internal state” (Piccinini 2007a, 514, italics added). The mechanistic “rule” also highlights this distinction. “A rule [...] is simply a map from input strings of digits, plus possibly internal states, to output strings of digits” (Piccinini and Scarantino 2011, 8). This suggests that digital computation proceeds from input D and possibly the internal states of the computational system to outp...

For certain sequences A of positive integers with missing g-adic digits, the Dirichlet series FA(s)=∑a∈Aa−s has abscissa convergence σc<1. The number σc is computed. This generalizes and strengthens a classical theorem Kempner on sum reciprocals sequence decimal digits.

We describe the extraordinary memory of C, a 21-year-old student who experiences synesthetic colors (i.e., photisms) when she sees, hears, or thinks of digits. Using three matrices of 50 digits, we tested C and 7 nonsynesthetes to evaluate whether C's synesthetic photisms influence her memory for digits. One matrix consisted of black digits, whereas the other two matrices consisted of digits th...

When C, a digit-color synaesthete, views black digits, she reports that each digit elicits a highly specific color (a photism), which is experienced as though the color was externally projected onto the digit. We evaluated this claim by assessing whether C's photisms influenced her ability to perceive visually presented digits. C identified and localized target digits presented against backgrou...