Knowledge Problems

Tuesday, April 11, 2006

The Lay of the Land




How can we ever know which of the above landscapes describes the relation between the physical world and our capacity to know that world? Does this matter in any practical sense? I suspect it does, because just as the topology of an error surface affects the convergence properties of optimization algorithms, the topology of the "knowledge surface" should affect the convergence properties of knowledge acquisition algorithms, i.e., science. Thus, we must find out what the landscape really looks like, but how?

8 Comments:

  • The topology illustrations you posted are confusing because of the first set {0,1}, which is composed of the the two elements 0 and 1, with the interval [0,1], which contains all the real numbers between 0 and 1. The latter set, unlike the former, is an infinite set, which, moreover, has the power of the continuum.

    By Blogger Enigma4U, at Apr 21, 2006, 3:53:00 PM  

  • Hmmm, you clearly know something about topology. Which is a good deal more than I know. I did not intend the drawing to represent a formal set-theoretic notion. It's just an informal suggestion that the asymptotic match between "the external world" and the "the world as described by a particular Knowledge Representation scheme" may have characteristics highly undesirable for inductive learning.

    By Blogger Big-S Skeptic, at Apr 23, 2006, 2:12:00 AM  

  • Ha! You're easy to fool! ;-) I know zilch about topology, and I did not understand much of your post (and I imagine most of your readers didn't either).

    My response was absolute gibberish (a takeoff on an old and infamous Alan Sokal prank). It sounds scientific enough, but it really means nothing.

    Don't feel too bad. Hard core scientists have fallen for this prank, too.

    By Blogger Enigma4U, at Apr 23, 2006, 11:26:00 AM  

  • So your point was just that my post was confusing? I will try to clarify the issues in some future posts.

    By Blogger Big-S Skeptic, at Apr 23, 2006, 11:50:00 AM  

  • Good question.

    However it may be better to illustrate in a multi-dimensional way, becuase we understand things on many different levels.

    Also each person processes information differently, so if we be both "know" the same thing we still don't know it the same way.

    By Anonymous Deep Thinker, at Jun 1, 2006, 11:10:00 AM  

  • Interesting observations, Deep Thinker. I agree on both counts.

    By Blogger Big-S Skeptic, at Jun 5, 2006, 10:10:00 AM  

  • I understand the dilemma presented here completely. Very well put. The answer, I think, is that we can't know what the topology is. One way to guess would be to enter the knowable space from different angles at different starting points and see if the two points fail to converge. Practically I'm not sure how you would do this. Totally a huge fan of your blog so far. I did a google search for "hierarchy of knowledge claims knowable unknowable meaningful" hoping to find something exactly like your blog. I'm looking forward to your next posts.

    By Blogger Robert, at Jun 11, 2009, 4:55:00 PM  

  • Thanks so much Robert. I'm glad you enjoyed it. I've been taking a bit of a hiatus, as you can see from the posting dates. Perhaps I will resume again in the next few months. Good luck with your continuing search for understanding! --Big

    By Blogger Big-S Skeptic, at Jun 14, 2009, 8:29:00 AM  

Post a Comment

<< Home