Fractional Reserve Banking as Economic Parasitism

A Scientific, Mathematical, & Historical Exposé, Critique, and Manifesto

Vladimir Z. Nurivznuri@yahoo.com

Abstract

This paper looks at the history of money and its mod-ern form from a scientific and mathematical point ofview. The approach here is to emphasize simplicity.A straightforward model and algebraic formula for alarge economy analogous to the ideal gas law of ther-modynamics is proposed. It may be something like anew F = ma rule of the emerging econophysics field.Some implications of the equation are outlined, de-rived, and proved. The phenomena of counterfeiting,inflation and deflation are analyzed for interrelations.Analogies of the economy to an ecosystem or energysystem are advanced. The fundamental legitimacyof “expansion of the money supply” in particular isre-examined and challenged. From the hypothesesa major (admittedly radical) conclusion is that themodern international “fractional reserve banking sys-tem” is actually equivalent to legalized economic par-asitism by private bankers. This is the case because,contrary to conventional wisdom, the proceeds of in-flation are not actually spendable by the state. Alsopossible are forms of “economic warfare” based onthe principles. Alternative systems are proposed toremediate this catastrophic flaw.

1 introduction

“An invasion of armies can be resisted, butnot an idea whose time has come.”

—Victor Hugo

The dynamics of money is an extremely complicatedsubject. It’s a foremost preoccupation of humans,

as in the way money system mechanics is intricatelywoven into major plotlines of complex and influentialpopular fiction works such as Rand’s Atlas Shrugged[52] or Stephenson’s Cryptonomicon [61]. Extrapo-lated, it even becomes a “social energy system” themein more futuristic or outlandish forms such as emerg-ing from the popular science fiction movie The Ma-trix.

Possibly the full leverage of focused worldwide sci-entific inquiry and attention has yet to be appliedto economics. Some evidence that the science isstill in its infancy are that new fields of “economicphysics” or “econophysics,” “computational finance,”also dubbed “phynance,” have been proposed onlyrecently. [4, 19, 18] Physicists are applying statisti-cal and computational modelling techniques to comeup with creative, ad hoc, or highly realistic theoriesof money flow in e.g. large economies or stock mar-kets. [20] Despite the overused cliché, objective scien-tific commentators sensitive to these kinds of shiftsand trends could easily identify all the signs of anapparent Kuhnian “paradigm shift” [38] in progress.

So the blaring headlines read, “Physicists try tobreak economists’ monopoly on financial theory” [4]and “Physicists attempt to scale the ivory towers offinance.” [19]

One major factor in the shift is increased compu-tational power due to the so-far-uninterrupted real-ization of Moore’s law over about four decades at theclose of the 20th century, i.e. exponential growth (ingates per chip or many other similar measurements).This awesome and accessible power has elevated thecomputer to the status of a new scientific instrument,roughly analogous to the invention of the microscope

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or telescope, which has rapidly transformed conven-tional scientific perspectives on laws of both natureand societies.

Complexity is the buzzword across multiple disci-plines, even as previously segregrated disciplines aremarried [12, 66] (e.g. in the case here, physics, fi-nance, biology, thermodynamics, etc.). It is likely keyinsights have not yet been totally realized, remainingpotential lying undeveloped. For example, virtuallyall economic theory of the 20th century was devel-oped largely without extensive computational exper-iments, modelling, simulations, and empirical analy-sis, so central to the new style of inquiry via the pre-miere, even transcendental instrument(s) of science—the computer and the algorithm. [13, 5]

The new breed of econophysicists are very open-minded in their metaphors, borrowing seemingly al-most indiscriminately (leaving them open to one ofthe major but predictable criticisms). A particularnew meme receiving heavy attention and advance-ment is the metaphor of the economy as an ecosystem.Such a view seems obvious in retrospect of various re-search delineating the parallels, but it was unfamiliar,novel, and even somewhat radical when first exhaus-tively and definitively proposed by e.g. Rothschild inthe seminal and foresightful book Bionomics: Econ-omy as Ecosystem. [55] It was not clear initially ifthe idea was just another shallow fad not so muchwith scientific merit but to be mostly appropriatedby those seeking to justify ulterior political or socialagendas. [7]

However, subsequent quantitative research, now afull decade after Rothschild’s manifesto, has pushedthe metaphor into reality and significantly strength-ened the case for its validity and correctness. Asa Wall Street Journal reviewer wrote, used as thefront-cover blurb for the book, “Revolutionary. . . afascinating and highly creative alternative to the wayconventional economics views the world.” The earlytour de force analysis by Farmer, “Market force, ecol-ogy, and evolution” [20] invokes and reapplies theimportant Lotka-Volterra differential equations orig-inally proposed for modelling population dynamicsto a stock market system (see Farmer’s work for anexcellent survey of the economy-as-ecosystem memethread in the scientific literature).

As usual with a paradigm shift, the perspectiveflip-flops. How can the economy possibly not bethought of as an ecosystem? In Farmer’s work, dif-ferent traders’ strategies are fluctuating adaptationsanalogous to evolutionary niches occupied by variousorganisms. The Lotka-Volterra equations originallyintroduced to explain oscillations in populations withpredator-prey relationships map readily into describ-ing capital (money) gains associated with the com-petitive speculative strategies utilized by inter- andindependent traders.

