Showing posts with label inference. Show all posts
Showing posts with label inference. Show all posts

Monday, May 11, 2020

Some Birthday Stories

Consider this story template to generate yes/no questions:
On May 12, [2020//1930/1890], [Emma/Charles] celebrated their [10th/20th/40th/80th] birthday in London. When their sibling [Charles/Emma] ate the [cake/pony/Faberge egg/iPhone], the birthday child cried. Does that surprise you?
Stories are surprising when the mix of ingredients does not go together. Some of these incongruencies would be temporal: An iPhone in 1930 (or a dodo bird at any of the offered points in time, having become extinct in the 16th century already). 

Some of these incongruencies would be structural: eating a pony or a Faberge egg is hard work and could not be accomplished quickly. 

Some of these would be social conventions surrounding emotions: a 40-year old man in 1890 London, that is Victorian society, would be expected not to cry over the loss of a birthday present, but a 40-year old woman may well be expected to. 

Some of these might be unusual but acceptable: though a Faberge egg cannot be eaten (despite what it name seems to imply to a noun tagger), it is also an odd present for a 10-year old (possibly excepting upper aristocracy). Eventually, as the age of the celebrated person increases, the presence of a sibling itself becomes unlikely without additional information.

Meandering and the Asymmetry of Overdetermination

The meandering nature of historiographical reconstruction has occurred to anyone who has worked in that field at all. One starts out at a general topic, such as the sources of a historical painting or the origins of Mendelian experimentation, and finds oneself, a couple of units of effort later, in the middle of contemplating the household receipts and textual editions (not to mention X-rays of the painting under consideration) or computing the total number of pea plants that the Moravian monetary garden (plus glass house) might have held or the names and origin of Mendel's four assistants (mostly lay brothers).
How did one get there?

Perhaps the most straightforward suggestion is afforded by David Lewis and his observation on the asymmetry of overdetermination of actual worlds (1973). The observation here is the plurality of traces that causal events leave and the point is to allow the philosopher by comparison to establish the causal relationship with respect to the effects. 

At issue is not the correctness of Lewis' observation per se but the proposal that actions in the real world that are causal leave a plurality of traces that extend into the historical record in a bewildering variety of ways. (The image of ripples on a pond is usually exercised at this point in the discussion.) All the same, time is the great destroyer and as the spans increase and other ripples chase across the pond, the traces become effaced. The artist's studio has disappeared, and so have his tools, materials and assistants; the Mendelian fields and glasshouse, should they have survived at all, were preserved only due to the conservative nature of the institution where he experimented. The historian is thus faced with "temporal cluster bombing" that works counter to the very tracing of the effect chains the historian wishes to undertake. At the same time, if the event was "big" enough (the extinction of the dinosaurs by meteorite comes to mind) the large number of traces prevents the erasure of every single detail---too much shocked quartz, too much iridium, too little volcanic activity in the Deccan traps.

My mother still remembers where she was and what she was doing the day John F. Kennedy was assassinated in Dallas, even though she was then an Austrian teen. It would be difficult to erase all traces, to spill damnatio memoriae on all the causal lines, that reverberated through the global village of modern media when that US president died. Diaries, letters, mementos, not to mention an avalanche of conspiracy theories all take their origin in that event. 

It is this situation that is both the possibility of performing historiographical research over the ages and the impossibility of focusing the ontology of investigation up front, as the lack of readier-made traces and the ability to decide between competing interpretations will push the historian farther and farther down the causal chain to refute some of the interpretations (and herein lies the underdetermination of historical reconstruction, as Tucker pointed out) and strengthen the others (where the notion of strengthening may be related to Lewis' similarity metric, a point that needs further analysis). Here Lewis' points of world become relevant again. 

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".