A comment on: ‘On some contradictory computations in multi-dimensional mathematics’

Abstract

In this paper we analyze the status of some ‘unbelievable results’ presented in the paper ‘On Some Contradictory Computations in Multi-Dimensional Mathematics’ [L.A.V. Carvalho, On some contradictory computations in multi-dimensional mathematics, Nonlinear Anal. 63 (2005) 725–734] published in Nonlinear Analysis, a journal indexed in the Science Citation Index. Among some of the unbelievable results ‘proved’ in the paper we can find statements like: (i) a rotation T θ : R 2 → R 2 , θ ≠ n π / 2 , is inconsistent with arithmetic, (ii) complex number theory is inconsistent. Besides these ‘results’ of mathematical nature, [L.A.V. Carvalho, On some contradictory computations in multi-dimensional mathematics, Nonlinear Anal. 63 (2005) 725–734] offers also a ‘proof’ that Special Relativity is inconsistent. Now, we are left with only two options (a) the results of [L.A.V. Carvalho, On some contradictory computations in multi-dimensional mathematics, Nonlinear Anal. 63 (2005) 725–734] are correct and in this case we need a revolution in Mathematics (and also in Physics) or (b) the paper is a potpourri of nonsense. We show that option (b) is the correct one. All ‘proofs’ appearing in [L.A.V. Carvalho, On some contradictory computations in multi-dimensional mathematics, Nonlinear Anal. 63 (2005) 725–734] are trivially wrong, being based on a poor knowledge of advanced calculus notions. There are many examples (some of them discussed in [A.L.T. Carvalho, W.A. Rodrigues Jr., The non sequitur mathematics and physics of the ‘new electrodynamics’ proposed by the AIAS group, Random Oper. Stoch. Equs. 9 (2001) 161–206. http://arxiv.org/abs/physics/0302016; E. Capelas de Oliveira, W.A. Rodrigues Jr., Dotted and undotted algebraic spinor fields in general relativity, Int. J. Mod. Phys. D 13 (2004) 1637–1659. http://arxiv.org/abs/math-ph/0407024; W.A. Rodrigues Jr., E. Capelas de Oliveira, Clifford valued differential forms and some issues on gravitation, electromagnetism and “unified” theories, Int. J. Mod. Phys. D 13 (2004) 1879–1915. http://arxiv.org/abs/math-ph/0407025; W.A. Rodrigues Jr., Q.A.G. Souza, An ambiguous statement called ‘tetrad postulate’ and the correct field equations satisfied by the tetrad fields, Int. J. Mod. Phys. D 14 (2005) 2095–2150. http://arxiv.org/abs/math-ph/0411085; W.A. Rodrigues Jr., A comment on Emergent Gravity, http://arxiv.org/abs/gr-qc/0602111]) of completely wrong papers using non sequitur Mathematics in the Physics literature. Taking into account also that a paper like [L.A.V. Carvalho, On some contradictory computations in multi-dimensional mathematics, Nonlinear Anal. 63 (2005) 725–734] appeared in a Mathematics journal we think that it is time for editors and referees of scientific journals to become more careful in order to avoid the dissemination of nonsense.