The nerdy version:
The Vector Space is a 100% analogue vector computer. It takes three CVs (-5V to +5V or 0-10V, selectable by switch) and uses them to calculate a point within a unit cube in vector space. It simultaneously calculates seventeen CV outputs: Eight corner voltages which correspond to the point’s proximity to the eight corners of the unit cube, six plane voltages which are skewed towards the positive and can (but don’t always) double the frequency of a cyclic CV input, and three sphere outputs which correspond to the distance of the point from the centre of the cube, the inverse of that distance and the distance of the point from the closest point on the unit sphere within the cube. The outputs all have bipolar LED indication of output voltage.

The regular version:
Vector Space builds on the concept of the Wiard JAG and moves into three dimensions, as well as adding additional complex outputs, letting you generate seventeen interrelated voltages from three CV inputs. Use it to generate a large number of complex modulations from a small number of simple sources, and vastly increase the amount of modulation you have in your system. Try running three sequencers or stepped voltages to the inputs and then running the plane outputs to a number of VCO frequency inputs for complex countermelodies, run LFOs or random voltages in to get complex modulation voltages out, it works particularly well feeding the outputs back to modulate the speed/shape/etc of what’s being fed in, things can get very complex very quickly. The switches shift the inputs from +-5V to 0-10V to use with either bipolar or unipolar sources, or use the switches as another input source by switching them in real time.