Is the main point of this post that people should play around more with numbers and estimation? If so, then I agree with it, but there are two aspects of the post that I found distracting.
One was the overly broad use of the word “arithmetic”. Arithmetic and algebra have substantially different histories, and they occupy somewhat different roles in contemporary society. (Especially for young math students.) Consequently, I think it’s best to avoid using the words interchangeably.
The other is the repeated emphasis of dimensional analysis. Although it was probably worth mentioning once, it doesn’t appear to be any more relevant than methods for sanity-checking literal arithmetic, and I don’t think that either is central to your epistemological claims.
Is the main point of this post that people should play around more with numbers and estimation? If so, then I agree with it, but there are two aspects of the post that I found distracting.
One was the overly broad use of the word “arithmetic”. Arithmetic and algebra have substantially different histories, and they occupy somewhat different roles in contemporary society. (Especially for young math students.) Consequently, I think it’s best to avoid using the words interchangeably.
The other is the repeated emphasis of dimensional analysis. Although it was probably worth mentioning once, it doesn’t appear to be any more relevant than methods for sanity-checking literal arithmetic, and I don’t think that either is central to your epistemological claims.