An operation is an action done on numbers, such as, counting. Numbers are not only used for counting as one, two, three, etc., but also to indicate sequence as first, second, third, etc.
As numbers are counted they stand for increasing quantity. This may be represented pictorially on a number line, where numbers are placed at equal distances on a line. These numbers increase sequentially from left to right. One may then use this representation to compare numbers, or to demonstrate how numbers may be combined to obtain new numbers.
Numbers may be visualized as sets, or collections of objects. A pile of pennies may be used as a set for demonstrating basic operations with numbers.
The combining of two numbers together is called addition. This may be done by counting a number to the right from another number on the number line. It may also be demonstrated as combining two piles of pennies together.
Taking a smaller number away from a larger number is called subtraction. This may be done by counting a number to the left from another number on the number line. It may also be demonstrated by breaking a pile of pennies in two smaller piles and taking one of those piles away.
Such opertions may help one develop a sense of estimating quantities without having to count each object.
By pairing pennies from a pile one may determine if they are even or odd. Numbers of pennies may also help one develop a sense of relative value, especially when they are presented as different coins. Here are some exercises in this subject for the kindergarten level.
“Numbers and Operations” introduces the basic operations with numbers and how such operations may be executed with skill. That is the sense underlying the word ARITHMETIC (from arithmos number + techne skill).
There is only the human being. And that human being has the potential to be spiritually awakened. God is merely an extrapolation by the mind. There is no higher being or power that sits in judgment over man’s destiny.
Man’s emancipation depends on his own realization of Truth, and not on the benevolent grace of a god or any external power as a reward for his obedient good behaviour. Each person must develop himself and work out his own emancipation.
Do not be led by reports, or tradition or hearsay. Be not led by the authority of religious texts, nor by mere logic or inference, nor by considering appearances, nor by the delight in speculative opinions, nor by seeming possibilities, nor by the idea: ‘this is our teacher’. It is proper to have doubt, to have perplexity, for a doubt has arisen in a matter which is doubtful.
When you know for yourselves that certain things are unwholesome, and wrong, and bad, then give them up. And when you know for yourselves that certain things are wholesome and good, then accept them and follow them.
A disciple should examine even the Teacher himself, so that he (the disciple) might be fully convinced of the true value of the teacher whom he followed.
The root of all evil is ignorance and false views. There must be doubt as long as one does not understand or see clearly. Doubt is not a ‘sin’. In order to progress further it is absolutely necessary to get rid of doubt and see clearly.
Just to say ’I believe’ does not mean that you understand and see. To force oneself to believe and to accept a thing without understanding is political, and not spiritual or intellectual.
Let all listen, and be willing to listen to the doctrines professed by others. Whosoever honours his own religion and condemns other religions, does so indeed through devotion to his own religion, thinking “I will glorify my own religion”. But on the contrary, in so doing he injures his own religion more gravely.
Truth needs no label. It is neither Buddhist, Christian, Hindu nor Moslem. It is not the monopoly of anybody. Sectarian labels are a hindrance to the independent understanding of Truth, and they produce harmful prejudices in men’s minds.
When we label a human being as English, French, German, American, or Jew, we may regard him with all the prejudices associated with that label in our mind. Yet he may be completely free from those attributes which we have put on him.
The love of a mother for her child is neither Buddhist nor Christian: it is mother love. Human qualities and emotions like love, charity, compassion, tolerance, patience, friendship, desire, hatred, ill-will, ignorance, conceit, etc., need no sectarian labels.
To the seeker after Truth it is immaterial from where an idea comes. In fact, in order to understand Truth, it is not necessary even to know whether the teaching comes from the Buddha, or from anyone else. What is essential is seeing the thing, understanding it. If the medicine is good, the disease will be cured. It is not necessary to know who prepared it, or where it came from.
Emphasis should be laid on seeing, knowing, understanding, and not on faith, or belief. One must have (a) full and firm conviction that a thing is (b) serene joy at good qualities, and (c) aspiration or wish to achieve an object in view.
The question of belief arises when there is no seeing (seeing in every sense of the word). The moment you see, the question of belief disappears. If I tell you that I have a gem hidden in the folded palm of my hand, the question of belief arises because you do not see it yourself. But if I unclench my fist and show you the gem, then you see it for yourself, and the question of belief does not arise.
