**6. Summary and conclusion**

This paper reviewed the evidence for long-range contextual modulation and concluded that it implied cortical convolution at the scale of the visual field. This resulted in the need to address the problem of how such long-range convolution could be accounted for with known cortical connectivity and within known time constraints. The paper proposed a solution to the problem that emerged from a mathematical analysis of cortical connectivity to account for the implied constraints of long-range convolution. In particular, it was argued that the known distribution of the long-range patchy connections and extrastriate connections is adequate to provide the means by which the global visual signal can be transformed into frequency space where the convolution can be performed. The main thrust of the argument was that these long-range connections facilitated the transformation of the signal into and out of the frequency domain via a new fast Fourier transform named PaSH-FFT. A mathematical proof of the most general form of this FFT, GOSH-FFT, was provided in the appendix along with MatLab-like pseudo-code to facilitate the implementation of GOSH-FFT in computer software.
