__Why It Is Impossible Neither To Prove Nor Refute That Machines Evolve Towards Ideal Machine__

*Y. B. Karasik, *

Thoughts Guiding Systems Corp.,

Ottawa, Canada.

e-mail:karasik@sympatico.ca

Some people believe that Altshuller
first conceived the notion of Ideal Machine towards which all machines evolve and
THEN converted it into a practical problem-solving tool called IFR.
In reality it was the other way around. He first invented a heuristic problem-solving tool IFR and
THEN put "scientific" foundation under it by inventing the notion of Ideal Machine and conjecturing
that all machines evolve towards it.

Unfortunately the latter conjecture is
impossible neither to prove nor refute.
Indeed, one can speak about convergence of a sequence {X_{n}} to X
only when a norm || X - X_{n} || is defined.
Altshuller never defined such a norm to enable verification of his law.
He was a clever man.
On the contrary, Simon Litvin & Zlotin noticed the gap and hastened to fill it.
Their norm was trivial: specific weight or any other specific characteristics
[1]:

||X - X_{n}|| = (W(X) - W(X_{n}))/(V(X) - V(X_{n})),

where W(X) means weight of X and V(X) means volume of X.
Then deviation of a real machine M
at the n-th stage M_{n} of its evolution from the ideal machine IM is equal to

||IM - M_{n}|| = (W(IM) - W(M_{n}))/(V(IM) - V(M_{n})) = W(M_{n})/V(M_{n}),

because W(IM) = 0 and V(IM) = 0.

Altshuller probably felt that under this norm
there is no convergence of machines {M_{n}}
to Ideal Machine and he resisted all who proposed it.
But being not a mathematician he could not explain why he felt this norm was not good. He just kept rejecting it.
And Litvin and Zlotin perceived his stubbornness as a whim of an old fool.
To them the norm seemed to be obvious and natural !

Devising a norm under which machines converge to Ideal Machine is an open
problem in mathematical foundation of TRIZ. It is quite possible that such norm
does not exist. But proving or refuting it is also an open problem in mathematical foundation of TRIZ.