The Lost Denominator

The Washington Post had an interesting article by Rick Weiss on the unraveling of the Chimpanzee genome which had a little problem with the math that it shares with many popular science articles. The conclusion of the article is that the chimpanzee DNA differs from the human in only 1% of the active DNA.

All told, the two sequences differ by 4 percent. But three-quarters of the differences seem to be in non-functional parts of the genome, suggesting that a mere 1 percent variation makes all the difference.

It's pretty clear that if you take 1/4 of 4% you get 1%. But from what the article says we can't say if that's the right approach. Suppose there are 3 billion letters in the genome. Then the article is saying that there are about 120 million differences in the total genome. About 90 million of these are in the non-functional part of the genome and 30 million are in the functional part. So far we're on pretty solid ground. But can we calculate the fraction of differences in the functional part?

What we don't know is what the size of the functional part is. I'm not a specialist in the field, but this article suggests that in one particular area about 39% of the genes are non-functional (and not all of the DNA sequence is in genes).

It may be that there is some new and different definition of non-functional that's being used in this latest article but I've certainly seen other articles indicating that most of our DNA is non-functional. It would sure have been nice if the author had thought to describe the change in the size of the denominator when he implied that the ratio of changes in the functional area of the genome was only 1%. I'd be a lot more willing to believe it.

The Federal Deficit: A big number with a little problem...

What does it mean? One of the most common misuses of numbers is publishing data that makes a nice headline, but has little meaning in and of itself.

The federal debt is the total amount of money the federal government owes. The federal deficit is the amount spent beyond revenues each year: it's the yearly change in the debt.

There's been a lot of talk about the budget deficit recently giving the latest numbers on the Federal budget deficit. The current estimate from the CBA is that we'll have a 331 billion dollar deficit in 2005. Ignoring the issues of inappropriate accuracy (can it really be estimated to 1/3 of a percent), it's not clear that this is a useful number at all.

Currently the federal debt stands at just under 8 trillion dollars according to the debt clock. Also, according to the latest numbers inflation over the past year has run at about 3.2%. So just adjusting the debt for inflation we'd expect a nominal deficit of about 256 billion dollars. I.e., if we owe 8.25 trillion dollars in 2005, we owe about the same amount of goods and services as 8 trillion dollars in 2004.

A 'nominal' deficit of 250 billion dollars actually represents a balanced budget.

By this calculation the real deficit, the additional goods and services that we owe, corresponds to a 'mere' 80 billion dollars.

So is the deficit $331B or $80B? Which number is right? Undoubtedly neither!

Of that 8 trillion dollars about 40% is owed to the federal government itself in fictions like the Social Security Trust fund. We can only really count the inflation on the 'real' debt owed outside the federal government. That's about 4.8 trillion dollars implying about 150 billion dollars of the deficit is simply inflation of the debt. That leaves a 'real' debt of about $180 billion.

So now we have three numbers ranging from a measly $80 billion to $331 billion.

It's not even the case that we can say "Well the number may not be correct, but by looking at the trends we can see what's happening." When we correct for inflation on the debt, we're taking the difference between two rather comparable quantities: the very sign of the deficit can, and in many years does, change.

It would seem elementary to correct basic discussions of economics for simple effects of inflation, but in general it does not seem to be done. Doubtless things are a lot more complex than the simple analysis done here. Nonetheless it's pretty clear that the debt numbers that see and hear discussed are not very helpful in understanding the real fiscal situation of the government.

Words on Numbers

Why this blog? There are excellent discussions of innumeracy on the Web, e.g., Innumeracy.com, but I haven't seen any blogs which discuss innumercy issues on a continuing basis. This blog is intended to be a venue where I can vent my own frustrations at seeing numbers and mathematical concepts misunderstood or distorted and to express pleasure on the occasions when we can see an insightful analysis. Numbers can be fun, but they are important enough in today's society to be dangerous toys.

I hope that in discussing issues with numbers and mathematics I can try to make constructive suggestions and in some small way raise awareness of issues. The topics I hope to talk about range from the great social issues of the day, e.g., the profound and deliberate misuse of numbers on all sides of the Social Security debates, to tiny issues that gratuitously make an issue difficult to understand.

My own sense is that only a small fraction of people really feel comfortable and like playing with numbers. The goal here is not to frighten people into numerical correctness, but to share the pleasure of using mathematics in daily life.