# Arithmetics of Ideality

## G. L. Filkovsky, Nomura Securities International,New York, USAe-mail:Gfilkovsky@us.nomura.com

With the letter to the editor [1], a new direction of TRIZ research has been opened: to find a most meaningful combination of meaningless symbols. The meaningless symbols of course are S(u) and S(h), since it is still unknown how to add up usefull functions or harmful effects numerically. Nevertheless, there are two formulas proposed, based on these undefined numbers:
1. I = S(u) / S(h)
2. I = S(u) - S(h)

Staying on the same level of simplicity, i.e. without using any higher math, let me propose two more:
3. I = (S(u) - S(h)) / S(u)
4. I = S(u) / (S(u) + S(h))

Let me explain. The advantage of both of these formulas is that an ideal system, i.e. a system with useful functions and without harmful effects, has the full and complete ideality: 1! An advantage of formula 4 is that it measures ideality on a scale 0 to 1, where a useless system with harmfull effects has 0 ideality, while a system with some useful functions is always somewhere in between. On the other hand, formula 3 makes an ideality negative if a sum of harmful effects is greater than a sum of useful functions. (Whatever that means.) By both formulas, ideality of a system with no useful function and no harm is undefined. That makes sense.

I'd also like to make an interesting observation regarding all the formulas: they open new ways of increasing ideality! The formula authors always consider increasing ideality by increasing sum of useful functions and/or decreasing sum of harmful effects only, but there are other possibilities:

Formula 1. Ideality of a "positive" system, i.e. a system with more use than harm, can be increased by subtracting equal amounts from both the useful and the harmful components. Example: if S(u) = 20 and S(h) = 10, then I = 20 / 10 = 2; subtracting 5 from the both makes I = 15 / 5 = 3, i.e. increases ideality 50%! Accordingly, adding equal amounts to both components can increase ideality of a "negative" system, i.e. a system with more harm than use.

Formula 2. It behaves in a different way: ideality of a "positive" system increases twice by doubling both components, while ideality of a "negative" system increases by halving both.

Now, this goes beyond just an exersise in math - it could be a research project:
Since systems evolve toward increasing ideality, if a research of "positive" systems showed that both their useful and harmful components tend to shrink, it would give a point to something like formula 1; if, on the other hand, it showed that both components tend to grow, it would support formula 2 and alike.

Anybody is ready to pick up the challenge?

R E F E R E N C E S:

1. Letter to the editor, From: Mark Barkan, The TRIZ-journal, September 2003.