Thank you for reminding me. I get the basic idea, but perhaps not fully through and through yet. It might help if I had three formulas, one defining a in terms of c and w, one defining w in terms of a and c, and one defining c in terms of a and w. I should probably do it myself as an exercise.Dave Keenan wrote: ↑Mon Jul 06, 2020 4:21 pm...I remind you that, with this scenario, the log base is not constrained by the data. You can lock it to whatever you want and you will find the same minimum. You only have to scale w and c by log_{new_base}(old_base). ...

So this is a 4-parameter metric.

Would it not have to be a condition that all of the parameters to the coapfar for which c is a coefficient be the same as the parameters to the soapfar with the related a and w? Well, but a and w are among those parameters, so should those be excluded? Yeah, I am finding ways to get confused about this relationship. Nothing I shouldn't be able to figure out through controlled experimentation with the dials and knobs I've built though.

I think this means that I waste resources searching for metrics which use all three. I should always leave one out and then pick reasonable ranges for the remaining two. Leaving w out means setting w = 0. Leaving c out means c = 0. Leaving a out means... wait, this one's tougher, because there is no identity base (as there is an identity exponent, which is 1). So if we're pretty well set that a logarithmic a is good, perhaps I should default to leaving out c, since that eliminates two "chunks" of complexity: the c, and the coapfar it coefficiates.

I believe the notion that this is a 4-parameter metric is what you were getting at earlier, and I just didn't grasp it yet. I took the conversation of defining a parameter in terms of complexity when we share this metric out. But this is a more urgent definition of parameter: in terms of finding the metric in the first place.

I agree that finding the correct scale factor on our metric to make it as similar as possible to SoPF>3 where it counts most is a good idea. I'm not positive that I'll want to include it in the metric itself; I may prefer to have a SoPF>3-scaled version of it for when it is needed.Dave Keenan wrote: ↑Mon Jul 06, 2020 6:39 pmThat suggests another question. What scale factor do we have to apply to your winning metric above (in its log_{2}version), to make it give almost the same values as sopfr, for the first few ratios? (Looks like we have to multiply it by about 5.7) And can we then describe it as a correction-function applied to sopfr?

I don't understand your last sentence here, though, at all. Sorry. Please say more.