Fuzzy Math, Texas Style

Let me begin with some numbers: in this year's first presidential debate, held on Oct. 3 in Boston, Texas Gov. George W. Bush used the phrase "fuzzy math'' four times to disparage the arguments of Vice President Al Gore '69. Of these four instances, one concerned an accusation Gore made about the coverage middle-class senior citizens would receive under Bush's Medicare reform plan, and the other three addressed claims that Bush's tax reform plan includes disproprotionately large benefits for the wealthy. In addition, Bush used similar dismissive phrases such as "phony numbers'' three times. Curiously enough, though, out of all of these incidents, in only one case did Bush actually dispute the particular numbers that Gore cited (namely, when Gore claimed that Bush was proposing a $1.9 trillion tax cut, rather than $1.3 trillion). This led me to wonder what exactly was meant by this mysterious word "fuzzy'' and its various cousins.

At first, I suspected that "fuzzy math'' simply meant "inaccurate numbers.'' But Bush flatly refused to replace Gore's fuzzy numbers by clean-shaven ones of his own, so eventually this idea began to seem untenable. Then, for awhile, I concluded that "fuzzy math'' was code for "high-fallutin' Washington-style use of numbers instead of words.'' But I was also unable to hold on to this belief for too long, because Bush himself cited plenty of numbers as the evening progressed.

Later on, I entertained the notion that Bush was suggesting that some subjects, such as the length of Gore's tax plan, are best debated in the language of numbers, whereas actual statistics about how much money will be spent on specific programs are simply too crass to be repeated in the exalted format of a presidential debate. This argument didn't make terribly much sense either, since a tax plan is actually composed of a collection of numbers, and so it seems slightly disingenuous to discuss only the vaguest of guiding principles while masking the actual outcome.

So, at the conclusion of the debate, I was at my wit's end. I was led to suspect that this was merely a manipulative use of the word "math'' to dodge serious political discussion, and as a mathematician, I felt slightly cheapened. However, upon further reflection, I've come to a much happier conclusion. I think it was a complex and sophisticated political move that simply needs some further explanation.

You see, Bush's knowledge and intelligence have been under attack since the beginning of the campaign, and these criticisms continue to dog him, in spite of his occasionally successful attempts to correctly pronounce the names of foreign heads of state. It has been one of his primary goals to refute this accusation, and conventional tactics have fallen flat time and time again.

His recent stroke of genius was to realize that demonstrating an understanding of contemporary trends in mathematics would surely be a convincing way to conquer these ghosts. Indeed, in fuzzy mathematics he has found a hot topic--it has beem the subject of more than 4000 research articles since its invention in 1965. Unfortunately, Bush's use of fuzzy arithmetic to explain Gore's positions, while an inspired political move, was somewhat lacking in detail. So, for the mathematically uninitiated, I'd like to spell out exactly what was meant by "fuzzy math.''

Let me begin with an analogy. Suppose you set your thermostat to 70 degrees in the wintertime. This basically means that the thermometer tells the heater to switch on when the temperature dips below 70, and to turn off otherwise. This system, while perfectly successful at keeping the house at a reasonably consistent temperature, isn't especially efficient: The heater is forever being turned on and off, which is a waste of energy.

A much better system would be to use a sliding scale, so that rather than always being either on at full-blast or completely off, the heat could be operating at a lower level when the temperature is close to 70 degrees. This way, there would be many fewer sudden changes to the system, which would be much more energy-efficient, not to mention easier on the heater itself.

Unfortunately, it is mathematically quite complicated to determine a precise formula to govern the behavior of a heating system which is both energy-efficient and heats the house quickly. Fuzzy math is aimed at exactly this issue: It provides a set of tools to find optimal solutions to problems by analyzing hybrids between several different alternatives.

Simply put, fuzzy arithmetic is the mathematics of compromise.

Armed with this knowledge, we can quite easily guess what Bush was driving at with his repeated comments about fuzzy math during the debate. Consider, for example, the issue of taxation. The non-fuzzy, black-and-white approach is to send the bulk of the money in our economy to one place, whereas the fuzzy solution is to attempt to spread wealth throughout society.

Thus, Bush is completely accurate in accusing Gore, whose proposed tax plan includes no cuts for families making over $300,000 per year, of fuzziness. In contrast, Bush's plan is strikingly unfuzzy: He believes that families earning $300,000 per year ought to receive a 9.7 percent tax cut, in spite of the widening disparity between the wealthiest and poorest Americans.

Moreover, although Bush only began to use the word "fuzzy'' recently, his record as governor of Texas demonstrates a long and storied history of unfuzzy policy decisions. For example, in the spring of 1999, he pushed a $2 billion tax cut through the Texas legislature, a move which he has often trumpeted as evidence of his opposition to taxation. In fact, this was a spectacular example of unfuzzy policy: The cut, which came mostly out of property and sales taxes, was directed straight at the wealthiest Texans, and was financed in part by a $250 million cut in the education budget, one of whose primary effects was the tabling of a proposal for free mandatory kindergarten for Texas children. Presumably Gore's proposed increases in spending on education, especially those which target public schools, some of which are attended by children from poor families, would also be labeled as fuzzy.

This is truly a ground-breaking moment in political history: It is the first time that a major candidate for the American presidency has used mathematics as a justification for a political philosophy.

My only confusion is why Bush, who is apparently opposed to all fuzziness, doesn't take these beliefs to their logical conclusion. Why should we tax the wealthy at all? And certainly, if we want to keep children from low-income families poor, it would be best to not educate them at all. We can only hope that Bush will gradually iron out these inconsistencies in his agenda, so that eventually, if he becomes president, only Texan oil billionaires will be able to feed their children. Until this happens, we are reduced to surmising where exactly Bush's philosophy of unfuzzy politics will take him.

In the meantime, I know that on Nov. 7, I will be casting one extremely unfuzzy vote for Al Gore.

Daniel K. Biss '98 is PhD candidate in mathematics specializing in algebraic topology at the Massachusetts Institute of Technology.