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WHY DO WE MULTIPLY FROM RIGHT?

Why do we multiply from right to left?

Multiplication is one of the arithmetic operations that we all use to study in our early classes. It makes our calculations easy and fast and helps us in finding patterns hidden in the number system. With the help of multiplication, we are able to perform our daily calculations very conveniently.

Going into the method of multiplication and as the title of says: -“Why do we multiply from right to left”? Is this the only way of doing multiplication? Is it predefined in the rulebooks of mathematics? Ahh! a lot of confusions.

Let us first try to figure out the meaning of multiplication. Multiplication as we know it, is repeated addition of the same number into one another. In order to get rid of adding, again and again, the same number or to make the calculations easy, we devised one more arithmetic operation known as multiplication. Through this operation, we can find the sum when a number is added to itself tens of thousands or even millions of times, in a very small unit of time and doing very fewer calculations. (Again the mathematics is fulfilling its need of making calculations easy. Here mathematics is making mathematics easy).

The approach that we follow to carry out multiplication of numbers, is what we have learned from our childhood. Let us understand by an example:

Say we want to multiply the number 32 by 4 :
We first use to write this down in the form like:
Then first multiply 4 by 2  to get 8 and then multiply 4 by 30 to get 120 . And write the answer as .

Now in doing this calculation, what we are performing is multiplying the unit numbers first and then the tens number and then add them together.

On the hidden part, we are using the distributive law.
i.e.,

4×(2+30)=4(2) + 4(30) .

\ \ \ \ \ \ \ \ \ \ =8+120 .

\ \ \ \ \ \ \ \ =128 .

This method now seems natural to us, as it’s been inculcated into deep our minds and understanding.

But we never argued, why do we always use this method of multiplication? Is there any other method also by which we can multiply any two numbers?

Let’s now take the title of the article seriously and raise the question “Why do we multiply from right? Why not from left? Why not from the middle or why not from anywhere?

When we multiply from right we used to decompose the multiplier into units, tens, hundreds, thousands and so on and so forth in increasing order, and then use to the multiply the multiplicand by all of the decomposed numbers and add the results to get the final result.

Multiplication from the left would be the same as multiplication from right, just the difference will be in the order of multiplication from the decomposed numbers and the addition.

For example, for the same question done above, the multiplication from the left would be like this:
Say we want to multiply the number 32 by 4:

In this we first multiply 4 by 30 to get 120 and then multiply 4 by 2 to get 8. And write the answer after addition them together as: 128. .

Now in doing this calculation, what we are performing is multiplying the tens number first and then the unit number and then add them together.

On the hidden part, we are using the distributive law. .

i.e.,

4×(30+2)=4(30)+4(2) .

\ \ \ \ \ \ \ \ \ \ =120+8 .

\ \ \ \ \ \ \ \ =128 .

The approach would be the same, just the order has been changed in this approach. We are using here a property that addition holds, which is a commutative property of addition.

According to this property the order doesn’t matter for doing addition:

i.e., for any given numbers a or b: .

a+b=b+a .

For example: .

2+30=30+2 .

32=32 .

So, there is no difference in performing the multiplication from the left or from the right.

Same kind of approach would be followed in performing multiplication from anywhere in between in the number, and there will be no difference in the solution.

Let’s understand by an example:

Say we want to multiply the number 425 by 3:

In order to perform multiplication from anywhere, we first decompose the number 425 into its units, tens, and hundreds:

i.e.,

425=400+20+5 .

First we can multiply the number 20 by 3 to get: 60 .

Then multiply the number 400 by 3 to get: 1200 .

Then multiply the number 5 by 3 to get: 15 .

Now, adding the results of all we get: .

425 \times 3 =1200+60+15 .

425 \times 3=1275 .

And, in this way, we can perform the multiplication from anywhere in the number.

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Can We Ever Stop Reading?

Human all through the process of evolution has tried to find new ways to communicate. The yearning to convey something to someone has been a very fundamental force driving them. There has never been someone who has in some way or the other not tried to communicate and express themselves. E.g. We go to a mountain, get absorbed and dissolved in the beauty of the mountains and then come back to the usual life. We then try to convey the sense of beauty to someone,  it may be in the form of poems, conversation, story, pictures or any other means. So we try to somehow capture the experience of some extraordinary phenomenon into something fixed.

Some people say that we are social animals and to communicate is one of the most fundamental needs of social beings. Even the most primitive living beings with no developed faculty of thinking like human beings find different ways to communicate. Be it some sounds, some uniform, and special gestures, they all try to convey some meaning or desire to the other.

