How do we arrive at a proof?
Without proof, are we left with only belief? And is that too bad?
Proofs exist only in mathematics, nowhere else. Experiments, real or computational, only provide a piece of evidence in favor or against a proposition.
For example, in Physics, take the case of classical mechanics. Try to prove Newton's second law of motion. We know it works, given an abstract concept of mass and force (only directly calculable quantity is the kinematic quantity called the acceleration), that's all. Similar is the case with the Maxwell's equations of classical electrodynamics, they are just embodiment of a few phenomenological observations. Can you prove the equations? No. In quantum mechanics, a proposition is made whereby position of particle and its momentum cannot be determined precisely together simultaneously. Can one prove this proposition? Again, a resounding no. However, quantum mechanics is known to work very well for microscopic observables very well.
Talking about proof, yes one can prove the Shannon-Nyquist theorem, with a couple of assumptions, using the theory of Fourier transforms. One of the assumptions has to do with the input continuous (analog) signal being extended in time from infinite past to infinite future. This signal is then read discretely with a particular sampling frequency. The theorem then shows under what conditions a bandwidth-limited signal that is also continuous in time is finally recoverable.
In practice, the analog signal to be discretized/digitized exists for a finite amount of time, and hence the assumption of the theorem is NEVER valid. I have tried already to explain these things in two of my posts:
1)
http://www.hifivision.com/phono-tur...-vinyl-sounds-better-digital-4.html#post37340
2)
http://www.hifivision.com/phono-tur...-vinyl-sounds-better-digital-5.html#post37385
Actually, there can be serious artifacts in real life due to violations of the assumptions of the theorem. This is discussed in my post
http://www.hifivision.com/cassette-tape-decks/12804-vinyl-better-than-cd-6.html#post178184
and in the links given in that post.
BTW, these are very well known facts for the last hundred years. The sampling of 44.1kHz IS a serious limitation, believe it or not or whatever the CD-gurus would like one to believe. Serious interpolation between discretized data points is the order of the day, because getting an infinite amount of data (the final continuous analog output) is NOT possible from a finite number of discrete data (input to DAC).
I have no problem with beliefs provided it is an honest one and is one which is respectful of other beliefs. I have also no problem with religion provided it is not a fundamentalist concept. What is unacceptable though is disrespect in the name of pseudo-science or pseudo-logic.
I honestly think the current debate is pointless to a large extent and that's why I do not like to take part in it. Whenever I see these sorts of debate, I remind myself of the goal of our hobby which is about primarily about music, and not basically about equipments. A little bit of musical appreciation can clarify many doubts in listening, and it takes a life-long journey to acquire that musical appreciation through hard work, and it is not available on the net or in any textbook.
BTW, I listen to 3 kinds of sources:, CDs, audio cassettes, and vinyls. Lately more than 80% of my listening is from vinyls in my modest stereo rig.
Regards.