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One in a trillion

March 4, 2010

The time has come to have a word about trillions. The subject has been ignored for too long.

I say this because of a question my youngest asked me the other night. He wanted to know if I'd ever heard trillions mentioned other than in a discussion of the federal budget deficit.

As a matter of fact, I had. A month previously I had purchased a one terabyte hard drive for one of the family computers. A terabyte is one trillion bytes.

Just a coincidence? Perhaps. But that got me to studying the matter. Consider the following facts.

Here's a chart of growth in hard drive size over the past 30 years:

Source: WikiMedia

And here's a chart of long-term growth in the national debt:

Need I say more?

You may object that there's no obvious causal link between hard drive size and the national debt, and that the astonishing and seemingly parallel growth of both over the past three decades is coincidental and will stop any time now. Maybe it will. However — and I don't mean to be alarmist about this — if I've been watching the sun come up every morning for thirty years, I can reasonably conclude it'll do so tomorrow, too. 

What does this tell us about the future?

You might suppose — hope, perhaps — that there's an upper limit to hard drive capacity. No doubt there is. I feel certain Planck's constant figures in this somehow. However, after some research, it's evident we have a ways to go. Right now we're still talking cobalt-platinum grains as the basic medium for digital information. Tomorrow, God help us, it may be spin on the fermions.

Perhaps you've heard of Moore's Law, which predicts a steady increase in the number of transistors the Intels of the world can cram onto a microprocessor chip. (Currently it's about two billion.) Well, there's also Kryder's Law, which predicts that the capacity of hard drives will increase 40 percent a year for the foreseeable future. A 4 terabyte drive has been announced for 2011, I see talk of 40 TB drives, and theoretical developments suggest we're looking at 400 TB. In the fullness of time no doubt they'll be plucking petabytes from the quantum foam.

You can see where this is headed, and it's not good. Today the annual federal deficit is in the trillions of dollars, and the national debt in the tens of trillions. Tomorrow, what? Quadrillions? Googols? (OK, maybe not googols, which is more than the number of atoms in the known universe.) But I bet it's going to be a lot.

Optimists will now say: as the national debt goes up, the cost of memory goes down. Therefore, it all evens out.

Let's think about that. In ~1987, I paid $130 a for 30-megabyte hard drive. Last month, that 1 terabyte hard drive cost me $110. In fact, as I think about it, every hard drive I've ever bought cost around $100, give or take thirty bucks. We may thus calculate that I can buy 33,333 times as much storage for my hundred dollars as I could 23 years ago.

Is this an impressive increase? Yes. However, let's be frank. Am I 33,333 times happier? Not to sound like a malcontent, but no. As I see it, more memory basically lets me stay even with Windows code bloat. Meanwhile, by 2011, my share of the national debt will be $34,000.

It will surely get worse. At least with hard drives we know that, ultimately, there are physical limits. That isn't true in the world of finance. Consider, for example, that in 2009 the notional value of over-the-counter derivatives was $605 trillion, more than four times the value of the entire earth.

I think I'm perfectly entitled to panic in light of these facts. If you prefer to stay calm, be my guest.

— Ed Zotti

He's choosing the panic option

Dear Ed:

I read your revelations regarding trillions with alarm. I tend to get all swimmy headed when numbers begin to exceed three digits. The concept of a million of anything confounds me — and then a thousand million — and a thousand billion. Where will it end? It's the work of the devil, I tell you. Deep, deep down I don't think there's really a trillion of anything. I mean, where would you put it? I certainly don't have a closet that would hold a trillion of anything. Do you? Martha Stewart could never knit enough cozies to contain a trillion, and they certainly wouldn't fit into those nifty compartmented and stackable storage boxes. The messiness of it all — a million behind the couch, a couple hundred million more slipped down behind the bookcase — would be so distressing. No, I just won't have it. Take your trillion (if you really have such an amount of anything) elsewhere and secrete it (or them) in an abandoned salt mine or one of Bernie Madoff's villas. I'll have no part of it. It's devil's work, and I'll have none of it.

— Jim Kepler, Rogers Park

Dear Jim:

A million? You're getting freaked out by a million? Please, Jim, you're giving panic a bad name. The truth is, you've barely begun to grasp the seriousness of the situation. To give you an idea, someone recently mentioned to me that we're not the first people in the world to deal with trillions; something similar occurred during the legendary hyperinflation in Germany's Weimar Republic in the 1920s, when the price of an ounce of gold reached 87 trillion marks.

However, this was mere inflation. In the end, the Germans simply chopped 12 zeros off prices, and there they were, good as new.

We can't do this. Yes, we're dealing with trillion-dollar deficits. But meanwhile, when I go to Starbucks for a triple toe loop latte to soothe my jangled nerves, I get pennies back in my change. In other words, I need to keep track of hundredths of a dollar, and hundreds of trillions of dollars, and everything in between.

This taxes the capacity of the mind. The other day I read that President Obama was introducing a $1.5 billion program of foreclosure relief. My initial reaction, based on matter-of-fact discussions of $800 billion stimulus packages, was: that's it? You can't remodel a bathroom for that amount of money. Silly me, I'd gotten my billions and millions mixed up. (And yes, I realize for $1.5 million you can easily get two bathrooms remodeled.) We primates lack sufficient whorls in the neural circuitry to process numbers across this range. Once you understand that, the only rational response is hysteria. Till then, suck it up.

— Ed   

Follow STRAIGHT DOPE CHICAGO on twitter, assuming Little Ed remembers to send the feeds out, and if nothing else observe his fumblings with a technology that is obviously beyond him.

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