Don’t see what this has to do with math.
Nobody claims the bits are altered.
Noise generated by electronic components has nothing to do with math
I don't think you can say "nobody" claims the bits are altered. But my statement wasn't a reply to everyone specifically in this thread.
It was a reply to the "general idea" of an
Appeal to Authority...
To answer specifically why I'm extremely skeptical about the "electrical noise" postulation, with anything approaching a modern PC, is that the overhead for decoding FLAC is so
absurdly low that if the system was impacted by problems like this, there would be all kinds of other situations where it would be impacted, randomly, regardless of whether you are playing FLAC or WAV.
No matter what you do with a PC, your computer is always doing a whole bunch of stuff in the background. Even if you go crazy and try to "super-optimize" services and whatnot (which is a terrible idea unless you're a Microsoft engineer), you won't be able to turn it all off.
So... Why would it uniquely happen when playing FLAC versus WAV (versus a wide variety of other lossless formats)?
The only performance tests I've seen with decent numbers show that FLAC decode performance has
almost zero chance of of impact. I've seen one decent set of benchmarks showing CPU usage for FLAC decoding, and that was a contrived test using ancient AMD hardware. That article was a few years ago, and used a contrived hardware setup to be even able to show a repeatable decode impact measurement (the CPU was a slow AMD low-end part, now years and years old, which was a cruddy one when it was first released, artificially limited to a single core, and so on and so forth). In all other cases, all of the exact same electrical noise environment stuff would be identical (or indistinguishable from noise) between FLAC and WAV decoding.
And I have seen plenty of test measuring output and doing difference analysis on them and aside from clock skew (which would apply equally to all media types) they came out identical time and time again. Someone linked one of these tests above. There are a ton more out there if you look.
The placebo effect is incredibly strong. It can "cure"
serious diseases. Convincing you that you hear a difference is child's play, unless you are extremely careful with your testing environment and setup.
That's why doing science is hard.