1. Your first statement is not technically correct. There is no "precise curve that proves your results are random".
2. You seem to have missed the point of my second point. It doens't matter what shape curve you get or where it is centered. No matter how many students do or do not pick out the Strad... or how you analyze the resulting data...
You WILL NOT learn with absolute certainty whether a certain specific student can or cannot do so. It is simply the wrong sort of test if that's the data you're looking for.
3. ... So, based on all of that, I would say that it's reasonably likely that nobody can run a mile in two minutes.
1. Here we go again. My first statement IS technically correct while yours is a deliberate LIE!! You've made-up your own (incorrect) statement, falsely attributed it to me and asserted I'm incorrect.
2. No, I did not miss your point and again, I did not mention "absolute certainty"!
3. And here we are yet again. Firstly: On what basis would you say that "it's reasonably likely that nobody can run a mile in 2 minutes"? It's certainly NOT any sort of rational or even common sense basis! The world record for the mile in the late 1960's was 3:51 and today it stands at 3:43. Even with all the modern scientific advancements in training that's still only an improvement of just 8 seconds in over 50 years, so a further improvement by another 103 seconds (to 2:00) is NOT "reasonably unlikely" it's incredibly unlikely and almost certainly utterly impossible (without artificial enhancements)! Secondly, what if we say a 10 times improvement over what anyone has ever demonstrated, a mile run in 22.3 seconds, how likely would you say that would be? Would you really not be "certain"? If not, that would put you in a tiny group of cranks/nutters! Many of the differences reported by audiophiles are more than ten times beyond what has ever been demonstrated.
I understand, you make and sell relatively expensive amps. It's vital that you somehow justify that extra expense and therefore you have no choice but to obfuscate the likelihood that the differences between your amp and a much cheaper one being audible but this is the wrong forum for such marketing tactics, this is the sound science forum, as you well know!!!
[1] However, do you really believe two amplifiers with the electrically totally equal scheme, but built to a vastly different price point - SOUND THE SAME ?
[2] That additional would buy the customer better and more precisely toleranced electronic components in the circuit itself, better power supply - or even supplies, as in mono blocs; better chassis ( there is such a thing as microphony in amplifiers ... - and better, sturdier cabinets are there not only for looks, but can actually aid in better sound quality ), and so on and so forth.
[3] The law of diminishing returns is very much still alive - as is the edge the pricier amps have over the lower priced. [3a] Saying that both perform and sound equally is simply not true.
1. You're joking right? On the one side we've got numerous reliable/controlled tests, plus objective measurements indicating differences are below/well below audibility. On the other side we've got a bunch of marketing, plus numerous uncontrolled tests and anecdotal audiophile "impressions", all of which vanish when subject to reliable/controlled testing. So of course I "really believe" they sound the same, I'd need to be an irrational nutter to believe otherwise!
2. All of which are irrelevant unless those more precise tolerances, better power supplies, etc., collectively make a big enough difference to be audible. Therefore, all you have to do is provide some reliable evidence that they are audible!
3. The law of diminishing returns (for amps) is dead, it's been dead for several decades! Audiophile amp manufacturers have had to develop strategies to get around this fact, which would otherwise put them out of business. The two most common appear to be: 1. Carry on incrementally improving amp specifications ever further beyond the threshold of audibility and then obfuscate (or outright lie about) what is the threshold of audibility. 2. Deliberately (colour) lower the fidelity of the amp's output by an amount greater than the threshold of audibility and then claim it is better/higher fidelity.
3a. If it's "simply not true" that they sound the same, then it's "simply" a matter of providing some reliable evidence to support your assertion. However, despite your promises you NEVER provide such evidence and therefore the only rational conclusion is that you're either simply lying or simply deluded.
"all amps sounds the same" is false. it's easy to disprove as we just need one case where 2 amps do not sound the same within all existing amps and all existing conditions.
No one is saying all amps sound the same without any conditions, such a statement would obviously be ridiculous. For example: A 10w amp will sound very different to a 2000w amp when driving say 1000w speakers at a reasonable level, a deliberately audibly coloured amp should sound different to an amp designed for accurate/high fidelity, a broken/non-functioning amp will obviously sound very different to a fully functioning one. The conditions for the statement that amps sound the same are relatively self-evident; for example: The same appropriate load, functioning well within specifications and designed for accurate amplification/reproduction rather than deliberately coloured.
G