# Mathematics.. A discovery or an invention?

I believe the primary responsibility of a BI (Business Intelligence) practitioner is to comprehend and quantify a phenomenon through data and make it accessible for decision-making. Understandably, numbers form an important part of his life. Numbers and more fundamentally Mathematics has long intrigued me. Is mathematics a product of human thought or is it a reality that humans stumbled upon? While there have been many perspectives around this question, I’ll cite the perspectives of 2 great physicists. In 1960, Eugene Wigner articulated the unreasonable effectiveness of mathematics in Natural sciences, reflecting the deep connection that he observes between sciences and mathematics. Albert Einstein held the following opinion –  ‘As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.’ While answering my own question is certainly beyond my capacity or imagination at the moment, this blog is my attempt to find those mathematical laws and crucial numbers (those I have come across) that have evolved out of reality. In a way, all of us experience these or use these for our decision-making. Again these laws and numbers are purely empirical.

Number 7 is the magical number when it comes to decision-making.  Originally conceived by cognitive psychologist George A Miller, this is referred to as Miller’s Law. Miller articulates that when it comes to humans processing information, the number of objects an average human can hold in working memory is 7 (range is between 5 to 9).

The bell curve (binomial and normal distribution) is an effective way to describe and imagine a random process. The empirical rule or the 68-95-99.7 rule states that in a normal distribution, approximately 68% of the data falls within one standard deviation of the mean, 95 % of the data falls within two standard deviations of the mean and within three standard deviations of the mean, we should fine almost (99.7%) the entire data. There are many contexts, where in we could see this at work or made to work. In his theory – Diffusion of Innovation, Everett Rogers places 34% of the community as the early majority and another 34% (68% total) as the late majority. A more personal example could be its association with Performance Evaluations (see Vitality curve) in an enterprise. Performance evaluations in many enterprises will most likely recognize no more than 30% of the group as high and low performers placing the remaining 70% close to the mean i.e. those who perform well to meet expectations.

The 80-20 rule or the Pareto principle is a commonly used one to explain cause and effect. Originally conceived by Pareto in 1906 when he observed that 80% of the land in Italy was owned by 20 % of the population. We could observe this phenomenon in business as well wherein 80% of the business is most likely to come from 20% of the clients.

Another concept that was born out of breakthroughs in technology and communication is the ‘six degrees of separation’. Per this concept, the social distance between any 2 random people in this universe is approximately 6 i.e. through my friend I can connect to his friends and when I go down this chain 4 more times I’m most likely to reach most of the people in this world. When we say ‘ It is a small world’, we exactly mean this. Again in an enterprise, there will most likely be no more than 6 levels of hierarchy between any employee and the ultimate decision maker (the CEO maybe).

The last one is the Zipf’s law, which is another curious and a mysterious reality. Originally proposed by linguist George Kingsley Zipf, this law states that given a corpus of natural language occurrences, the frequency of any word is inversely proportional to its rank in the frequency table.  For example, the most frequently used word ‘the’ is used almost twice the number of times the next frequently used word ‘of’. It is mysterious because, this pattern is evident in the population of world cities as well.