Rss Feed
Linkedin button

The Science of Economic Growth: Part 2

The Science of Economic Growth: Part 2

This is a multi-part post on the science of economic growth.  Standard economic theory has failed miserably to define the source of economic growth, which means it is impossible for it to provide rational policies to restore economic growth.  This series of posts defines a scientific theory of the source of economic growth.

Part 1 

Part 2 

Part 3 

Part 4 

Part 5 


Homo Economicus, Entropy, and Invention

Homo sapiens also consume food and create shelter to overcome the effects of entropy.  Unlike other living organisms, homo sapiens organize their environment to minimize the effects of biological entropy.  For instance, humans have invented agriculture to increase their supply of food (energy).  Humans also harnessed the physical strength of animals, created internal combustion machines, electric lights, electricity, washing machines, tractors, computers, the internet, email, lasers, fiber optics, etc.  All of these are inventions.  Humans alter their environment by creating inventions.  This is different from every other animal.  For instance, our bison standing on coal will never be able to harness the potential energy in that coal unless the species evolves to eat the coal.

The distinguishing characteristic of homo sapiens is their ability to reason.  Man is a rational animal according to Aristotle’s classical definition.[1]  Man uses his reason to alter his environment (invent) and increase the energy available to him.  Note that I am not limiting myself to the arcane definition of invention provided by the law.  Anything that man creates to solve an objective problem is an invention.  If a device/service is not found in nature separate from man then it is an invention.  For example, the ability to create fire or harness it is an invention of man.  No other animal has the ability to create or harness fire.  Man did not have some sort of inherent knowledge of how to create or harness fire.

If humans did not invent, then studying economics would be the same thing as studying the evolution of humans.  While trade is also unique to humans, trade is not the fundamental basis of economics.  Trade is an invention of man.  If everyone produces the same thing, then there is no reason to trade.  For instance, if we all produce wheat, then there is no reason or ability to trade.[2]  It is only because someone has invented a new product that trade becomes a rational choice.  For instance, one group of people may have invented a process for skinning animals and using them as clothing.  They may have traded this with people who had access to flint and invented a system for making simple axes.  Invention has to proceed production, which has to proceed trade logically.  Of course, without trade the value of invention and production is severely diminished.


Diminishing Returns: Sustainability Isn’t Sustainable

Biological entropy implies diminishing returns.  For all species of life there is a limited supply of the resources (free energy) and conditions necessary to sustain a particular form of life at any point in time.  The concentration or ease of extracting these resources varies as a result of the non-homogenous nature of the universe.  A species of life thrives where it has a high concentration of resources (low biological entropy for the species) and as its population expands it has to expand to areas of low concentration of resources (high biological entropy), which results in diminishing returns.  The species are then constrained by the Malthusian Trap.

The way this is expressed in economics is that the use of any one resource results in diminishing returns for that resource.  The question of limited human resources has been the subject of Economics since Malthus and David Ricardo.  I will explore the idea of diminishing returns and its relationship to invention, by examining the idea of sustainability.  Sustainability is an attempt to overcome or at least manage diminishing returns.  There are numerous and conflicting definitions of what sustainability means.  However, most sources point to the World Commission on Environment and Development (WCED), also known as the Brundtland Report.  According to the 1987 Brundtland Report, sustainability is: “Meeting the needs of the present generation without compromising the ability of future generations to meet their needs.[3]  This definition is not testable and is incredibly vague.  What are the “needs” of the present generation?  Do we need the Internet, satellites, SUVs, etc.?  How do we know if this will compromise future generations ability to meet their needs?

Since this is not a productive path of inquiry, let’s take the word “sustainable” literally.  A sustainable technology would be one that can be used indefinitely by humans without side effects and without any diminution in its effectiveness.  This definition violates the laws of physics.  According to the second law of thermodynamics, entropy always increases in a closed system.  As a result, any use of technology at least produces waste heat – a side effect.  Sustainability taken literally is an attempt to create a perpetual motion machine.  Even the Sun’s energy will not last forever and it is not infinite.  This is true whether we are talking about absolute entropy or biological entropy.  Is the sustainability movement unrealistically optimistic?