A man has a faith. If he says “This is my faith”, so far he maintains truth. But by that he cannot proceed to the absolute conclusions: “This alone is Truth, and everything else is false”.
To be attached to a certain view and to look down upon other views as inferior – this the wise men call a fetter.
It is unnecessary to discuss metaphysical questions, which are purely speculative and which create imaginary problems.
Discuss those things that are useful, fundamentally connected with the spiritual holy life, and conducive to aversion, detachment, cessation, tranquility, deep penetration, full realization, and Nirvāna.
To measure a distance would be to determine how close or far a location is, such as, the distance of school from home. To measure a size would be to determine how small or big something is, such as, the size of a house. To measure capacity would be to determine how much something can hold, such as, the capacity of a pool. In short, to measure is to determine the extent, size, capacity, etc. of something.
To measure anything we need a unit. For example, to measure the length of a table, we may use span as a unit. To measure the size of the floor we may use square tile as a unit. To measure the capacity of a tub, we may use bucket as a unit. In short, the unit used in measurement is a small but definite amount of what is being measured.
Suppose we want to know how long a football field is. We may walk the length of the field and count how many steps it took. This will give us the number of steps that fit in that length. We can then say that the measure of the field is so many steps. Here a small length called ‘a step’ is the unit used to measure the length of the field.
If we want to compare two lengths then we must measure them using the same unit, and the unit must be of the same size each time it is applied. To be able to compare measurements around the world, we must use the same unit the same way anywhere in the world. Thus, we have standard units of meter for length, kilogram for weight, hour for time, etc. Here are some exercises in measurement for the kindergarten level.
The measurements make the numbers meaningful. It is important to get the sense of numbers in terms of units by measuring as many things as you can, using as many different types of units as you can.
This issue is now obsolete. For latest reference please see:Universe and Awarenessand subsequent issues linked to it.
This issue simply established that we shall never be able to know this Universe in an absolute sense. The two links provided here are better explained by Chapter 3 of the book The Tao of Physics. We shall never fully know what is there through logical associations.
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No matter how much you know, there is always something unknown beyond it. And that is wonderful because that makes one strive farther to achieve a deeper understanding. Understanding, in my view, is bottomless.
It is this condition of never being able to know something in an absolute sense, which I like to refer to as Unknowable. Here are some definitions of unknowable on Internet: unknowable.
TV Mohandas Pai was a Director at Infosys until recently. He is a Chartered Accountant, but his views as a well-informed outsider to the IIT system, are quite relevant. The article was published in The Economic Times.
IITs may become less relevant By Mohandas Pai
The IITs have completed 50 years and have helped build India. They were set up for producing high quality technical human capital for India and have met their objectives. But, as is the character with such institutions, they have not changed with the times and are not providing India with what she now needs. They have remained largely teaching institutions , as they were set up, not transforming into research based, innovation driven agents of change for the India that is now emerging.They seem unwilling and unable to change – overburdened by work, driven by a small vision, starved of adequate resources and owned by an apathetic master. They seem to be in a state of perpetual decline though there are some bright spots, but not large enough to meet the needs of time.Very recently, a Union Minister made a statement that IITs are known for their world class students and their world class alumni, of which he presumed himself to be one but not world class faculty. Partly true, but forgetting that he and his ilk are largely responsible for this outcome. The IITs today enjoy substantial academic autonomy but lack adequate administrative and financial autonomy . The IIT boards and the directors are unable to take any financial decision which they deem fit without the approval of the government . Even for an overseas travel of the director or the faculty, permission is needed. They are subject to austerity measures of the government, a perfect situation to emasculate an educational institution.
The demand for an IIT seat is enormous and has spawned a tutorial industry that earns more revenues than the IITs themselves. This has resulted in large number of students spending up to two years of their youth going to cramming schools learning pattern recognition, forgetting the art of thinking and problem solving knowing that their lives are made once they get entry into the hallowed portals. Today about 60% or more of the intake is from the coaching mandis. This has also resulted in many bright young Indians deciding not to undergo the ordeal and go overseas for higher education. 250,000 of them study overseas, over 110,000 in the United States, about 45,000 in the UK spending about $ 6bn on fees and costs annually, depriving this country of much needed resources for education and talent, adding to the wealth of those countries. The IITs too have steadfastly refused to change. They remain small by global comparison . They are between 6,000-9 ,000 students in size, with an annual intake of about 500 PhDs, and about 1,000 undergraduates.
