cant observe it. We dont see ourselves attracted towardswall. This is because our masses are very low, so gravitational pull becomes


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very low. This is the reason why earth attracts moon and why sun attractsearth. This observation gives us the idea that the gravitational force workson larger scale which is the reason why planets and stars are large. We needthis calculation of this force to send satellites on space. This is the first

unified law, because it unifies the reasons behind lots of phenomena. Nowon e interesting question comes in mind: If earth attracts apple, why doesnot it go inside the ground? Why does it stop on ground? Why do we stay onthe ground even when such powerf ul force is attracting us?

The answer lies in the second most fundamental law of nature orforce of nature known as electromagnetic force. Its combination of electricand magnetic forces because both forces are codependent of each other. Itssays that two charges attract each other or repel each other on the basis of

their property of being negative or positive by a strong force (strong incomparison to gravitational force ) which is proportional to the their chargesand inversely proportional to square of distance between them. This can beexpressed mathematically as,

Where k is the constant of proportionality. Here, we would need to definecharge too. A charge is the property of a matter due to which it attracts orrepels other matters with charge. This charge can be positive or negative.Two positive or two negative charges repel each other while two oppositecharges attract each other. Electrons are supposed to be of negative chargewhile protons are supposed to carry negative. So at sub atomic level, smaller

particles or subatomic particle carry two properties: mass and charge. Due tomass we feel gravitational force while due to charge we feel electromagneticforce. Electromagnetic force is very very strong than gravitational force.Electromagnetic force happens in smaller scales. This is the responsible forcefor all the natural phenomena happening in nature. This force is responsiblefor human existence and for existence of all animals and plants. Since thisforce is a smaller scale force, we humans, plants and all other animals are


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smaller than planets and stars where the driving force is gravitation. Thisforce does not cause any significant phenomena in larger bodies because incase of large bodies, their whole charge which is sum of all positive andnegative charges turns out to be zero or neutral

. This force is responsible for one of the biggest achievement of ourscientific history: Electricity. And all the modern science equipments like tv,refrigerator works due to this force. This force is responsible for friction dueto which we are able to walk on surface and due to which all vehicles run.Natural phenomena like rainbow, lightning etc happens due to this force. Allthe chemical reactions, which are basically interchanging of electrons tomake other compounds and elements, happen due to application of thisforce.

Now if we come back to our actual problem which was If earth attractsapple, why does not it go inside the ground? Why does it stop on ground?Why do we stay on the ground even when such powerful force is attractingus? The answer would be due to electromagnetic force. When we standon the ground, the earth certainly attracts us but at the same time, our legswhich are in contact with the surface interact with the surface in a magicalway. When we stand on the ground, the atoms on the outer surface of ourlegs interacts with the atoms on the surface of earth. They are so close to

each other that electromagnetic force comes in the power. These atoms andtheir sub atomic particles collectively interact with each other in such waythat they create a repulsive force. Now since electrons and protons of surface interacts with the electrons and protons of our leg, there should befour interactive forces, force of attraction between electrons of surface,protons of legs and force of attraction between protons of surface andelectrons of legs, force of repulsion between electrons of surface andelectrons of legs and force of repulsion between protons of surface andprotons of legs. But the resultant of these all four interactions comes out to

be repulsive in nature. And it turns out that these electromagneticinteractions create a repulsive force which is equal but in the oppositedirection to gravitational force. So surface of earth pushes us upwards in thesame amount of force with which earth pulls us inwards. So the total force iscanceled out and we remain on the ground.


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By giving these examples and nature of the natural laws, I am trying toshow how beautifully and elegantly our world works. Only two mathematicalexpressions are there to explain lots of mysterious phenomena of nature.And one interesting thing is here that these two laws are very similar to each

other mathematically.

This tells us how beautiful our nature can be if we try to figure out what ishappening out there and why is it happening. It becomes interesting todoubt and then to find out. What we need most importantly is to widen ourthinking spectrum and start doubting things. We need to see more to findout hidden beauty.

Knowing the names of the things alone does not mean anything. We

dont learn by just memorizing names. Let me explain it to you. When wetalk about a flower, if we just know the name of that flower, we dont knowanything about the flower. We just know the name given to it in thatlanguage. Knowing the flower means lot more. And to learn more, you needobserve the flower. You need to be curious about the flower and start usingimagination to find hidden beautiful details in it. One can imagine a complexbut elegant web of cells inside the flower; cells collectively forming tissuesand then organs. Every organ system has given a structured work. One canthink of how flowers interact with nature. Flowers are evolved with colors

because they need to attract insects towards them for the reproduction.Different flowers evolved with different shapes and colors so that it becomeseasy for insects to differentiate between them. Also it tells us that theinsects have ability to see colors. It just need to think differently and learningfrom the very basic fundamentals.


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History of UsNow, I would like to take you on a tour of our history. And by history, I meanhistory of everything in the universe. I mean history of large galaxies, stars,our solar system, earth and us. I think its very important to understand the

process of formation of universe to understand the core meaning of ourlives. It tells us from where we started, where are we, and where are wegoing. It would help us to connect with scientific laws. We thus need abroader history of universe. This would reveal a sense of unity amongeverything around us and put meaning to almost everything.

Lets travel back in time to 13.7 billion years ago. There was nothing. Imaginethe darkest silence. There were no existence of space and time. Everythingwas meaningless because you need to have something to give meaning. And

then suddenly universe appears with a huge blast. This is called Big Bang; thebang which started the universe. This universe is very very small and highlydense. It contains tremendous amount of energy. There are not even atomsin this universe. It is vibrating with lots of energy and it is expanding veryrapidly. Within a fraction of second, fundamental forces of nature appears.The same forces we talked earlier. Due to these forces energy started toform matter in the form of protons, neutrons and electrons. Still there are noatoms in the universe.

Around 400000 years after the big bang first atoms appeared in the formof hydrogen and helium: the atoms with lowest mass. But still this universe ishighly dense. Small clouds of hydrogen and helium atoms started to form.This happened due to gravitation force. Since universe is dense, gravitationforce is more powerful here. Due to gravitation force, the density of hydrogen-helium clouds start increasing. These clouds became denser anddue to high density they started attracting smaller clouds towards them tomake even more dense clouds. Due to very high density, these atoms cameso close to each other that their fusion occurred. This was very spontaneous

and a lot of energy released. This was our first star. After around 200 millionyears after the big bang, lots of stars began to appear.

When a star dies, it releases lots of energy and due to this energy,temperature increases a lot too. So in these highly volatile conditions, thenuclei of hydrogen and helium started to fuse and due to their permutation


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and combination different nuclei appeared. These nuclei have more numberof protons and neutrons in them. Then at the same these nuclei attractedrequired number of electrons to neutralize their charges and hence newelements started to appear. First, elements with small masses appeared then

elements with large mass began to form. Small clouds of elements started toform around stars. These clouds of elements started to merge with eachother due to gravitational pull. Different elements started to react chemicallyto form different compounds. At this time our universe was highly chemicallyactive. When these clouds of elements and compounds make sufficientlylarge volume, we call them planet. Our solar system was formed about 4.5billion years ago.

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What is Learning and Why is It Important