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.
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updated: 19/12/2016
by Garry Morrison
email: garry -at- semantic-db.org