# Subtractive cancellation errors in the lab

I am quite familiar with the problem associated with loss of significance in numerical analysis. This problem seems to be an even bigger problem in the science lab, where subtracting one physical measurement from another produces potentially tremendous error because the uncertanties in the measurement don't subtract, but add.

Question: Is there a special name for this type of error associated with subtraction when applied to the physical measurement? Does anyone know any resources that specifically target this problem?

• I have only encountered "cancellation". Why do you think there is a special name for it? – Anders Sandberg Apr 2 at 21:36
• Because the error can be so enormous. It has a special name in numerical analysis (subtractive cancellation, catastrophic cancellation, loss of signficance) so I figured that there would be a term for it in physics. – Roger Dodger Apr 2 at 21:39
• I would argue that that kind of mistake is much less common in a laboratory setting, mainly because it is much more obvious when you are about to make it. Suppose that I need to know the width of a hair. I might think to drive my car from Cleveland OH to one edge of the hair, then drive from Cleveland to the other edge of the hair, and take the difference between the two odometer readings. Sounds silly, but a novice programmer, unfamiliar with the nature of floating point arithmetic, and unable to visualize what the numbers mean, actually could make a mistake of that magnitude. – Solomon Slow Apr 2 at 21:54
• The mistake doesn't just arise when finding the changes in physical properties, it also appears in vector summation when two vectors are pointing in the same direction. It showed up in our collision theory class, where some students' loss-in-momentum calculations were larger than others'. It was purely from the order in which they summed numbers. – Roger Dodger Apr 2 at 21:57
• It is important to differentiate between absolute and relative errors. Subtraction does not produce catastrophic errors but cancellation can produce singular behaviour in terms of relative errors. – Paul Childs Apr 2 at 22:16