You can definitely plot all three points on the same graph—you can even plot them such that the distance from “there is no god” to “there is a god who created every kind of living thing ex nihilo” is greater than the distance from “there is a god who gets involved in biological evolution” to either of the two aforementioned points. That can all be done perfectly sensibly.
My claim is simply that the three points can’t be colinear on that graph.
It seems to me that you can plot them wherever you want to, so this is really a question of aesthetics more than anything else. Or is there some actual consequence that follows from one or another answer to this question?
Yes, very familiar with complex numbers, thanks. But, I repeat, you can plot what you want however you want; the question is whether it’s helpful, and that will depend on the application. (Suppose the values taken by your dependent variable are all on the circle of radius 1/sqrt(2) centred at (1+i)/2. Then plotting 0, 1, and i collinearly may make a whole lot of sense, though you might actually want to call them −3pi/4, -pi/4 and pi/4 respectively.)
(Suppose the values taken by your dependent variable are all on the circle of radius 1/sqrt(2) centred at (1+i)/2. Then plotting 0, 1, and i collinearly may make a whole lot of sense, though you might actually want to call them −3pi/4, -pi/4 and pi/4 respectively.)
I reluctantly concede the point, but firmly maintain that calling them −3pi/4, -pi/4 and pi/4 respectively would make a lot more sense.
You can definitely plot all three points on the same graph—you can even plot them such that the distance from “there is no god” to “there is a god who created every kind of living thing ex nihilo” is greater than the distance from “there is a god who gets involved in biological evolution” to either of the two aforementioned points. That can all be done perfectly sensibly.
My claim is simply that the three points can’t be colinear on that graph.
...I hope that makes it a bit clearer.
It seems to me that you can plot them wherever you want to, so this is really a question of aesthetics more than anything else. Or is there some actual consequence that follows from one or another answer to this question?
...it would be a bit like plotting 0, 1 and i colinearly. (I assume you’re familiar with complex numbers?)
Yes, very familiar with complex numbers, thanks. But, I repeat, you can plot what you want however you want; the question is whether it’s helpful, and that will depend on the application. (Suppose the values taken by your dependent variable are all on the circle of radius 1/sqrt(2) centred at (1+i)/2. Then plotting 0, 1, and i collinearly may make a whole lot of sense, though you might actually want to call them −3pi/4, -pi/4 and pi/4 respectively.)
I reluctantly concede the point, but firmly maintain that calling them −3pi/4, -pi/4 and pi/4 respectively would make a lot more sense.