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PONTIFICIAE ACADEMIAE SCIENTIARVM SCRIPTA VARIA - 28 
LEONTIEF 
The structure of an analytical system which one decides to use in 
any particular instance must to a very large extent depend on the 
type, that is, amount and accuracy of factual information actually 
available for its implementation. Refinements of statistical methodo- 
logy are often wasted on all too crude raw material of primary data. 
FRISCH 
I have been listening with interest to the discussions in a field in 
which I took great interest some yars ago and which I think I was 
at that time qualified to speak. Today I do not think I am qua- 
lified, quite to the same extent, but since I have been called upon 
let me just give one example which is connected with what Pro- 
fessor LEONTIEF said right now. Suppose for a moment that you 
have a curve whose mathematical form you actually know. . It is 
for instance a second degree parabola. For a moment you forget 
this mathematical knowledge and you look for some numerical data 
to determine the tangent at a specific point A. You have observa- 
tion in the vicinity of this point. Let each of these observations 
be affected by an error of measurement. In order to have actually 
the tangent (not the secant) in the point considered, you want to 
use observations that are as close as possible to the point A. If 
you really want the tangent (not the secant) at this point you would 
have to creep up to the point A as close as you can. But in so doing 
you expose yourself more and more to the inaccurancies involved 
in the numerical observations and if you get two points that are 
very close to A you get something absolutely absurd. So you have 
to make a compromise between. giving up a little of the ideal you 
are looking for, i.e. the tangent instead of the secant, you have to 
do it in order to get a method which is more robust. You must 
make a compromise, and a practical man will understand more or 
less intuitively how far he should deviate from the mathematical 
ideal in order to have a result which is useful for his purposes. 
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Wold - pag. 70