> I think this should be front and center. To that end I propose "magnitude notation"[0] (and I don't think we should use the word logarithm, which sounds like advanced math and turns people away from the basic concept, which does make math easier and more fun).
The only reason that "logarithm" sounds like advanced math is because it was so useful that mathematicians, well, used it. Since this terminology is just logarithms without saying the word, if it is more useful it, too, will probably be used by mathematicians, and then it will similarly come to sound like advanced math. So what's the point of running away from a name for what we're doing that fits with what it's actually called, if eventually we'll just have to make up a new, even less threatening name for it?
(I'd argue that "logarithm" is frightening less because it sounds like advanced math than because it's an unfamiliar and old-fashioned-sounding word. I'm not completely sure that "magnitude" avoids both these issues, but it's at least arguable that it suffers less from them.)
It's written like ^6 and said like "mag 6", which sounds like an earthquake (and this is basically the Richter scale writ large). One syllable, sounds cool, easy to type/spell, evokes largeness. "Logarithm" is 3-4 syllables, hard to pronounce, hard to spell, sounds jargon-y.
People virtually never say “logarithm” in use though. They either say “log” or they say “lun” for natural log. Notice that both log and lun are one syllable, easy to pronounce etc.
Magnitude is an existing and important concept in maths - it would be extremely confusing to just overload it to mean something else.
The log of 3.1m is 6.5. How do you say "10^6.5"? I say "mag 6.5" and it is clear. The Richter scale famously uses "mag 6.5" exactly like this. If that was ever confusing, then we've managed to work past it, and this just expands the Richter scale to cover basically everything.
There's nothing particularly special about the Richter scale in that respect. All logarithmic scales (eg dB) work that way. Both the Richter scale and decibels (and other logarithmic scales) are also famous like other nonlinear scales[1] for being widely misunderstood so I'm not sure a lot of people would think your way is clearer than the current usage, which is just to say "3.1m" if that's what you mean. That said, I like log scales and logarithms in general so if you want to campaign for this scale, knock yourself out. I don't like that you're calling it magnitude though, because magnitude means a specific thing (the first coordinate of a vector in polar or spherical form).
The only reason that "logarithm" sounds like advanced math is because it was so useful that mathematicians, well, used it. Since this terminology is just logarithms without saying the word, if it is more useful it, too, will probably be used by mathematicians, and then it will similarly come to sound like advanced math. So what's the point of running away from a name for what we're doing that fits with what it's actually called, if eventually we'll just have to make up a new, even less threatening name for it?
(I'd argue that "logarithm" is frightening less because it sounds like advanced math than because it's an unfamiliar and old-fashioned-sounding word. I'm not completely sure that "magnitude" avoids both these issues, but it's at least arguable that it suffers less from them.)