Tarantola's new physics book

This is kindof an interesting idea (just recently read the intro to this book):  You know how vectors are defined independently of any coordinate system -- they're specific points in space regardless of how you name those points, and e.g. their sum and so on is the same regardless of coord system.  For those who've done a little higher level physics you've seen this is true for tensors in general.  Well, so Albert Tarantola's point in his new textbook Elements for Physics (having only read the intro, mind you) is that our laws of physics are all derived or empirically found in a particular coordinate system, but the quantities they describe needn't be -- for example a scale of temperature could be quantified via the temperature value, the inverse temperature, log temperature, etc., but any given value of one of these quantities is still talking about a particular hotness/coldness.  And his thought is that rather than have one equation that relates temperature to say heat flux, another equation to relate the inverse temp, and another for log temp (even though these particular examples might be simply related), he would go derive the equivalent of those which instead relates the invariant quantities and try to learn something more fundamental about their relationship in the process.  At the end one can always take the invariant quantity and express it in a given coord system.  Ideally that would produce the original historical physics law, and in his examples generally did but at least once apparently didn't (heat flux vs temp, Fourier's Law), which is surprising, not sure came of that.  Anyway, as with his wonderful inverse theory textbook he offers this one in a PDF file free online, with the understanding that if you can afford it and use it then please buy it...