That was a painfully bad explanation of why random errors cause an over-estimate of distances. There&#x27;s a much better visual explanation:<p>Suppose you have the true location for both points. Draw a circle with a center at the first point that goes through the second. Replace the second point with a circular distribution of errors around the original location. Any error outside the original circle increases the measured distance, while any error inside the original circle decreases it. More points are going to be outside the circle, since that&#x27;s the direction it curves.<p>This explains a qualitative feature about the formula given - that the error tends towards zero as the distance between two points increases. It also maps well with the case where d approaches zero, where any measurement is simply the result of the random effect.