# Mean girls model

 Above left: a modern human molecule pressure volume element labeled depiction of the hall scene from the 2004 Mean Girls, where the alpha female (alpha molecule) “queen bee” Regina George α (Rachel McAdams), in pink, causes a volume expansion: students reactively move away giving her more personal space; a natural phenomenon verified and measured by sociologists (Nancy Etcoff, 1999). [3]
In hmolscience, mean girls model refers to the social physics stylized premise of applying the physics-based models of “pressure”, as in social pressure or lateral pressure (see: Niccolo Tartaglia), and “volume”, as in social volume, to the stereotypical social clique based social spaces, personal spaces, and volumes of the scenario of a typical American high school; the 2004 comedy film Mean Girls (Ѻ), conceptually taking place in Evanston, Illinois (Ѻ), which is based on the 2002 self-help book Queen Bees and Wannabes (Ѻ), being the launching point for discussion.

Volume change | Models
The following are three volume change models:

Above left: Daniel Bernoulli’s 1738 depiction of "pressure", the original definition of pressure, as the average rate at which the particles of a containing vessel collide with its walls and push out against the atoms, particles, and molecules of the surroundings (in this case the weight of the atmosphere, a 72-mile high Karman line column height of primarily oxygen and nitrogen molecules). [4] Above middle: Enrico Fermi’s 1938 method of thermodynamically quantifying pressure volume work energy for “irregular shapes” in terms of volume element differentials: surface element (d-sigma) and the displacement element dn. [5] Above right modern kinetic theory depiction of particles pressing outward against their containing boundary (see: dW = PdV).

Objections
On 25 Aug 2011, American electrochemical engineer Libb Thims made an 11:23-minute video “Pressure Volume Work and Mean Girls”, posted to the HumanChemistry101 channel of YouTube, and sometime thereabouts added the video still image shown adjacent to Hmolpedia. [9] Some took objection to this depiction and formulation.

In 2011, Irish biochemistry student Ryan Grannell, in his blog series on “Human Chemistry”, posted the following objection to the mean girls scenario: [1]

“Your claim that “social pressure” is synonymous with “pressure (physics definition)” in your ‘mean girls’ video is fallacious; it is entirely based on the lucky coincidence that they share a similar name; subbing “social ostracism” (which is not a numerical quantity) for pressure would be more obviously plain wrong.”

In 2012, American ecological thermodynamicist Jeff Tuhtan posted the following objection about the mean girls depiction: [2]

“Regarding the fundamental Gibbs equation: Yes, this is the correct mathematical treatment, but I don't see it in your examples, instead you provide 'mean girls' expansion work ('human PV work'?) examples. You are correct on the one hand, if you are talking about the PV work done on the atmosphere by the lifting of the water line when I enter a swimming pool, but on the other seem to want to boil everything down into a single expression using the Gibbs free energy. Why don't you make this distinction more explicit?”

Discussion
The issues or objections, such as raised above, seem to revolve around the assumed equating of:

Physical pressure = Atmospheric pressure

such as would be measured using a barometer, that many people hold in their mind, to the effect that “pressure” is solely defined as the weight of the atmosphere pressing down on the surface of the earth; possibly something along the lines of Dutch-born Swiss mathematical physicist Daniel Bernoulli’s 1738 Hydrodynamica visual depiction of “pressure”, shown above, as the average rate at which the particles of gas collide with the walls of the container or cylinder with a weight (mass) adjustable piston top and thus push out against the surrounding particles of the earths atmosphere.
 An artistic rendition of humans as human particles, bouncing off walls like gas molecules, in effect creating a version of social boundary pressure. [8]

The general objection, if this is the case, then, seems to have to do with an inability to see the derivation backwards to its fundamental roots, which are namely the original definitions of force and movement of bodies, in the 17th century works of Isaac Newton and Galileo Galilei, as codified in Newton's laws of motion, which are not soley "only" applicable to gas particles, moving about under the simplified model of the principle of elementary chaos, but to any and all bodies in the universe, namely that: a force has to act on a body in order for it to move, and when the force is applied normal to a surface, the effect is called by definition pressure:

$P = \frac{F}{A} \,$

or force per unit area; and hence, by rearrangement, the force will be given by:

$F = PA \,$

where A is the surface area on which the force normal acts; whereby, then, according to French physicist Gustave Coriolis' 1829 principle of transmission of work, the work done by (or on) the body will be given by the product of the force and the distance of the surface is moved:

$W = Fd \,$

a distance moved that will be dh in the piston surface example or dn in the social boundary surface (boundary surface) example:

and with substitution of force from the third previous equation, the quantification of social pressure volume work (pressure volume work) becomes:

whence, noting that the volume differential for the social expansion (volume expansion) is:

where A is surface element , we have:

