We're divided over "Affirmative Action". Pete Wilson, Governor of California, former Presidential candidate, would replace Affirmative Action with "complete merit testing". Does "merit" testing represent our social functions and responsibilities?

Suppose I'm your financial adviser. Unknown to you, I can advise three types of investments. A: businesses whose products contribute nothing to daily life but promise investor dividends. B: businesses whose products threaten your wellbeing, environment, or rights, but promise dividends. C: businesses whose products promise dividends and improve the quality of your life. But I've advised only A and B investments, which may pay monetary dividends but daily penalties. Am I a good financial adviser? HAVE YOU A CHOICE?

Replace "financial adviser" by "math teacher" or "college entrance tester" or "hiring tester". Replace "A" by technically understandable math problems unrelated to daily life, but solutions might "get you into college" or "hired". Replace "B" by intimidating problems, but "winging it" just might get you chosen. Replace "C" by problems whose solutions both facilitate your daily life and might get you chosen. Am I a good math teacher or a good tester? DO I GIVE YOU A CHOICE? What are these C-problems?

For citizens of a democracy and consumers in a market economy, role- playing resides in CHOICE. A citizen needs choices as to representation and achieving rights to differ from a collectivist clown. A consumer needs purchasing choices in a market economy, to differ from a medieval peasant. Citizen-consumers need education about all options for choosing the desirable, to differ from nonentities. YOU ARE THE CHOICES YOU CAN MAKE! YOUR ARE THE ROLES YOU CAN PLAY!

"Choice-mathematics", or combinatorics (also called "counting without counting"), BEGAN some 250 years, from foundations 2500 years old. (It is the "C" in "The Mathematical DNA", which I prescribe for children.) Yet our schools don't teach applied combinatorics! Why? Why bother? College entrance and hiring tests ignore combinatorics. Why study a subject you won't be tested on to get into college or get a job? Especially, when no one told you the importance of combinatorics in your every day life!

Why isn't COMBINATORICS taught? Why can't we CHOOSE it? Is combinatorics too complicated to be taught and applied?

No. COMBINATORICS USES ARITHMETIC ALREADY TAUGHT! In fact, I've explained combinatorial strategy to third-grade children in my Yes, it's true that two combinatorial subjects (combinations and permutations) are abstractly taught in high school or college "algebra" classes. Thus, given n distinguishable items, their COMBINATIONS COMPREHEND ALL CHOICES WITHOUT REGARD FOR ORDERING. YOU SEE, ORDER-CHOOSING IS KNOWN AS PERMUTATIONS.. Formulas for both permutations and combinations involve ratios of the "factorial" combinatoric. What is "factorial"?

Frinstance, "factorial 5" (written "5!") equals 5 x 4 x 3 x 2 x 1 = 120 (choices). A child should discover the 120 ways of counting fingers of one hand. From 5 children, 120 basketball teams can be chosen, From 9 children, 9! = 362,880 baseball teams. From 11 children, 11! = 39,916,800 football teams. Etc. "Kids, you're rich!" You're even richer. You've just learned the key to a vast field of math which has created some powerful physics and created millions of jobs (say, in electronics).

All permutations for n choices constitute a mathematical group, which models conservation laws of physics. I've taught the ideas to third-grade children in "The Creeping-Baby Group" and in "Colored Multiplication Patterns -- Colored Conservation Laws".

Committees and groups often select "the most meritorious" candidates for jobs or contracts, in contests, etc. My mathtivity, "Trap the Wild Word", teaches, say, sixth-grade children in binary search for a defined word designated by "the leader" from a dictionary of around 1000 pages. Asking 15 questions, answered "Yes" or "No" by the leader, "traps the wild word". But nobody teaches you this. NOCHOICE!

Sieving, perhaps most useful (and inclusive) combinatoric, is ancient (and includes searching). I've taught children to "sieve out" prime numbers from composite numbers by flipping tags hung on a wire. This models diagnostic testing and strategies for repairing cars, TVs, etc. "Were all possibilities (choices) considered?" NOCHOICE STRIKES AGAIN!

Statistics and probability derive from event combinatorics. A statistical t-test answers such "your-money's-worth" questions as: "Does a 9 tomato-can sample have an arithmetic mean weight 'close enough' to the advertised 14.5 oz.?" NOCHOICE STRIKES AGAIN!

