Curse of Living in the Meso-scale…

This comic makes a point – albeit clumsily – that has been on my mind lately. As I’ve been mentally composing posts that involve discussions about very large numbers (and sometimes very small numbers), I find that it’s difficult to express to a literate but non-scientific audience issues of relative magnitude. Or even absolute magnitude. Our options are remarkably limited.

1) Common names. Most people understand thousands well enough, but go beyond millions and things get very dicey. The first problem is the so-called short scale and long scale used by different nationalities. In America “billion” and “trillion” differ by factors of a thousand, while in France they differ by factors of a million. Thus an American “trillion” is equivalent to a French “billion”, and they have some “milliards” and “billiards” thrown in to patch the holes.

2) Exponential notation. You probably learned exponential notation in fifth grade and promptly forgot it once the test was over. These are numbers of the form “something-point-something times ten to the something.” The “something-point-something” part is a decimal fraction somewhere between one and ten, and the “ten to the something” part tells you where to put the decimal. It’s a great way to express big numbers (“3.5 times 10 to the 11” is 350 billion) and small numbers (“1.0 times ten to the -6” is one one-millionth) but unless you learned to live and breathe these kinds of numbers in college science they mean nothing.

3) Standard prefixes. Somewhere between the science and the lay lies the Greek. “Kilo” for thousands, “Mega” for millions, “Giga” for billions, “milli” for thousandths, “micro” for millionths and “nano” for billionths – these are terms that have specific meanings and can be employed widely. Unfortunately they have also been bastardized by popular culture such that “mega” just means big and “micro” just means small. Indeed there has been inflation in their usage so that advertisers now have to resort to “giga” and “nano” to make customers take notice. “Tera” and “pico” can’t be far behind.

4) Standard common names. Even if we pick a system of common names, say the more logical short scale, we can very easily get names for values that are well out of the middle range for which these common names are useful. Who can visualize the 602 sextillion molecules in 18 grams of water? It doesn’t really help to call it 602 billion trillion either, as no one can honestly grasp what it means to have a trillion of something, let alone if that something consists of a billion of something else.

5) Comparisons to other things. So we’re finally left with the hokiest of all options, the “football field” comparison. Take some incomprehensible number, like the cost of the Iraq War so far (6.5x10¹¹ dollars), and convert it to something tangible, like quarters. This would make a stack 2 million miles tall (1.8x10⁶ miles), which is like going to the moon and back 4 times. And the distance to the moon is about as long as an airport security line composed of every living person their carry-on and pets, which – even with a thousand scanners running full time – would take 2000 years to process. And if you took your mother and her mother and all your female ancestors going back 2000 years and had them stand hand in hand, they’d be the length of a football field, which is finally a largish thing that everyone can visualize.

- jack*

Comments

[vfwh]

I don't get this "oh my god how can we explain to people how big this is?" meme that's been going around the media, that keeps reinforcing in people the idea that we're all really too dumb to get the point of important policy decisions.

There's a perfectly simple way of putting it: hospitals or schools. How many hospitals or schools would this be able to fund the annual budget for? Or how many patients medical bills would it pay for? How many pupils would it educate?

Then, to compare, give the number of hospitals or schools currently in operation in the US, or the world, or California, whatever, or the number of pupils or patients treated per year... you get the point.

Enough with the pile of quarters or stacks of singles already. Being able to visualize masses of quarters on a football field does not get people any closer to understand how much wasted value this represents.

Figuring out how many hospitals or schools this would pay for would give people more of a sense of reality, in terms of actual things that we care about.

For instance, I'm in Paris, I just checked quickly. The annual budget of a single hospital is on average 160M euro, about 200M dollars.

One trillion dollars would therefore be able to fund:
1,000,000,000,000 / 200,000,000 = 5,000 hospitals for a year, or 5 hospitals for a thousand years. Or 50 hospitals for a century.

I'm guessing there are about (order of magnitude) 750 important general hospitals in the US today.

So one trillion dollars would be able to fund all the general hospitals in the US for 1,000,000,000,000 / (200,000,000 * 750) = 6.7 years.

Assuming the cost of the bailout will be about 3.5 trillion (some say more, but let's remain conservative), then the bailout could basically provide free healthcare to most americans for 3.5 * 6.7 = 23.5 years.

I'm sure the numbers are wrong in several places, but not in orders of magnitude. So there would be no money for healthcare coverage, but banks can get the equivalent of over 20 years of healthcare for almost all americans. That means no medical bills for you, your neighbours, your friends, even the folks you don't like, for 2 decades.

Doesn't that make it a little more real? I just did this with a couple of Google searches and a little extrapolation in under a half-hour. Surely someone with actual resources and time, like a media outlet, could figure out more accurate numbers, and also run school scenarios. I wonder why they don't.