A human being cannot count to one billion!

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

25 March 2007

John Muriuki wants to know how long it would take to count from one up to one billion, counting one number per second. The easy answer is found by dividing 1,000,000,000 seconds by 60 to get 16,666,666 minutes. This is divided by 60 again to give 277,778 hours. Dividing this further by 24 yields 11,574 days, which is equivalent to about 31 years and eight months.

But that is not realistic at all: one needs to sleep, eat and take short breaks in between. Thus, we can expect the person counting to following the normal working hours starting at 8am, breaking for 30 minutes at 10am, taking one hour lunch at 1pm, breaking for another 30 minutes at 3pm and finally continuing until 6pm when he rests for the day. That is, eight hours per day.

Therefore, we should actually divide the 277,778 hours by eight to get the number of days. The result is 34,722 days which is a little over 99 years. Judging from the number of people aged above 99 years, we can conclude that it is highly unlikely that a normal human being can count to one billion within a lifetime.

Still, the assumption that you are counting one number per second is a gross underestimate. To understand, read out the following number aloud: 652,326,781. It is “six hundred and fifty two million, three hundred and twenty six thousand, seven hundred and eighty one” Now, can you say that in one second? Obviously no!

To find out how long it can take to say a nine-digit number aloud, count from 652,326,781 to 652,326,789 and time the duration. Then divide this by nine. I took 51 seconds to do the counting, thus I spent about 5.5 seconds on each number.

Now, there are “only” 899,999,999 nine-digit numbers; from 100,000,000 to 999,999,999. Not all of them are difficult to say out loud (for example, 300,000,000 takes about one second) thus we can assume that each takes about 5 second on average.

Therefore counting from 100,000,000 to 999,999,999 would take a total of 4,499,999,995. To simplify matters, let’s call it 4.5 billion seconds. By the same token, eight-digit numbers are also difficult to say out loud.

If it takes 5 seconds to say a nine-digit number, it will probably take 4.5 seconds to utter an eight-digit figure. There are 89,999,999 such numbers, thus it would take about 400 million seconds to count them. Therefore it would take about 4.9 billion seconds (4.5b plus 400m) to count from the number ten million to one billion.

When the same arguments are applied to the other multiple digit numbers, it turns out that counting to one billion would take about five billion seconds. If the count is done eight hours per day, then it would last about 500 years. Thus we can conclude categorically that no human being can count from one to one billion!

Perhaps the question can be turned around to ask: what is the largest number that one can count in a lifetime? Well, that is a story for another day.