**Subject: **Re: "fuzzy math" reference in US debates

**From: **Vladik Kreinovich (*vladik@cs.utep.edu*)

**Date: **Wed Nov 08 2000 - 12:05:52 MET

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Date: Tue, 07 Nov 2000 11:52:34 -0500

To: vladik@cs.utep.edu

From: Diversions <diversions@nytimes.com>

Subject: Article from today's New York Times

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November 7, 2000

Yes, Candidates, There Is a Fuzzy Math

By BART KOSKO

LOS ANGELES -- They've been at it for weeks: the presidential

candidates accusing each other of using "fuzzy math." George W.

Bush first threw this dirty snowball in the debates, attacking Al Gore's

analysis of the Bush budget plans. Mr. Gore threw it right back and kept

throwing it. He even got audiences at campaign stops to shout "fuzzy

math!" when he asked them to describe Mr. Bush's budget projections.

Both candidates plainly use the term as the ultimate logical putdown.

What neither seems to realize is that there really is such a thing as fuzzy

math, and we use it every day.

Fuzzy math and fuzzy logic are fields of mathematics and engineering, like

chaos math or probability theory. Scientists hold international

conferences on fuzzy math and publish in journals of fuzzy math. Scholars

write textbooks and monographs on getting computers to reason with it.

Two of the largest fuzzy research centers are in Governor Bush's own

state, at Texas A&M University and the University of Texas at El Paso.

And in Vice President Gore's home state of Tennessee, General Motors

puts fuzzy math to use in new Saturns.

The math of fuzzy math is not, itself, fuzzy. It is as black and white as the

columns of budget numbers that we all want computers and accountants

to add up correctly -- and that each candidate suggests the other side

wants to obfuscate. What fuzzy math does is let us -- and our computers

-- reason with shades of gray. It is a branch of machine intelligence that

captures human expertise in software or computer chips.

A good example of a fuzzy concept is cool air -- it has a clear meaning,

but it is not black or white. Fuzzy logic builds rules out of such fuzzy

terms and then embeds those rules in a computer. One rule might be "If

the air is cool, then set the motor speed to slow." Another might be "If

the air is warm, then set the motor speed to high." Fuzzy math lets an

expert program a computer in English, but helps the computer interpret

"cool" according to a number of interacting variables -- just as a human

being does.

Both candidates say that their top priority is education. Both say they

favor increased training in science and mathematics. Both rely on

advanced technology to solve social problems that range from cleaning

up oil spills to fighting information warfare at home and abroad. Yet both

reflect the sorry state of scientific literacy in this country.

The rest of the world rightly laughs at the all-powerful Americans who

still base their unit of length on the bottoms of men's feet. More tellingly,

a famous 1989 study at Oxford and Northern Illinois Universities found

only half of American adults knowing that the Earth orbited the sun and

took a year to do it. Bush and Gore supporters may not be so naïve as

that, but if Americans were, as a rule, more sophisticated about what's

going on in science, candidates who threw out the "fuzzy math" charge

would find the laugh was on them.

Bart Kosko, a professor of electrical engineering at the University

of Southern California, is author of "The Fuzzy Future."

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