Why?
Why did I start down this road? I was not particularly good at Math, but I remember enjoying it in my formative years. One reason could be that I used to enjoy rhymes & poems and the multiplication tables just seemed to be more or less similar. Something which you rattle away, keeping rhythm, learning by rote.
My perspective changed through the years, as it with any aspect of life. From learning tables “by heart” , from learning algebraic fomulas, solving theorms, to complicated rules in calculus, to proportions & statistics. But once I was out of the “learning as a means to get marks” phase, it suddenly started getting interesting…
Learning the history and anedotes behind various strides in Math, realising the birth of concepts and their consequence, sparked a lost curiosity into the nature of things. Starting enjoying books by Simon Singh, started following “Numberphile”, dug up multiple math documentaries, all the while relishing someone else’s fun journey through challenges to epiphanies, until I glimpsed upon a juicy one myself…
Why Math?
In most cases, when possessed with an idea, I gladly dive into the deep oceans of Google and Wikipedia to satisfy my urges. But this time I felt, its best to check my bearings, align my direction, perhaps start with few specific questions:
Q 2.: Do animals process math the same as we do?
Q 3.: Could thought/technical prowess improve without math?
Q 4.: Is math an eventuality for evolution?
Q 1. Why did we get Math?
I loved Marcus Du Satoy’s “Story of Maths”. It showed how usage of Math arose from the need to measure fields for taxation purposes, as with early Egyptians. It also seems that long before that our ancestors from the mid palolithic age marked slits in bones (vis Ishango bone) as a means of counting. So our need for counting obviously predates our need for measuring stuff. But why count?..
If I’m a hunter/gatherer, would I need to count my kills? or even my kids? Would it be a means to keep track of things? Its difficult to imagine their situation, working without a notion of unity, duality, singular or plural.
[reaches back to the cave]"Honey, I got 'more' deer, that should be enough".
"Dear, before you leave, remember we have dinner with Ugabooga family today".
"Ok Honey, I'll bring 'more' deer"
"But Dear, 'more' is only enough for us. You need to bring 'more'.. 'more'"
"What do you mean 'more-more'???""
[points to the skulls of the last deers on the cave floor] "That was 'more'" [pats the empty space next to it] "That's 'more-more'"
"Aah.."[starts etching small groovers at the base of his axe-bone] "... deer ... more-deer .... more-more-deer"
"Ok Dear, i'll get more more deer"
[few months later]
"Boy, Get me moh-moh sticks"
"Mother says we dont have moh-moh sticks, we only have moh sticks"
[sigh]"FINE !!"
Soon, as the need for counting increased, ‘moh’,’moh-moh’ would have evolved to ‘two’,’three’ and more symbols to designate larger numbers. But there would have been a need for “comparison” as well. ‘moh’ was inherently smaller than ‘moh-moh’. But if there ‘moh’ set of ‘moh’ then they are larger than ‘moh-moh’. And the need to ‘Equate’ would have arisen from the need to match deers to diners. With enough practice, our humble caveman would have noticed patterns, how two and three became enough for five. How the same patterns applied to deers, sticks, so long you count them as ‘individually’. The more generic the symbol, the more easier the application of pattern.
Now let’s fast-forward by many thousands of years to the coastlines of Nile, flourishing civilisation, lush fields, bustling city, all powered by the fertile banks of Nile. A municipal tax collector is on his way to collect levy from 2 neighboring farmers. Both farmers are managing a usual yield from their farms, managing toiling workers/cattle, meticulously harvesting and storing grain bushels, to be sold at the market. With one minor difference, the 2nd farm is smaller.
"Salutations Officer. Its not easy this time to pay the levy. This whole region has gotten only medium yield and I need to take care of my family, cattle, workers. I hardly make any profit"
"This is becoming a habit Joe. You should be more like Jack, who always pays up promptly. You default on the levy one more time and I would have to take away the irrigation canal to your field"
"But Officer, Jack's farm extends from lane all the way to the canal. [gestures with his hands outstreched] but my land is only at the corner of the settlement border. Surely you see Jack's stack of bushels is much higher than my own. He can pay the levy while able to feed his family"
"He also needs to pay more workers"
"his farm also takes a lot more water. You should increase his levy and reduce mine"
"Hmm .. I have 5 houses to cover today [holds up his right hand with outstreched fingers] so I need to take back 10 talents[holds both his palms fingers outstreched]. I cannot go back to the pharoh with less talents. Joe & Jack have 2 farms in total, so I need to get 4 talents. Any ideas, Scribe?"
"Sire, Perhaps we can count the number of steps we need to walk end to end in both farms. The farm with the more steps, should mean more ground, taking more water, hence more levy"
Counting steps, or covering longer distance with smaller units (fitting generic patterns again), would have been truly a leap of genius. We started ‘measuring’ attributes of objects beyond just tangible objects. Measurement of physical field area evolved from ‘length’ to ‘area’ where the field was comprised of smaller fields of unit length. A unit increase in length meant an increase of smaller areas by the unit ‘breadth’.
meter = Late 18th century: from French mètre, from Greek metron ‘measure’.
acre = Old English æcer (denoting the amount of land a yoke of oxen could plow in a day), of Germanic origin.
Some talented scribe would have started noticing patterns in adding the same breadth over and over again. He would have started noting down these repeated answers for the same breadth (to ease his calculation and to simplify future measurement) perhaps giving rise to the first multiplication tables.
Similar problems to be solved in the local bakery (As Satoy wonderfully elucidates) in distributing bread to dissimilar number of patrons led to the notion of division, where the larger object progressively becomes smaller with each division, but its count increases.
So, arising from the need to solve practical problems, balancing and allocating resources, comparing situations, driven by rising complexities and need to simplify (get to answer in shorter time), lead to a series of steps, patterns, rules and recepies, which eventually became Math.
Q 2. Do animals process math the same as we do?
test
Q 3. Could thought/technical prowess improve without math?
what actually drove the progress? Was it necessisity or curiosity or simply pleasure?
Q 4. Is math an eventuality for evolution?
sample changes
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