This is a joke. Severe apologies if you actually expected this to calculate Fourier transforms for you. This calculates 'fourier' and 'fouriest' transforms instead. See Zach Weiner's paper for an explanation of the mathematical concepts involved.
How to use
bash-3.2$ irb irb(main):001:0> require 'fouriest' => true irb(main):002:0> class Integer; include Fouriest; end => Integer irb(main):003:0> puts 624.fouriest_didactic 624 has a four-count of 1. The bases in which 624 has a higher four-count are: 5, in which it is [4, 4, 4, 4], with a four-count of 4. 12, in which it is [4, 4, 0], with a four-count of 2. 155, in which it is [4, 4], with a four-count of 2. Obviously, the highest four-count among these is 4. The bases which yield this four-count are . These are the bases of its fouriest transform! => nil irb(main):004:0>