A key issue for the sustainability movement is the use of so called non-renewable resources, such as the use of fossil fuels and the using up of other natural resources (diminishing returns).  The way this is often phrased today is Peak Oil, Peak Water, Peak _____ (Pick Your Favorite Resource).  Peak Oil (natural resource) occurs when the amount of oil that can be extracted reaches its maximum or the point at which we reach the maximum net energy output from oil.  The alternative definition takes into account that even if we can extract more oil, this is irrelevant if it takes more energy to extract the oil than we receive from the oil.  The supposed solution for our Peak Oil problem is to develop renewable energy resources.  The Clean Energy website provides the following definition “Renewable energy is natural energy which does not have a limited supply.  Renewable energy can be used over and over again, and will never run out.”[4]  What is a natural energy?  Either all energy is natural, comes from nature, or only animal muscle power is natural.  The natural qualification is complete nonsense – unless they really want us to go back to animal muscle only.  The “never run out” qualification violates entropy.  All energy resources will run out.  All energy sources, fossil fuels, solar, hydroelectric, tidal, biomass, hydrothermal, fission, fusion, etc are solar or at least stellar.  For instance, hydroelectric energy is the result of the Sun heating the oceans or other large bodies of water.  As the water evaporates and then condenses in the form of rain or snow on land masses it is collected in dams.  The dams convert the gravitation force of the water into electric energy.  Fossil fuels are created by plants converting sunlight into biomass (including animals).  The biomass is trapped underground by sea sediment and the pressure and heat converts the biomass into oil, coal, natural gas, etc.[5]  Fission is the process whereby heavy elements, generally Uranium, are split into lighter elements and energy is released.  These heavy elements were created in a star that has long since expired.  Thus, all energy is Solar or at least stellar.  The Sun will not last forever and does not provide unlimited energy.  The concept of renewable energy that “will never run out” and “can be used over and over again” is false.  So was Malthus correct?  Are humans doomed by entropy to eventually return to the Malthusian Trap or worse?  Is the defining characteristic of economics that diminishing returns (entropy) will always force humans back to the point that we are on the edge of starvation?  If so, will evolution pass humans by and humans will become extinct?

This concept of peak resources is not new.  You can find numerous examples of “Peak Oil” historically.  For instance, the fertilizer crisis of the 19th century.  In 1830 it was discovered that bat guano was an excellent fertilizer.  Population exploded, as guano was used in Europe because of the additional food (energy) produced as a result of this excellent fertilizer and mechanization.  The best sources of guano began to run out fairly quickly.  People predicted the equivalent of “Peak Guano.”  The question was not whether we would have “Peak Guano,” but Peak Fertilizer.  In other words, we did not have a guano problem we had an invention problem.  The Haber-Bosch process was invented in 1909, which allowed fixing nitrogen in air and solved the “Peak Guano” problem.[6]

Reason magazine in the article Peak Everything? discussed how logical, scientific projections showed we would run out of lithium, neodymium, and phosphorus.[7]  Peak lithium was going to limit the batteries necessary for electric cars.  In fact, we would run out of lithium faster than we would run out of oil.  The solution is a new invention that replaces lithium with zinc air batteries.  Note the solution was not a better way to extract lithium, but to make the supply of lithium irrelevant.  New invention creates a paradigm shift.  Peak neodymium is going to limit our ability to build the electric motors of hybrid cars as well as other products.  Interestingly, neodymium magnets were invented to overcome the problem of peak cobalt.  In the area of permanent magnets, it appears that a new induction motor will eliminate the need for permanent magnets.  Peak phosphorus is a repeat of Peak Guano.  Peak phosphorous threatens our ability to provide enough fertilizer for our agricultural needs.  One solution is to expoit human waste.  Phosphorous is a byproduct of human urine.  The phosphorous can be recycled using a no mix toilet.

