Better to be roughly right than precisely wrong

Posted by Concettina Sfienti on April 24, 2015

Science is fundamentally about measuring the physical universe.
Whenever you actually measure something there is always a chance that you can make an error. In our daily experience an error is something wrong we have done. However in science “error” does not mean the measurement was wrong: it is all about its accuracy, i.e. how close the measured value is to the actual (true) value. Errors merely reflects the condition that our measuring instruments are imperfect, they translate in numbers the uncertainty which accompanies every measurement. Uncertainty estimates are necessary for assessing quality of data, comparing data and verify theoretical predictions.
A measurement without a consideration of this inherent uncertainty is meaningless.

So how do we deal with uncertainty? All we can do is to try to ensure they are as small as possible and to have a reliable estimate of how large they are.

(that’s a short summary for physics students who need quick review)

Error analysis is the study and evaluation of these uncertainties, its two main functions being to allow scientist to estimate how large they are and reduce them when necessary. The analysis of uncertainty is therefore a vital part of any scientific experiment. Unfortunately when learning about the details of error analysis we might miss the big picture, losing sight of the forest for the sake of the tree.

By a comparison of the results of accurate measurements with the numerical predictions of the theory, we can gain considerable confidence that the theory is correct, and we can determine in what respects it needs to be modified. It is often possible to explain a phenomenon in several rough qualitative ways, and if we are content with that, it may be impossible to decide which theory is correct. But if a theory can be given which predicts correctly the results of measurements to four or five (or even two or three) significant figures, the theory can hardly be very far wrong. Rough agreement might be a coincidence, but close agreement is unlikely to be. Furthermore, there have been many cases in the history of science when small but significant discrepancies between theory and accurate measurements have led to the development of new and more far-reaching theories. Such slight discrepancies would not even have been detected if we had been content with a merely qualitative explanation of the phenomena.” (Keith R. Symon, Mechanics, Second Edition, 196)

A thorough evaluation of the uncertainty shows that even though our measurement lacks of perfection, we can unfold the mysteries of the Universe. In some sense uncertainties in measurements are the peephole Nature left us after shutting the door.
No matter how beautiful and clever an experiment can be in reaching for a fundamental question on the character of Nature, it is only through the complete assessment of its uncertainty that we can unlock that door… To err is human; to describe the error properly is sublime.“(Cliff Swartz)

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