Here is the BKO:

spikes |wave-1> => range(|0>,|1000>,|1>) spikes |wave-2> => range(|0>,|1000>,|2>) spikes |wave-3> => range(|0>,|1000>,|3>) spikes |wave-4> => range(|0>,|1000>,|4>) spikes |wave-5> => range(|0>,|1000>,|5>) spikes |wave-6> => range(|0>,|1000>,|6>) spikes |wave-7> => range(|0>,|1000>,|7>) spikes |wave-8> => range(|0>,|1000>,|8>) spikes |wave-9> => range(|0>,|1000>,|9>) spikes |wave-10> => range(|0>,|1000>,|10>) spikes |wave-11> => range(|0>,|1000>,|11>) spikes |wave-12> => range(|0>,|1000>,|12>) spikes |wave-13> => range(|0>,|1000>,|13>) spikes |wave-14> => range(|0>,|1000>,|14>) spikes |wave-15> => range(|0>,|1000>,|15>)Now, load that into the console:

sa: load make-ft-spikes.sw sa: simm |*> #=> 100 self-similar[spikes] |_self> sa: map[simm,similarity] rel-kets[spikes] |> sa: matrix[similarity] [ wave-1 ] = [ 100.0 50.05 33.37 25.07 20.08 16.68 14.29 12.59 11.19 10.09 9.09 8.39 7.69 7.19 6.69 ] [ wave-1 ] [ wave-2 ] [ 50.05 100.0 33.33 50.1 20.16 33.33 14.37 25.15 11.18 20.16 9.18 16.77 7.78 14.37 6.79 ] [ wave-2 ] [ wave-3 ] [ 33.37 33.33 100.0 25.15 20.06 50.0 14.37 12.57 33.53 10.18 9.28 25.15 7.78 7.19 20.06 ] [ wave-3 ] [ wave-4 ] [ 25.07 50.1 25.15 100.0 20.32 33.47 14.34 50.2 11.16 20.32 9.16 33.47 7.97 14.34 6.77 ] [ wave-4 ] [ wave-5 ] [ 20.08 20.16 20.06 20.32 100.0 16.92 14.43 12.94 11.44 50.25 9.45 8.46 7.96 7.46 33.33 ] [ wave-5 ] [ wave-6 ] [ 16.68 33.33 50.0 33.47 16.92 100.0 14.37 25.15 33.53 20.36 9.58 50.3 7.78 14.37 20.36 ] [ wave-6 ] [ wave-7 ] [ 14.29 14.37 14.37 14.34 14.43 14.37 100.0 12.59 11.19 10.49 9.09 8.39 7.69 50.35 6.99 ] [ wave-7 ] [ wave-8 ] [ 12.59 25.15 12.57 50.2 12.94 25.15 12.59 100.0 11.11 20.63 9.52 33.33 7.94 14.29 7.14 ] [ wave-8 ] [ wave-9 ] [ 11.19 11.18 33.53 11.16 11.44 33.53 11.19 11.11 100.0 10.71 9.82 25.0 8.04 7.14 20.54 ] [ wave-9 ] [ wave-10 ] [ 10.09 20.16 10.18 20.32 50.25 20.36 10.49 20.63 10.71 100.0 9.9 16.83 7.92 14.85 33.66 ] [ wave-10 ] [ wave-11 ] [ 9.09 9.18 9.28 9.16 9.45 9.58 9.09 9.52 9.82 9.9 100.0 8.79 7.69 7.69 7.69 ] [ wave-11 ] [ wave-12 ] [ 8.39 16.77 25.15 33.47 8.46 50.3 8.39 33.33 25.0 16.83 8.79 100.0 8.33 14.29 20.24 ] [ wave-12 ] [ wave-13 ] [ 7.69 7.78 7.78 7.97 7.96 7.78 7.69 7.94 8.04 7.92 7.69 8.33 100.0 7.79 7.79 ] [ wave-13 ] [ wave-14 ] [ 7.19 14.37 7.19 14.34 7.46 14.37 50.35 14.29 7.14 14.85 7.69 14.29 7.79 100.0 6.94 ] [ wave-14 ] [ wave-15 ] [ 6.69 6.79 20.06 6.77 33.33 20.36 6.99 7.14 20.54 33.66 7.69 20.24 7.79 6.94 100.0 ] [ wave-15 ]I guess that is it. I leave it up to the audience to interpret the matrix results. I guess the main point is that if a wave has frequency f, then it is somewhat similar to a wave with frequency k*f for k an integer, and by "wave" I mean a very spiky wave.

Actually, we can visualize this with a couple of examples:

sa: table[wave,coeff] coeff-sort similarity |wave-2> +---------+--------+ | wave | coeff | +---------+--------+ | wave-2 | 100.0 | | wave-4 | 50.1 | | wave-1 | 50.05 | | wave-3 | 33.333 | | wave-6 | 33.333 | | wave-8 | 25.15 | | wave-5 | 20.16 | | wave-10 | 20.16 | | wave-12 | 16.766 | | wave-7 | 14.371 | | wave-14 | 14.371 | | wave-9 | 11.178 | | wave-11 | 9.182 | | wave-13 | 7.784 | | wave-15 | 6.786 | +---------+--------+ sa: table[wave,coeff] coeff-sort similarity |wave-3> +---------+--------+ | wave | coeff | +---------+--------+ | wave-3 | 100.0 | | wave-6 | 50.0 | | wave-9 | 33.533 | | wave-1 | 33.367 | | wave-2 | 33.333 | | wave-4 | 25.15 | | wave-12 | 25.15 | | wave-5 | 20.06 | | wave-15 | 20.06 | | wave-7 | 14.371 | | wave-8 | 12.575 | | wave-10 | 10.18 | | wave-11 | 9.281 | | wave-13 | 7.784 | | wave-14 | 7.186 | +---------+--------+ sa: table[wave,coeff] coeff-sort similarity |wave-4> +---------+--------+ | wave | coeff | +---------+--------+ | wave-4 | 100.0 | | wave-8 | 50.199 | | wave-2 | 50.1 | | wave-6 | 33.466 | | wave-12 | 33.466 | | wave-3 | 25.15 | | wave-1 | 25.075 | | wave-5 | 20.319 | | wave-10 | 20.319 | | wave-7 | 14.343 | | wave-14 | 14.343 | | wave-9 | 11.155 | | wave-11 | 9.163 | | wave-13 | 7.968 | | wave-15 | 6.773 | +---------+--------+ sa: table[wave,coeff] coeff-sort similarity |wave-5> +---------+--------+ | wave | coeff | +---------+--------+ | wave-5 | 100.0 | | wave-10 | 50.249 | | wave-15 | 33.333 | | wave-4 | 20.319 | | wave-2 | 20.16 | | wave-1 | 20.08 | | wave-3 | 20.06 | | wave-6 | 16.915 | | wave-7 | 14.428 | | wave-8 | 12.935 | | wave-9 | 11.443 | | wave-11 | 9.453 | | wave-12 | 8.458 | | wave-13 | 7.96 | | wave-14 | 7.463 | +---------+--------+I guess that should make the results a little clearer.

Update: I wonder if the brain makes use of something like this?

Update: likewise, we should be able to use simm to measure distances.

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