Luis ArroyoIn existographies, Luis Balbino Arroyo Colon (1990-) (IQE:180) (CR:), referred to as “Arroyo Colon” (Ѻ), “Arroyo” (Ѻ), or “Balbino” (Ѻ), depending, is a Puerto Rican child prodigy turned physicist, economic thermodynamicist, lawyer, and political advisor, noted, in hmolscience, for his 2010 “A Thermal Model of the Economy”, an age 20 penned MS thesis in physics, wherein he platforms of Roegen (1971), Mimkes (2008), and Samuelson (1970) to outline a social services model of value, which although error filled, does have interesting points of originality.

Coupled heat engines
Some of the more interesting points of Arroyo’s thesis are as follows:

“It is important to quickly survey the model we are proposing. At this stage, we simply have two heat reservoirs and two thermal cycles. One of the reservoirs is the hot (or supply) reservoir with a temperature Ts. The other (demand) reservoir is colder and has a temperature of Td. As we discuss further in the appendix, a heat engine is basically a way of using heat to do work. In our model that process represents the act of turning resources into products and services, or production. Then that work is multiplied by what we call the ‘value multiplier’, or V which we will also discuss. Then that work is used to run a reverse heat engine, or refrigerator. That represents the flow of money as it goes back to the supply in the form of consumption.”
— Luis Arroyo (2010), “A Thermal Model of the Economy” (pg. 20)

“How will we define temperature? In physics, temperature tends to determine average energy per particle; high temperature results in higher energy per particle. In a similar vein, temperature would be a kind of energy density. This would point to temperature being a measure of the density of resources available to a reservoir, or group of particles which will do work through a heat engine. We can refer to a group of people as a reservoir, since people are or own resources. The higher the wealth of the people in the reservoir, the higher the average temperature will be.”
— Luis Arroyo (2010), “A Thermal Model of the Economy” (pg. 24)

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Overview | Thermal economics
In 2010, Arroyo completed his “A Thermal Model of the Economy”, a MS thesis on an amalgamation of economic theory and theoretical physics, at the University of Puerto Rico, Mayaguez, the abstract of which is as follows: [1]

“The motivation for this work came from an interest in economics (particularly since the 2008 economic downturn) and a desire to use the tools of physics in a field that has not been the subject of great exploration. We propose a model of economics in analogy to thermodynamics and introduce the concept of the ‘value multiplier’ as a fundamental addition to any such model. Firstly, we attempt to make analogies between some economic concepts and fundamental concepts of thermal physics. Then we introduce the value multiplier and justify its existence in our system; the value multiplier allows us to account for some intangible, psychological elements of the value of goods and services. We finally bring all the elements together in a qualitative system. In particular, we attempt to make an analogy with the ‘Keynesian multiplier’ that justifies the usefulness of fiscal stimulus in severe economic downturns.”

Arroyo's thesis was approved by the following committee:

● Jose I. Alameda Lozada | PhD economics (1996) (pdf) (Ѻ)
● Erick A Roura Davila | PhD theoretical physics / Computational / Quantum physics [7]
● Pablo J. Marrero Soto | PhD theoretical physics / Computational / Fine materials [7]
● Anand D. Sharma | PhD agricultural engineering (1980) (Ѻ)
● Hector J. Jimenez Gonzalez (Chair) | PhD solid state physics / magneto-optics (1992) [7]

In interview with the newspaper El Nuevodia, Arroyo, aged 20, commented the following on his thesis: “The issue (of the thesis) is a relationship between economics and physics applied to the current economic crisis. It is a bit complex and has taken me time to develop, but I graduate.” [3]

Difficulties: Human nature | Two natures?
Arroyo seems to believe that human nature is different from physical nature; the following evidences this:

Physics is a natural science, and it is both the most mathematical and the most exact. Economics, however successful, is at heart a social science. Human behavior is ill-suited to exactness and mathematical certainty by its very nature (see: human nature).”
— Luis Arroyo (2010), “A Thermal Model of the Economy” (pg. 7)

This statement seems to be in code for his Jehovah's Witness religious beliefs (Ѻ), which includes belief in free will (Ѻ), among other numerous issues.

