Arrival of another birthday (January 20) tends to make me extra-conscious of numbers – although I am a numbers guy anyway. Numbers – especially big numbers – are much in the national news, nowadays, so I thought it would be useful to my readers to examine some of the numbers we are currently seeing and hearing about.
How much is a billion? Most people know that a billion is the number 1,000,000,000. Mathematicians would say it is 10 to the 9th power. You can think of it as a thousand millions – or a million thousands, etc. But that’s different from understanding the number quantitatively. We know what a hundred yards is, or even what a mile is (5280 feet). These are graspable quantities. Think of it this way: if you could spend $1000 a day, how long would it take to spend $1 billion?
Answer: Just over 2700 years. Think you could do it (should you live so long)? Well, maybe. That’s really like an income of $365,000 a year. Some people do have incomes like that – not a lot of people, but there are some besides football players or film stars.
The example isn’t entirely accurate, though, since it doesn’t account for a small detail called “interest.” If you actually had a billion dollars, you would surely invest it in some kind of interest-bearing financial instrument. A modest rate of return might be 4%. That would produce interest of $40,000,000 a year! Whoa! That’s way over the measly $1000 a day you’re trying to spend. A bundle like that would fund handsome incomes of $400,000 a year for over 100 families, while leaving the principal intact. When we start talking billions, we are really talking about BIG money – way beyond the comprehension of most of us.
What about a trillion? It was not until the Obama administration burst on the scene that we started talking about trillions of dollars with any regularity. Politicians and the media now toss the number around nonchalantly, but can anybody really understand how much money that is? A trillion is 10 to the 12th power. That would be enough to give a share of $10,000 to each of 100,000,000 people – or a share of $3,333 to each of 300,000,000 people. (The latter is the approximate population of the USA.)
If that amount of money were invested at interest of 4%, the annual earnings would be $40 billion – a pretty nice income of $100,000 a year for 400,000 families. No matter how you slice it (to paraphrase the late Senator Evertt Dirksen): “…a trillion here and a trillion there - before you know it you’re talking about real money.”
How big is the ocean, etc.? During the past year the ocean got a lot of media attention because of the ruptured oil well in the Gulf of Mexico. There was much alarmism about the “destruction” of the Gulf’s ecosystem. Some alarmists said it might take decades – even centuries – for the Gulf to recover from the leaked oil. Some wild-eyed prophets said the Gulf would become a “dead sea” that would never recover.
There is no doubt that a lot of oil leaked out. Figures vary on the quantity, but 4.9 million barrels seems to be a consensus number. That’s 205 million gallons. In terms of pools of oil, this is an incomprehensible amount. We can write the number, but the amount of oil that represents boggles the mind.
Is it enough oil to “destroy” the Gulf. Probably not. Part of the problem both reporters and the general public have is a lack of understanding of how big the Gulf of Mexico – or, indeed, the ocean – really is. In a previous article (“Enhanced Crisis” – Atlantic Highlands Herald, 27 June 2010) I pointed out that the Gulf of Mexico contains 597,834 cubic miles, or 660 quadrillion (660,000,000,000,000,000) gallons of water. This puts the oil-leakage of last year in perspective. Yes, it was a lot of oil, but in the context of the amount of water in the Gulf, it is relatively little. Beyond the hugeness of the Gulf, the ocean’s primary defense against pollution is its ceaseless churning – a “grinding” action which “emulsifies” oil into microscopic particles that become lost in the sea’s vastness.
Of course, the entire ocean is much bigger than the Gulf of Mexico. The ocean’s volume is difficult to measure, so estimates vary, but 1.347 billion cubic kilometers – give or take a few million km3 – is probably about right. For readers who don’t think well in metric units, that’s 322,914,361 cubic miles – or 356.5 quintillion gallons of water (i.e., 356,492,494,080,000,000,000 gallons). This is where most readers’ eyes glaze over. (In fact, mine are a little glazed too.) What I want to convey is that the ocean is unimaginably vast. Grasping that fact – even if the numbers are beyond us – will help us to avoid being deceived by bogus claims of terminal catastrophe.
How Big is the Atmosphere? The preceding review of the size of the ocean is useful in the context of environmental discussions that have currency today. We know the ocean is vast because most of us have waded in it or swum in it or sailed in it. If you’ve flown high above it – with no land visible in any direction – you get some idea of how big it is.
But failure to grasp the size of the atmosphere is far more common. Part of our difficulty is that we “see” only a small “dome” of atmosphere from wherever we stand on the earth. If a person’s eyes are about six feet above the surface of the earth, then his horizon of visibility is typically about 3.4 miles away. This atmospheric “window” for the ordinary person is quite small, compared with the total atmosphere. Our misperception lets us be deceived about effects of pollutants whose quantity seems large.
Estimates of the atmosphere’s size vary considerably, depending upon how high you think it goes. One calculation puts the height at 10,000 km (about 6300 miles). This “exo-atmospheric” altitude gives a calculated volume of 4.14 quadrillion cubic miles, or 4.7 septillion gallons (that’s 23 zeroes after 47). Even using swimming pools as a unit of measure doesn’t help much here.
A lesser altitude of 8.2 km, cited by some sources, produces an atmospheric volume of just over 1 billion cubic miles – i.e., 1.1 sextillion (i.e., 1,111,557,888,000,000,000,000) gallons. Even this lower figure is three times the volume of the ocean. Furthermore, if you double the putative altitude of the atmosphere, the volume increases 8-fold. None of these volumes can be comprehended by most of us. But the knowledge that the atmosphere is far larger than the oceans should help us to understand that man and his “emissions” are relatively puny.
Scientists have noted that if humans stopped all carbon dioxide emissions, the reduction would constitute only 3% of all CO2 being released into the atmosphere. All the rest comes from natural sources. In other words, if all human life were erased, there would be only a trivial reduction in emissions and no measurable reduction in temperature.
We need to think about these things before we let lawmakers enact ruinous taxes to “stop climate change” or “save the oceans.”