Error Bars
also Uncertainty range
A documented range stating how far a measurement might deviate from the true value, which bounds quantitative error rather than removing it.
An error bar is the standard statistical way to handle variance: a stated range, such as x±y, expressing confidence (often 95%) that the true value lies within it. CF’s distinctive point is that this is not error correction in the strong sense. Error bars document how much error you might have; they do not remove or solve it. The error stays in the result, merely bounded and labeled.
The practical consequence is accumulation. Because each measurement carries its own bar, combining values combines their uncertainty, and the bound grows with every step. CF stresses that the growth is worse than people expect. Adding ranges 3–5 and 8–10 yields 11–15 (size 5), but multiplying them yields 24–50 (size 27): two narrow inputs produce a wide output. Addition scales variance linearly; multiplication scales it with the data, so it behaves like a percentage that compounds. Run 50,000 multiplications and the final bar is enormous. This is why CF treats quantitative error correction as having a built-in ceiling, and why bounded uncertainty is managed rather than eliminated.
Error bars cover only quantitative errors. They say nothing about qualitative ones, miscategorizing a thing, a non sequitur, an ignored factor, a vague premise. Those require explanatory error correction, which can decisively remove an error rather than bounding it. CF also rejects using a bar as an excuse for unjustified approximation: a shortcut needs an objective bound on the size or chance of error, not the feeling that a mistake seems “unlikely.” Properly used, an error bar maps a solution space honestly; misused, it disguises guessing as measurement.