Soul weighing
Circa 1500BC depiction of the weighing of the soul: a process in which the moral value, moral mass, or soul weight of a person's lifetime actions, right or wrong, are quantified numerically.
In religion, soul weight is a theory that the sum of one’s actions have a correlative moral mass, termed the soul, ba, or karma, that can be measured on some type of afterlife scale (the original being the scale of Maat) and thus quantified morally.

History
The concept of soul weight, or ‘ba weighing’ in its original namesake, originated in the Ra theology in circa 2500BC, as described in the Egyptian book of the dead and various other Pyramid texts, the mass being quantified by the actions, right or wrong, of 42 negative confessions.

An interesting aspect about this model is that soul is weighted against the force of gravity, although technically speaking "mass" is distinct from "weight", the latter of which depends on the planet on which the measurement is being made.

In circa 500 BC, the Ra theology based ba weighing concept diverged into two new religious derivative versions: B-ra-mha-ic “karma weighing”, a reincarnation based model, and Ab-ra-ham-ic “soul weighing”, a resurrection based model, the set of these derivative religions, in modern terms, dominate the moral philosophies of over 72 percent of the modern world.

Soul theorists
Into the modern scientific age, dozens of so-called ‘soul theorists’ have attempted to extend on the premise that the weight of one’s actions, in a right or wrong sense, or one’s ‘moral mass’ can be quantified, weighed, or explained theoretically in terms of modern science.
pineal gland
The pineal gland: a neurological mass and the supposed location of the soul according to French philosopher Rene Descartes.

Pineal gland
The most-famous of the so-called soul theories is French scientific philosopher Rene Decartes postulate in circa 1620 that the soul is found in the pineal gland of the brain, on the logic that this is the only brain organ not divided in two, i.e. into bilateral left and right hemisphere parts.

Soul snow
With the development of low temperature thermodynamics in the 1890s it became possible to liquefy all known gases, as epitomized in the work of British physicist James Dewar and his Dewar flasks. On this model, in circa 1895, to disprove the theory of the soul, German biologist Ernst Haeckel posited that if the soul exists it must be of a physical form, i.e. some kind of gas, and that using the correct technologies one should be able to liquefy the soul of a person and thus create a type of ‘soul snow’. Supposedly, because this had never been done, in Haeckel’s argument, the soul does not exist. [4]

21 grams
In 1901, in a letter to a friend, American physician Duncan MacDougall postulated that:

“If personal identity, and consciousness and all the attributes of mind and personality, continue to exist after the death of a body, it must exist as a space occupying body.”

To test this theory, later that year he famously began to measure or rather test for a possible change in mass of near-death patients, the seconds before and after their death point, according to which he found an experimentally determined value of 3/4th of an ounce (or 21 grams) as the mass of the “soul substance” leaving the body of a person at the point of death. [1]

Mass-energy equivalence
In 1905, German-born American physicist Albert Einstein introduced his formulation of the equivalence between mass and energy, in the form of his most-famous first law mass-energy equivalence: [2]

 E = mc^2 \,

and alternative second law of mass-energy equivalence:

 m = \frac{E}{c^2} \,

In the decades to follow, thinkers began to use the logic of these two equations to speculate on the possible idea that one's soul or after death moral mass might be associated with a type of energy and that this soul energy, being a measure of one's soul mass (or karma mass) might be able to be quantified or described scientifically or rather thermodynamically on the logic that according to a combination of Einstein's second law and either the conservation of energy, conservation of force, or first law of thermodynamics, that one's moral mass (or soul mass) at death might be conserved in such a way that it transforms into pure energy or is some type of moral energy at the point of death that mediates in some way in the structure of the universe.

One example of this type of approach being American chemical engineering physician Gerard Nahum’s 1998 “Proposal for Testing the Energetics of Consciousness and its Physical Foundation”, in which he postulated that at the time of death mass of one's soul would transform into energy to the information content of one consciousness, according to thermodynamic versions of information theory (e.g. Shannon entropy, negative entropy, etc), should be able to be measured by finely tuned electromagnetic detectors, and thus be quantified. [3]

Bond energy
In 2003-2007, American electrochemical engineer Libb Thims worked out a prototype theory called cessation conservation hypothesis, reasoning to the effect the moral essence of a person, at the point of termination, might be able to be quantified in terms of the energetic content, moral or amoral, of the summation of one's interpersonal human chemical bonds, left residual at death (cessation), thereafter becoming continuity bonds or transformed bonds or effects in the minds and post-cessation reconstructed bonds of the next generation. The basic model assumes that (a) human chemical bonds exist, (b) that all chemical bonds have a quantifiable amount of bond energy, (c) that energy is conserved according to the conservation of energy, whereby, accordingly, at any given moment, on average, a person's total bond energy can be quantified by the following formula:

