You know how people who are bad in mathematics or logic always try to hide their dumbness by classifying mathematics as a subject of theoretical and academic pursuits only. “Oh, I am more of a creative person” , or “Oh I am more right brained”. The best one is “I am more of a people person. I understand people better than numbers. Numbers are just theory. People are more real, interesting and diverse due to their varied personalities”.
Well, sir/ma’am, here is some news. Numbers are no less “people” than “people”. You don’t believe me? Alright then, take this journey with me.
So let’s see. At beginning we have the “whole” numbers (or the “natural numbers”). Nothing complicated about them. Simple minded folks like 1,2,3,4… Easy to add, subtract. Easy to understand. Just like that perfect boy who takes all his lectures regularly, very dedicated to his family, job, friends; very dependable; easy to hang out with; has clean ideas of fun like watching a movie or a travel with family; keeps his teeth and shoes shining all the time and can enjoy a fine wine every now and then. Some are ‘even’ and some might be ‘odd’ but overall kind of simple minded.
Then comes “fractions”. Now things get tricky. Well, somewhat. I mean, they are not as clean as “whole” numbers but you can live with them or at least you know the ones you can live with. A “1.5”, sure I can take it. I know how to understand that. A “1.33333…”, mmm, that’s dangerous and best to be avoided. The point is you know the kinds you like and the kinds you don’t and its easy to make the choice.
For every alpha there is an omega. For every good, there is evil. For every God, there is a devil. Life works on the principles of ‘duality’ and hence for every “positive” number, we a “negative” number. The dark side. So you have a -1,-2,-3…as well as -1.5, -1.25, -1.33. Nobody likes negativity but its a hard fact of life. The only was is learn to deal with it.
It’s easy to understand good or bad but then what happens when good becomes “irrational”. Yup, someone can be good but “irrational”. Thats where we talk of “rational” or “irrational” numbers. Mathematically speaking any number that can be described in the form of p/q where p and q are whole numbers (with a minor exception, which we will see later), it is a rational number. And anything that’s not rational is irrational. I mean, what would you say if I tell you that you can have a perfect whole number defining one side of a right-angled triangle and the exact same number defining other side but you just can not find the exact length of the third side. Pretty irrational, i would say. Similarly I give you a circle. You can see it’s circumference and measure it. You can also see that it’s diameter is a finite length. Yet you can not describe their ratio. Man, what has the world come to? How irrational can you get? As if positive and negative was not enough, now we have rational and irrational too?
Between this positives and negatives, sits the aptly neutral “0”, the Switzerland of numbers, the arya-putra. No wonder it got discovered by someone named “Aryabhat”. It’s neutrality gives it interesting properties. If you simply hang around with it (add/subtract), it doesn’t change you at all. It takes you for what you are and leaves you as it is. But it keeps its borders open so if you want to merge into it, you will become like it. It doesn’t take sides and therefore can not be used for any divisive purposes. And that’s the exception to rational numbers i.e. q can not be 0.
Alright, so we have all these positive, negative, whole, fraction …whatever. Fine, it’s tricky but it’s all real. One can see and follow these based on geometry. Of course it is, because we haven’t yet reached an “imaginary” number. Try mixing some of these irrational numbers with a negative number and you land in the territory of “imaginary” numbers. You see there is a whole number and when you multiply it with itself, you get it’s square. So for e.g. square of 2 is 2 X 2 and that is 4. Similarly square of 3 is 9, so on and so forth. For negative numbers also, the squaring results into a positive output because you know, two negatives just cancel each one out. So -2 square is also 4. Now reversing this operation is called the square root of the number. Thus Square root of 4 is 2. What would be square root of “-4”? Can’t imagine, right? That’s why they are “imaginary” numbers. Just like that childhood friend that you had but you never had. Just like all those villains whose ass you kick when you are imagining you are the superhero. They are but they are not. They exist but they do not.
Throw in an imaginary number with a real number, and what do you get? ..Gosh, can’t you keep it simple? Of course not, and thats why we have “complex numbers”. Half true half untrue. Real and imaginary. Awake and dreaming. Simple yet complex.
Tired? Oh c’mon. You maybe a people person but haven’t you seen those ‘lone rangers’ who are just happy with themselves? Very hard to read them and impossible to decompose them. Yup, they are the “prime” numbers. They are completely happy with themselves or whatever notion of unity they believe it.
Although don’t confuse the ‘prime’ types with the egoist types. The ‘primes’ are happy with themselves but the ‘egoist’ are full of themselves. Those are called the “narcissist” numbers’ i.e. a number that is the sum of its own digits each raised to the power of the number of digits. See, so full of themselves. Although be careful with the “radical narcissist” types. You never know, you know.
Boy, is their anything called perfect? Well, I don’t know about people but surely numbers can be “perfect” numbers. Beat that now.
And then above all there is the “god” number. The one number that answers everything. The one number that answers the ultimate question of life, death, universe and everything. It took a supercomputer nearly 7.5 million years to compute that and the number is “42”. Why “42”? Well, either you know it or you don’t :)
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