“You cannot get something from nothing”.

“Nothing comes from nothing”.

“Nothing cannot turn itself into two things: +1 and -1”.

Once +1 and -1 have turned one another into nothing by mutual negation, they are gone for good.

In quaternion mathematics, once i has turned j into k and j has turned i into -k, k and -k cannot turn one another back into i and j. The rules for squaring k taken with the sign multiplication rules, coded in XOR, ensure that k turns -k into +1 and -k turns k into +1: nothing (0) in units of i, j and k. Application of the same sign multiplication rule to both sides assures mutual destruction: two things become one nothing.

This violates common sense. Distinction must be conserved. Two numbers acting on one another must always produce two numbers.