0 10 then the monte carlo method is the most efficient when the dimensionality n u2267 21 if b is 0 5 and the required required accuracy is 0 01 then n u2267 152 for the monte carlo method to be the most efficient in the optical realization of the von neumann ulam monte carlo method a matrix with elements of exitance i ij is displayed on the crt input device 14 fig3 the matrix has n rows and n 1 columns we will take the m th row of the matrix to correspond to the m th urn described in the previous section also we will take each column of the matrix to correspond to a different type of ball the crt screen is imaged onto the photon event counting 20 detector the light level at the detector is reduced to an acceptable level by inserting a neutral density filter 30 or by stopping down the aperture of the imaging system with the pinhole camera 28 from eq 1 the probability p mi that a photoevent is detected at spatial coordinates x m y i is related to the exitance of the associated matrix element on the crt by the equation equ18 where i mi is the exitance of the matrix element in the m.