05 February 2014

The bend in the breadthless length



A line or rather a straight line is the shortest distance between two points.  That’s conventional wisdom.  Mathematicians would call it ‘geodesic’.  In the seventh grade geometry class we were told it is made of an infinite number of points.  Analytical geometry, if one got that far, would contend that it is ‘a set of points whose coordinates satisfy a given linear equation.  I like the Euclidian description best: ‘a breadthless length’. 

A few days ago my father had told my sister that her ‘little brother’ was a ‘Point A to Point B traveler’.  True.  If I have to drive, I factor in time, possible traffic issues, the stated needs of fellow travelers etc.  I contend that the problem is with the brief.  If I am told, ‘it’s all open-ended’ I will factor that in too.  I am not averse to deviation from ‘Plan’ as long as deviation is scripted in clearly.  My father’s statement got me thinking.  And remembering.

I remember a wet evening from more than 20 years ago.  Seven young boys were hiking from Horton Plains to Belihuloya.  That’s a 20 km trek if I remember right.  It rained most of the way from World’s End downwards, through two estates, Nagrak and Nonpareil.  All of us were carrying backpacks, the weight of which could be imagined considering we had camped for several days on the plains.  One had greater energy reserves.  Jayantha Jayman, spurred on by a mix of enthusiasm and perhaps misplaced sense of solidarity, went ahead of the pack.  Apparently someone along the way had told him that there was a bus leaving Belihuloya for Colombo at a particular time.  He wanted to get there and convince the driver to wait until his friends caught up.

Now Jayantha had spent some years out of the country and probably lost touch of things Sri Lankan. He was optimistic.  Very. We found that he had scratched some messages on the path detailing his intent.  The rain and a couple of tractors had all but obliterated his story.  We did catch up courtesy of a tractor-ride that gave our tired limbs some rest the last kilometer of the journey.  When we got off, we saw young Jayman making his way through the tea bushes down a hill.  We didn’t know what he was about, so we asked. He told us about the bus. 

‘What’s that got to do with you going into the bushes?’ someone asked.

‘I am going in the direction of Belihuloya.’

We burst out laughing.  He was peeved.  He was doing what he thought was best for his friends.  The shortest distance between two lines in the hills, in terms of travel-time, is not a straight line and this is ancient knowledge.  That’s why roads hug hills and more or less follow the contours.

There’s another Point A to Point B story that I remembered.  My older brother, Arjuna, who was one of the most talented young chess players in Sri Lanka in the early eighties gave up playing competitive chess after he ‘discovered that the shortest distance between two points is not a straight line’.  He claims chess taught him this.  This is his story.

Suppose you have just a bishop and knight and the opponent has no pieces on the board.  You have to use the two pieces supported by your king to checkmate the opposing king.  There are two points on the board where this could take place; you have to drive the enemy king to one of the two corners of the board which has the color of the squares your bishop controls.  Thus, if it’s a dark squared bishop that you have, the king has to be driven to either of the two dark squares (chess players would know these squares as a1 and h8).  Here’s the rub: you cannot push the enemy king across the board, rather you have to drag the king along the perimeter.  In other words, unless fortuitously positioned, you have to first drive the king to a light squared end before you can push it to the dark squared end.  It’s not a straight line.  My brother drew a philosophical lesson from it.

Eminently applicable to many life situations.  It is impatience, arrogance and ignorance that persuade us embrace straight-line logic as it were.  But as Euclid said, we forget often that even the straight line is ‘breadthless’.  It can leave us breathless, as it would have Jayman had we not stopped him, and for quite the wrong reasons. 



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1 comments:

Anonymous said...

Interesting.