Talk:Mimolok
People often claim that they're not good with numbers. What does this mean? Usually it means that the grunt work of adding (counting), multiplying (counting), dividing (counting) and subtracting (counting) strings of digits is not really their cup of tea. No wonder, it's laborious and boring - the real meaty fun of mathematics is in the logical jamming, in spawning a universe of truths from a couple of basic definitions (and maybe a paperclip). Unlike counting beans, mathematics is a creative activity; number is important, but only as labour-saving shorthand so more interesting stuff can be dealt with.
I'm willing to wager that if you show such a person even the most insightful, interesting, brilliant mathematics book, they will assume that it is beyond their ability to understand. They will assume this because they couldn't remember the 'LONG MULTIPLICATION' dance, or how to work with 'FRACTION NOTATION', or some other algorithm they've been told to remember in place of getting the logical sense of things. They will see the numbers, the a's, the b's and the plus and minus signs they have only been given the slightest clues about, and politely tell you to take your book somewhere else.
As stated elsewhere, the reader will not see anything they already categorise as 'mathematics', unless they have an existing interest in such things. They will see weird symbols heading off in all directions, soon, patterns will emerge, hey maybe this says something...maybe it's just a game?
Nothing in this book will be stated without proof, aside from the most fundamental definitions. We will begin our journey with something like 3 definitions that allow addition to occur. You might think that addition is fundamental enough not to warrant such wrangling - but without this care, a property as basic as A + B = B + A eludes formal proof (as opposed to verification with specific cases). This is all before we've encountered any numbers apart from 1 & 0 (if you want to call them that) - so there's not much to verify with anyway...logic is the only recourse! It turns out that a particular logic hammer can be used over and over in order to churn out great meaning from the simple definitions...with a minimum of effort. We are in good stead from the very beginning - multiplication will be the next target and then we can start talking about getting some more numbers.
I recall that this hammer was only fleetingly introduced towards the end of my high school years, the numbers, on the other hand, were well established before I started school! Maybe there are cognitive-development reasons for getting the order backwards? Perhaps children can relate better to the concrete, only to deal with abstracts at a later age? What if shackling mathematics to the real world at an early age is stunting everyone's mathematical growth?
What if they never get to play the awesome creative game because they lost interest in counting the beans?
