The traditional explanations

So far, three types of hypotheses have been made on the conservation of body plans. 

No new body plan has been invented after the Cambrian explosion because all ecological niches were already occupied. 

This is a very weak suggestion, because a high number of new ecological niches did become available after the Cambrian, and not just once but many times over. When animals invaded the land, for example, they had at their disposal absolutely virgin territories for hundreds of millions of years. And as for the sea, species have been literally decimated various times by great mass extinctions, which certainly created plenty of opportunies for new experiments in body plans. 

Body plans impose so many constraints on embryonic development that any novelty would disrupt too many characters and would bring development to an end. 

This seems a more reasonable hypothesis, but surely it cannot apply to Cambrian animals. They too had embryonic developments and body plans, and the Cambrian explosion means precisely that those ancestral plans were modified. If the constraints on embryonic development did not prevent the modification of body plans before the explosion, why should have prevented it after the explosion  

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At the same time we recall that, in an external field, the electrical mobility of the Li+ ion is unusually small and in this connection we should certainly discuss the passage just quoted. Although the Li+ ion has the smallest radius of all the alkali ions, it has the smallest electrical mobility. According to the traditional explanation, described in Chapter... 

The traditional explanation either leans on lack of norms and morals or rests the case on a disease concept. The former has ancient roots and is represented for instance by Plato "From the moment of their birth men have a desire for food and drink. Every living creature has an instinctive love of satisfying this desire whenever it occurs, and the craving to do so can fill a man s whole being, so that he remains quite unmoved by the plea that he should do anything except satisfy his lust for the pleasures of the body, so as to make himself immune to all discomfort." (Plato 1970,782). "Give a man correct education, and these instincts will lead him to virtue, but educate him badly and he ll end up at the other extreme," Plato states. Obviously lack of education is seen to be the core problem. Aristotle used the term akrasia, signifying the weakness of the will that makes man unable to resist temptations. 

The traditional explanation of the fact that carboxylic acids are much stronger acids than alcohols is that resonance stabilization of the conjugate base, which is more important than the charge-separation resonance in the acid, stabilizes RCOO-... 

Some of the same features affect the electrophilicity of tetrahedral electrophiles undergoing SN2 reactions. Thus some donor substituents on the carbon being attacked reduce the electrophilicity of alkyl halides, where the order of reactivity is methyl > ethyl > isopropyl > terf-butyl. The transition structure of an SN2 reaction is inherently electron rich, and donor substituents slow it down. Equally, steric hindrance to attack, the traditional explanation for this reactivity order, is greater for the more substituted alkyl halides. 

Not only is there a shortage of nebular gas in the Earth and terrestrial planets today but the moderately volatile elements also are depleted (Figure 1) (Gast, 1960 Wasserburg et al, 1964 Cassen, 1996). As can be seen from Figure 2, the depletion in the moderately volatile alkali elements, potassium and rubidium in particular, is far greater than that found in any class of chondritic meteorites (Taylor and Norman, 1990 Humayun and Clayton, 1995 Halliday and Porcelli, 2001 Drake and Righter, 2002). The traditional explanation is that the inner terrestrial planets accreted where it was hotter. 

It was also proposed that the significant s and p orbital contraction at row four (Cu) is caused by the post-transition metal effect (d contraction), caused by an increase of the effective nuclear charge for the 4s electrons due to filling the first d shell (3d). A similar interpretation is possible for the row six (Au). This effect is commonly called lanthanoid contraction due to the effect of filling the 4f shell. The traditional explanation for the smaller size of gold (compared to Ag) is the lanthanoid contraction. However, this effect is only sufficient to cancel the shell-structure expansion, to make Au (nonrelativistic) similar to Ag (nonrelativistic). 

Sodium, potassium, chloride, and calcium ions carry the currents associated with the action potential. The two that have seemed to be most important are Na and K+. According to the traditional explanation, the cell resting potential was maintained by a Na - K+ ion pump (figure). 

The traditional explanation of Hund s rule is as follows Electrons with the same spin tend to keep out of each other s way (recall the idea of Fermi holes), thereby minimizing the Coulombic repulsion between them. The term that has the greatest number of parallel spins (that is, the greatest value of 5) will therefore be lowest in energy. For example, the 5 term of the helium ls25 configuration has an antisymmetric spatial function that vanishes when the spatial coordinates of the two electrons are equal hence the 5 term is lower than the 5 term. 

Tropisms have been used as an exquisite test of the ability of a plant to selectively control its growth, since one side of a stem grows more rapidly than the other side of that same stem. The traditional explanation is the theory of the Lateral Transport of Auxin proposed by Went and Cholodny [32]. This theory states that the tropism induces lateral transport of lAA, thus causing more lAA to accumulate on one side of the stem than on the other. The theory is adequate, except there has been no explanation of how lateral transport of lAA is attained. We have developed a working theory to explain tropisms and lateral transport based upon our experiments, as described above, and upon the earlier studies of changes in the bioelectric potential of plant tissues induced by environmental stimuli. 

In a typical study, such as that of Wilkins and co-workers, this plot is linear. The traditional explanation for this is that 35< 2,[HTand 35 34, SO that Eq. (3.77) simplifies to Eq. (3.78), which will give k 2 as the intercept and slope. 

Comparing the acidity or basicity of related compounds in the gas phase and in solution one finds that in some cases the acidity or basicity order is the same while in others the order may be very different or even totally reversed. In fact the reader who sees the values for the first time and is well versed in the traditional explanations of factors influencing acidity and basicity will experience a few shocks on examining the gas phase values. 

This suggests, it seems to us, that the traditional explanation for the superiority of variational methods must be incorrect. From the previous two subsections, we see that the main difference between the two variational methods, the SVP and the NVP, and the nonvariational method MMAD, is that for a given basis size, the variational methods find a far more accurate wavefunction than the nonvariational method. The variational methods also differ fixim the nonvariational ones in that the former are characterized by a stationary principle. Let us now examine the consequences of this aspect of variational methods, taking the SVP functional as an example. 

The traditional explanation for the superiority of variational methods over nonvariational ones has been that an error of order in the wavefunction is transformed into an error of order in the computed stationary quantity. Implicit in this explanation is the... 

The traditional explanation for the occurrence of the g = 4.3 line goes back to the classic paper by Castner et al (1960), where only second order terms in equation (22) are considered. Castner et al (1960) considered the limiting case of extreme rhombicity as governed by the condition D = 0, E 0 and possible symmetry arrangements which could lead to its fulfillment. It can easily be shown by a permutation of axes that an exactly equivalent condition is E/D < 1/3. From many points of view it is useful to maintain the convention, E/D < 1/3, which covers all possible situa-... 

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