The analysis presented here will be heavily depen-dent in places on the economy-as-ecosystem conceptand mostly take it as unequivocally justified and vir-tually proven, even though it is not a common per-spective among mainstream economists, and the un-derlying research agenda is clearly only beginning.Nevertheless, building on it, an important additionaltheme proposed and explored here is that of economicparasitism.

Along these lines, another paradigm shift is go-ing on in the field of parasitology. Researchers areonly recently beginning to appreciate the full implica-tions of parasites in and on ecosystems, via similarlyboundary-crossing interdisciplinary scientific collab-orations, all forcing a serious re-evaluation of the“big picture.” [70] In fact the study of biology is inmany ways the study of parasites; by one estimate, onplanet earth parasites outnumber ‘freeliving’ speciesfour to one!

New realizations are manifesting around the ubiq-uitous and crucial role(s) that parasites play inecosystems. In many ecosystems parasites are farfrom inconsequential, insignificant, or innocuousstowaways, but in actuality, despite their relativephysical and scientific invisibility, drive entire ecosys-tems. Parasites have been a domininant force, andmaybe even the dominant force in the evolution oflife! [70] So. . . given their forefront role, what is thepresumable link to economics?

The third major theme pursued here in naturalconjunction with bionomics and parasitism is a largescale economy seen as an energy system. While againthis concept may seem obvious, the full understand-ing stemming from this perspective appears not yetavailable. There is a strong parallel between eco-

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nomics equations and e.g. thermodynamics or elec-tronics formulas that does not seem to have beenexplored systematically by researchers so far. More-over, if the economy is an energy system, then vari-ous laws governing it can be analyzed and regulatedbased on solid engineering principles, and the mys-tery of economic dynamics should be minimized ine.g. the same way engineers understand the construc-tion of buildings based on applying Newton’s law.

So far econophysicists have tended to focus onthe dynamics of markets. However it is possibly in-evitable that they will soon arrive at a reconsidera-tion of the classic questions of economics, one of thechief ones being the question of the optimal policy forexpansion or contraction of the money supply. Hope-fully new scientific light can be shed on this age-oldquestion and definitive rather than speculative an-swers are within reach. This paper has been writtenwith that main goal in mind.

2 brief history of money

adult: Our government borrows money ev-ery year.

child: Where does the money come from?How can we always be in debt and nothave to pay it off?

adult: We’re in debt to ourselves.child: That doesn’t make any sense!adult: It’s based on fractional reserve bank-

ing. Banks do not have to have all themoney that they lend.

child: I still don’t understand.adult: You’ll understand it when you get

older.

Paper money was not used by Europeans until themiddle ages, partly on the discovery of its success-ful use in China by Marco Polo in the 13th century.The Greeks and Romans used coins. Some standardterminology is useful: (see e.g. [32] or [50])

commodity money Money that is made out of acommodity e.g. typically a precious metal, ei-ther gold or silver, i.e. coins.

receipt money This is also called “fully backedcommodity money” in [50]. A goldsmith orbanker issues paper receipts or certificates al-ways redeemable for an exact quantity of pre-cious metal and the receipts may be traded in-dependently.

fractional money Money that is backed by a com-modity only at a fraction of the face value. Alsocalled “fractionally backed commodity money”in [50]. Also called “bank money” or “bookcredit” in [17]. For purposes here, the exact frac-tion is considered to be fixed in perpetuity.

fiat money Money that is declared “legal tender”by a government with no commodity backing.Or for purposes here, arbitrary manipulationrather than fixed commitment to any fractionof backing.

paper money For purposes here, money made outof paper. Depending on backing it could be ei-ther receipt, fractional, or fiat money. Many au-thors use it as a synonym for fractional or fiatmoney to contrast it with commodity money.

electronic money For purposes here, money as re-duced to an abstract accounting process in-volving ‘blips,’ no longer requiring a physicalmedium for transfer. Also called “digital cash”or “cybercash.” Depending on backing it couldbe either receipt, fractional, or fiat money.

As e.g. Griffin [32] and Rothbard [54] explain, re-ceipt money was often turned into fractional moneyby bankers. They found they could temporarily loanout additional pseudo-certificates exceeding their col-lected inventory of gold and collect interest on theseloans. Rothbard notes that this practice was ruled le-gal by courts in some historical cases. Griffin assertsthis practice invariably leads to an inherently unsta-ble money system and periodic runs on banks, withmany historical examples to make his case. Griffinalso asserts that fiat money always leads to hyper-inflation and worthless currency. These views willbe carefully reappraised here with slightly differentconclusions.