Paul Romer has observed, “Every generation has perceived the limits to growth that finite resources and undesirable side effects would pose if no new recipes or ideas were discovered.  And every generation has underestimated the potential for finding new recipes and ideas.  We consistently fail to grasp how many ideas remain to be discovered.  The difficulty is the same one we have with compounding: possibilities do not merely add up; they multiply.”[8]

The computer industry has also been beset by predictions of impending doom, when it could no longer achieve Moore’s law of doubling the number of transistors every eighteen months.  Ray Kurzweil has shown that if you restate Moore’s law as computational power, every time a technology reaches its limit to improve computational power a new technology takes over.  Using this he shows that computational power has been growing exponentially since 1900.  The first computational devices were electromechanical.  When these devices reached their limit, they were replaced with relay devices; these were replaced with vacuum tubes, then transistors, and finally integrated circuits.[9]  However, if you trace the speed of machines beginning with the invention of the steam engine, it peaks at around supersonic flight.  It is hard to determine if this is an economic/technological limitation or political limitation.

Diminishing returns for a given natural resource in a technology static scenario occurs because high order areas of the natural resource are exploited first.  It takes more energy to extract lower order areas (high biological entropy).  For instance, man first exploited gold nuggets picked up from the ground.  Eventually, man dug for the gold or panned, which required more energy because it was less ordered.  Note that even this change required new (additional) technologies – a shovel and pick or a tin pan.  Modern techniques of gold mining, e.g., cyanide leaching, have allowed formerly unprofitable mines to be reopened.  This is because the new technology allows us to exploit even lower order areas of gold.  Diminishing returns only apply in a technology static environment.  These diminishing returns can be modeled as a decaying exponential.


Are Inventions Subject to Diminishing Returns?

Every invention is a combination of known elements – you cannot create something from nothing.  This follows from the natural law conservation of matter and energy.  As a result, every invention opens up the possibility of more inventions by building on earlier inventions.  Creating these inventions takes energy, but the number of potential inventions we can conceive of increases with every invention we create.  As a result, the number of potential inventions grows factorially.  There are four ways in which inventions could be subject to diminishing returns: 1) the number of inventions are limited, 2) the inventions in a narrow area of technology are limited 3) the returns on devoting more resources, as a percentage of total resources, to inventing declines, and 4) the cost of creating the next invention in any technology could increase.

The number of potential inventions, however,  is not subject to diminishing returns.  In fact, the opposite is true.[10]  The number of potential inventions grows factorially as new inventions are created.

Inventions in a narrow area of technology are subject to diminishing returns.  Early inventions would appear to provide the greatest return and latter inventions appear to provide more limited returns.  Ray Kurzweil has studied this and found that new technologies appear to follow an S-curve with the greatest return in the middle of the S and eventually declining in return.[11]  Cross pollination between the primary area of technology and other areas of technology appears to prevent diminishing returns in a narrow area of technology, similar to how substitute resources prevents diminishing returns for natural resources.[12]

Would it logically follow, if a greater and greater percentage of a country’s or the world’s resources were devoted to discovering inventions you would hit a point of diminishing returns?  The answer is no country has ever come close to testing this hypothesis.  Countries throughout history have under invested in inventions and provided little or no incentive for inventors.  Those countries that have devoted the most resources to inventing, have seen the greatest economic returns.  The U.S. has historically devoted the most resources to invention.  It has historically had the strongest laws protecting the rights to inventions, which has resulted in greater resources being devoted to invention.  England had some of the strongest laws protecting inventors at the beginning of the Industrial Revolution and it was the hotbed of invention at that time.  The Italian city states of the 15th and 16th centuries had some of the first laws protecting inventors and they had a much higher standard of living.  Among their inventions were modern glass making techniques and a modern banking system.  There is a minimum amount of resources that must be devoted in a country to agriculture and maintenance just to keep up with the decline due to human biological entropy.  If inventive activity were so large as to crowd out those activities necessary to overcome biological entropy, you would have to assume that there are diminishing returns at that point.