Difficulties: Roegen
The first main citation for Arroyo's theory is Nicholas Georgescu-Roegen (1971), whose economic model forms the platform for his theory; Roegen's "material entropy" model, however, is a conceptual misinterpretation of bound energy and free energy of chemical thermodynamics applied to economic resources; Roegen's model, in short, is fallacious and without basis. Arroyo, in fact, not only sites a defunct model, but does not even understand the so-called “Roegen model” correctly, but only generally (i.e. factory = heat engine); this is evidenced by the following (pg. 9) statement:

“This correlation of turning resources into products and entropy reduction is the heart of the [Roegen] model. This allows us to clarify the relationship between the economic point of view and the physical perspective in the model proposed there. Economically, a factory exists to produce higher value material than what came in. Physically, it is impossible to create energy, but we can decrease the entropy of part of the material. Therefore, Georgescu makes the connection between value and entropy. The lower the entropy, the higher the value.”

Arroyo, firstly, seems to think that Roegen modeled the output of a factory, e.g. a child’s toy or transistor, as a “low entropy” type of matter, which is not the case. Roegen conceived the fossil fuel, which powers the factory, as being “bound energy” (i.e. low entropy matter, in his mind) and the factory waste (e.g. burnt exhaust fumes) as being “free energy”, e.g. coal or oil burned to power a factory and converted into disordered energy of fumes, or something along these lines. This entire model, however, is not how free energy (Gibbs energy) and bound energy (entropy) are defined by chemical thermodynamics. The root of the error, of course, being that Roegen was a mathematician who learned most of his thermodynamics out of a dictionary.

Arroyo, secondly, from Roegen, gleans a connection between entropy and value: something along the lines of:

Value function (Arroyo)

This, however, is incorrect. If Arroyo had studied the historical usage of human thermodynamic variables tables, he would have known that John Neumann (1934), in discussion of French physicist-economist Georges Guillaume's 1932 PhD dissertation (turned book) On the Fundamentals of the Economy with Rational Forecasting Techniques, wherein thermodynamics models are utilized, had equated free energy to cash value, and that Australian organic chemist and commerce theorist James Reiss (1994), in his chapter "Comparative Thermodynamics in Chemistry and Economics", building on the previous work of Bela Lukacs (1989), more recently and precisely defined value as a function of Gibbs energy follows:

Human thermodynamics variable table (Reiss 1994)

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Factory (Fairborn)
In 1915, American chemical engineer William Fairburn was the head of the Diamond Match Factory and as executive penned his human chemical theory stylized Human Chemistry, according to which the "factory" was conceptualized as a giant retort or continuous stirred tank reactor (CSTR), in modern chemical engineering terms, which produced matches via the controlled reactions of its factory workers, conceived as human chemicals, the foreman conceived as the master "human chemist" according to Fairburn. [11]
Factory | Heat engine vs Retort
In comparing the Reiss model to the Arroyo model we see the "factory" not modeled as heat engine, but equated to "concentration", which seems to be more along the lines of the William Fairburn (1914) model of the factory as a continuous stirred tank reactor (CSTR model) where the foreman is the "human chemist", according to which entropy or human entropy is defined, by Fairburn, as follows: [11]

“As each chemical element is an entity, differing and distinct from any other, so is each human element and entity and a personality, which, when guided by a human chemist to do work and perform his peculiar function in life, feels and acquires what no inert substance can ever acquire, namely moral stimulus of responsibility. A classification based on a [human element’s] relative electricity or relative energy or enthusiasm would not of itself help us much, for misapplied energy and wasteful application of human forces are common. The classification of entropy, referring to temperature changes which can be likened to coolness, passion, explosiveness and frigidity, are all interesting but of themselves prove little.”

In any event, Arroyo, platforming off Roegen’s model, jumps to the following human-human interaction model (pg.11) of entropy:

“In our times, the service sector has become the true center of growth for the world economy. As its very name points out, services do not produce physical goods that have entropy. Services performed reduce entropy on other bodies, and they have an energy cost, much like the production of physical goods. However, to quantify that entropy reduction in services is much more difficult than the more purely physical entropy reduction on the inputs of a production process. When a factory produces goods, it is (in theory, ignoring the obvious complications) straightforward to do a strict accounting of the energy that came in, and the energy that came out. However, when a service is performed on a human being, the question of calculating the entropy change in the human is an imponderable.”

