- #1

- 18

- 0

Assume,

**x**and

**y**represents occurrence of two distinct actions. Also, assume that

**x**and

**y**are related in such a way that if

**x**occurs 2 times,

**y**occurs 4 times, if

**x**occurs 3 times,

**y**occurs 9 times. In other words,

**y**=

**x**

^{2}

Square is a special case of multiplication. We can say or write that,

**y**=

**x***

**x**.

Now, if we forget about Mathematics in its present form, it is quite easy to understand a fact that occurrence of some action

**A**can cause occurrence of another action

**B**in such a way that

**B**will occur as many times as

**A**occurs. Or in simple Mathematical term, we can write (occurrence of

**B**) = (occurrence of

**A**) or simply

**B**=

**A**.

But it is bit hard to grasp a fact like

**y**=

**x***

**x**. How it may happen that occurrence of

**A**causes occurrence of

**B**as many times of occurrence of

**A**as

**A**actually had occurred itself. It seems like some other thing is also happening apart from

**A**and that unknown thing is influencing the occurrence of

**B**, too.

If we write

**y**=

**x***

**z**and

**z**=

**x**, it also yields same result as

**y**=

**x***

**x**does if we assume z as the occurrence of a third thing in such way that its occurrence is influenced by

**x**, and

**z**itself influences occurrence of

**y**.

So,

**y**=

**x**

^{2}may signify the following fact.

Occurrence of

**x**causes occurrence of

**z**in such a way that

**z**occurs as many times as

**x**occurs.

And occurrences of

**y**is dependent on

**x**and

**z**in such a way that

**y**happens as many times as

**x**occurs if

**z**was not there at all or

**y**happens as many times as

**z**occurs if

**x**was not there.

So, if we find a situation in measurement where we find a relation involving square of something, we can think (as there is no harm in thinking) that may be we are missing one influential factor. And unknown factors drive human crazy :)

Since square of integer is discussed, its worth mentioning viewing square of 1 with different eye. For

**y**=

**x***

**x**=

**x***

**z**, it means if

**x**happens 1 time,

**z**also happens 1 time and

**y**happens 1 time. Well, it is more weird than to understand 3

^{2}=9 with the light of above way of thinking. Though I am not entirely convinced myself, but I think we can view 1

^{2}=1 fact in the following way.

Making relation between occurrence of

**x**and

**y**will involve some sort of measurement. Measurement is just comparing something with some another thing or simply called unit. But before measuring something you need to first observe the occurrence of something. Without first observing something it is hard to be enthusiastic to go for measuring that thing. 1 may represent the very start or basis or unit of measuring of that observed thing. So, we can think that “

**if x=1 then y=1**” may represent that very beginning of measurement.