oh for heavan’s sake! .. the cursory glance at Maria’s post shows she has pinched the thought in my mind, regarding Lord Acton’s dictum. Not really, I wasn’t really inclined to write about power in the normal sense, but I will take a stab. I choose a different path. As I’d indicated elsewhere, the third R of education interests me. Not something Ramana, would have suspected when he suggested this most arduous of topics.

I am inclined to elucidate on something called the power law. It is a term to describe a general mathematical relation, where a quantity depends on another quantity raised to the power of some constant. Such a relation is said to follow the power law. The law of gravity

**G = **SomeConstant** x**** R ^{-2}**

can be thought of as following a power law. So this means that farther you go from the sun/earth the gravitational pull will fall very quickly. Another manifestation of a power law is that there are many more towns with smaller populations than towns/cities with larger populations.

However it is useful to know of the existence of this sort of relations, as many entities in nature are subject to power laws. This law (it various strength or power) rules over many things. This is the reason I write about the power law, as an awareness of this law gives one the power to understand and handle situations which otherwise would be mysterious and hence upset calculations. Pareto’s 80/20 rule is also a power law, in form, though it is often explained in a colloquial manner. Summed up snappily by ‘the vital few and the trivial many’ whereupon we obtain a perspective of power holding, if not power.

An interesting aspect of the power law (or even Pareto’s law) is that it is scale free. Which means, if you take the 20%, even within this, 80% will have relatively small impact vis a vis the 20%. That is 20% of the 20% (ie 4%), will make up 80% of the 80% (ie 64%) of impact/effect. This can be extended indefinitely, but the next step means that the 1% will be worth about 50% of the whole.

{ If you’d like to know more about Power laws, Pareto etc…. here is a good explication. Apparently, each additional equation included in a book for the general reader, will halve sales. I hazard loosing interest very quickly by including the equation above. This also seems to be an illustration of a power law, but not really, it is even more difficult to picture. As an aside the current pandemic, isn’t guided by the power law, but by an even more beastly mathematical relation the *exponential*, which decent people shouldn’t have anything to do with, but unfortunately still are affected by anyway. But that is not for this post.}

I feel that the other other Friday bloggers will have a more engaging, but less mathematical perspective, and surely as interesting a view to offer: Sanjana, Padmum, Raju, Maria, Shackman , Ramana and Conrad.

rummuser

Oct 10, 2020@ 19:32:21It does not surprise me but, it certainly stumps me. The third R unfortunately has always been my weakest and I had to take special lessons to get by in Business School where we had to use Statistical Models!

https://www.rummuser.com/tribute-to-a-great-teacher/

Conrad

Oct 11, 2020@ 04:59:19Srinivas, you are so mischievous in your thinking. I had not thought in terms of the powers of numbers when considering power and my mind went to those regions first, that of physics but not to math per se. I liked how you inched the reader to perilous precipices without endangering anyone’s sanity.

Maria

Oct 15, 2020@ 04:05:47I have to admit, my friend, that the third ‘R’ fills me with terror. Okay, ‘Rithmetic is good, but the science part of maths? Oh, man! Keep it far away from me. Sorry about Lord Acton, but great minds and all that. I suppose I really should try to overcome my maths phobia. It is a nuisance in so many ways,