Naked Numbers

When I was taking heat transfer as an undergrad one aspect of problem solving that was vital to making sure you arrived at the proper answer was the need to be consistent with your units of measure. It was drilled into us that naked numbers were of absolutely no value, a number didn’t mean anything without its complete set of units. The reason was simple we had a dizzying array of units floating around our equations—to the point where my subscripts had subscripts—that it was easy to lose a unit and come up with a number that made no sense. We don’t often think too heavily of the importance of units in normal conversation we often believe the context bespeaks the units. For example if someone is asked how much their car cost it is perfectly normal for them to respond with something like fifteen thousand. From the context of the conversation it is obvious that we are speaking in dollars but theoretically they could be talking cents, in which case it’s only a hundred fifty dollars, or euros in which case we are talking more like twenty thousand dollars. The point is a number with no units leaves it up to the listener to imagine what that number means, and its actual magnitude.

Currently across the country we are having a discussion about the fiscal crises states and municipalities are experiencing. A lot of big numbers are being thrown around, for example 1.5 trillion dollars is the shortfall in pension obligations some people are estimating facing all the states combined. At first glance this sounds like a tremendous shortfall and nothing could possible be done to close this gap. This however is an example of a number walking around half naked. Much like in life half naked can often be a lot more distracting than totally naked. That 1.5 trillion dollar number demands a lot of context that is almost always left out. Don’t believe me? Ask yourself is this number referring to the amount of money they need to output this year, over 5 years, over 10 years? Is this number based on last year’s tax revenue or on projections of this year tax revenue, on the stock market today or ten years from now? This is the equivalent of declaring a budgetary crisis because you only have ten thousand dollars in your bank account but you owe one hundred thousand dollars on your house. If you leave off the fact that you are given thirty years to pay back that money you are leaving out an essential fact about your financial situation. While it is true that both sides of the political spectrum employ this tactic of naked or half naked numbers to score political points in the current discussion of fiscal policy it is the right who have been barraging us with a horde of scantily clad numbers.

Maintaining units is all about giving the proper weight and context to a particular number. It is this context that we are almost always missing, and are left to assume. Take for example the canard that America has one of the highest corporate tax rates in the industrialized world. If you simply look up corporate tax rate you will clearly see we are only second to Japan in terms of corporate taxation. This number though fails to jibe with the equally real number that shows corporate tax revenue as a share is GDP is at a thirty year low. The only way to explain this is to dig deeper and realize that over the last thirty years the amount of non-taxable business activity has shot up to nearly 35% a nearly three fold increase. This has the effect of lowering the effective tax rate to only 13.4% putting us near the bottom of the totem pole of industrialized nations in terms of corporate taxation.

With the fiscal problems facing the nation, it is crucial that these politicians show all of their work like our math teachers made us, so that we can adequately asses their understanding of the situation and grade them appropriately.