Monday, October 6, 2008

Million vs. Billion – A Drift To Innumeracy...

The first time I heard the term innumeracy was in 1991. I was in college and had a psychology professor who was going on and on about how people today don’t understand the magnitudes of numbers. He had a point. I maintain it’s because practical application ceases once the numbers grow to be larger that what we encounter in our everyday lives. Most people I encounter (and I’m in the banking and finance industry) don’t have a clue what large numbers mean and what their impact is on whatever they are being applied to; whether it be financing for large projects, balancing budgets, timeframes, or even how many fish are in the sea.

I wrote this post to illustrate in real-world examples (by showing the unknown in terms of familiarity) how large numbers relate to each other and the impact and magnitude they have on us. I was compelled to write it based on a conversation I had recently with a friend of mine who (it became apparent) hadn’t the slightest clue as to what they were talking about; not because they were incapable or because they had a differing opinion from mine; but because they were utterly ignorant to the magnitude of the numbers they were throwing around – my friend was innumerate...

At some point, (and I suspect it is different for all of us) numbers transition in our minds from quantitative units to mere language so there is, therefore, a loss of quantitative understanding when the transition threshold is reached. I say transition because it is less of a shift and more of a drift. If the drift should be graphed we would see, I suspect, a gradual curve down, towards innumeracy, as we drift from understanding the numbers… through sort of getting the numbers… to not having a clue. This numeracy curve is a sliding scale based on a person’s grasp of large numbers that begins with zero and drifts toward infinity. At some point on each person’s curve the threshold is reached where the numbers have lost quantitative value and are nothing more than words in the subjects mind. I call this point the numeracy threshold. In this country we have a very low numeracy threshold. It is the reason most people can’t grasp the quantitative values and realities of large numbers. It is also the reason the government can pitch astronomically high dollar amounts past the taxpayers like fastballs…

Saying, “I walked 5 miles,” allows most of us to understand the magnitude of that accomplishment because we have a frame of reference. Saying, “I walked 1000 miles,” is similar because the reference frame is there, but there is a disconnection from experience so the true impact of the accomplishment is lost until we map 1000 miles from, say, our home – then we suddenly realize the magnitude of the accomplishment. Now saying, “I walked 10,000 miles,” I imagine would cause most people to glaze over, then change the subject completely as they start singing the pop song remake by the Proclaimers – which, by the way, never actually mentions 10,000 miles but somehow we all think it does anyway… This is what I mean by the drift towards innumeracy. Now, I’m not saying you need to count to some ridiculously large number to understand its quantitative value, but it might just help…

I could probably write a dissertation on this subject. One that would span many pages, but this isn’t a master thesis it’s a blog so I’ll spare you and get to it. What I want to do is apply familiar comparisons to large numbers so that you might find their quantitative value. Numbers that we regularly encounter but are rarely able to reference; numbers that are in the news daily, but mean very little to us because they are merely words to most people – they exceed the numeracy threshold.

Over the last few weeks I’ve asked various individuals I’ve run into to tell me the difference between a million and a billion. Try this for yourself and you’ll get some very diverse answers (some even comical) ranging from cleverly uninformed to the ignorant to the very innumerate. Answers like “a few zeros,” or “a third comma,” or a favorite of mine, “a ‘B’ and an ‘M’.” One person cleverly said, “37 years of McDonald's served.” It was actually the 8 years from 1955 (one million served) to 1963 (one billion served). But that’s one more illustration of not having a reference or a framework to put it in… the result is that innumeracy affects many people’s grasp of time as well. I suspect the reason McDonald's stopped counting in 1994 after 100 billion burgers had been sold was because they realized if it took them 8 years to go from a million to a billion it would take them much too long to get to a trillion and the marketing ploy would lose it’s luster. Actually, at their current rate of 75 burgers a second and current tally of about 120 billion sold, it would take another 372 years to sell the trillionth burger… feeling innumerate?

So let’s get on with it. Below you’ll find some reference points that might help you the next time you read about a billion or a trillion dollars being spent here or there…

What is the difference between a million, a billion, and a trillion?


If you had a million dollars in a stack of bills one foot high, by the same denomination a billion dollars would be a stack the height of the Eiffel Tower. A trillion dollars would terminate just outside the airlock of the International Space Station during an average orbit.


If you were to travel back in time a million seconds you could relive the past 12 days. A billion seconds sends you back 32 years and would allow you to celebrate our country’s bicentennial all over again – in 1976. A trillion seconds of time travel and you could witness, first hand, the final extinction of the Neanderthals 31,710 years ago.


If you laid a million US pennies out flat in a tight, single-layer carpet you would cover about 4000 square feet or less than one tenth of an acre – roughly the area of a high school basketball court. A billion US pennies laid out in the same fashion would cover 89.7 acres – roughly 68 football fields. A trillion US pennies would cover 89,675 acres or 141.1 square miles. They would carpet the entire city of Philadelphia, Detroit, or Washington, D.C. – not that they don’t waste enough money in that town as it is… Incidentally, the first penny was minted in 1887. The US Mint estimates there have only been 300 billion pennies ever produced… ever. At that rate, the US will mint its one-trillionth penny sometime in the year 2290.


If you wanted to walk a million inches you could walk around the perimeter of Central Park almost 3 times (15.78 miles). At an average walking speed of 2 miles per hour, total walking time would be about 8 hours. A billion inches and you could walk from Central Park to Los Angeles and back almost 3 times (15,782 miles) and total time on the hoof would be roughly 11 months. A trillion inches would take you from Central Park to Central Park via the North and South Poles as you circumnavigate the Earth more than 634 times and the trip would take around 901 years of constant walking. For those of you more theoretically minded, a trillion inch stroll would also take you from Central Park to the Moon and back – 33 times.

Liquid Volume

If you had a million 12-ounce cans of beer you could fill 3 residential in-ground pools with frosty libation. A billion 12-ounce cans of beer and you could fill 3,125 pools or 1.5 commercial oil supertankers. A trillion 12-ounce cans and you could fill 1,488 commercial oil supertankers, or the Houston Astrodome roughly 150 times.

Dry Volume

If you stacked a million 12-ounce cans of beer you could build a life-size replica of Big Ben or 5 city buses. If you stacked a billion 12-ounce cans of beer you could replicate 4,600 city buses or the Washington Monument close to 14 times. Stack a trillion 12-ounce cans of beer and you could either build 13,631 Washington Monuments; or 161 life-size replicas of the Great Pyramid at Giza; or the Great Wall of China 1.5 times; or both towers of the World Trade Center 124 times… each.

We seldom stop to think about the magnitude of the numbers we encounter everyday on television, or in the papers, or on the radio. We hear of this company or that company’s record profits, how congress has earmarked another absurd amount of money for something or other, or national debts… but the true quantitative value of the numbers is lost on most people because it exceeds their numeracy threshold.

The next time you encounter a number you believe could be beyond your numeracy threshold, hold it up to the light of something you can quantify – it might surprise you… or even scare you...

1 comment:

  1. AMAZING POST! I have never thought of it like that. Congress will throw millions and billions of dollars around for seemingly unimportant side-projects while we as normal citizens only know the true magnitude of maybe 50-500 thousand dollars. We as Americans should see and attempt to understand the actual numerical and real value of OUR money being spent on a daily basis. This money is being spent by elected officials that we appointed and that work for us. You would not see a Vice President of a company taking money from the President of the company and spending it on research for the effects of lipstick on monkeys in Antarctica. That may be a little absurd, but what they are spending OUR billions on is not much better. Great Post. Sorry so long but you really got me thinking.