Some basics

Recently, I stumbled upon a video at Gregory Chaitin's site where he is one of the commentators about four people (BBC) who were ahead of their times. These were Cantor, Boltzmann, Gödel, and Turing. One theme of the presentation was that things are 'topsy-turvy' (Chaitin's characterization) due to uncertainty (and its power, so to speak). Chaitin takes it further to show how the computer exacerbates the problem.

The video is worth the time (which says a lot from someone who would rather read the transcript) if only to allow one to recognize the importance (ignoring, for now, T-issues, though they are alluded to in the video's narrative) of the four views. As we sit here in 2009 (or so), it is very easy to forget the basis underlying what we take for granted. In some senses, the underpinnings are very weak.

Ah, one might say that this is a motivation for truth engineering, in part, as we really ought to keep the principles (their formulation and foundation and failings) in mind. In fact, computational intelligence, which is what we deal with almost ubiquitously, demands such.

I first got interested in Chaitin's work from reading his view on mathematics and its limits. At the time, my day-to-day focus was applied AI and computational mathematics which ought to be sufficient to allow admittance of uncertainty, usually under the name of undecidability (cloaking the issue under a numeric framework does not eliminate the problem). Chaitin made sense as there was a resonance with what I had observed.

Some of this may appear to be too philosophical or academic, yet we can relax, a little, the rhetoric and point to a concept already used multiple times here, namely quasi-empiricism (see Wigner, et al), which was first expressed under an operational framework.

So, expect that there will a few posts that lay out some basics, such as the Incompleteness Theorem, the Decision Problem, and more. There too will be other concepts such as those related to complexity and NP. That last is why brute force cannot work, as we saw with truth maintenance.

Remarks:

04/03/2011 -- Need to look at some background issues.

09/09/09 -- We'll need to look at UUUN, as a framework.

09/02/2009 -- Quants (both financial and engineering) ignore complexity.

07/05/2009 -- As said, couching things numerically does not remove these problems.

06/17/2009 -- Theme of the basics continues.

Modified: 04/04/2011