Analysis for Challenge 10

Clearly, the first task will be to convert 25 nanoacres to a square of manageable (recognizable) dimensions.

We first define a term:  The Acre Edge (AE=acre1/2).  If the reader can accept this terminology, then the edge dimension is given by

    (25×10-9 acres)1/2•(208.71033 ft/AE)•(12in/ft)•(2.54cm/in) = 1.0058 cm

                                                                                         = 0.010058 meter

Philosophical Commentary

The absolute fastest signal-traverse would necessarily be limited by the speed of light.  In a realistic circuit the signal path would include circuitry (which would slow the propagation).  If only a wire (or light pulse) was needed (no signal management, no amplification, etc.), the integrated circuit would not be required.

The Calculation

Per Wikipedia, the speed of light (with certain qualifying conditions) is given by

                                 c =  299,792,458 meters/sec 

Thus,

                    tProp(min) = (0.010058 meter)/(299,792,458 meters/sec)

                    tProp(min) = 33.6 picoseconds

which is about one-thirtieth of one nanosecond.  This represents, then, a figure of merit for best-performance.  Any practical circuit whose line-of-sight signal path is approximately 1cm must necessarily be slower:

   1.  The actual signal path (up, down, over, under, around, and through) will be greater than 1cm
   2.  Signal movement will be slowed because of the need to charge & discharge junctions, etc.
   3.  The medium is not the vacuum of space