I had ideas for a application of nupic technology.  But first, I need to know a 
few things.

HTM currently learns sequences.   So:
Can it learn a sine wave, given that HTM neurons are just on and off?  

A sine wave is a smooth curve, and if I were to represent it with my own binary 
code, I would use two numbers (all numbers can be expressed in base-2 as 
binary) – one would be the amplitude (y-axis) and one would be the angle 
(x-axis).  But I doubt sparse representations would represent it that way.  

Secondly, sine waves go on forever.  Would HTM predictions be affected by that?

There is a cell phone application that recognize tunes.  You hum it into the 
cell phone, and it tells you what the tune is.  Obviously the frequencies in a 
taune are more complex than just a sine wave – they vary in phase and 
frequency, and there are several frequencies occurring together, and then some 
stop, others start.   Would this overwhelm HTM?  

The above is actually not what I want to work on, (since it has been done 
already, though not with nupic) but it is related to the idea I have.

Yet more questions, taking this tune-recognition application further:
1)
Perhaps you would need several levels of regions, the lowest that would tease 
out the basic frequencies, and a higher one that would put them together again?
2) 
Also, if you were to associate a song title with the song, that raises a whole 
new question.  Suppose I have 2 regions.  One is presented with the title.  The 
other is presented, over time, with the tune.  Both feed into an upper layer, 
and the upper layer has feedback to the lower layers.   Would that setup 
associate a song title with a tune?
The same issue would be for learning language in general.  If you learn a word, 
it is just an arbitrary set of sounds associated with a concept.  So you would 
have to feed the word to one region, the concept to another, and somehow they 
would have to communicate.

Thanks in advance
Gid

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