non-linear resonance

The idea is this. The brain stores a vast collection of patterns, and in the BKO scheme we store these patterns as superpositions. But then given an input pattern the brain can resonate if it detects a specific pattern. In the extreme case of a "non-linear resonance" the pattern has to be very precise to trigger the resonance. Though we can have weak resonance too, in which case even a loosely similar pattern can trigger a resonance.

Anyway, words are boring, lets give an example in the console:

-- load up this data:
sa: dump
----------------------------------------
|context> => |context: non-linear resonance>

non-linear-resonance |*> #=> 1000 drop-below[0.99] simm(""|_self>, ""|g>) |g>
weak-resonance |*> #=> 200 drop-below[0.6] simm(""|_self>, ""|g>) |g>

 |g> => |a> + |b> + |c> + |d>

 |f1> => |a>
 |f2> => |a> + |b>
 |f3> => |a> + |b> + |c>
 |f4> => |a> + |b> + |c> + 0.9|d>
 |f5> => 0.95|a> + |b> + |c> + |d>
 |f6> => |a> + |b> + |c> + |d>
 |f7> => |a> + |b> + |c> + |d> + |e>
 |list> => |f1> + |f2> + |f3> + |f4> + |f5> + |f6> + |f7>
----------------------------------------

where g is our incoming pattern, and f_k are our stored patterns.
And we have defined our weak-resonance and non-linear-resonance operators (where we need at least 60% similarity for the weak-resonance, and 99% similarity for the non-linear-resonance, and the amplitude of the non-linear-resonance is much higher).

And then, let's look at the resulting table:

sa: table[pattern,weak-resonance,non-linear-resonance] "" |list>
+---------+----------------+----------------------+
| pattern | weak-resonance | non-linear-resonance |
+---------+----------------+----------------------+
| f1      |                |                      |
| f2      |                |                      |
| f3      | 150 g          |                      |
| f4      | 196.15 g       |                      |
| f5      | 198.10 g       | 990.51 g             |
| f6      | 200 g          | 1000 g               |
| f7      | 160 g          |                      |
+---------+----------------+----------------------+

I'm not sure how that table looks to others, but to me it is very, very beautiful. It is showing hints of stuff I have been thinking about for a long, long time now.

Anyway, some comments:
1) the patterns can of course be anything. eg, a very specific sequence of sounds could non-linear resonate with the "frog" neuron. The specific sequence of letters for "beach" might weak-resonate with the "sun", "sand", "waves" and "beach-goers" neurons.
2) the above of course has a lot of similarity with the similar[op] operator.
3) I suspect something very similar to that table happens in the hippocampus. But that is for later!

Update: the above is essentially a 1-D version of the landscape function:
L(f,x) = simm(f,g(x))
Though here we have f and g swapped, so it is:
L(g,x) = simm(g,f(x))

Update: on reflection, I don't think the "beach" thing is a good example of a weak resonance. I'll have to see if I can think of a better example.

Update: we can also have a "square resonance":

square-resonance |*> #=> 200 clean drop-below[0.6] simm(""|_self>, ""|g>) |g>

Now, look at the table:

sa: table[pattern,weak-resonance,square-resonance,non-linear-resonance] "" |list>
+---------+----------------+------------------+----------------------+
| pattern | weak-resonance | square-resonance | non-linear-resonance |
+---------+----------------+------------------+----------------------+
| f1      |                |                  |                      |
| f2      |                |                  |                      |
| f3      | 150 g          | 200 g            |                      |
| f4      | 196.15 g       | 200 g            |                      |
| f5      | 198.10 g       | 200 g            | 990.51 g             |
| f6      | 200 g          | 200 g            | 1000 g               |
| f7      | 160 g          | 200 g            |                      |
+---------+----------------+------------------+----------------------+

Anyway, that should be clear enough. And of course, we can make (almost) arbitrary permutations of the shape of the resonance.

Also, we could call "weak resonance" a "fuzzy resonance". Ie, the pattern only has to be fuzzy close, yet it still resonates.