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John Doe Meets Big Numbers

John Doe Meets Big Numbers

These days we often talk about Gigabytes, Terabytes and Petabytes of data without missing a heartbeat. We know that 1 Gigabyte is 1 Billion or 109 bytes of data, 1 Terabyte is 1 Trillion or 1012 bytes of data and so on. But do we really have a feel for how large these numbers are? Mind you, I am not talking about data sizes – I am just talking about comparing the magnitudes of these numbers to the ones that we typically come across elsewhere.

Consider the example of John Doe. John works with a technology firm as a senior Big Data developer. The application he works on processes Petabytes of data regularly, and John has scant respect for data sizes less than a Gigabyte. In fact, he had got so used to the Big Data world that, till recently, any power of 10 where the index was less than 9 looked like a small number to him. This perception was altered one day when John’s younger cousin, who had recently graduated from High School and had a liking for numbers, pointed out some interesting facts to John:

  • At 30, John is already older than most of his teammates. He was surprised, however, to find that the total time he had spent since his birth was only about 9.5 x 108 seconds. Since his birth, John’s heart has beat about 3.7 x 107 times (it beats approx. 70 times per minute); the number of breaths he has taken so far total up to 8.4 x 106; and the total number of meals he has eaten is somewhere in the range of 30,000 to 40,000!
  • When John learnt the idea of a countably infinite set for the first time, he associated it with the number of hair on his head – having tried in vain to count them earlier. He was surprised to find that the number of strands of hair on an average human head is only of the order of 105!
  • John drives to work and is irked by the increasing traffic in his city. The ever increasing number of cars on streets appear to him like another example of countably infinite objects. He was amused to find that when he bought his car in 2013, it was one of approximately 65 x 106 cars produced in the entire world in that year.
  • The distance from the Earth to the Moon is about 3.84 x 105 KiloMeters (Km). When John compared this to his monthly driving average of 1000 Km, he realized that it will take him over 30 years to cover a total driving distance equivalent to the distance to the Moon. Alternatively, if John were to drive 500 Km per day and continue driving day after day non-stop, it would still take him more than 2 years to cover this distance! It would take John several lifetimes of driving if he attempted to cover a distance equivalent to that from the Earth to the Sun (approximately 1.5 x 108 Km).
  •  The length of the Earth’s circumference is about 4 x 104 Km. If John attempted to cover this distance with a daily driving of about 500 Km, it would take him about 80 days to do so – which reminded him of Jules Verne’s classic novel Around the world in eighty days.
  • John is fond of reading books and has read close to a thousand books in his lifetime. He knows that this is but a tiny fraction of the total number of books available out there, but was amused to know that the total number of books ever published in this world was estimated at about 1.3 x 108 in 2010!
  • Finally, John realized that if he were to start counting natural numbers at the rate of 1 per second, and continued counting day and night without taking a break, it would still take him over 30 years to count up to 1 Billion (109)!
  • Today John Doe continues to excel in Big Data technology, but he now harbors a healthy respect for numbers which don’t look large in the context of data sizes.

Sources of stats
http://mathworld.wolfram.com
http://www.oica.net/category/production-statistics/2013-statistics
http://www.space.com http://mashable.com/2010/08/05/number-of-books-in-the-world/
http://bionumbers.hms.harvard.edu

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About Nilesh Karnik

Nilesh is the Chief Data Scientist at Aureus. In this role, he is responsible for development of algorithms and mathematical models that help large organizations with advanced analytics solutions. His PhD dissertation made a substantial contribution to the theory of Type-2 Fuzzy Logic Systems and his work is still widely referenced.

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