Related articles: Boolean Sorcery
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This month’s HackerBox features digital logic circuits, reminding me of a design I have been contemplating for a while. The mathematical foundation of digital electronics, Boolean algebra, is based on three logical operations: conjunction, disjunction, and negation. The gist of Boolean sorcery is applying these and derivative operations to magical objects (it may help to visualize how these operations apply to polygons).
I envision a box having a rotary switch for selecting the Boolean operation to perform, a power switch, and a Venn diagram having two pairs of electrical contacts (one for each circle) and an LED in the center of where the circles intersect. Two magical objects are sculpted in conductive or resistive play-dough (the name-brand stuff is conductive but you can make your own conductive and resistive doughs, adding small quantities of magical ingredients as desired; I typically use food coloring to color my conductive dough red and resistive dough blue), and then placed on the pairs of contacts. The selected Boolean operation determines whether or not the objects together light the LED. E.g., to amplify a quality shared by two things, the sorcerer would select the AND operation, sculpt both things out of conductive play-dough, place one sculpture on the pair of contacts labeled ‘A’ and the other on the pair labeled ‘B’, then toggle the power switch — electricity would pass through both pairs of contacts connected to an AND gate, and the LED would light up. To rid herself of some quality, the sorcerer would select the NOT operation, sculpt an image of herself in the conductive dough and place it in ‘A’, and use the resistive dough to sculpt an image of the quality to be subtracted, which she places in B — when the power is switched on the LED will light because electricity is conducted through A but not B. You need not be an adept sculptor to do this; you could simply form crude disks (or use a cookie-cutter) and inscribe magical words or sigils into them.
Below is a diagram showing an AND gate circuit using a 7408 semiconductor. If both doughs are conductive then the LED will light; if either dough is resistive then it will not.
More complex relations between objects could be made with multiple gates (or by using a microcontroller or other computer), and the output could be something other than an LED. Appropriate talismans may be drawn on the box or placed within it.