Sunday, June 8, 2014

The Problem of Analogical Back-Off

Since historical information almost never contains the nugget of information that you need to make your point, one finds oneself making analogous arguments that proxy for the missing evidence.
  • I cannot show that Joseph Smith Jr believed X, but I can show that the Book of Mormon says X, and I can show that Smith Jr is considered its author or translator (depending on denominational affiliation). 
  • I cannot show that the pioneers of the Upstate New York city of Palmyra did Y, but I can show that the pioneers in the proximate city of Rochester did Y, and that's only K miles away in an ecological homogeneous setting. 
  • I have no survey that shows me how the citizens of Palmyra felt about the approaching Erie Canal in 1817, but I have a newspaper editorial that suggests to me that this was something that was being discussed. 
  • I cannot show for 1830 that the citizens of Palmyra felt outclassed by the booming manufacturing center of Rochester, but I can show it for 1857. 
In all these cases, we are doing a type of "flood fill" search across a continuous space to interpolate the missing data point. However, what if the space in question is not contiguous but qualitatively fragmented? How does one deal with parameter spaces that are mathematically contiguous but not qualitatively? For example, in the village case, where we have a mathematically contiguous dimension like space, 20 miles is OK, but say that in 40 miles distance, a new type of ecological habitat starts and there the analogy might no longer automatically hold. Or similarly, for much of the US of A, going from 1864 to 1863 is fine, but going to 1859 is tricky, because then you fall out of the Civil War era, and things are really very different along some dimensions.

I took the liberty of asking Professor Ken D. Forbus, Head of the Cognitive Systems division at NWU, who has published widely and for a long time on qualitative reasoning, and he recommended the following literature to me.
In the accompanying email, Ken also observed the following:
The QR version of this is differences in qualitative state, which are typically demarked [sic!] by changes in limit points that then indicate different model fragments are active, or for spatial phenomena, that a place boundary has been crossed. How those limit points (which are just 1D boundaries) and place boundaries are defined is very domain and even task specific (in the case of qualitative spatial reasoning).  
Ken also noted that Paritosh and Klenk's work was relevant in showing that one "should use differences in qualitative state to guide estimates".

No comments:

Post a Comment