And May Be We Need New Numbers

numbers

I remember the discussion I had last month with my college seniors about what we all mean by being or making something perfect. I was told that there exists nothing like perfect. Its not possible to make nearly anything perfect and its all about the point of view of someone towards something or someone. I made a counter argument saying, what if I decide to earn 100 rupee in next ten days and on the evening of the tenth day I count my collection and it turns out to be exactly 100 rupee,will my statement and the effort I made be not counted as perfect!. Then I had  believe that this argument of mine was also not perfect since it was just according to my point of view. May be there was some other way of making 100 rupee with less effort than I had made in these 10 days. After some more discussion one of my seniors said perfection is like the speed at which the light travels and had to rest my case since in the physical world there is nothing that travels at this speed.

When I came back to my room, my mind was still occupied by all those thoughts and arguments we just had. Suddenly one thing struck into my mind, wait they said there exists nothing like perfection at least in this physical and observable universe, but they also said, perfection is like the speed at which light travels, Tadaa!!! I win . They accepted there is at least one thing which is perfect: “The Speed of Light“. Might be that there is something which can travel fast enough to beat the light.Why not! Truly possible, its just that we have not figured it out yet.But at the moment I can think myself the winner.

 

Now, how does the above talk relates to numbers. Well! recently I have been reading about mathematics especially numbers in books and on the web too. I always thought the maths is all about perfection. If I say “This is one apple“, for instance, the number 1 can exactly represent one apple, no less and no more than one. As I read more about numbers several question started to bug my mind,like what exactly the number 0 (zero) represents, why can’t I perform all the mathematical operations on zero, which I perform on other numbers, for example, dividing the number by itself. I don’t know what exactly the result should be if zero is divided by zero.

Another such number is Infinity.May be its not even a number, but then what exactly Infinity represents to. May be I can think of a number for Infinity; how about the total number the smallest particle, that can exist on its own, in the whole universe. To me it makes at-least to some extant. But then the question arises of the number represented by negative Infinity.What could the negative Infinity represent. Again I rest my case.

As I read further I came across several other numbers like what exactly the 1/3 tells us.0.3333333…... so on. In computers and even in scientific calculations such numbers are sometimes rounded to some value beyond which there number has negligible effect on the calculation. Similarly, the concept of imaginary numbers also occupied some space in my mind.

And then I came across several mathematical constants like the Pythagoras’ constant √2, the Euler’s number e, and the most talked one: Archimedes’ constant π. I am sure every one has had an encounter with these numbers. It is the constant π which took a lot of attention of mine. A fun fact about several mathematical constants is that they do not even have an exact value; for example, the exact value of π has not derived yet. The value of π has been calculated to several hundreds of thousands of decimal places, but no exact value has been derived so far.  Although, there are several mathematical formulas present to to calculate this constant, none of them has been able to give some exact value. All the mathematician and scientists do is just use its value up to a significant position.

Now, when I look back on to these numbers and try to find the exact values for them, it looks like I am trying to square a circle. My mind then forces me to think whether the numbers that we use are enough to represent everything. May be not. May be there is a need of another set of numbers which can accommodate all these mathematical constants. It might be possible to have a number which can represent the 100% exact value of π. May be there is some value which can help derive the 1/3 of every number. May be there is something more to the number zero which we have not been able to find so far. Surely, there can be(and a need too for) a whole new concept of new number system other than the decimals or binary or hexadecimals, which can help providing solutions to these unsolved questions.

 

P.S.: Here is an interesting relation between the constant √2 and a normal A4 size paper which we use for normal printing:

The lengths of sides of a full A4 size paper have a ratio of √2. Now if you fold the paper from the middle of the longer side, the resulting sides are still in the ratio of √2 and it continues.

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