$dW = PdV \,$

whereby, if the volume change is measured, such as by slow motion video measurements of the displacements of bodies, or via GPS tracking devices, etc., the integration can be written in the form of the a definite integral, having a definite measurable initial state volume V1 and final state volume V2:

$W = \int_{V_1}^{V_2} PdV \,$

and if the social pressure can be gauged, such as by the invention or construction of a social barometer, then a social pressure volume indicator diagram (social indicator diagram) can be graphically constructed, and hence the human molecular social pressure volume work expansion done by the alpha molecule system (four socially-affined human molecules: one alpha, two betas, and one competing alpha) on its surroundings (students of the hallway) can be calculated and graphically represented by the shaded area under the PV work diagram curve; a generic example of which is shown adjacent.
 A PV diagram showing a "system" transforming from an initial state 1 to a final state 2, where the representative work W done is indicated by the shaded area under the curve.

Gas molecules | Surface molecules
A salient often-unstated point here to be noted is that humans are surface-attached motile molecules and not gas molecules, such as depicted artistically above. The equations will apply equally to both, the only difference is that while gas molecules will expand radially and spherically outward, human molecules will only expand cylindrically outward. The force is the same in both cases: the electromagnetic force.

Data
The following volumetric changes are known in regards to the social space a tall person and a short person will be given:

Tall = 22.7 inches
Short = 9.8 inches

the numbers of inches being in regards to how far the average person will stop away from the given person before "feeling" uncomfortable. Data for physically attractive individuals has been measured as well, and are expected to be similar in magnitude. American attractiveness researcher Nancy Etcoff summarizes the findings as such: [3]

“Very attractive people of any size are given bigger personal space and territory; which they carry around with them.”

In other words, in the context of human molecular orbital theory, physically ‘hot’ molecules, in the visual sense, trigger volume increase (volume expansion) be it a gaseous molecule or a human molecule. [6]
 A timeline depiction of the 2008 Russia-Georgia “five day war”, an armed conflict in August between Georgia on one side, and Russia and separatist governments of South Ossetia and Abkhazia on the other, which can be likened to the collisions of gas particles on the containing vessel boundary of Dutch-born Swiss mathematical physicist Daniel Bernoulli’s 1738 moveable piston head (above)—which, in the context of war thermodynamics, however, the moveable piston head becomes replaced by the heavily-fortified territorial boundaries of the “conflict zones”, as shown above (in purple) according to which the Russian human molecules to the North and the Georgian human molecules to the south create a type of social-political-governmental territorial pressure at the boundary, that can be measured in SI units. The depiction here is similar to the 1970-74 Chimpanzee war, the result of which, in the end territorial expansion resulted.

Russia-Georgia war | 2008
The adjacent depiction of the 2008 Russia-Georgia five day war, and the various troop movements and boundary fortifications, gives an idea of who the four-molecule system mean girls example scales up to the million+ human molecule system level, in regards to social pressure and boundary regulation at national boarders.

The adjacent depiction can be likened to the 1970-74 chimpanzee war, the result of which, in the end, destruction (dereaction) of the smaller faction of chimpanzee molecules (genocide), one one side of the territorial boundary, resulted, pressure (social pressure) thus reduced, and the territory of the larger faction expanded outward.

Rise and fall of civilizations
War thermodynamics
Human thermodynamic instruments
Integration and segregation thermodynamics

References
1. Grannell, Ryan. (2011). “Category: Human Chemistry”, Bag of Many Things, WordPress.com (Jun 26 –Jul 22).
2. Tuhtan, Jeff. (2012). “Ecological Stoichiometry”, Hmolpedia threads, Jun 4.
3. Etcoff, Nancy. (1999). Survival of the Prettiest – the Science of Beauty. New York: Anchor Books.
4. Bernoulli, Daniel. (1738). Hydrodynamica, Sive Vivibus et Motimus Fluidorum Commentarii. Sectio Decima: “De affectionibus atque botimus fluidorum elasticorum, praecipue autem aeris.” (pgs. 200-204; piston and cylinder, pgs. 319). Argentorati, Sumptibus Johannes Reinholdi Dulseckeri.
5. Fermi, Enrico. (1936). Thermodynamics (pgs. 5-6). Prentice-Hall.
6. Thims, Libb. (2007). Human Chemistry (Volume One) (pgs. 223-33, ch. 9: Human Molecular Orbital Theory, pgs. 247-95) (preview) (Google books). Morrisville, NC: LuLu.
7. (a)
2008 Georgia-Russia crisis – Wikipedia.
(b) 2008 South Ossetia war – Wikipedia.
8. Macrone, Michael and Lulevitch, Tom. (1999). Eureka!: 81 Key Ideas Explained (section: Entropy, pgs. 129-33; image pg. 130). Barnes & Noble Publishing.
9. Thims, Libb. (2011). “Pressure Volume Work and Mean Girls”, HumanChemistry101, YouTube, Apr 25.