The Concept of Freedom

The concept of freedom plays an important role in order to understand the derivation of the phase rule. Therefore, we repeat a few terms concerning this aspect here. 

---

This chapter is in this sense philosophical. My aim is to account for how uncompelled and therefore free addictive behavior might exemplify a limitation upon our freedom of the will. This aim requires a clarification of two basic notions, addiction and freedom of the will. I start with the latter and move on to the former. The reason for starting here is simply that we are not even sure we can make precise, or precise enough, sense of the concept of freedom of the will. If we cannot do that, this route to the elucidation of addiction is not available. 

The conception of freedom of the will I allude to raises many problems.2 Obvious questions concern the understanding of the phrase "to have the will one wants to have." 1 believe there are two related but distinct questions here. One question concerns what it is to possess freedom of the will, to be a free and responsible person. A second question concerns what state one is in when one fails to have the will one wants to have. The approach to freedom of the will 1 briefly presented earlier may collapse these two questions into one. 

Condorcet s key idea is to link the concept of freedom to equality, so that real or full freedom for individuals presupposes equal participation in the making of laws and the equalising of their chances of influencing them. Aware that it is impossible to avoid some arbitrariness in the application of these terms and that his own account is relative to our current state of enlightenment , he proceeds to distinguish between senses of freedom - what it means to be free with respect to different aspects of life (natural, social, political and personal) to which different rights correspond - and how they relate to one another, and in what ways peoples can be free as distinct from individuals. He also raises the question of how to identify degrees of freedom. 

If we consider Condorcet s view in relation to modern discussions of the concept of freedom and if we are to use the now conventional categories of negative , positive and republican liberty, then it clearly counts as republican ( a man can be called free when he is subject in... 

The concept of molecular structure implies a reduction in the freedom of motion for the involved atoms. Thus an indirect strategy for identifying structured segments is to search for restricted motion for contiguous sets of amino acid residues. Relaxation of the 15N nucleus in the peptide bond provides a quantitative measure of the rates and angular range of motion experienced by individual amino acids under equilibrium conditions (Palmer, 2001). 

The specific fundamental idea formulated in paper [1], which found most applications in biophysics, is the concept of incomplete equilibrium, of kinet-ically frozen degrees of freedom. This idea is at the base of modern concepts of enzyme functioning [135-137], and in many cases it is clearly formulated as one originating from the paper [1] of I.M. Lifshitz. 

In optimization using a process simulator to represent the model of the process, the degrees of freedom are the number of decision variables (independent variables) whose values are to be determined by the optimization, hence the results of an optimization yield a fully determined set of variables, both independent and dependent. Chapter 2 discussed the concept of the degrees of freedom. Example 15.1 demonstrates the identification of the degrees of freedom in a small process. 

More than 93.5 percent of the variance is explained by the first two components, which tells us that two degrees of freedom describe most of the natural isotopic variation with the five chronometers. This observation has led to the concept of the Mantle Plane of Zindler et al. (1982), since a plane is defined by only two independent variables, and has been extensively discussed by Allegre et al. (1987). 

As the auto met America s need for transportation, cars released people from train and streetcar schedules, allowing them the freedom to travel at their own pace. Automobiles were marketed using this concept of freedom. Advertising also stressed the comfort of automobiles free from the problems of snow or rain. Independence was the message being conveyed. 

Because the mapping approach treats electronic and nuclear dynamics on the same dynamical footing, its classical limit can be employed to study the phase-space properties of a nonadiabatic system. With this end in mind, we adopt a onemode two-state spin-boson system (Model IVa), which is mapped on a classical system with two degrees of freedom (DoF). Studying various Poincare surfaces of section, a detailed phase-space analysis of the problem is given, showing that the model exhibits mixed classical dynamics [123]. Furthermore, a number of periodic orbits (i.e., solutions of the classical equation of motion that return to their initial conditions) of the nonadiabatic system are identified and discussed [125]. It is shown that these vibronic periodic orbits can be used to analyze the nonadiabatic quantum dynamics [126]. Finally, a three-mode model of nonadiabatic photoisomerization (Model III) is employed to demonstrate the applicability of the concept of vibronic periodic orbits to multidimensional dynamics [127]. 

We have seen in section 3.1 the application of the concept of the harmonic oscillator in the interpretation of vibrational properties of crystals. For a unidimensional harmonic oscillator, there is a single degree of freedom ... 

In his derivation, Frieden uses the concept of a number-count set nm, each member representing the number of photons counted in a spectral interval. The total number of photons m= x nm is taken as known to be N. In terms of frequencies vm, the values of the object spectrum are given by om = nmhvm, where h is Planck s constant. The number of normal modes or degrees of freedom available for occupation by photons of frequency vw is labeled zm. The Bose-Einstein degeneracy factor... 

Frankfurt, Harr). 1971. "Freedom of the Will and the Concept of a Person." Journal of Philosophy 63 5-20. 

For an additional degree of freedom of a particle that defines one of the two possible states in which it exists, we shall apply now the concept of isospin (in analogy with the theory of the nucleus where the isospin doublet includes protons and neutrons, which are treated as two states of the same particle - the nucleon [122]). For a pair of states (a,/ ) we introduce the isospin operators... 

Another example of a quantal repeat—but with considerable variation in sequence—is seen in the keratin-associated proteins (KAPs). In sheep, these display pentapeptide and decapeptide consensus repeats of the form G—G—Q—P—S/T and C-C-Q/R—P—S/T—C/S/T—C—Q—P/T—S, respectively (Parry et al., 1979). Some of the positions, as indicated by the presence of a consensus sequence, contain residues that occur much more frequently than others, but the absolute conservation of a residue in any position is not observed. The decapeptide consists of a pair of five-residue repeats closely related, but different to that displayed by the pentapeptide. Although the repeats have an undetermined structure, the similarity of the repeat to a sequence in snake neurotoxin suggests that the pentapeptides will adopt a closed loop conformation stabilized by a disulphide bond between cysteine residues four apart (Fig. 5 Fraser et al., 1988 Parry et al, 1979). Relative freedom of rotation about the single bond connecting disulphide-bonded knots would give rise to the concept of a linear array of knots that can fold up to form a variety of tertiary structures. The KAPS display imperfect disulphide stabilization of knots and have interacting... 

---