Linear Decomposition

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You hit the nail on the head, when you speak of the information contained in the result. The number “100” has less information than “50 ones and 200 quarters”, even though the quantities are equal. That is why factoring is inherently harder than multiplication. But I have never seen a professor quantify this distinction. I am curious if there is such a subject, and what it is called. It seems to apply to countless things.

vwcanter
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I am amazed! The prior clip that demonstrated adding the Bach prelude and MLK's Dream just snuck up on me. Even though I understood the idea, I expected the added sounds to be jarring or noisy somehow. Had to laugh at myself when it just became a sound editing function. Pretty obvious that you would end up with a "soundtrack for the speech" as we hear it.

But then...the excellence of these two sounds individually got to me. Hearing the audience responses drew me in. I have always loved Bach. But, but but but... the way that these two complement one another emotionally! What a great choice! I even became suspicious about MLK doing this intentionally. I can imagine him sitting and writing with this music in the background. Even the key change at the end seemed to match both physically and emotionally to me.

Well. I don't care to correlate emotions with numbers at the moment. But this lecture experience is reminding me of the premise of Hermann Hesse's Glass Bead Game. It appears that the physical properties of tone, cadence, volume would yield to this snalysis to reveal what I am hearing and being... uh, "transported" by. A linear transformation. These correlations are exactly of the same cultural and interdisciplinary type that Glass Bead Game players are described as exploring in that beautiful novel.

Simply brilliant. I am indebted to you. Many deep thanks.

haniamritdas
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My understanding is that pitch discrimination is performed by the cochlea of the ear, which is a coiled up row of resonator cells, lined up in such a way that different wavelengths will excite different resonators of the cochlea. Additionally, the cochlea is ideally constructed to distinguish timbres. Timbres are partly distinguished by the fact that they share a similar set of frequencies, either harmonic sequence for musical sounds, or no harmonic series for other sounds. That focus on timbre is what allows you to clearly hear one piano voice and one speaking voice in the combined recording. People who have perfect pitch hearing report in studies that they have a much better focus on subtleties of timber.

vwcanter
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beautifully chosen Clips, especially for the way the rythm of the Music and of the speech Support eachother

oliverhulesch
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I don't know. Watching again I can't help feeling something deeply philosophical is being asserted here, and yet it falls short somehow.

I guess it centers around the distinction you draw between objects which have 'richness' and those that don't - the common isolated number in this case. For vectors themselves are largely dealt with as components describable by numbers are they not.

I think you are onto something with the idea of information conservation in sound but it is difficult to see in the example of measurement of a simplistic amplitude of a voltage applied to a speaker.

Ultimately I guess what I'm driving at is 'the nickel and dime' problem seems to lie ( but not ) / remain in the realisation of each component of a vector. Why is it the 0.567.. whatever volts is separable ?

Hythloday
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"Your browser does not currently recognize any of the video formats available"
Thanks, YouTube ;P How hard is it to encode a video in a standard-compliant way? ;P

scitwi
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Is this an LA course, or should I say a mind blowing one?

laliborio
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should have seen your videos some 30 years ago. Maybe then I would have taken more care of my ears by listening to music not as loud as I did :D

compphysgeek
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I don't think the ear / brain is decomposing sound literally. Unless trained to recognise and remember, I or you couldn't tell the difference between 5 or 8 harmonious notes played at one time except for the different experience. The reason i recognize MLK over a classical  piece I would say is simply due to relative amplitudes / dominance of signals and the brains ability fill in / predict. I don't think our ability to change our focus onto the lower amplitudes is enough to demonstrate 'decomposition'. See sin wave speech.
Also, it is a bad analogy to compare supposed richness of music with money problem. Given 4 denominations and 4 equations you can determine the decomposition.

Hythloday