Communication theory and the constellation hypothesis of calculation

It is assumed that in translation tasks the brain behaves as an information-processing system for which the time-requirement (t) of a translation is strictly proportional to the information which must be handled in performing it. Writing Qcalc] for the information-requirement of a given calculation, the problem is to define a procedure Q which may be applied to calculations involving various arithmetical operations on numbers of varying magnitudes, such that Qcalc] ≈ k.t. The constant k would then give the information-handling rate.

Experiments with six subjects on seven types of simple addition-sum lead to a definition of Q which satisfies this condition for 25 out of 42 observations. Of the other 17 observations, 14 are accounted for by a modified definition of Q and at least one more on the assumption that “redundant information” may be handled in some cases. The main hypothesis, with these two subsidiary assumptions, accounts well for all observations in a further experiment with four subjects on six types of addition, subtraction and multiplication.

The definition of Q is next generalized by analogy to deal with more complex multiplications. A prediction concerning multiplications of the type x. log x] is borne out by 11 out of 12 subjects and the subsidiary assumptions are not required. Information-rates found by this rapid method range from 2.07-5.78 binary units of Qcalc] per second (BU/sec.) and there is reason to believe that 1 BU is equivalent to 1 bit.