Now, it is part of the hypothesis Pecsd that PG J. From this it | 
is easy to deduce that J[C‘PG P,,, or that reC‘P.9,.2P,. a | 
Moreover, it follows from the definition of P,, that yPx and yP..@ | 
448 Mr Norbert Wiener, A Contribution to the 
are incompatible hypotheses, and hence that Bete |P..%. Thm 
fact, combined with (1), gives us 
27> 27 CS 
PAP eel se eOUP s 2) 5 Ue. mn seca 
SO) Ue Gam E88 =P | Pye Ba Doe Yl ae 2) 
From (2), (8), and the definition of tp, we have 
ro/Peg@d,aweGvP.>- 
minp‘P,, ‘7 = p*P,.“‘minp‘ P,,‘« . D . Minp Pema 
This is the desired proposition. 
It will be observed that the only portions of the hypothesis _ 
of Pecsd of which we actually make use in this theorem are 
PGJ and P| P,,.€ P| minp|P,,. The theorem ensures us that | 
t.CSP Cs‘rp: that is, in the case of time, that each event shall | 
be at some instant—the instant at which it begins. For, since | 
= 
PGJ, IF} CPCP,,. This ensures that ce P,,“2. Moreover) age 
v v=— 
we have just seen, a+ P| P,,x, or we — P“P'x. Therefore, if 
> vy > - 
ceCP, xe P,,'aan CiP — P“P,,‘a, or xe minp‘P,,‘2. As we have | 
—p 
proved in *0:21 that minp‘P,,‘ve7Tp, we get the formula 
POEMS S*Tp. 
I now wish to prove that inst“‘esd C comp. 
*0°22. |. inst*‘esd C comp. 
Proof. 
As we saw in *0'1, (1), 
Dace 20 0a pee a, ane oe. 
(Hv, y)-vea.yeR.aPy. 
Since FR ecsd, by definition, implies & € &| R,, | R, this gives us 
ne elcsde > tens tela 6 a> 
=> => 
a=pP..“a.B=p'P. 8. (Ha, 7) = 2 eo. Vie Gm) 