As lotteries, off-track betting, legalized casinos proliferate, America becomes Americasino. For 30 years I've advocated "How to Gamble If You Must" in public schools. No wonder there's a sucker betting every minute! NOCHOICE STRIKES AGAIN!

Combinatorics also exposes our limits-- such as no perfectly "fair" rule for "round robin" tennis tournaments. Brown eliminates Adams while Davis eliminates Curtis. Curtis might eliminate Brown, but won't get the chance. Any sports, hiring, or promotion decision-making with implicit "round robin" structure suffers the same bias: denial of choice. How many sports fans, registrars, or supervisors know this? NOCHOICE STRIKES AGAIN!

The same combinatorics explain the impossibility of perfectly "fair" rules for apportioning representation to states or other political entities. Let students discover there's no method for rounding fractions to integers with a given sum that satisfies three natural conditions: "The House of Representatives Problem". Discover that majority rule is certain only in two-candidate elections. Kenneth Arrow, 1970 Economics Nobelist, proved the impossibility of a voting system satisfying five reasonable conditions. NOCHOICE STRIKES AGAIN!

Merit testing perpetuates ignorance of citizen-consumer richness of choice on the one hand, limitations on the other. PERPETUATES NOCHOICE!

If evolution operates socially as well as biologically, is it surprising that "merit tests" favor Governor (NOCHOICE?) Pete Wilson's favorite meritists, who are "well-prepared" white males?

How are our sophisticated citizens and consumers worse off, in this respect, than an ancient illiterate Shepherd?

To explain, I must explicate the term "calculus". Don't flinch! I don't mean that math course involving limits, derivatives, and integrals. The word derives from the Latin for "stone" or "pebble". The physician calls a gallstone "a calculus". Mathematicians refer to many algorithmic devices as "calculi". (For example, the "truth-table" method for determine the validity/invalidity of a statement is a "logical calculus".) For an ancient illiterate Shepherd, the calculus was a pebble in a little bag to represent a sheep.

When the Shepherd allowed a sheep from the pen, he would put a pebble into the little skin bag: one pebble for each sheep exiting the pen. When the pen was evacuated, the Shepherd tied the bag to his belt, took up his crook, and herded the sheep to graze in greeny mountain fields. Upon herding the flock back to the pen, the Shepherd removed a pebble from the bag for each sheep entering the pen. If all the sheep were enclosed and the bag was empty, the Shepherd's "books were balanced". But if all returning sheep were enclosed and one pebble remained in the bag, the Shepherd knew he must look for "the lost sheep" (in the famous parable of Jesus).

Elsewhere I explain the "rationality" problem facing economists and political scientists. This ignorance of consumers and citizens regarding number of choices confounds the irrationality of voting and buying. If a citizen or consumer had rejected or balked over x choices and then noticed "one or more choice in the bag", the more rational nature of his/her decision process would assist the political scientist or economist in evaluating and understanding that decision process. And perhaps make for better predictions.

Also elsewhere, I've described the difference between "epistemic" ("Whaddya know, Joe?") and "ontic" ("What's real, Neal?"). What you know or don't know about a process is epistemic, and (at least, theoretically) is correctable or modifiable. What is "built into the process or built into reality" is ontic, and cannot be corrected or modified. I've explained elsewhere that economic and politcal activity (like sports) depend upon the two relations of "competing" and "preferring". And -- like it or not! -- neither relation is transitive -- the essential PRECONDITION for putting choices (or whatever) in order of "best" and "least". If Team A beats Team B, and Team B beats Team C, will A beat C? Mebbee. Mebbee not. That's how some book-makers get gots and some bettors get got. If Yoda prefers bannanas to apples, and apples to oranges, but prefers oranges to bannanas, there's no "law" that says he's "inconsistent" in such a preference. (Remember? King Arthur built a Round Table at Camelot so that no knight would be "higher" than another.) So quasi-transitivity (sometimes works, sometimes doesn't) is built into competition and preference relations -- ONTIC! But the citizen or consumer not realizing that one more "choice in the bag" is an EPISTEMIC problem and, sometimes, correctable! Either force combinatorics on teachers and "merit testers", or give up "merit testing" as "being without merit in a democracy and market society"!

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