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Immediately upon any inquiry into money, the top-ics of debasement and counterfeiting arise. Someonecan take a gold coin, clip or shave it down, and passon that coin, or create entirely fake coins with no goldcontent. Complicating the picture is that the govern-ment itself may adopt debasement of the currency asan official state policy! Many authors have blurredthese cases. So a strict definition of these differentforms of debasement is required.

counterfeiting The criminal practice of debasingthe currency or creating fraudulent money.

publicly-owned money expansion At the knowl-edge and consent of citizens, the government de-bases the currency as a matter of policy for arevenue stream other than taxation, spent on le-gitimate government services.

privately-owned money expansion The situa-tion mentioned above where private bankerstransform receipt money into fractional money,and the practice is regarded as legal by thegovernment. Revenue is counted as ‘profit’ byprivate bankers.

Counterfeiting is equivalent to theft. The criminalobtains tangible assets as booty at the collective rob-bery of all who use the currency. However it is not anovert theft in which victim is readily aware of, as, say,when their car is stolen and missing. Embezzlementis more accurate, presuming it is eventually detected!

As is widely understood by economists and thegeneral public, both counterfeiting and publicly-owned expansion lead to, or more accurately, causewidespread inflation of prices and, if uncontrolled,destabilization of the integrity of the overall moneysystem. Often governments have had draconian lawsagainst counterfeiting practices as equivalent to actsof sabotage, treason, or war. Sometimes wars wereactually waged partly via the very effective techniqueof one country counterfeiting another’s currency and‘buying’ (in actuality confiscating) resources with it.In this sense it is a camouflaged seizure of assets, or,economic warfare. Whereas pillaging is sometimesthe goal of warfare, counterfeiting permits an invisi-ble pillaging with no arms or army required!

The third case above, privately-owned money ex-pansion, is not so sharply delineated in the eco-nomics literature or popular treatments and is typ-ically mixed up with the other two cases. This is acatastrophic error as will be considered below. Forreference, call this the cui bono caveat emptor error(Latin, “who benefits—let the buyer beware”).

The above account hides further detail and mixesterminology based on the modern perspective. Fromthe historical standpoint, a nation can have two kindsof banking or money systems:

centralized banking A universal, standardized, of-ficial government currency is controlled and is-sued by a central bank.

noncentralized banking Different banks may is-sue their own receipt money as currency, alsocalled “banknotes.” The different banknotes cir-culate simultaneously in the overall economy.

Most nations worldwide now have their own cen-tral banks based on complex historical economic andpolitical events. American history involves eras ofalternation between centralized and noncentralizedbanking systems, now currently centralized. In theU.S. the central bank is known as the Federal Reserveand was established in 1913. Note that the centralbank may either publicly-owned or privately-owned.Despite its name and management protocols the U.S.Federal Reserve is privately owned. The assumptionthat a central bank is always publicly-owned is thesame cui bono caveat emptor error.

seigniorage

“By this means government may secretlyand unobserved, confiscate the wealth of thepeople, and not one man in a million will de-tect the theft.”

—John Maynard Keynes

In economics literature, the word seigniorage is typ-

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ically used as a synonym for money expansion.

seigniorage: revenue or a profit taken fromthe minting of coins, usually the differencebetween the value of the bullion used andthe face value of the coin.

In a fractional money system the mechanism is dif-ferent (not associated with minting coins) but withthe same effect.

Here a very careful distinction must be made. Thefollowing are separate and distinct but are sometimesconfused by neophytes or unclear in some accounts.The terminology is somewhat arbitrary (remarkably,there does not seem to be a standard terminologydevised by other commentators).

straight borrowing A government borrows moneyvia issuing bills or bonds at a discount on facevalue, promising to repay the purchaser the facevalue at some specified date in the future. Theinterest rate is the difference between the facevalue and the purchase price.

expansion borrowing The government may also‘borrow’ via money expansion, either publicly-owned or privately-owned. Even though in thiscase the standard overt procedure of “selling abond” seems identical to the prior case of gov-ernment borrowing, the underlying mechanismsand effects of the transaction are fundamentallydifferent.

Note that both cases involve a “shortfall of funds”but the first case does not constitute seigniorage,whereas the second does. If a government’s expen-ditures exceed revenue (government revenue is gen-erally taxes) then it can make up some difference viaborrowing such that additional funds become avail-able via a free-market loan by bondholders. Demandof these bonds is mainly tied to the interest rate of-fered by the government; higher interest rates spurhigher demand. However, even after the “auction ofdebt,” the additional available borrowed funds maystill be inadequate to fully cover a budget deficit.In which case another last resort, other than rais-ing bond interest rates, is money expansion. Hence

the latter case can be considered in a sense a “doubleshortfall” (a shortfall of demand or buyers agreeingto loans).

A further key distinction must be made on moneyexpansion. A bank may lend funds either to individ-uals or the government. In the former case typicallythe “noncentral” bank lends funds deposited by otherindividuals. In the latter case, typically the govern-ment borrows money from the nation’s central bankwhich controls issuance of the nation’s currency, thatis, when the bank buys government bonds. In eithercase, if the bank has assets on deposit equivalent tothe borrowed funds, it’s “straight borrowing.” If onlya fraction of the loan is backed by assets, it’s “expan-sion borrowing.” This latter case is called fractionalreserve banking (or, lending, borrowing). The frac-tion of deposits-to-loans a bank is required to hold iscalled the reserve requirement.

