Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

Benoit_Essiambre comments on Artificial Addition - Less Wrong

36 Post author: Eliezer_Yudkowsky 20 November 2007 07:58AM

You are viewing a comment permalink. View the original post to see all comments and the full post content.

Comments (117)

Sort By: Old

You are viewing a single comment's thread.

Comment author: Benoit_Essiambre 22 November 2007 05:05:12AM 0 points [-]

Benquo, I see two possible reasons:

1) '2' leads to confusion as to whether we are representing a real or a natural number. That is, whether we are counting discrete items or we are representing a value on a continuum. If we are counting items then '2' is correct.

2) If it is clear that we are representing numbers on a continuum, I could see the number of significant digits used as an indication of the amount of uncertainty in the value. For any real problem there is _always_ uncertainty caused by A) the measuring instrument and B) the representation system itself such as the computable numbers which are limited by a finite amount of digits (although we get to choose the uncertainty here as we choose the number of digits). This is one of the reason the infinite limits don't seem useful to me. They don't correspond to reality. The implicit limits seems to lead to sloppiness in dealing with uncertainty in number representation.

For example I find ambiguity in writing 1/3 = 0.333... However, 1.000/3.000 = 0.333 or even 1.000.../3.000...=0.333... make more sense to me as it is clear where there is uncertainty or where we are taking infinite limits.