The idea that the cost per invention could increase to the point of diminishing returns, seems to have credence if we look at a narrow technological area.  For instance, the cost of improving the aerodynamics of airplanes is extraordinarily expensive.  However, modern electronics allow us to improve the aerodynamics of planes by putting in control systems that allow a plane to be unstable aerodynamically.  Commercial supersonic flight was not feasible economically in the 1970s because of aerodynamic drag.  This problem can be solved today fairly inexpensively with electronic control systems.  The cost of inventing in electronics grew tremendously with the advent of the integrated circuit.  The advent of personal computers and software have driven down the cost of inventing in electronics and a wide variety of other areas.  There is evidence that the cost of inventing is decreasing over time, if we do not limit inventing to a narrow area of technology.

Diminishing returns can be modeled as a decaying exponential.  Inventions across all areas of technology are not subject to diminishing returns.  Potential inventions grow factorially, which is much faster than diminishing returns shrink.  Thus, it is entirely possible to grow our technology faster than the limitations of diminishing returns.  However, it is not foreordained that humans will invent.  Humans are volitional beings and they can choose not to invent.  There is plenty of evidence that when humans choose not to invent then they become subject to diminishing returns and their society declines or becomes extinct.  For example, Jared Diamond’s book Collapse[13] argues that many societies collapsed because of environmental problems.


In a technologically stagnant society, entropy and diminishing returns will prevail and that society will become extinct. 


            It appears that the sustainability movement is overly optimistic, in a technologically stagnant society.  However, if humans choose to invent in broad technological areas, then they can escape this fate.  Invention is the key to escaping the Malthusian Trap and growing real per capita income.  This is consistent with Robert Solow’s paper “Technical Change and the Aggregate Production Function” paper and the subsequent work in this area of economics which shows all real increases in per capita income are due to increases in technology.[14]  It is also consistent with groundbreaking econometric studies of Jacob Schmookler, in chapter V, “Productivity Advance: A Case of Supply and Demand” of his book Invention and Economic Growth.[15]


In a technologically dynamic society, inventions will result in growth that outstrips entropy and diminishing returns.  People will escape Malthusian Trap and their per capita income will grow. 


The question about whether humans are doomed to a Malthusian existence, where economic growth cannot keep up with population growth, has been one of the most vexing questions since the beginning of economics.  Malthus was clearly correct for all of human history other than the last 200 years.  Even since then he has been correct for the majority of humans until the last 40 years or so.  On the other hand, critics of Malthusian theories have pointed to the West’s ability to overcome all predicted population bombs and resource limitations during the last 200 years.  Critics often point to the famous bet between Paul Ehrlich and Julian Simon over the price of commodities.  The reason this debate has been so contentious and has not been resolved is clear.  There is no predetermined answer.  It depends on whether large groups of people decide to invent fast enough.  I say large groups because Matt Ridley has shown in his book, The Rational Optimist, that small population groups cannot even sustain their initial level of technology.[16]  The book provides numerous examples of how various groups of humans regressed technologically because of inadequate population densities to support specialization, such as Tanzania.  The book summarizes the lessons by quoting economist Julian Simon “population leading to diminishing returns is fiction: the induced increase in productivity is scientific fact.”[17]


[1] The Philosophy of Aristotle, Adventures in Philosophy, 10/7/10.

[2] Some animal trade like items across time.  If I have extra wheat, I give it to someone who does not have enough and they return the favor later.  Usually this only occurs between family members in other species.

[3] Brundtland Commision, Wikipedia,, 11/7/10.