Overall , the 15 IITs graduate 7000 undergraduates, 6000 post graduates and about 1700 PhDs annually . Sadly only about 2% of the undergraduates go on to their masters and PhD in the IIT system. The IITs hold fast to the idea that by squeezing input they can get a quality output, an idea that has been consigned to the dustbin of history. Increasing the scale and size can give them the diversity of talent, the resources, the ability to have more quality faculty and the depth and width needed for an elite educational institution. Even the current increase in size was forced on them because of social initiatives. Contrast this with China. China today has about 1,000 universities, each between 25,000 to 40,000 students, running fully residential courses, turning out over 50,000 PhDs annually . China may, in the next 20 years, it will overtake the United States as the world centre of higher education.The Top Five Chinese universities , in the global top 50 now, have between 25,000-35 ,000 students and about 7000 PhD students each. China has invested for growth through quality institutions while India has lost out and is oblivious to it. Even in comparison to the engineering education system in India the IITs have become insignificant today. 10 years ago the IITs made up about 10% of India’s engineering output of human capital. Today they are less then 2% and declining further. India currently has about 3800 engineering colleges with an annual intake of 1.2 million, a size to rival China. Yes, about 50% of the colleges are of indifferent quality, some rank bad; but they are offering an answer to India’s youth. About 1,000 of them are of reasonable quality , very many have improved over time. No university or college was founded great, they evolved over time, so there is hope for India that these bad colleges will provide the sinews for India’s growth and answer the need of India’s young.In the meantime, the IITs will live in their ivory tower and possibly become less and less relevant to India’s need as neither are they meeting India’s need for more human capital nor producing the kind of PhDs India needs. What needs to be done to change this? The government has all the answers setting up many eminent committees, the latest of which is the Anil Kakodkar Committee of which the author is a member. The solutions are known to all, the government, the policy makers, the academics and the intelligentsia .
Total autonomy to the IITs, driven by a board of governors with a new vision, accountability through public opinion and transparency. Yet there is resistance to change, from government for the fear of losing control, from some part of academia because they become more accountable and lose the shelter of blaming the government for all ills and for inadequate performance and from some opinion makers who believe that the existing feudal system should continue since they have a disproportionate influence on them.
The best solution is to open up the education system and allow competition, the dreaded word in academics, to come forth. India should revise her educational policies and allow the private sector to set up “innovation universities” granting them all that they need. Full autonomy, academic, administrative and financial to chart their own future. Some safeguards are needed, as this is a public good. A large corpus of say Rs 100 crore, an open merit based admission policy, a faculty compensation policy based on minimum UGC scales and an assurance that they will aim to be amongst the top 100 in the world over the next 25 years. To ensure access to the merited we need a national scholarship scheme which will fund students. India needs to trust the genius of her citizens to create institutions that are world class and not look at them through myopic eyes with suspicion.
India’s future is too important to be left to the benevolence of an apathetic, insensitive government which has destroyed academic excellence over the years, driven her young out and even today shows callous indifference. See the state of our universities today, so many have fallen from the high standards they had, see the state of the Presidency Colleges, it is indeed sad! Most policy makers and leaders have solved their personal issues by sending their children out to get a good education, so they are not impacted by the poor quality of higher education in India. It is the middle class and the poor who suffer, because they love their country more and see their future here; maybe they too want to take flight but do not have the resources to. As the saying goes “Yankee go home, but take me with you.” But will competition work? Yes, it will indeed.
The engineering colleges have opened up, very large numbers set up by political influence and plain bribery but they have served another purpose. Today there is a flight to quality. The bad colleges are dying since students have a choice, they are voting with their feet. The good ones are expanding and seeing greater demand. The market mechanism has worked, not by design but by serendipity. So there is hope. Look at various other sectors today. Bharti has made BSNL redundant and has given us a choice, Jet has overtaken Air India and given us a choice, the power system in Mumbai is still the best, and in education the Indian School of Business has turned our IIMs inside out. The IIMs actually want reform, expansion and are concerned about their future .
Competition and an open liberal environment for higher education will work . India’s best higher education institution, the Indian Institute of Science , was started by a private citizen many years ago and is still the best we have. India’s needs in higher education are too large to be met by the government , they need the genius of India’s citizens to meet them.
