What is the stretch of human mind's imagination?

Imagine that you placed two gold coins on the first square of a chess board. If you kept doubling the number of gold coins for each and every square, how many coins do you think will be there on the last square(64th)? I asked this question in a more story oriented form to my 4th grade kids while I was at TFI(TeachforIndia). When I finally wrote down the answer on the board, hoohs, haahs and large exaggerated gasps followed. I did get what I wanted : got them totally captivated!!(I can promise you how difficult it is to keep them that way for more than 10 minutues) Coming back to the question: 18 followed by 18 zeroes it is!!! 

  

18000000000000000000

Can you imagine that number in your head? I mean I can visualize 2 birds, 5 trees, 10 buildings, a few hundred people, even a few lakhs and crores of money(Rajas and Marans set new records though!). Malcom Gladwell articulates this very principle through the concept of 'Tipping Point' brilliantly through a lot of social examples. His main idea in the book is how little unprecedented things can actually create a social movement and the factors which lead to that critical mass for the movement to explode. To further break it down for a school going child, human mind does not have the cognitive ability to comprehend geometric progressions or in other words, big socially impactful movements(read World Wars, computer, internet etc.)

There are a few other mathematical theories to highlight the same principle(Long Tail, Butterfly effect etc.) but I will focus on one which really appealed to me - The Black Swan theory

 

                                              

The Black Swan Theory or Theory of Black Swan Events is a metaphor that encapsulates the concept that The event is a surprise (to the observer) and has a major impact. After the fact, the event is rationalized by hindsight.
The theory was developed by Nassim Nicholas Taleb to explain:

1. The disproportionate role of high-impact, hard to predict, and rare events that are beyond the realm of normal expectations in history, science, finance and technology
2. The non-computability of the probability of the consequential rare events using scientific methods (owing to the very nature of small probabilities)
3. The psychological biases that make people individually and collectively blind to uncertainty and unaware of the massive role of the rare event in historical affairs

Black Swan Events were characterized by Nassim Nicholas Taleb in his 2007 book (revised and completed in 2010), The Black Swan. Taleb regards almost all major scientific discoveries, historical events, and artistic accomplishments as "black swans"—undirected and unpredicted. He gives the rise of the Internet, the personal computer, World War I, and the September 11 attacks as examples of Black Swan Events.

Black Swan  is an event with the following three attributes. First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme impact. Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable. I stop and summarize the triplet: rarity, extreme impact, and retrospective (though not prospective) predictability. A small number of Black Swans explains almost everything in our world, from the success of ideas and religions, to the dynamics of historical events, to elements of our own personal lives.

My single biggest learning from this is simple - Do not limit your GOALS in life. We have all heard the adage "Nothing is impossible". Maybe, this will give you some mathematical confidence now. None of our past so far is an indicator or predictor to what we can achieve in the NOW. Yes, planning the small steps is important but do not predict the leaps. Maybe, that's why they say " Take a leap of faith!!" Who knows, you and me might get to see the Big Bang or the one-trillionth of a second!!!