Draw a distinction in a medium made of the same stuff as your mark
If you miss, can you tell?
The distinction creates two states; the unique prime field over two states is ๐ฝโ.
Odd primes means the beats die
Extensions require more than one bit
Neither can exist
The minimal perfect code over ๐ฝโ is Hamming(7,4)
Thus unique geometry of a boundary where signal and noise are the same thing is PG(2, ๐ฝโ)
Everything else is ...
Geometry