 E_S = \frac{1}{2} \sum_{n=1}^L E_n \,

where Es is the bond energy or "energy signature" of a person or human molecule embedded in a larger connective matrix-style transforming social structure, L the number of total acquaintance bonds in ones existence (200 being the average number on one's social network, e.g. friends, family, work associates, etc) 300 to 5,000 being the number of people one knows by name), and the ½ factor quantifying the factor that bonds between atoms and molecules are typically shared bonds, hence bond energy will be divided by two, on average. [5]

Coupling theory
The modern way we interpret the Egyptian theory of the "ba", the idea that each person has a moral weight (called the soul or karma), the mass of which is based on the sum of each person's total set of actions (good or evil) in their existence, which if light enough will allow the person to either (a) get afterlife and transcend to heaven (Ab-ra-ham-ic version) or (b) escape samsara and achieve nirvana (B-ra-hma-ic version), is to re-interpret good and evil in terms of the thermodynamic terms "natural" (good) and "unnatural" (evil), the essential outline of this view first presented in English thermodynamicist Edward Guggenheim's 1933 Modern Thermodynamics, the structural details of which are extensive to say the least.

The gist of the model, is that in thermodynamics, "free energy coupling theory", as was first outlined in terms of Lewis thermodynamics in German-born American biochemist Fritz Lipmann's famous 1941 "Metabolic Generation and Utilization of Phosphate Bond Energy", which itself was based on previous scatters works on the puzzle as to how to explain the energetics of frog leg movement, posits that according to the following equation:

free energy coupling
which is called the Lipmann coupling inequality, that as long as the sum of the Gibbs free energy changes for all "natural", symbol  N  \, , processes or reactions (good processes and reactions, in anthropomorphic speak), in a given coupled system, plus the the sum of the Gibbs free energy changes for all "unnatural", symbol  \tilde N  \, , processes or reactions (evil processes and reactions, in anthropomorphic speak), in a given coupled system, is negative or has a measurement value less than zero then the process as a whole will be natural and spontaneously progress or occur.

In modern times, this is known popularly as the "free energy coupling" model of driven energy transformations, the textbook example being the model of ATP as a type of "energy currency".

References
1. Fisher, Len. (2004). Weighing the Soul: the Evolution of Scientific Beliefs. London: Weidenfeld & Nicolson.
2. Wilczek, Frank. (2010). Lightness of Being (pg. 19). Basic Books.
3. (a) Nahum, Gerard. (1998). “A Proposal for Testing the Energetics of Consciousness and its Physical Foundation (25-pgs)”, Presented at an international meeting in Tuscson, AZ called Tuscon III: Towards a Science of Consciousness.
(b) ibid, Nahum. (2005). “A Proposal for Testing the Energetics of Consciousness and its Physical Foundation (33-pgs)”, Submitted for review to Consciousness and Cognition.
(c) Nahum, Gerard. (2010). “A Proposal for Testing the Energetics of Consciousness and its Physical Foundation”, Journal of Human Thermodynamics, 6: 1-25, March.
4. (a) Connor, Steve and Leslie, Esther. (2009). “Master’s and Doctoral Program in Humanities and Cultural Studies Courses: Coldness: Toward a Political Thermodynamics of Culture”, LondonConsortium.com.
(b) Haeckel, Ernst. (1895–1899) Die Welträthsel ("world-riddle"); also spelled Die Welträtsel. Jena: Publisher.
(c) Haeckel, Ernst. (1905). The Riddle of the Universe: at the Close of the Nineteenth Century (ch. VI: The Nature of the Soul, pgs. 88-108; ch. XI: Immortality of the Soul, pgs. 188-210; ch. XII: The Law of Substance, pgs. 211-32; soul-snow, pg. 201), trans. Joseph McCabe. Harper & Brothers.
(d) The Riddle of the Universe – Wikipedia.
5. (a) Thims, Libb. (2007). Human Chemistry (Volume Two), (preview), Ch 16: section "Cessation Thermodynamics", (693-699). Morrisville, NC: LuLu.
(b) Thims, Libb. (2003). Human Thermodynamics, VIII (manscript). Chicago: Institute of Human Thermodynamics.
(c) Thims, Libb. (2005). Cessation Thermodynamics (manuscript), 100 printed copies. Chicago: Institute of Human Thermodynamics.
(d) Cessation Thermodynamics (Origin of) - Institute of Human Thermodynamics.
(e) Thims, Libb. (2007). Human Chemistry (Volume Two), (preview), Ch 13: "Human Chemical Bonding", (515-560). Morrisville, NC: LuLu.

Further reading
● Roach, Mary. (2005). Spook: Science Tackles the Afterlife (Gerry Nahum, pgs. 97-106, 290, 297). W.W. Norton & Co.
● Roach, Mary. (2006). “What Happens After You Die?”, New Scientist, Nov. 18.
● Roach, Mary. (2005). “A Soul’s Weight: What happens when a man (or a mouse, or a leach) dies on a Scale?”, Lost Magazine, Dec. No. 1.

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