Visualizing BIG Numbers

Millions, Billions, Trillion; we hear these terms used about large values so often people have become numb to their actual meaning. I heard a fellow employee asked one time what he would do if he won a million dollars in the lottery. He replied, “a million isn’t enough to do anything.” He had no clue how much a million is. So, let’s take the most common object and use it to illustrate what these values are.

A dollar bill is .0043 inches thick. A stack of 1000 one-dollar bills would be 4.3 inches which are also 109.2 millimeters. For the sake of mathematical simplicity, I will be using the metric system from here on. I will convert the here and there so people using “Standard” and are not familiar with the metric system can understand. I will also round-up from 109.2 cm to 110 mm because by the time we get to billions, trillion, and beyond that small difference becomes negligible (if you’re picky, you can go back and use the precise value I’m just too lazy to deal with it).

Back to our stack of a thousand one-dollar bills. A 1000 one-dollar bills are 110 mm. A million, which is one thousand, thousand one-dollar bills (1000 x 1000) on top of each other would be 110,000 mm tall, or 110 meters high (see why metric is easy? 1000 mm = 1 meter). 110 meters is approximately 120 yards, longer than the length of a football field. That’s a million one-dollar bills stacked one on top of the other. So much for my fellow employee’s statement.

A billion is one thousand million. 110 meters is .11 kilometers and when you multiply that by a thousand, to get one billion, (.11 kilometers x 1000) you get a stack of one dollar bills 110 kilometers (approximately 68 miles) tall. Mount Everest is 8.85 km (5.5 miles). 110 km is almost 12.5 times the height of Mount Everest. Twelve and a half Mount Everest mountains on top of each other would equal a stack of one billion one-dollar bills. Presently, there are 7.5 billion people in the world. What if each dollar bill represented one person alive today that stack would be 825 km (approximately 513 miles) tall or 93.75 times the height of Mount Everest! This is the height most low orbiting satellites travel at.

 Take a moment to think about this. A stack of one billion one-dollar bills stacked on top of each other representing each person would be tall enough to reach space. I’ll wait.

That’s a lot of people living on Earth today.

This is why I find apocalyptic scenarios that speculate the complete extinction of human being so far-fetched. One billion is a large number and seven and a half, well, you see. Even if you were to kill off 99.99% of the human population there would still be 750,000 people alive. 750,000 is the estimated number of humans alive 10,000 years ago at the dawn of agriculture and city-states. From 750,000 to 7.5 billion in just 10,000 years, a blink of an eye in geological time! Hardly an extinction event in human terms. Nothing human beings have created thus far can kill every man, woman, and child on this planet. Yes, the human loss would be devastating but not complete. We are as indestructible as the worst of any infestation. Considering the number of species that have become extinct by our hands, beginning with the megafauna around 12,000 years ago, animal life on Earth has more to fear by our presence than any other natural event. By the end of the 21st century, if present trends continue, the human population on this planet will reach 10 billion! Not even climate change will kill us all off but the human suffering will be incalculable. Now, let’s take it up a notch and see what a stack of one trillion one-dollar bills would look like. That is if we can.

A trillion of anything is thrown around these days with as little true meaning as a billion was decades ago. A trillion is, in fact, a huge number. We just saw that our stack of one billion one-dollar bills would reach outer space. Doing the math as we have done before, multiplying by one thousand, our stack is now 825,000 km tall (512,630 miles). The distance to the moon is 363,100 km (238,900 miles). That would make our stack a little over two and a quarter-time the distance from the earth to the moon. Another way to think of it would be to make two equal stacks reaching the moon with a lot of change leftover. The stack laid on its side would circle the Earth a little over 33 times! The United States’ national debt is now at $28.3 trillion and growing every year.

I’ll give you another minute to think about that one.

$28 plus trillion dollars is an amount in debt your great, great, great-grandchildren would barely make a dent in paying it off. And like I said, it grows every year. The United States would have to run on a balanced budget up to its quadricentennial to pay it all off. It’s just impossible. Yet, politicians are always talking about how cutting a million here, or a million there makes them fiscally responsible. Who are they kidding if it’s not their constituents? Quibbling over a billion dollars, and cutting vital programs in the process, seems a little like trying to empty an ocean with a teacup.

Now, I’m going to skip a great deal of order of magnitude and discuss another term widely used but little understood by the general public, infinity. Just what does infinity mean? To most people, it means “something that goes on forever”. But can anybody truly picture what “forever’ means? Is it to the end of time? Well, no. Because the universe has a beginning, the Big Bang and, if physicists are correct, there is an end. One theory states that the “End” will come when the universe has expanded so far that star formation will come to a complete halt because the matter will be so thinned out no material could clump to make new stars a quadrillion years in the future. That’s one followed by fifteen zeros. What stars are left would form black holes that would eventually, due to the escape of Hawking radiation, will slowly fade away in ten to hundred quintillion (one followed by nineteen or twenty zeros) years from now. The only thing left at this point is a thin soup of basic particles that too will eventually lose energy and decay after a huge amount of time (1 followed by 200 zeros years from now). At this time, in the far, far future, with no movement, no particles, not even enough energy to register, time cannot be said to have any real meaning, and, so, it can be considered the “End of Time”. But this is not infinity for it goes on forever. This is why physicists hate infinity for to them it means simply “I don’t know”.

There you are, working on equations that will solve the Grand explanation of Everything and after years of work your answer comes out as “infinity”. Talk about frustration. Yet, the general public throws it around like it’s a household word. There are Infinity Stones, infinite multiverses (redundant, really), infinite possibilities (but, really, only a few possibilities). Infinity is, in human terms, an unknown and one that, by definition, can never be known.

-A. M. Holmes

Author’s Note; I’m not going to include any citations for the piece because I went to Google for such things as “how tall is Mount Everest” and “how far is the moon”. If I could do this, so can you if you have any doubts. I do think my math is pretty sound but if I did make mistakes please point them down in the comments along with the correct answer. -A. M. Holmes

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