i wonder if interest in measuring error of previous calculations is what encouraged this direction of computational rigor respecting accuracy encourages a self

i wonder if interest in measuring error of previous calculations is what encouraged this direction of computational rigor respecting accuracy encourages a self awareness with an almost conscious stead ignorant error i am always intrigued when it is discussed how a calculation began and the error of the initial values the first known attempt at measuring the speed of light(o) had an ignorant error of ~26% the first known attempt at measuring the circumference of the earth(i) had an ignorant error of ~15% > our planet Earth.. the circumference .. > .. would .. be if you used the limited version of pi above? > It would be off by the size of a molecule. our conscious error is the size of a molecule, but what will our ignorant error be? how will its significance manifest? the ignorant error is a result of the tools of measure, in this case observable measurements and numerical approximation for those who calculated using pi equal to 22/7, for the circumference, their error would only be ~.04% of the 15 digit rounded value >>>2*(22/7)*(7926/2)>>> 2*(22/7)*(7926/2) 24910.285714285714 >>> 2*(3.141592653589793)*(7926/2) #from the article 24900.2633723527 >>> 24910.285714285714/24900.2633723527 1.0004024994347707 >>> (1.0004024994347707-1)*100 0.04024994347706645 (o) https://en.wikipedia.org/wiki/Speed_of_light#First_measurement_attempts https://en.wikipedia.org/wiki/Speed_of_light#First_measureme... (i) https://en.wikipedia.org/wiki/Eratosthenes#Measurement_of_the_Earth.27s_circumference https://en.wikipedia.org/wiki/Eratosthenes#Measurement_of_th... .. edit, percentage error, left out the *100