The notion that one grain of sand on a beach is not important, but one hundred are, is dubious to say the least.

My argument was actually that 1 grain of sand on a huge beach is almost never important. I made no statement about how many grains of sand result in what other level of importance. And I don't hear you refuting the claim that one grain of sand on the beach is almost never important (and so people dealing with such situations should expect to have to do a tiny bit of extra work). And I doubt anybody will argue with an assertion that the first significant bit is almost always important. There is, of course, no clear "line" where the bits on one side of the line are clearly important while those on the other side are clearly not important. Yet, in a 'double', we have at least 1 bit that almost always matters and at least 1 bit that almost never matters.

First: it's not about print really. It's about stringification.

Sure, I was talking about the default stringification which I sometimes referred to as 'print' as a shortcut.

Perl scalars can get pPOK from "action at a distance"; and stringification is currently lossy.

Certainly stringification can happen for subtle reasons. You seem to be implying that you can get a loss of precision due to "action at a distance". No, stringification is not lossy in that way. What is lossy is taking the default stringification and then converting that back to a number. A Perl scalar getting stringified does not cause any loss of precision in that scalar (the original numeric value remains along side the stringification).

Frankly, this sounds like you are discouraging perl use for scientific work

Perhaps you jumped to that conclusion because you thought that Perl's default stringification could cause numeric values to lose precision due to "action at a distance"? I certainly was not arguing that Perl is inappropriate for scientific work. I was making the point that just pasting the default stringification output from one set of calculations as input to another set of calculations can be inappropriate in scientific work. But then, my experience is that scientists are aware of this. Though, most scientists are calculating how many significant bits they can claim from their calculations and those are almost always quite a bit fewer than 15 anyway (even 15 digits of accuracy in the measurements going in to the calculations is almost unheard of in science in my experience).

Someone scientifically minded will of course understand the caveats of floating point, but at the same time expect roundtrip accuracy.

What?! You think scientist are prone to take digit strings output from one calculation and paste them in for further calculations and not realize that some precision is lost? My experience is the opposite of that. Though, my experience is also that 15 digits of precision is so far above the significant digits in most scientific calculations that "15 vs 17 significant digits" is something that will often be ignored by a scientist.