millions, billions, trillions - who cares!

There is an old joke about the planetarium lecturer who tells his audience that in 5 Billion years the Sun will swell to become a bloated red giant, engulfing the planets Mercury and Venus and eventually consuming the Earth.
An anxious member of the audience corners the lecturer:
“Excuse me, Doctor; did you say that the Sun will burn up the Earth in 5 billion years?”
“Yes, more or less.”
“Thank God. For a moment I thought you said 5 million.”

Over the past 7 days, since writing about Chess, geometric progression and exponential notation in my last blog entry, few people expressed to me that millions, billions, quintillions have little bearing on our personal lives. Although they creep into our everyday language, but the meaning is progressively blurred and distorted. Confusion among millions, billions, trillions is still endemic in our daily life. I couldn't agree more so let's spend few minutes on them.

Back in the 60s/70s the enormously rich were millionaires. Anyone who had few "thousands" could bring unnecessary attention from the income tax department, having few "hundreds" in your pocket meant you could close a deal, having few "tens" meant you could paint the town red with your friends and having few "ones" meant you got a rich daily allowance from your parents.

The population of the earth at the time of Jesus was approximately 250 million people. There were almost 4 million Americans during the constitutional convention of 1787. 132 million people by the beginning of World War II. It is 93 million miles (150 million kms) from the Earth to the Sun. Approximately 40 million people were killed in World War I. There are 31.7 million seconds in a year. This was the “millions” millennia.

Times have changed and the world is now in the company of Billions and Billionaires. The age of the Earth is well established at 4.6 Billion yrs. The human population is above 6 Billion. Every birthday represents another billion kilometers around the sun. A few inches are a billion atoms side by side. And there are all those billions of stars and galaxies.

Trillions are in fashion now. World military expenditure is now close to nearly $2 Trillion a year. The total indebtedness of all developing nations to Western Banks is pushing $4 Trillion. The annual budget of the U.S. Government is also approaching $4 Trillion. The distance from our Solar system to the nearest star, Alpha Centauri, is 25 trillion miles (bout 40 trillion kms).

For a long time, the British word “Billion” corresponded to the American “trillion”, with the British using “thousand million” for a billion. In Europe “milliard” was the word for a billion. I still have a used plane ticket (Moscow - Delhi – Moscow, bought in Feb, 93 in Kiev, Ukraine) at the height of inflation after the Russian military coup of 1991 and subsequent collapse of communism. The cost of ticket reads “44,000,000.00 рубли́”.

The names are almost never used above trillions. You could count one number every second, day and night, and it would take you more than a week to count from one to a million. A billion would take you half a lifetime. And you couldn’t get to a quintillion even if you had the age of the universe to do it in.

Once you have mastered exponential notation though (write down 10; then a little number, written above and to the right of the 10 as a superscript, tells how many zeros there are after the one. Thus, 10⁶ = 1,000,000; 10⁹ = 1,000,000,000; 10¹² = 1,000,000,000,000; and so on), it becomes effortless to deal with immense numbers such as the microbes in a teaspoon of soil (10⁸); of grains of sand on all the beaches of the Earth (maybe 10²⁰); living things on earth (10²⁹) etc.

Indian arithmetic has long been equal to large numbers. Das = 10; San = 100; Hazaar = 1,000; Lakh = 10⁵; Crore = 10⁷; Arahb = 10⁹; Kharahb = 10¹¹; Nie = 10¹³; Padham = 10¹⁵; and Sankh = 10¹⁷. The Hindus held that the age of the Universe is 8.6 x 10⁹ years old – almost right to the button. And the third century B.C. Sicillian mathematician Archimedes in his book The Sand Reckoner, estimated that it would take 10⁶³ grains of sand to fill the Cosmos.

You do the math.