Given an infinite number of paperclips what are the design constraints?
Paperclips designs are the "string theory" of physical construction.
Ideas in 1 dimension
Obviously you could make a single one-dimensional line of paperclips. This raises the question of multiples sizes of paperclips. Can we make an ever smaller paperclip progression in an interval?
Ideas in 2 dimensions
One could make a 2-dimensional regular fabric of paperclips. The 2D fabric could be made from regular shapes like hexagons instead. How many ways can a plane be tiled, especially if we vary sizes
Ideas in 3 dimensions
One could make a 3 dimensional solid of paperclips. The 2D hexagons could be extended in 3D forming a "bee hive" effect. A 3D paperclip array could have holes and voids forming structures. In 3D the paperclip can vary in size and shape. Bent paperclips arise.
Paperclips don't need to be made of steel. Suppose some are non-conductive so we can form circuits. A non-uniform paperclips could, for example, be a capacitor.
Are there interesting "vibration modes", like waves in a sea?
Ideas in 4 dimensions (varying in time).
Paperclips can move independently. One could clearly make "paperclip wheels". Can we build a timepiece in paperclips?
Tools.
We need to make a solid modeling tool to handle paperclips. We need an MCP server to allow the AI to use the tool. We need a trained AI to "think in paperclips". We need "alignment training" so the results fit our needs.
Further thoughts.
Suppose we go to the moon and find the moon has ideal paperclip material. Might it be efficient to construct a single paperclip factory? Then everything has a common structure and is easily maintained and repaired.
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