Hence money expansion can be localized to a givenbank’s own banknotes in the noncentral system, oraffecting the entire nation’s currency in the case ofa central bank. In the cui bono caveat emptor error,most economics literature does not apply or blurs theconcept of the central bank owning assets to back thegovernment loans, not using the idea of a “reserverequirement” relative to it.

The above establishes an important direct corre-spondence between commodity or receipt money tostraight borrowing, and fractional or fiat money toexpansion borrowing. Moreover the two types maybe practiced by either noncentral banks or a centralbank. The banks may further be either publicly-owned or privately-owned. An even more precisedistinction requires more sophistication than thisoverview and will be pursued further below.

In economics literature and popular accounts, thefollowing two cases are also not always carefully dis-tinguished. Current prices in an economy may shiftunder two separate and distinct key factors:

supply and demand Demand for a particulargood or service may fluctuate due to chang-ing economic conditions. This is the “invisiblehand” of Adam Smith’s theory. The value ordemand of the underlying assets has changed.

money manipulation In a fractional money sys-

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tem, money units can be shifted or modifiedbased on money expansion. The value or de-mand of the underlying assets is not changed.

This paper will focus on the latter case and reservethe word inflation exclusively for it. (To add to theconfusion, many authors refer to the latter case asthe supply and demand of money.) The distinction isalso roughly between extrinsic and intrinsic factors,respectively.

The economist Keynes helped analyze the processof publicly-owned money expansion and consideredthe ensuing inflation as a pernicious “hidden tax”on the masses. However, many monetary reformistshave proposed publicly-owned money expansion as avery useful means of taxation superior to alternatives,presuming it is limited and erected at full knowledgeand political consent of citizens (see e.g. [27]). Viasuch a system:

The state can obtain spendable revenue that re-quires no vast, complex, and cumbersome ac-counting system in e.g. the way the income taxdoes.

It also is an extremely uniform taxation system;representing a percent of every dollar in circu-lation, in contrast to every reported dollar, orevery dollar in only particular types of trans-actions. Conventional taxes on the other handhave uneven effects which are notoriously diffi-cult to anticipate by a legislature.

Tax evasion is essentially impossible underpublicly-owned money expansion!

money policy

“All the perplexities, confusion and distressin America arise, not from defects in theirConstitution or Confederation, not fromwant of honor or virtue, so much as from thedownright ignorance of the nature of coin,credit and circulation.”

—John Adams

In 1849, in a racist screed championing the righteous-ness of slavery over free market economics, Thomas

Carlyle lambasted supply-and-demand ideology as“the dismal science” in the first reference ever. [41] Inmodern form the preoccupations of “the dismal sci-ence” are over money expansion and inflation but theroot issues are timeless. After centuries of commen-tary and reaction, it seems an utterly poorly under-stood, mysterious, intractable, and at times incom-prehensible subject. How should money expansion beregulated? New theories arise regularly. For examplethe major trend of monetarism advanced chiefly byFriedman came about in the second half of the 20thcentury in response to dissatisfaction with existinggovernment policies regulating money expansion.

This lack of consensus seems tremendously ques-tionable and unsettling given that the health of entireworld economies is at stake. Routine money expan-sion has become the modus operandi of virtually allmajor and minor governments worldwide. Regard-ing different policies on its regulation, no school ofthought seems to have tangible proof of its supremacyof interpretation and guidance. Here maybe econo-physics research can eventually untangle the tangledmess of conflicting and contradictory approaches.The following is a rudimentary “first cut” in this di-rection representing in parts a radical departure fromconventional dogma.

3 mathematical analysis

“Better cut my pizza into four slices, I’mnot hungry enough to eat six.”

—Yogi Berra

What is needed to cut through the legacy of am-biguous verbiage and claims on money expansion andinflation phenomena is a correct, preferrably simplemodel. Extremely complex models of money expan-sion effects on the economy have been proposed re-cently with the help of computational simulations,and researchers will presumably continue to pursuethese directions to yield new insights. [6, 35] As themodels reflect, the interplay between taxation, pro-duction, and expansion is surely tremendously intri-cate. However, while these are admirable analyses,complicated models are only necessary if simple mod-

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els do not give correct or accurate results for the pur-poses or questions at hand.

The approach here will be to take perhaps the sim-plest possible model(s) imaginable, with the fewestoverall “moving parts,” and derive straightforwardconclusions. These models are offered as plausiblebut falsifiable hypotheses to serve as a base for fur-ther research rather than a definitive or final anal-ysis. They’re mainly a vehicle for introducing somekey metaphors and analogies to guide intuitive think-ing on the subject. (Also, in the following presenta-tion, the prose will fully explain the meaning of themathematical equations, leaving the latter optionalfor nontechnical readers.)

Economics’ basic equation for “money demand” isthe “equation of exchange” outlined by Irving Fisherin his 1911 treatise, The Purchasing Power of Money :[50, 17]

MV = PY (1)

where

M is the stock of money

V is the velocity of money

P is the price level

Y is the level of real output in the economy, e.g.the GDP, Gross Domestic Product.

The velocity is typically assumed constant by the“standard behavioral proposition;” it may also betaken as a measurement of individuals’ preference forsaving vs. spending.