This last point about calculating the entropy change in a human or of a human in a given state or during a given interaction, is not “imponderable”, but only is an engineering problem; the subject of calculating entropies, enthalpies, and or free energies of humans being an historical subject of its own, dating at least to the Bridgman paradox (1946) if not before.
Box spring model (Henderson)
American physiologist Lawrence Henderson's 1938 "box spring model" of the Pareto-Gibbs sociological extrapolation of the Le Chatelier principle (see: social Le Chatelier principle) of equilibrium restoration of the system after small modification to the system, which he defines as an equilibrium of forces. [12]

Mimkes | Samuelson
Arroyo, after his Roegen platform, then cites Jurgen Mimkes (2008) and Paul Samuelson (1970), digging into the general premise of being to formulate “equilibrium” in an economy via differential inflection points. [9]

Arroyo then jumps into the box spring model for forces and equilibrium of springs. Here Arroyo would have been keen to study the earlier box spring model of equilibrium outlined by Lawrence Henderson, in terms of free energy, as this is the more accurate model of value, as pointed out by Neumann (1934) and Reiss (1994), as discussed above. In 1938 to 1942, Henderson, in his “Sociology 23” lectures was citing Vilfredo Pareto's version of equilibrium and expanding on this definition, as applied to equilibrium in social systems, as follows: [12]

(1) A ball which is in a cup, and struck a blow that is not too hard, will return to its original position;
(2) A candle flame which is deflected by a draft that is not too strong will resume its original form;
(3) A trout brook that is ‘fished out’ will, if carefully protected, regain its former population of fish;
(4) An infant, according to Hippocrates, after a disease that is not too sever will gain in weight until that weight is reached which is approximately what would have been reached if there had been no sickness.

Henderson elaborates that these are examples of “stable equilibrium” but comments that there are other phenomena that resemble: unstable equilibrium, neutral equilibrium. He then comments that both the Pareto and Hippocratic models of equilibrium restoration are like of a box spring mattress after being sat on in that the underlying theory of equilibrium is an equilibrium of forces and force restoration: [12]

“In both cases—Hippocratic analysis and Pareto’s equilibrium—there is the underlying theory that equilibrium, for instance, in a box spring; that a small modification leaves the forces substantially intact; and that the forces tend to reestablish the state that would have existed if no modification had occurred, just as a box spring which has been depressed when someone lies down on it resumes its original form when one gets up.”

Henderson, as example of this, then cites the Feb 1937 Louisville flood, the earthquake and fire in San Francisco, and the devastation of the war of 1914 to 1918 in France. It is doubtful, to note, that WII, as Henderson seems to see things, was an example of stable equilibrium restoration, rather it would have been something as follows:
WWI + WWI Gibbs landscape
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Difficulties: Lucas
Arroyo also cites Robert Lucas; Lucas, however, has been lambasted by Noah Smith (Ѻ) as someone whose economic equations fail to make predictions as to where an economy is headed in the same manner as physics’ equations of motion can predict where a cannon ball will land.

Difficulties: Other
Other difficulties in Arroyo's thesis are his opening ontic opening discussion of the Heisenberg uncertainty principle along with information (possibly information theory) discussions of entropy.

IQ 200 | Prodigies
Arroyo, cited with an IQ of 200 at age 15 (Ѻ), interestingly, can similarly be grouped with two other IQ:200+ cited child prodigies, namely: William Sidis (1898-1944), IQ:250-300 cited, and Christopher Hirata (1982), IQ:225 cited, who each, with similar background in math and physics, applied thermodynamics to the deeper questions as teenagers, Sidis at age 16 and Hirata at age 18.

Arroyo stated that he cannot remember whether he learned to read at two or three years, but what he does remember is how he was “bored” in class when their teachers in elementary school tried to teach colors and letters: [6]

"Yes, I was bored in kindergarten ... I was bored because I knew almost everything they said. I had many problems with the teachers because I knew what they were saying and got up a lot. It was frustrating, it bothered me, but nothing; I kept going to school because I liked being with the kids my age and playing.”

Arroyo recalls, in kindergarten, how he had unpleasant experiences owing to the lack of intelligence and insecurities of his teachers, e.g. one time when he asked what a “diphthong” (Ѻ) was, he was scolded by his teachers for asking such questions: [6]

“I remember in kindergarten, I asked a teacher what were the diphthongs, because the index of the book said some diphthongs and Iit sounded weird. I asked what it was and they scolded me, told me I did not have to ask that, that was for later. Sometimes they threw me the room that was moving a lot.”

