The Neutral Theory of Evolution (NTE) proposes mutation and random genetic drift as the most important evolutionary factors. The most conspicuous feature of evolution is the genomic stability during paleontological eras and lack of variation among taxa; 98% or more of nucleotide sites are monomorphic within a species. NTE explains this homology by random fixation of neutral bases and negative selection (purifying selection) that does not contribute either to evolution or polymorphisms. Purifying selection is insufficient to account for this evolutionary feature and the Nearly-Neutral Theory of Evolution (N-NTE) included negative selection with coefficients as low as mutation rate. These NTE and N-NTE propositions are thermodynamically (tendency to random distributions, second law), biotically (recurrent mutation), logically and mathematically (resilient equilibria instead of fixation by drift) untenable. Recurrent forward and backward mutation and random fluctuations of base frequencies alone in a site make life organization and fixations impossible. Drift is not a directional evolutionary factor, but a directional tendency of matter-energy processes (second law) which threatens the biotic organization. Drift cannot drive evolution. In a site, the mutation rates among bases and selection coefficients determine the resilient equilibrium frequency of bases that genetic drift cannot change. The expected neutral random interaction among nucleotides is zero; however, huge interactions and periodicities were found between bases of dinucleotides separated by 1, 2... and more than 1,000 sites. Every base is co-adapted with the whole genome. Neutralists found that neutral evolution is independent of population size (N); thus neutral evolution should be independent of drift, because drift effect is dependent upon N. Also, chromosome size and shape as well as protein size are far from random.