No monetary authorities appear to have ever re-marked on the striking correspondence between thisformula and the ideal gas law from thermodynamics,which holds for gases at low density. The equationsthat follow are mainly adapted from [65]:

pv = nRT (2)

where

p is pressure measured in dimensional units offorce/length2 (i.e. force/area)

v is volume measured in length3

T is temperature,

R is a conversion constant

n is the number of particles (atoms or molecules)

The product p·v has units force·length, i.e. energy,also analogous to heat and work in thermodynamics,measured in units of joules.

The correspondence is established and metaphorrevealed when eq. 1 is written in the form1/P ·MV = Y . The analogies are:

1/P ⇔ pMV ⇔ vY ⇔ T

The above seems to constitute something of avery important “bridge theorem” between economicsand statistical physics (specifically thermodynamics).From this parallel many new insights are immedi-ately available. The mass economy can be seen assomething like a given volume of gas under pressure.For example, if the volume is increased, the pressureper area decreases, assuming constant temperature;analogously, if the money stock is increased, pricesincrease (being inversely proportional to pressure),assuming constant GDP.

In thermodynamics a process involving no heattransfer between the system and environment istermed adiabatic. For ideal gases, a related processoccurs at constant temperature, called isothermal.The thermodynamic equation for the special case ofconstant temperature is known as Boyle’s law:

p1v1 = p2v2 (3)

Quite probably, economic transactions between in-dividuals are the parallel to atomic collisions in theideal gas. This hypothesis and direction are veryrecently being pursued by pioneering econophysicistDoyne Farmer: “[our] results suggest that some ba-sic properties of markets can be explained by a the-ory much like statistical mechanics, in which each

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trade imparts an impact to prices, much like a molec-ular collision.” [21] This concept also has strong par-allels to fascinating new research by econophysi-cists Bouchard and Mézard into economic models ofPareto’s law of wealth distribution related to temper-atures in directed polymers. [11, 8]

Another link can be found in the extremely im-portant Black-Scholes equation for derivatives (op-tions) pricing which was actually initially adaptedfrom a heat transfer formula from mechanical engi-neering. In it, price differentials become analogous toheat variations. An overall stock market behaves as aheat diffusion system. It seems likely that stock mar-ket results directly correlate with general economictransactions, although this link has apparently notyet been systematically explored.

On the local, microscopic level, the collisions andtransactions are random and statistically distributed.On the macroscopic level, a simple global propertyemerges as one of the best scientific examples of the“law of averages” realized. This will surely be avery fruitful line of inquiry for future econophysicsresearch.

Apparently then, prices are an instantaneous mea-surement of money-energy denominated in units ofcurrent pressure, which economists sometimes referto as “underlying value” vs. “nominal value.” Theproduct p ·v, pressure times volume, gives a quantityof money-energy. Boyle’s law states that under “con-stant temperature” (constant GDP), money-energyis conserved under changes in the money stock; thismight be called the law of conservation of money-energy.

In thermodynamics the direct analogue wasdemonstrated by Joule in a classic two-chamber airtransfer experiment, which shows the internal energyof an ideal gas is a function of temperature only (i.e.not pressure and volume), written

u = f(T )

Now suppose that the money stock, v1, (denom-inated in e.g. units of dollars) is increased by anamount v2 = v1 + x. Then p1v1 = p2 · (v1 + x),or, (assuming constant GDP)

p2 =(

v1v1 + x

)p1 (4)

The new “pressure per dollar” is a fraction of the oldpressure, and a greater “volume of dollars” is requiredto obtain the same level of money-energy. This is thesimplest scientific and mathematical explanation ofthe fundamental phenomenon of inflation.

intuitive analogies

This new framework and vocabulary is not merelya superficial restatement but a very important newinsight into money expansion and an answer to thequestion, what exactly is money? A nice analogyfrom introductory engineering emerges here. In en-gineering the concepts of weight vs. mass, which ini-tially seem synonymous and are sometimes casuallyinterchanged, are carefully distinguished.

Mass is a fundamental unit and property of mat-ter. Weight, measured in units of force, is an amountof mass relative to a given gravitation, i.e. masstimes gravity (acceleration), typically presumed to beEarth’s. Analogously, “underlying value” or money-energy is a fundamental property of economic trans-actions, whereas price is a quantity of money-energymeasured relative to a given volume or pressure (pres-sure times volume). The same mass has differentweights on different planets just as the same money-energy has different prices within different volumesor relative to different pressures. In economics andpopular literature, lacking strict terminology, confu-sion easily arises as writers often use the single term‘money,’ or others, to connote the two distinct mean-ings depending on context.

On the other hand, remarkably, much literatureanticipates the thermodynamical equivalences estab-lished here without actually taking the slight extrastep of articulating them directly or formally (i.e.mathematically). For perhaps centuries, many com-mentators have talked about the volume of money,the pressure of a deal, or the heating up of an econ-omy.

