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Relations December 11, 2006

Posted by amahabal in Uncategorized.
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Relations in Seqsee play a role similar to that played by bonds and bridges in Copycat and Metacat. As mentioned in the previous entry relations in Seqsee need to be generalized to take care of what I called weak relations. Because of this transition, this entry is tentative but not very much so.

 
 

Let us stay concrete with an example. Let group A be [2 3 4] and group B be [3 4 5], with neither having yet been seen as ascending groups. Then the function “find relation” returns empty-handed: in Seqsee, all relations are based on categories shared by the two ends. Without a common category, no relation is discovered.

 
 

Let us proceed to a subsequent time when both groups have been seen as ascending. Now the function “find relation” does succeed and discovers the relation based on this shared category: in going from group A to group B both the start and the end have gone up by one. ‘Start‘ and ‘end‘ are words that are applicable to things that are ascending groups. For mountains ([3 4 5 6 5 4 3], for example), applicable words include ‘peak‘, a word that would scant make sense for ascending groups.

 
 

This restriction of sharing a category in order to be related might seem restrictive. However, several relations are of this type. Those that are not include the relation between George W. Bush and the United States. One is a country and the other is not. At least in the domain of sequences, though, this restriction does not seem crushing. There are also good reasons why similarity must play a role in describing differences. A quote from Michael Agar’s “language shock” has vividly stuck in my mind. He was describing the classic experiment of Berlin and Kay where they tried to make sense of differences in color terms in different languages. Using the spectrum, they asked natives to pinpoint what the central example of the color red was. I quote from page 75:

 
 

Berlin and Kay made sense of differences between languages in terms of similarities that humans share. Before their work, linguists used the spectrum to highlight the differences. What Berlin and Kay did was to show how the differences showed up against the background of human universals of color perception, abilities wired into the eye and brain.

 
 

Categories in Seqsee provide just such a backdrop of similarity with which to compare. To drive the point home—at the risk of repeating myself or of stating something obvious—let me point out that a question like “how does evolution differ from gravity?” is silly, unless you make both the things being compared belong to the same category, say, the category “scientific theory”. Now the two can be compared in terms of how much people believe them, how mathematically quantifiable they are and so forth.

 
 

So far so good. Let us go into deeper waters. Consider the groups [ [2 2] 3 4] and [3 [4 4] 5] where the ‘2 2’ has been seen to be just a funny 2, and the two groups have been seen as blemished versions of [2 3 4] and [3 4 5] respectively. How do we now describe what changed? Another quote from Michael Agar from the same chapter is relevant (page 82):

 
 

[…] similarities are always too simple and differences are always too complicated. The academic tendency is to put together a framework of similarities and then go forth and understand the world in terms of it. With a good framework, you can understand something of each piece of the world, no doubt about it. But each piece of the world will not just consist of that similarity; it will consist of that similarity plus plenty of other things working within the system where the similarity is found.

 
 

The author was not talking about a program understanding sequences, to be sure, but rather about people trying to understand other cultures. That does not make the quote any less true here.

 
 

Relations in Seqsee are programmed to note several other characteristics like the blemishes present and their positions. This does give it some framework in which to describe differences. This framework needs to be at the same time stronger and more flexible. Relations like that between [3 4 5] and [8 9 10] are not supported yet. I did not reach the stage of talking about weak relations as I had expected to, but I will get there in the near future.

Comments»

1. A change of terminology: no more relations « Seqsee Diary - December 12, 2006

[…] In the post “relations” I described how the relations Seqsee notices have both related objects sharing a category, and also mentioned exceptions in the world around us: George W. Bush and the United States do not share obvious categories, and yet, the question “how is Bush related to the United States?” is not inane and has an answer. […]

2. Michael Tim - February 28, 2009

I love your site!

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