Logarithmic Scale

***Addendum:
By no means do I think debt is a bad thing and must be eliminated. Debt is a lot like milk: drinking some everyday helps bone growth and keeps you healthy, but take on too much too quickly, if you've seen/done a gallon challenge, and you'll end up puking it out all over the place. Another case for why the US could be closer to Japan than Greece or Italy is that the US has control over its own currency. If all else fails, the US can inflate the debt away by printing crisp new Benjamins for its debtholders (but it would still be a disaster for all of us)
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You've undoubtedly been asked before "On a scale of 1-10..." how tasty is the food / how hot is that girl / how much pain are you in? If you're a math nerd like me, you respond by asking first if it's a linear or a logarithmic scale. It's a fair question, especially if you want to compare a '5' to a '10'. On a linear scale, a '10' would be roughly twice as good/strong/etc as a '5'. On a log scale, it would be 2⁵, 10⁵, or 1024⁵ times stronger depending on the base of your units.

For instance, the scale system used to measure earthquakes, the Moment Magnitude Scale (inaccurately called the Richter Scale, even though it's a modification of it) is a log based 10 scale of the wave amplitude on a seismograph. In terms of energy, it is roughly a base 31.6. This means a magnitude 6 quake releases 31.6 times the energy of a magnitude 5 quake, and a magnitude 7 quake releases 1000 times the energy of a magnitude 5. The Great San Francisco quake was a 7.9, and last year's quake in Japan was a 9.0, 1 million times more energy than a 5.0 quake, and 5.0s do considerable damage already.

But there's a more ubiquitous application than earthquakes that we use everyday that is really a log scale and not a linear scale: scaling large numbers whether it's populations or sums of money by the thousand, million, billion, trillion, quadrillion ... They even have nice little Latin prefixes for 'two', 'three', 'four' that make them seem smaller than they are. We don’t think of 1 million being 1000 times greater than 1 thousand. When we try to visualize 1 trillion, the tricks we use aren’t even very helpful at all. How many people truly understand what a stack of 1 trillion sheets of paper stretching from the earth into space looks like?

With the gross public debt ("public debt" + "intragovernmental debt") sitting around $15,850,000,000,000, how much is that exactly? True, it's possible we can sustain it as long as we remain the strongest economy in the world and keep growing. With public debt at around $11,000,000,000,000 and our GDP at around $15,500,000,000,000, the oft-cited Debt-To-GDP ratio is about 70%. I bet you can see why people would not want to talk about Gross Debt to GDP, which is at about 101%. The scary part is that in 2001 the Gross-To-GDP ratio was only 56% according to the Office of Management and Budget, which means that ratio has nearly doubled in 10 years. Before we laugh too hard at the Greeks and their lazy, tax-dodging lifestyle, they started having trouble in 2009 when their Gross Debt-To-GDP ratio hit 120%. Ditto with Italy this year at 120%. Considering the accelerating pace of debt growth due to increasing budget deficits and interest on the debt ($450,000,000,000 in 2008), we don't have much time.

But wait, you might ask, what about Japan? They've been running at a gross debt-to-GDP ratio of 200% and they're still chugging along. Well the difference is that around 95% of their debt is held domestically while we're at around 65%, which means they have a much safer and more captive audience for their IOUs than we do.

So next time, think again when politicians want to slap on $500 billion dollars to our national public debt like it's nothing. Think again when they trumpet a balanced budget like a panacea. It's certainly a step in the right direction, but for the debt to go down, we need a primary surplus of at least $450 billion. Don't let the rhetoric and seemingly small number of $0.5 trillion fool you (see what I did there?)... or we could be a lot closer to Greece than you think.