[5] Note that have been some alternative explanations proposed for how oil is produced that does not involve this biomass conversion

[6] Mark Ridley had numerous “Peak Oil” examples in his book The Rational Optimist: How Prosperity Evolves, Harper Collins, 2010, New York, pp 121 -156.

[7] Bailey, Ronald,, Peak Everything?, April 27, 2010,, 10/16/10.

[8] Bailey, Ronald,, Peak Everything?, April 27, 2010,, 10/16/10.

[9] Kurzwiel, Ray, The Singularity is Near: When Humans Transcend Human Biology, Penguin Books, 2005, p 67.

[10] If there is a limited amount of matter and energy in the Universe, which is open to debate, there may be a limitation to the number of potential inventions.  However, this limitation would be so large as to be meaningless for all practical purposes.

[11]  Kurzweil, Ray, The Singularity is Near: When Humans Transcend Human Biology, Penguin Books, 2005, p 44.

[12]  Kurzweil, Ray, The Singularity is Near: When Humans Transcend Human Biology, Penguin Books, 2005, p 44.

[13] Diamond, Jared, Collapse: How Societies Choose to Fail or Succeed, Penguin Group,New York, 2005.

[14] Solow, Robert M, Technical Change and the Aggregate Production Function, The Review of Economics and Statistics, Vol. 39, No. 3 (Aug., 1957), pp. 312-320

[15] Schmookler, Jacob, Inventions and Economic Growth, Harvard Press, 1966, pp 86-103.

[16] Matt Ridley in his book The Rational Optimist shows that self sufficiency is an economic dead end.  Only large groups of humans can afford to have people specialize so some or all their time is devoted to inventing.

[17]  Ridley, Matt, The Rational Optimist: How Prosperity Evolves,Haper Collins,New York, 2010,p. 83.


  1. Dale,

    I don’t want to waste my finite energy debating with you whether Malthus was right, whether Peak Oil will (has) happen(ed), etc.

    At the end of the day, DNA is a pattern of information that changes (due for example to evolution) where the pattern is either successful in fighting against environmental challenges or the pattern (and its host, the creature) goes extinct.

    Similarly, the compilation of technologies, and other informational patterns that a civilization has, need to adaptively change to successfully fight the good fight against evolving environmental challenges or the pattern (and its host, the civilization) goes extinct.

    A strong and vigorously encouraged patent system is one way that a civilization can keep its adaptations going.

    On this, I think we can agree. (Basically, a long and winding story made short.)

  2. Agreed – I think the important point is a technologically stagnant society is doomed to subsistence living or worse.

  3. A “technologically stagnant” society is not the only one in the competitive global village.

    Hence the more tech-wise competitive other societies will quickly eat it for lunch.

    Have you heard much lately from our Neanderthal cousins? They don’t seem to call much any more.
    Problem is; lately I’ve been looking in the mirror and asking, Who’s the Neanderthal now?

  4. True, but it does point out that we want to have policies that encourage invention. In order of importance we need policies that encourage invention and then production. We do not need policies that encourage consumption. In other words, Keynesian prime pumping is snake oil.

  5. Ronald Raygun trickle trickle is also snake oil. We need to “invent” a new paradigm that fairly gives a piece of the pie even to those who are not capable of inventing. We also need to discourage the inventing of more lethal forms of bird flu. We need to discourage the production side mass production of planet killing toxins. Do I have the silver bullet magic answer to all this? Sorry. No. I’m not that smart.

  6. Fairness is a subjective concept. The only real definition is equality under the law and the recognition that you own yourself and the product of your labor. Anything that interferes with that is immoral and unfair.

  7. Ah. The old biblical debate resurfaces.
    Am I my brother’s keeper? (And is he mine? And what if he’s a slacker?)

  8. The morality of Slavery “Am I my brother’s keeper?”

Leave a Reply

Subscriber Count


Advertise Here

Your Ad

could be right


find out how


Coming Soon