Another analogy is extremely helpful. Imagine acompany stock trading on an exchange, with somequantity of shares publicly owned. The founders

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decide to issue additional stock. As is well knownthis “secondary offering” dilutes the share price. Onecould say that the supply and demand of the stockchanged, but this is not a change in supply and de-mand that is related to market effects or change inunderlying value of the company. It’s a simple varia-tion on money manipulation as defined in the previ-ous section.

Eq. 4 is immediately applicable and gives the newprice per share after some adjustment period, assum-ing no other factors. v1 is the initial number of shares,x is the number of new shares, p1 is the original priceper share, and p2 is the final price per share. Theexact dynamics and timing of the transition wouldrequire further empirical study and is an excellenteconophysics research topic. This also suggests thatstock markets could be a very nice model for expan-sionary bank lending and government monetary ad-justment (i.e., a microcosm of the fractional reservesystem).

Cui bono? The issuers of the new stock shares thenown a greater share of the company even after theprice depreciation of their previous shares. All othershareholders have lost real value in their holdings atthe abstract redenomination. Caveat emptor!

Now obviously this analogy extends further. Evi-dently a nation’s currency actually represents sharesof the economy of that country (the GDP) and moneyexpansion is exactly analogous to issuing new shares.But how are additional shares allocated? Cui bono?Who owns them? Caveat emptor!

counterfeiting vs. seigniorage

“The process by which banks create moneyis so simple that the mind is repelled.”

—John Kenneth Galbraith

These algebraic formulas often taught in high-school-level physics may seem trivial. But they are a basic,useful, rarely applied tool for analyzing some simpleeconomic situations. For example, in the previoussection it was asserted that counterfeiters embezzleat the expense of all currency holders of an economy.This seems intuitively obvious, yet what are the un-derlying mechanics? Exactly what is embezzled, and

how much?Remarkably, the above straightforward formula for

the simplest case, eq. 4, is again immediately appli-cable. x can be taken as simply the number of coun-terfeited dollars spent into circulation; v1 is the totalnumber of dollars in circulation. The formula givesthe final value of all dollars assuming the counterfeitdollars continue to circulate without detection, suchas with debased coinage. The counterfeiter obtainsmoney-energy by debasing the value of all dollars inthe system.

(If all the counterfeit dollars are detected and thoseholding the dollars must forfeit their loss then nomoney expansion occurs. But typically taxpayersmust make up for counterfeiting losses via a “write-off” which may be equivalent to money expansion.The formula correctly gives the instantaneous theo-retical loss.)

However, a very complicated question also imme-diately arises that cuts to the heart of this model.How much money-energy was actually obtained bythe counterfeiter? The counterfeiter spent x dollars,but was the money-energy obtained based on initialpressure pi, or final pressure pf? For insight, an an-swer can be related to the ideal gas metaphor. Boyle’slaw refers to the state of the gas at two separatetimes, such that it has reached an equilibrium in bothstates. Suppose that a significant volume change ismade in a very short time. Boyle’s law may not nec-essarily apply to all intermediate states.

Suppose that the counterfeiter spends the fake dol-lars slowly. Then each subsequent dollar will havea decreasing pressure associated with it, pi > p2 >p3 > . . . > pf . Apparently in the “best case sce-nario” the counterfeiter obtains x · pi money-energyif the money is spent rapidly with no further trans-actions, and as an asymptotic worst case with slowongoing transactions, x · pf . The actual precise quan-tity is also exactly the “invisible tax” levied uniformlyover all currency holders. The difference between thepn is related to how large the economy is and howquickly monetary perturbations spread throughoutit (another crucial and compelling econophysics re-search question). For later comment, call this phe-nomenon the decay rate.

Fig. 1 shows three hypothetical scenarios for a pres-

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p2

p1

t1 t2

pres

sure

time

linear paexponential pb

logistic pc

Figure 1: Three hypothetical scenarios pa(t), pb(t),pc(t) for decay in pressure p1 → p2 from volume ex-pansion during the time period t1 → t2, i.e. depre-ciation in asset value due to inflation from moneyexpansion via a gas thermodynamics model.

sure decay rate. The graph was generated for thescaled range [0..1] with t1 = p2 = 0 and t2 = p1 = 1via the following formulas:

pa(t) = 1− tpb(t) = 1e6tpc(t) = 1− 11+ 1

e12t−6

(5)

These formulas represent path functions for pres-sure change over time between the two intermediatestates. pc(t) is based on the S-shaped logistic curveused in many physical fields, such as for chemicalmixing or measuring population dynamics in biology.Their shapes are adjustable by varying the constantsand they’re readily adapted to the general case usingthe substitution

p(t′) = p2 + f(t′ − t1t2 − t1

)· (p1 − p2) (6)

Next, what about publicly-owned money expan-sion? Again, remarkably, in the simple analysis, theformulas are exactly the same. The ratio

r =p2p1, r < 1 (7)

is exactly equivalent to the seigniorage discount (anddepending on currency issue rates). r is clearly di-rectly analogous to a publicly-owned central bank re-serve ratio. v1 is the reserves, the entire nationaleconomy. The ‘revenue’ x accruing from the moneyexpansion can be spent on government services. Con-ceivably, here x could represent the entire governmentbudget. Again, different levels of money-energy areobtainable depending on the decay rate (analyzed inmore detail below).

