(March 9, 2014 at 1:02 pm)rasetsu Wrote: You're missing the point. Since the choice of scale was arbitrary, where something falls on that scale is arbitrarily chosen as well. If I were to choose a scale based on the logarithm using base 80 instead of 10, then something else would show up as the item at the center. Because the choice of scale is purely arbitrary and without sense, the result of what is at the center is without meaning or sense. We have ten fingers and use base ten math, so a base 10 logarithm seems natural. An animal with 80 tentacles might consider a logarithm using base 80 more natural. On top of that, depending on the size of the creature, it might be at the center of the scale using base 80, even though it's a different size than a human egg! So the fact that the scale can be fitted to the result rather than being a necessary choice makes it a second, deeper example of the Texas sharpshooter fallacy.
I boned up a little bit on logarithmic scales and I'm sure now that it would not matter what base you used or if you used a linear scale the midpoint would be the same.
The only way the scale gets fitted to the result is by arbitrarily choosing where it is bounded.
I'm afraid you are just plain wrong here.
