Personal Assessment – Maps Could have Helped Me in My School Studies

 Personal Assessment – Maps Could have Helped Me in My School Studies

Perhaps my learning is visual, at least not an insignificant part of it. The text books we were prescribed in my schools (between 1965 and 1970) had very few maps−for Asoka’s or Akbar’s empires, the zoom-out view of Indian rivers, the Cauvery delta region−perhaps two per book on social studies (history and geography) and science. 

Each map was congested, for example, the Indian Railways Train Guide showing details of railway lines, though only major stations named (when I was about seven years old, I thought there were only seven or eight stations that the then Janata Express, plying between Madras Central and Bombay VT, would stop at. The reality was it was many more than that (including Sholapur, where my mother would buy me ice cream, at about 11:00 in the morning!).

Had more maps been included, families of many students might not have been able to afford it; my own family had to sit down and seriously budget for the books for me and my brother(it might be so even now for at least some families, I am blissfully unaware!). I remember some of my cousins were handed down my books. That was my extended family then, in the 1960s.

We could not and did not learn, in any serious way, from which point River Ganga and River Yamuna (Gangotri, Yamunotri) started to flow (we did not worry about River Saraswati then, though we studied about Indus Valley Civilization!). We knew they all started somewhere in the Himalayas. Enough; why because a more detailed map would have made the books more expensive. It was affordability, affordability and affordability, of the parents.

To understand why maps are important, one has to project the map of the world, or the globe on the screen and ask the students why the flight paths of any aircraft, even the one going between, say, Madrid and New York (along almost the same latitude) is not a straight line (on the flat map) between the two cities, or not nearly along the latitude of the two cities on the globe. For Madrid and New York, the flight path would be concave towards the south.

The latter of the two demands an explanation. And, mathematics comes to the rescue, and the new term to be used is the Geodesic. A Geodesic cuts the earth sphere (which is actually an oblate spheroid, but a sphere is a good approximation for our purposes, but not for precise determination of where a satellite upon return would splash down, targeting ICBMs and such). The necessary point on the sphere of the earth is the centre of the earth. The other two points are the points on the surface of the earth, taking Madrid and New York City, say. These three points define the geodesic (now you would understand that it is the geodesic and not a geodesic when two points on the earth’s surface are the reference points), and more importantly, there can be only one geodesic for one set of any two points on the surface of the earth, excepting the combo North and South poles (any longitude is a geodesic!).

Along the geodesic that includes two points, the shortest/longest distances always, always,falls along that geodesic. Therefore, the flight path of a plane traces the shortest distance between two points. The flight between San Francisco (37.77o N) and Tokyo (35.68o N) “often travel close to the North Pole”. 

This, sailors of long ago knew, not in terms of analytic geometry but through empirical observations. That too was science, just an aside.

I would like to go beyond what the heading suggested, only about maps.In high school, we did some table top experiments and understood that light travels in a straight line. Strictly speaking, it is not so, we have nowfigured, unless light travels in a single medium without a boundary and  the medium is (nearly) unaffected by gravity.

Why are the angles in reflection the same? It is because, as we understand it now (science is always provisional!) the time taken for a light ray to travel from point S to O after being reflected takes the shortest time among all the other paths (actually, it is only very highly probable, and not definitely, as Richard Feynman figured out using path integral formulation that is based on the Lagrangianformalism). The same formalism holds the reins for refraction, with the additional parameter, Refractive Index, of the intermediate medium included.

The next time anyone hears something like light bends in an intense gravitational field, recognize that the same can be said that light travels between two points in a straight line, if, and this is the big if, the curvature of space time is taken into account. Or, it may be said that light travels, perhaps more elegantly, between two points in the shortest time! At the Schwarzschild radius from a Black Hole, time stops! Go figure that (use Schwarzschild coordinates)!

Why did I bring in this here? Merely to indicate that one can take an idea from a particular field (spherical geometry) and can understand it on a wider canvas, like optical geometry, but beyond a plane! Maps in text books could show the way for developing different perspectives. I could have understood better much of what was taught me in geography (particularly, the names of European countries and their capitals!) and history!

Raghuram Ekambaram