The quantity of extracted dollars x ‘levied’ by thestate can also be expressed in terms of the seignioragediscount rate r and the original money stock v1:

x =(

1r− 1)v1 (8)

This naive model has special meaning for x > v1, orcorrespondingly r < 12 ; those ranges imply a ‘levy’greater than the entire economy. The equation showsthe ‘tax’ is minimal as r → 1 (from below), maximalas r → 12 and infinite as r → 0 (from above).

So one is left with the perplexing question, how ispublicly-owned money expansion different from coun-terfeiting? Obviously, with e.g. coin debasement theunderlying mechanism is identical. The inescapableconclusion: the only difference is that in the lattercase, the funds are spendable by the state and serveas an official pseudo-taxation system, i.e. as exam-ined and partially endorsed in the prior section. Theother key difference between counterfeiting and tax-ation comes down to citizen knowledge and consent.

The simple overview of this publicly-owned expan-sion system is that the government issues x additionalshares of “stock” (dollars) of the GDP and uses the‘revenue’ to buy government services, paid for by in-flation.

privately-owned money expansion

“Thus, our national circulating medium isnow at the mercy of loan transactions ofbanks, which lend, not money, but promisesto supply money they do not possess.”

—Irving Fisher

Finally, consider the strange worldwide case of

10

privately-owned money expansion. Here a privatebank is allowed to debase its receipt money basedon fractional reserves, i.e. loan out more money thanit has in reserves, either to a government or citizens.The idea of money expansion as equivalent to a frac-tional reserve system is not an explicit observationof modern economics, but it’s transparently identi-cal. Again, the above formula for depreciated valueis still applicable except that the borrower must payback the loan.

With straight borrowing, a lender provides imme-diate money-energy in return for the money-energyreturned plus a fee at a future time. (That fee, “in-terest,” may therefore be regarded as the price ormarket rate of instantaneous money-energy per re-payment time; the complex subject of interest is pur-sued below.) But by the money-energy conservationprinciple, no money-energy is provided by the lendervia privately-owned money expansion—this holds re-gardless of changes in GDP. The ‘illusory’ money-energy that is spent by the borrower is accumulatedvia the depreciated value of the lender’s fractionalmoney—inflation. Ergo, ‘pseudo-lending.’

In short, in this situation all money holders’ as-sets denominated in terms of the fractional moneydepreciate relative to the bank’s assets. If the bank’sfractional money is universally standardized as witha central bank, then for simplicity the groups “moneyholders,” “taxpayers,” and “citizens” can be taken toall overlap and be roughly interchangeable.

Mathematically, this means approximately that ifa government borrows x dollars into circulation viaprivately-owned money expansion (x is the shortfallafter straight borrowing), all dollars depreciate at theratio v1/(v1 + x) during and after the governmentspending. However, in contrast to publicly-owned ex-pansion where there are no further obligations, withprivately-owned expansion the government and itstaxpayers are additionally required to ‘repay’ the bor-rowed quantity of x dollars to the private pseudo-lender(s).

In one plausible scenario the government spendsthe money quickly and obtains money-energy atthe undeflated pressure p1, and taxpayers repay thepseudo-loan later at the deflated pressure p2 (inflatedvolume v2). Therefore total money-energy cost to

taxpayers is

E1 = xp1 + xp2 (9)

If the economy measured by v1 is extremely largerelative to x, then p1 ≈ p2 and the bottom line isapproximately 2x dollars cost for x dollars worth ofgovernment services! This bizarre and irrational ‘sys-tem’ is known as “monetizing government debt.” Un-der it, where privately-owned money expansion cov-ers government budget deficit(s), the taxpayers effec-tively ‘repay’ the value of the pseudo-loan twice, firstthrough inflation, a second time through taxation!

The total energy extracted by the private bank canbe taken as x · p2, which from eq. 8 can be expressedin terms of total money stock and the central bankreserve ratio:

E2 =(

1r− 1)v1p2 (10)

But since p2 = r · p1,

E2 = (1− r)v1p1 (11)

This extraordinary equation shows that via the sys-tem, the pseudo-bank extracts the proportion 1 − rquantity of money-energy from the original economyEi = v1 · p1, leaving only r remaining!

Even more shocking, in the modern privately-owned money expansion system, the lending bankis essentially allowed to count the ‘loan’ as an as-set, immediately, not being required to wait until theend of the repayment period of the pseudo-loan todo so. In this case the pseudo-lender then essen-tially immediately extracts x · p1 money-energy fromthe overall economy (i.e. via the device of a centralbanking system) at the initiation of the pseudo-loanof zero money-energy, and the taxpayers more accu-rately obtain x · p2 worth of government services (at2x · p2 energy cost). In this case the money-energyextracted by the private bank is

E3 =(

1r− 1)v1p1 (12)

Note that if r < 12 then x > v1 and E3 exceeds theentire initial energy of the economy—this represents

11

net indebtedness by all money holders to the privatebank! Evidently, economics is in fact the scienceof heat transfer of money-energy; E > 0 representswealth or assets, E < 0 represents indebtedness.

