How much can be measured -- and how much cannot?

"How important do you think measurements are?"

Important, but do not tell the whole story. Not likely that they ever will in the foreseeable future.

"Are the ears really the only true arbiter?"

In the end, for the end user, yes. No two ears along with the rest of the human auditory sensing system behind them are exactly the same, just like stereo gear. What else could possibly take their place?

Specs and measurements are most useful to help determine what gear might/should play well together up front during the decision making process, but its all you and your ears from there.

"The final of the Sibelius 2nd will give me goose bumps on certain speakers. I know of no measurement that will tell me which speaker will do that for me."

No, but to Almargs point, when shopping for gear with the best chance of doing it, impedance specs allow matching from output to input that if accurate and applied properly as a factor in the decision making process is more likely to result in better dynamics and lower distortion, two attributes that are generally desirable from a goosebumps perspective regardless of what speaker is used.

"Despite audiophile claims to the contrary the science of of sound reproduction is extremely well understood"

No doubt. One is always at risk when proven scientific principles are ignored or not applied in solving a problem.

Here are the most useful audio specifications/measurements for me that I tend to always take into consideration:

Input and output impedance so these can be matched between components for better dynamics and lower distortion.

In addition, for amps, I look at power ratings, damping factors and current delivery related specs to get an idea of how well an amp might be able to drive a particular set of speakers.

Sensitivity related information can be useful as well,especially when dealing with various phono section designs and speakers.

I do not usually pay too much attention to distortion specs. I will look at various charted lab measurements if availble from a reliable source in order to gain more insight when possible.

That's mostly it that I can think of off hand.

I would say that a basic understanding how to interpret and apply audio metrics is a very advantageous skill for any true audiophile who wants a systematic means of improving their sound reliably to develop. It's something I am still working on and I try not to lose any sleep over these things though I probably have in practice from time to time.

"I agree with your clear reasoned examples, they will certainly have value in determining likely(or unlikely) compatability. They won`t help in determining the sound quality of various component matching."

Disagree somewhat.

Accurate impedance specs or even estimates are more likely to help assure quality of certain attributes (like dynamics and distortion) of the resulting sound than anything else.

However true that there is no guarantee that specs are accurate and the complete nature of the resulting sound still cannot be known until heard regardless.

Perhaps it would help to look at certain specifications and their application (like impedance matching)as a form of quality control one can practice before buying, though as has been stated repeatedly, the complete final results cannot be known until heard.