I disagree. Well written and abstracted code makes mathematical formulas easy to scan and proofread.

Your code should look like this:

    angle = acos( ( a . b ) /
                  (|a|*|b|) )

If it looks like this . . .

    angle2 = Math.acos((a.x*b.x + a.y*b.y + 
      a.z*b.z)/Math.sqrt(a.x*a.x + a.y*a.y + 
      a.z*a.z)*Math.sqrt(b.x*b.x + b.y*b.y + 
      b.z*b.z))

. . . you're likely to miss the error*

Bad code compiles. Good code works right. Great code is so obviously right you don't have to wonder.

*Those are the same formula, though the second one is missing some critical parentheses. I use the example because I have done exactly this and been bitten by exactly this, and now am fanatical about keeping my mathematical formulas clean and obvious.

I suppose the tie-in is simply that we hackers think differently from scientists. It's much easier for us to visualize a complex tree of logic than for people who are not accustomed to it. The second purpose of the anecdote was to illustrate that there is a complete lack of software testing knowledge within the scientific community, or even the recognition of the need for it. All of the "testing" they do is on production data. There is no unit testing anywhere.

I bet that they would have been more likely to have found the problem themselves had the code been cleaner and better documented.