Social Avogadro number

In human thermodynamics, social Avogadro number is a number between one and the current human population that is the social system equivalent to the Avogadro’s constant NA for calculations of quantities such as Gibbs free energy, entropy, internal energy, or enthalpy.

In 1995, American chemist Jay Labinger, in his “Metaphoric Usage of the Second Law”, in commentary on the American mechanical engineer Joseph Klein's 1910 "human applicability" supposition, stated the following: [4]

Klein’s [human applicability assertion] suggests that a minimum requirement for applicability of the second law is a sufficiently large number of elements—an Avogadro's number of people, perhaps?—as well as hinting at issues such as free will versus random actions.”

In 2003, Hungarian sociologist Babics Laszlo made an attempt at a representative particle unit number equivalent for sociological thermodynamics calculations and therein calculated what he called a "sociological Avogadro's number" of:

 A = 60 \,

In the initial stages of his derivation, to note, Laszlo also reasoned that the mean population number of:

 A = 6.01 \times 10^7 \,

for each of the top 87 of the world's countries (a typical reactive human social system), which in sum constituted 97 percent of the world's population, could serve as a representative A, although he considers this value to be too high for meaningful calculations. [2] In honor of Laszlo's effort, being that he seems to have been the first to address this issue (although his calculations are nearly incorrigible) it would seem customary to designate the symbol NL (verses NA in chemistry) to be representative of the social equivalent of the Avogadro number in human chemistry and human thermodynamics. This, however, is only a preliminary idea as still more work needs to be done to find a more meaningful useful equivalent number, as the number 60 isn't essentially based on anything other than the incorrect idea that the 6.022 part of Avogadro's number is significant (with a power of ten roundup to a useful socially significant number of people).

In 2006, American chemical engineer Libb Thims had discussed the Avogadro number issue with Russian physical chemist Georgi Gladyshev during a meeting in Chicago (and via email), during which Thims alluded to the idea that the value should be around 1,000 and possibly be called the Gladyshev number (or Gladyshev constant), being that Gladyshev was the first to do some of the pioneering work in sociological thermodynamics (1977) calculations of Gibbs free energy, which has units of J/mol. Gladyshev, however, did not (at the time) have much commentary on this topic. Thims also suggested that term ‘mol’ should be termed ‘hmol’, short for 'human-mole', for calculations of Gibbs free energy, entropy, internal energy, or enthalpy for human reaction processes between people. In this scheme, Laszlo number (in namesake) plus the term 'hmol', we would have the preliminarily concept of:

 N_L = 60 \bigg( \frac{human(molecules)}{hmol} \bigg) \,

just as Avogadro’s number, in modern terms, is defined as the number of atoms in a twelve gram sample of carbon twelve:

N_{\rm A}=6.022 \times 10^{23} \left (  \frac{entities}{mol}  \right ) \,

although, at this point, until further studies can be made, the number 60 is still rather arbitrary. Another useful version could be the number of people in two different military units reacting in combat during wartime.

The central issue here is that humans aren't typically measured in groups by mass. In short, the standard SI base unit for 'amount of substance' is not applicable to calculations of reactions involved in larger systems of interacting humans. One could say, for instance, that in a 1,000-kg sample of average humans (70-kg) that there are about 14 human molecules on average, but his approach is rather nonsensical. Using an alternative methodology, for instance, one could say that the Laszlo number could be the average number of students in a typical US elementary school, which in the 2001-2002 school year was 477 students.

The issue here is that historically, in chemistry, chemical reactions and processes were measured and quantified in units of grams. This concept evolved into the gram-molecule, being the number of atoms or molecules in a gram of substance. The term gram-molecule was truncated to the term ‘mol’ in 1893 by German chemist Wilhelm Ostwald. In the decades to follow, it was determined experimentally that there are about a septillion atoms in a gram of gas such as air: [1]

 10^{24} \,= number of atoms in a gram of air

Subsequently, the equations of modern chemistry, physics, and thermodynamics are all septillion-based particle count units of the mol. In studies of reactions and processes between human molecules, however, the total population is only in the near ten billion range, hence a new SI base unit is needed for studies in the fields of: human chemistry, human physics, social physics, etc.

In this context, units for quantities such as entropy (or social entropy) or free energy (or social free energy) of thermodynamic calculations involved in either reactions between human molecules or of transformation processes of systems of human molecules would be:

 S (units) = \bigg( \frac{J}{K \cdot  hmol} \bigg) \,
 G (units) = \bigg( \frac{J}{hmol} \bigg) \,

and so on.

Dunbar number
Another related number is the Dunbar number (150) which is the number at which human groups (e.g. social clans) can maintain stability using only social peer pressure as the cohesive principle, sizes above which the group tends to split apart.

1. Names of larger numbers – Wikipedia.
2. (a) Laszlo, Babics. (2003). “A Tomegtarsadalmak Mechanikajaes Termodinamikaja”, 92-page manuscript. Feb 10.
(b) Laszlo, Babics. (2003). "The Mechanics and Thermodynamics of Mass Societies", English trans. by Vera Tanczos, 85-pages.
(c) Laszlo, Babics. (2010). “The Mechanics and Thermodynamics of Mass Societies”, Journal of Human Thermodynamics, Vol. 6, pgs. 39-46, Aug.
3. Dunbar number – Wikipedia.
4. (a) Klein, Joseph F. (1910). Physical Significance of Entropy: or of the Second Law (humans, pg. 89-90). D. van Nostrand.
(b) Labinger, Jay A. (1995). “Metaphoric Usage of the Second Law: Entropy as Time's (double-headed) Arrow in Tom Stoppard's Arcadia”, Presented at Nov meeting of the Society for Literature and Science, Los Angeles; in: The Chemical Intelligencer (pg. 32), Oct. 31-36, 1996.

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