Arroyo, as a child, envisioned that he wanted to study physics and law. Sometime thereafter he began to be cited in newspapers as the “boy genius of Moca”. [3] In 1999, Arroyo, age 9, in third grade, was being referred to as a as a “child genius”, by those who competed with him in mathematics and calculus. [4]

Luis Arroyo (2001 and 2006)
Left: Arroyo, age 11, during first day of college, at the University of Puerto Rico, being greeted by teacher Pablo Rodriguez, the interim rector at the time. Right: Arroyo, age 16, at college graduation, BS in physics (4.00 GPA), shown holding the three awards he received, namely: the Luis Stefani Rafucci Prize, the highest academic award given for acts of conferring of degrees from the college, the prize of the Faculty of Arts and Sciences bestowed students greater academic index, and the Enrico Fermi Award as best student of the physics department. [2]
In 2001, Arroyo, age 11, completed high school (4.00 GPA), and then set a record for youngest person to enter the University of Puerto Rico; the following is a retrospect news clipping: [3]

“The 11-year-old surprised everyone by graduating from high school with a high honor and become the youngest person to enter a university in Puerto Rico person. With an IQ that surpassed scales designed to measure the intelligence of children, child Moca spent his time studying the quantum theory and the movements of the stock market, while other children their age probably preferred to play wrestling.”

Shown adjacent, is a photo of age 11 Arroyo during first day of college in 2001 being greeted by teacher Pablo Rodriguez, the interim rector at the time. [2] In 2005, Arroyo, age 15, was being cited, by, as having an IQ of 200. [6]

In 2006, Arroyo, age 16, completed his BS in physics, at the University of Puerto Rico, Mayaguez, with a 4.00 GPA, winning a number of awards, which he holds in the adjacent photo, including: the Luis Stefani Rafucci Prize, the highest academic award given for acts of conferring of degrees from the college, the prize of the Faculty of Arts and Sciences bestowed students greater academic index, and the Enrico Fermi Award as best student of the physics department. [2]

In 2010, Arroyo, completed his MS in physics + economics, with a thesis on “A Thermal Model of the Economy” and was being blogged about, by his former classmates, as a genius. [4]

Luis Arroyo (2010) (genius)
A photo of Arroyo from a 2010 blog by one the students he competed with in calculus in elementary school. [4]
In 2012, Arroyo, age 22, obtained his JD from the Eugenio María de Hostos School of Law and passed the bar exam. In 2013, Arroyo, went to work for Senator Angel Rosa, one of his former professors from college, who approached Arroyo for help with drafting a bill aimed at job creation. It took the name “Proposal for jobs and prosperity for Puerto Rico”. Arroyo, stated that he envisioned physics applied to politics, while working on his thesis; Arroyo commented the following on his in interview: [5]

“Many models of the economy emerge from physics. I think my knowledge in the economy may be useful to help develop ideas to bring benefits to Puerto Rico. Especially ideas that do not cost.”

Presently, he is legislative director at Senator Angel Rosa’s Office.

Religion | Science
In 2005, Arroyo, age 15, during an interview with Mabel Figueroa of, stated that he was raised as a Jehovah’s Witness, and when questioned about the collide of faith and science, stated that he was “conservative” in his religious beliefs and that faith was “very important” for him; the following is the interview dialogue on this:

Arroyo: I am conservative in my religious beliefs

Figueroa: How Important is the faith to you?

Arroyo: It's very important.

Figueroa: But how faith can be understood by the head of a scientist? ... It's not something you can try.

Arroyo: I Do not think that religion and science are uneven ...

Figueroa: But there are scientists who do not think so ...

Arroyo: I think that what the Bible says can be taken as reality.

Figueroa: But by faith, not as something tangible ...

Arroyo: Well, I think that some things can be checked in a tangible way in the Bible.

Figueroa: Like what?

