and by an elementary reasoning known in physics as “dimensional analysis”, dividing a number of issues by another number of issues cannot give us an ROI
This is just being nit-picky, but from a dimensional analysis point of view, both “dollars per dollar” and “issues per issue” are dimensionless figures, and are thus in fact the same dimension.
While writing I was wondering if I should clarify that or if my meaning would come through even if I was somewhat imprecise—thanks for settling that.
My point here is that ROI is a ratio of something gained (or saved) over something invested, and while you can reasonably say you’ve “saved” some number of issues it’s silly to talk about “investing” some number of issues.
It doesn’t really matter for the rest of the argument, since the steelman tries to reconstruct investments and gains from the numbers given, but I’ve amended my sentence to say “something similar to dimensional analysis” instead.
What you said in the above comment is not what you wrote in the article. I’d encourage you to rewrite that section to be what you said here, as its a valid argument but one that’s very different from what you wrote. And for me at least, your dimensional analysis point made me stop and go “huh?” and now I’m reading comments instead of the rest of your otherwise quite interesting article.
Thanks for the additional prod towards clarity. Removed mention of dimensional analysis altogether and updated with the content of the comment I wrote to defend the weak spot. (It’s galling, but this is a technique I actually try to teach others from time to time—when you feel the need to write something in defense of your writing, put that into the original piece instead.)
There are cases in which you can relate dimensionless units. For instance, moles is a dimensionless unit, it just means times 6.022*10^23. But you can relate moles to moles in some cases, for instance with electrolysis. If you know how many electrons are being pumped into a reaction and you want to know how much Fe(II) becomes Fe, then you can compare moles of electrons to moles of Iron, even though neither moles, elements, or electrons can be related directly to one another in the conventional sense of m/s. In the same way one can relate dollars of one thing to dollars of another and get a meaningful answer.
You are right to point this out though, it is skirting very close to the gray areas of dimensional analysis without being explicitly mentioned as doing so.
This is just being nit-picky, but from a dimensional analysis point of view, both “dollars per dollar” and “issues per issue” are dimensionless figures, and are thus in fact the same dimension.
While writing I was wondering if I should clarify that or if my meaning would come through even if I was somewhat imprecise—thanks for settling that.
My point here is that ROI is a ratio of something gained (or saved) over something invested, and while you can reasonably say you’ve “saved” some number of issues it’s silly to talk about “investing” some number of issues.
It doesn’t really matter for the rest of the argument, since the steelman tries to reconstruct investments and gains from the numbers given, but I’ve amended my sentence to say “something similar to dimensional analysis” instead.
What you said in the above comment is not what you wrote in the article. I’d encourage you to rewrite that section to be what you said here, as its a valid argument but one that’s very different from what you wrote. And for me at least, your dimensional analysis point made me stop and go “huh?” and now I’m reading comments instead of the rest of your otherwise quite interesting article.
Thanks for the additional prod towards clarity. Removed mention of dimensional analysis altogether and updated with the content of the comment I wrote to defend the weak spot. (It’s galling, but this is a technique I actually try to teach others from time to time—when you feel the need to write something in defense of your writing, put that into the original piece instead.)
There are cases in which you can relate dimensionless units. For instance, moles is a dimensionless unit, it just means times 6.022*10^23. But you can relate moles to moles in some cases, for instance with electrolysis. If you know how many electrons are being pumped into a reaction and you want to know how much Fe(II) becomes Fe, then you can compare moles of electrons to moles of Iron, even though neither moles, elements, or electrons can be related directly to one another in the conventional sense of m/s. In the same way one can relate dollars of one thing to dollars of another and get a meaningful answer.
You are right to point this out though, it is skirting very close to the gray areas of dimensional analysis without being explicitly mentioned as doing so.
“Issues” are kind of dimensionless already.