Originally Posted by ralphp@optonline
Perhaps simplest way to address this issue is just to ask exactly what part of the Nyquist–Shannon sampling theorem is it that one disagrees with and to please provide mathematical proof of the error in the original theorem.
Seems like a good idea in theory but this approach still has problems:
1. Many don't understand what a theorem actually is, or how this particular one applies to digital audio. Many theories exist to explain some observed natural phenomena and may or may not be correct or entirely correct. This doesn't apply to digital audio though, because digital audio is a technology invented from the theory, not something which existed naturally and then a theory was invented to try to explain it. A fairly subtle but important difference which many audiophiles can't or don't want to grasp.
2. Physical audio equipment (ADCs and DACs) cannot perfectly apply the Nyquist-Shannon sampling theorem, there are real world engineering constraints which make it effectively impossible, a fact which the better educated audiophiles and audiophile equipment marketing departments are happy to exploit. In practise, real world engineering constraints still allow us to get very close to a perfect implementation of Nyquist-Shannon and any imperfections which do exist are (or should be) many times below audibility.
3. You assume, incorrectly, that Nyquist-Shannon automatically applies to all digital audio but this isn't always the case in the audiophile world. There was a trend at one point (I don't know if it still exists) by a few audiophile DAC manufacturers to market "filterless" DACs. This deliberately breaks the Nyquist-Shannon theorem, which specifically requires a band-limited signal (a signal which does not exceed half the sampling rate).
4. To some/many audiophiles their perception is sacrosanct, hearing is believing and they "trust" their hearing. Because this belief is sacrosanct and therefore unquestionable, anything which does question (or worse, disagrees with) it, MUST be incorrect. No matter how proven Nyquist-Shannon is, or how impossible to disprove, it just doesn't make any difference, it MUST somehow be wrong or it (and any other part of accepted science) MUST have missed something. Unquestionable belief in a perception is an irrational position to take and even more frustratingly, rational arguments are typically ineffective against irrational people. In fact, the more rational/proven/accepted the facts presented, the more irrational/ludicrous the responses have to become in order to preserve the sanctity of their belief, and this inevitably results in accusations of a complete lack of basic education or of actual insanity. As personal attacks are forbidden here, and this site largely exists to cater to audiophiles, the only option is to effectively ban science and rationality from any discussion. We end up with a hobby/passion entirely based on science but where the discussion of that science is effectively forbidden (except in this sub-forum), a thoroughly bizarre state of affairs!!
I'm usually all for letting sleeping dogs lie and allowing people to accept any old nonsense they want to support whatever beliefs they want. The problem is that many of these dogs aren't sleeping! Many/Most who come to this site come here for information and immediately become targets for indoctrination by these (very awake) dogs and the manufacturers/retailers who make a living from them (and their shills). All of which is incredibly frustrating for those of us who actually love audio. [/rant]! :)