In an attempt to circumvent the University's punishment of writing out lines, the student wizard "Rubber" Houser scrounged some bits of wood and stripped a mattress of its springs to design the Graphical Device. This device began as a four-line writing machine, but eventually became capable of writing sixteen and thirty-two lines at once. Houser's invention became extremely popular- students would break rules so they could have a go at using the Graphical Device (for threepence to use it and a penny to help wind it up). Eventually, Houser's experiments came to an end when someone opened a wrong door and the pent-up force of his prototype 256-line writing machine propelled Houser out of a fourth floor window.
What is being described here appears to be a pantograph, a device which may be used to trace exact size copies of artwork, or scale copies as desired, by adjusting its settings.
More sophisticated versions can even do 3-d copies: an example exists in the British Museum of a pantograph that could follow the lines on a much over-sized design, and engrave it accurately on an actual-size coin blank for stamping currency.
The idea of escalating in powers of two also appears to ape computer memory progressions... in certain applications in Windows, ie when trying to delete more than one image file at a time, I have noticed that the computer can "go rogue" and assume that rather than delete thirty-two large image files, I am asking it to copy them. Before the dust settles and I can properly stop it, I might end up with 256 or even 512 unwanted files to delete with baroque names like "Copy of a copy of a copy of copy 2 of IMG3504"