Expressing Mathematically.

 

These days writing has become a bit difficult for me. It’s not that I don’t write, but I am generally writing about teaching math, and that too mainly about introducing concepts and trying to break them down for teachers, so that students are able to conceptually get it.
One day I could be thinking about algebraic expression, while another day about division. And yet another day about add or subtract, and yet another day about basic number sense. How do we get a sense of numbers? It still baffles me how little kids are able to decode numbers, such an abstract concept. Numbers are something we cannot touch, feel, taste or see, but we still get it that we are talking about one. Kids are able to figure this out even before coming to school. Researchers have done studies on other animals, and have found that they possess some basic number sense. Apparently crows can decipher upto number 3. Isn’t that amazing? Little kids play with dice, and can decipher numbers up to 6. Thanks to the expertise of pattern recognition that we have. They may not conceptually understand a 4, 5 or 6, but perceptual understanding is there. When they come to school we work on this conceptual understanding. They learn the language of math.
Learning the language of math is not only understanding it’s grammar and syntax. It’s much more than that. Through theĀ  digits 0 to 9 and the little decimal, we can create any number in the world that is possible. No combination of numbers is a gibberish. Every number, yes every number makes sense, and represents something unlike any other language in the world. Throw in some operations with the digits, and then see their power. They start making each other. Each number can be instrumental in making another. The digit signifying nothing, zero, sometimes it has power to kill when it’s armed by multiplication operator, while with add, it bites the dust, can’t to a thing to others. At yet another time, when armed with division, the smartest of mind can’t figure out what it does to the other number.
And look at its neighbor 1, it’s powerless with the armor of multiplication or division. It can’t change the number in any way. But still it tends to be a keeper of neighborhood relationships. Armed with the operators of add or subtract, it will immediately take the number to its neighbors. We need such properties in humans also, all over the world.
Come to think of it, zero also tend to be friendly many times. It never mind it’s place been take by another digit for a short cut representation. For example, 100 and 30 and 5 can be written in short cut form as 135. Have you ever seen zero raise a hue and cry about it. It sacrifices being written at three locations, but it never complains. It’s another matter that we totally forgot that we have snatched it’s place, and that creates a lot of problem for our kids, because our students don’t know that we took away it’s place for a short cut.
Zero is friendly many other ways. Let’s think of another number 1035. No digit has taken hundreds place yet. Zero doesn’t mind. It says, you could put me there as a place holder, so that everyone known that 1 is a thousand, and not a hundred. Imaging if zero was not cooperative, how would we have distinguished between a 1035 and 135?
Have you ever thought about the size of smallest particle, or the size of a microbe, an ant, earthworm, dog, zebra, elephant, dinosaurs, earth, sun, solar system, milky way or the universe? Guess what, these digits from zero to 9 can combine together to tell you that, and that too in one straight line and not scattered all over the place. And they are only ten of them. Let’s count the decimal in, the four main operators, the fraction bar, the percentage and the equal to sign. It still makes only 18 symbols. These are the ones that we tend to use in our daily life. Only 18, and they take care of all our financial expressions: How many people are coming for dinner, how much to cook today, how much water, how much milk and sugar in tea, how much money to take out to from the bank. Did she get the fair wages, did I make a profit or a loss. What fraction of the wealth is mine when we divide, how many litres of petrol is needed to hit that far. It’s an endless list. But look at the power of these 18 symbols. Add a few more to them, and the mathematicians write equations for nature. When alphabets start collaborating with digits and operators magic happens… We almost start to feel that we are getting close to the key to understanding nature. It might be a very long path, but these ten digit in collaboration with some others seem to hold this power of expression within them.