For humans, this desire to communicate coupled with highly developed cognitive schemas led them to develop various means to communicate. Language and its development still perplex the greatest minds as to how a very young child understands the whole semantics and attaches meaning to words. Recent works by a famous linguist Noam Chomsky has attributed an innate faculty to humans which help him to grasp the rules and nuances of language. This says that with evolution we have the very evolved structure of the brain that can help a person to make meanings. This is a highly complex process as it not only conveys the information in its most crude forms but also convey the emotions, feelings, love which appear to be indiscernible to the scientific paradigm.

In this whole pursuit to develop new means to communicate, reading and writing became the most important tools and method. This not only helped to communicate ideas to proximate places and time but could trespass these geographical and chronological constraints. The importance of reading and writing can never be underestimated. This has, in fact, become one of the major parameters for judging the literacy of humans. The linguists put special emphasis on the whole structure, the correct usage. This can be seen in the extra effort of the teachers in trying to teach the child to write properly. While teaching in one of the schools in Delhi, I saw one of the teachers trying to train a girl to participate in the debate. The way it was happening looked as if the thing that must be debated is not important and the manner and style were only needed. The student was just reciting or repeating the whole thing exactly as the teacher was doing. The student was meekly repeating without any intelligent or conscious thinking. She was not only copying the words but also the expressions and the bodily gestures.

In classrooms, this is also evident in the manner in which the answers are expected in the language papers (or even in the more technical subjects). This can be further seen in the higher education institutes where there is a particular and accepted method of writing papers and answers. In such an environment and approach,  the entire effort of the student is put in trying to imitate the style and adapt to the particular way. Little or no consideration is paid to the thing that is been said. However, In order to bring more content and credibility to the piece of writing, what is generally suggested is to read more and more books and literature around it. This is true not only for the technical disciplines where knowledge of a particular person is always limited and needs more grounding in theories and available body of knowledge, but is also true for the disciplines that are highly subjective, e.g. Psychology, sociology, and philosophy. But what happens in the process of this approach is that the person loses the touch with what is, and tries to bring it in the ambit of the available terminology and experience. This experience is past and therefore many times not true. I insist on it being not true in the sense that it loses the presence and actuality and beingness.

For many academicians and educators ( this is not leaving other people,  but stressing more on this community), this(reading and quoting people) is the only means to earn the daily bread and butter. Apart from that reading more characterizes his whole being, professional survival, and intellectual continuity.

However, in this piece, I would like to ask if such an important and revered act be looked from a different perspective. Can we ever be done with reading and stop it? Can there be a point in life where we feel that now we will see the things as they are and not through the lenses provided by someone else? Can we ever make a decision to feel the things as they are and mark a full stop to the act of reading itself?

This may sound very strange and lunatic to some, as to forgo such a beautiful act of reading which exposes us to so many new things and cultures, be altogether left. But this is what I want to ask here. What will actually happen if we stop reading anything?  This may not be done at a particular or specific time but can anyone at their own convenience and point in life say goodbye to this skill. What will the consequences be?  Will this mean an intellectual death? Will this stop the continuity of the stream of thoughts that we so highly prize? Will it make us any less?

So for a moment, let’s look at this possibility. Why do we want to hold on to the things that we believe in? The beliefs are characterized and shaped by the experience, our own conditionings and exposure. II am here referring to the reading or the literature that I connect or associate with. It could be scientific, philosophical, social. It could be the literature of a particular Person, some ideology or some theory. What is the whole stake of losing it? What is the thing that we lose?

I believe that such an act brings us face to face with the fact that we in ourselves are still empty. Empty in the sense that we are always defined by what we associate with. It could be a community, a particular belief, a situation, an image, a god, a theory or anything that gives us a continuity. And since my whole being requires something or the other to associate itself to, so I constantly need something to maintain this continuity. This continuity is what makes the Me, the I.  So cessation of the activity or the thing that I associate with is not the only cessation of the thing, but of the Me. And in this absence, there is the complete sense of isolation and fact that the idea of me is losing grounds.

Since we have never been in the space where this uncertainty and nothingness is experienced, so this appears like a death. This becomes evident in some of the actions of people( all of us) but especially the ones who want to make the most out of life as they feel that the activities give the life a continuity and therefore a purpose. And therefore I am always active, (activity meaning the escape from what is to what I want it to be). And this brings a tremendous conflict, dissipation of energy and all the misery that we see around us. So we see the social workers, the politician, the educator, and all of the humanity constantly engaged in something and this engagement creates the illusion of the purpose. It could be to create a better world.

So this piece not only concerns with just leaving the act of reading but also the act of letting go. Can we let go with what we have, or is this a wrong question?