A little kid, who does not know what 'color' is, comes across a bag of

*colorful*billiard balls. what would be his reaction? His childish curiosity drives him towards the bag. He is attracted by the appearance of the balls...I mean, the*colors*, though he doesn't know what it is....Most children stop there. But, imagine, an extraordinary( hypothetical, if you feel so) child, who can proceed further. The next thing he would do is, look for

*similar*balls (balls which look*like*each other) The child has a way to tell whether two balls look*like*each other or not, by visual inspection. (looking*like*each other in our language means same*color*).Next, the child can divide the bag of balls in to groups of

*like*balls. Every pair of balls within a group would look*alike*. Hence, each group can be represented by a single ball. If the child is given new balls, he can easily put them in to respective groups. Or, if it doesn't look*like*any of the group representatives, it makes a new group.Now, he is close to defining

*color.*The representatives of each group are not balls, they are*colors.*He can name each group at his will. This is precisely what man did, over generations. The names he gave were*red blue green et al.*Now, a formal look at the procedure adopted by the child. An important comment to be made at this point is about the way the child decides if two balls are

*alike.*If balls 1 and 2 are*alike*, and balls 2 and 3 are*alike,*inevitably, balls 1 and 3 will fall in the same group. Hence, they should look*alike.*Formally speaking, his definition of*alike*should be*trasitive.*By using '*two balls look alike',*and not '*one looks like the other',*I have already meant that the*like*is*symmetric.*A little more thought will convince you that the*like*needs to be*reflexive*as well, for successful classification. Thus, it gives a reason to the mathematical definition of*equivalence relation.*Formally, those*groups*arising out of the equivalence relation are called*classes.*Once the classes are made, a mathematician may do various things with his classes....order them etc.This is how most of the seemingly undefinable terms like

*color, size, mass, charge, cardinality, etc*are*defined(?).*The purpose of this blog is to express my thought flow, which at the moment says,

*mathematics is a way of thinking, formalized.*
A very gud one.....cheers!!!!

ReplyDeletenice thoughts!!but can a machine do it??

ReplyDeleteOops, seems like my comment didn't appear the last time i posted it.

ReplyDeleteGreat one anna, keep them coming!

Needless to say, Mathematics is the Language of all sciences! :)

nicely built up !! go on..... we may now define a machine

ReplyDelete