Dirac and sign errors in odd number of places

Question

I recently came across this Dirac anecdote. How does one prove that signs must have been wrong in odd number of places? Does this follow from parity? Now for example if I calculate 1+2+3+4 I get 10 and if I make sign mistake in even number of places like 1-2-3+4 I do not get 10. Sign mistakes in even number of places do not cancel out. What am I missing? Or am I getting the whole thing wrong? What does Dirac mean mathematically?

Answer 1

I agree that if your things are added together, then you can't tell that there has been an odd number of sign errors. However, in pysics, it is much more common that quantities are multiplied together. And in that case, you can indeed tell whether the number of sign errors is even or odd.