Arroyo: For example, in the Bible god he tells Job that he was dwelling above the circle of the earth. The Bible says that the earth was spherical and not a square. There is talk of some mathematical discoveries, such as the ratio of the circumference of a circle and its radius. There are physical things you can demonstrate ... Although the Bible is not a book of science, scientific things in the Bible can be checked.
Measure of the fish (labeled)
An example of mathematics in the Bible: the 200AD parable of miracle of Jesus catching 153 fish with a large net (Ѻ), in waters where no fish resided, and feeding the hungry, originating in the story of the 510BC miracle of Pythagoras regarding 153 as a sacred number and catching that number of fish; the ratio 265/153, being the height-to-width ratio of the intersection of two circles (called by Archimedes in 250BC the "measure of the fish"), being the nearest whole number approximation to the square root of three, the controlling ratio of the equilateral triangle, supposedly utilized in the design of the pyramids. [8]

Interesting here to see the collision of physics and faith, at such a young age, by someone who attributes his accelerated intellect to "an ability to learn some things faster". Arroyo would be keen to watch the "Zerotheism for Kids" (2015) lecture series, to see how religio-mythology studies and chemical thermodynamics cleanses false religious beliefs.

There is, to note, some truth to what Arroyo says here about mathematics in the Bible. The so-called "measure of the fish" is a mathematical formulation, supposedly attributed to Pythagoras (and or Archimedes, according to some accounts), who, in 520BC, according to the aretalogy, written by Porphyry, is reputed to have performed the supernatural feat of helping his disciples catch a large number of fish, 153 to be precise. Further, the Pythagoreans regarded 153 as a sacred number due to its use in a mathematical ratio called "the measure of the fish" (Ѻ), which produces the mystical symbol of the vesica pisces, the intersection of two circles which yields a fish-like shape. This was re-written, by someone, to the rescript that Jesus miraculously helped his disciples catch a large number of fish, precisely 153, at the Sea of Galilee (John 21:11). (Ѻ) Another book explains how the number has to do with the size of the net, squaring the circle, and the design of the pyramids.

1. (a) Arroyo-Colon, Luis B. (2010). “A Thermal Model of the Economy” (abs) (pdf) (79-pgs), Master’s Thesis, University of Puerto Rico, Mayaguez.
(b) Poudel, Ram. (2016). “Email to Libb Thims (on Arroyo)”, Feb 10.
2. Rosa-Velez, Mariam Ludim. (2006). “He Graduated from College at Age 16” (SpanishEnglish), Press Rum, Jun 9.
3. Staff. (2010). “Not So Young, But Still Genius: Balbino Luis Arroyo Colón, the small Moca who entered college at age 11, and soon complete his Masters” (Spanish → English), El Nuevodia News, Jul 13.
4. Anon. (2010). “The Genius of Luis Balbino: a Retrospect at the Human Intellect” (Ѻ), El Encuevao, Blogspot, Jul.
5. Staff. (2013). “Luis Balbino ‘the Genius of Moca’ Ventures into Politics” (Ѻ), El Nuevodia News, Jan 5.
6. Figueroa, Mabel. (2005). “Balbino Luis Arroyo Colon in Kindergarten Asked what was a Diphthong” (Ѻ),, Oct 8.
7. Faculty (physics) – University of Puerto Rico, Mayaguez.
8. Freke, Timothy and Gandy, Peter. (1999). The Jesus Mysteries: Was the Original Jesus a Pagan God? (pg. 16). Three Rivers Press.
9. (a) Mimkes, Jurgen. (2008). “Differential Forms: a New Tool in Economics from Biological Models to Econophysics” (Ѻ) (pdf), Paderborn University.
(b) Samuelson, Paul A. (1970). "Maximum Principles in Analytical Economics", Nobel Prize Lecture.
10. 10. (a) Lukacs, Bela. (1989). “Once More about Economic Entropy, Acta Oeconomica, 41:1-2, pgs. 181-92.
(b) Reiss, James A. (1994). “Comparative Thermodynamics in Chemistry and Economics”, in: Economics and Thermodynamics: New Perspectives on Economic Analysis (ch. 5, pgs. 47-72) edited by Peter Burley and John Foster. Boston: Kluwer Academic Publishers.
11. Fairburn, William Armstrong. (1914). Human Chemistry. The Nation Valley Press.
12. Henderson, Lawrence. (1942). "Sociology 23", in: L.J. Henderson on the Social System (pgs. 28, 73-74). University of Chicago Press, 1970.

External links
Luis Balbino Arroyo – LinkedIn.
Luis Balbino Arroyo – Wikipedia.
Luis Balbino Arroyo – Twitter.

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