The entire prior analysis proceeded without ref-erence to the concept of interest. Evidently inter-est relative to private-based money expansion is sim-ply inapplicable, because regardless what interest feeis charged, even zero interest, the pseudo-lender haslevied a real charge for a pseudo-service of no realvalue.

Usury is defined as “the act or practice of lend-ing money at an exorbitant or illegal rate of inter-est.” Similarly, practices identified as predatory lend-ing have been outlawed in various jurisdictions. Butthis situation does not qualify as usury or predatorylending; it’s fundamentally different and far moreinsidious because no money-energy is actually pro-vided. So the analysis and conclusions stand gen-erally independent of considerations on interest—it’sirrelevant.

A slight variation is the possibility of a hybrid sys-tem in which the money expansion is both publicly-and privately-owned at some ratio; this appears tobe the case with the U.S. Federal Reserve. How-ever exactly the same conclusion applies, i.e. that anyamount of privately-owned expansion is illegitimate.

In short, the government can finance its operationsoutside of taxation via borrowing, or money expan-sion. However privately-owned expansion reduces toan illegitimate combination (“borrowed expansion”?)with disastrous ramifications. Cui bono caveat emp-tor.

good vs. bad money

In standard economics and banking r is also called thereserve requirement, and the inverse 1/r is known asthe money multiplier. [17, 50] In examples a typicalrate is given as r = 0.1. [32] gives a banker’s rule-of-thumb ratio of 4:1 circulated (debased) receiptsvs. deposits corresponding to r = 0.2. These are ex-tremely low and in the previous (primitive) model fallinto the range r < 12 that results in net indebtednessof all money holders to the bank.

However, the previous generalized formulas do not

attempt to model money that circulates outside thebanking system, such as would occur with one bankissuing fractional money in much a larger economy.In this new scenario there is an amount of “nonbank”cash, say v0, in addition to the bank reserves v1, andv0 � v1. A ratio can be defined to give the amountof bank vs. nonbank cash in the economy:

s =v1

v0 + v1(13)

s can also be taken as the savings rate. From this,

v1 =(

s

1− s

)v0 (14)

This time the bank reserve ratio is logically definedas

r =v1

v1 + x(15)

which implies

x = v1

(1r− 1)

(16)

In this scenario, instead devaluation is based on thisformula:

(v0 + v1)p1 = (v0 + v1 + x)p2 (17)

Using the higher estimate for money-energy obtainedby the bank, x · p1, and eq. 16,

E4 = v1

(1r− 1)p1 (18)

Substituting in the equation for v1, eq. 14,

E4 =(

s

1− s

)v0

(1r− 1)p1 (19)

That gives the energy extracted as a fraction of theoriginal nonbank cash economy v0 · p1. Or equiva-lently

E4 = s(v0 + v1)(

1r− 1)p1 (20)

This equation bears a remarkable resemblance tothe prior full economy money-energy transfer quan-tity E3 (eq. 12). It shows that for a bank holding the

12

fraction s of the entire economy in reserves, the en-ergy extracted from the total initial economy, givenby (v0 + v1) · p1, varies according to the ratio

r2 = s(

1r− 1)

(21)

For this equation, r2 < 1 even for small r if s is small.That is, in contrast to eq. 12, total money-energyextracted is now proportional to s or the proportionof money deposited in the bank relative to the entireeconomy. Still, for small r and s, the ‘leverage’ ishigh and E4 entails the entire economy. More exactly,r2 ≥ 1 if s ≥ r/(1− r) (or r ≥ s/(1 + s)). For r = 0.2this is at s = 0.25; for r = 0.1 this is at s ≈ 0.11.

This all appears to be one possible mathematicalrepresentation of Gresham’s law, which states “badmoney drives out the good.” In other words, if onebank circulates debased receipts into the economy,all money depreciates based on eq. 17 and energy ex-tracted from the overall economy is based on the sav-ings rate and fractional reserve ratio of the individ-ual bank. The equation appears to show that moneyholders may defend against mass money depreciationby minimizing their savings!

Moreover, eq. 20 seems to shed new light onFisher’s equation of exchange, eq. 1. Recall from theearlier discussion that the thermodynamical v waschosen as analogous to the Fisherian term V ·M whereV is velocity and M is the stock of money. It appearsto be possible that velocity of money V and savingsrate s are being mixed up in the classical theory, ı.e.possibly

s · (v0 + v1)⇔ V ·M (22)

From this, if savings rate decreases, money circulatesmore in the nonbank economy v0 than is stored inthe bank reserves v1, apparently decreasing the ve-locity. The classic quantity of velocity may actuallybe measuring nonbank money circulation relative toa fractional reserve bank. Maybe nonbank moneyvelocity increases as the bank extracts more money-energy from higher savings.V is a somewhat mysterious quantity in classical

economics, sometimes assumed constant or not, used

in multiple contexts, and its thermodynamical cor-respondence is not so obvious. However, some rela-tion to savings rate does seem plausible. Thermo-dynamics does have equations for molecular veloci-ties derived from statistical mechanics that it may berelated to—altogether, another key item for futureeconophysics analysis.

A more sophisticated analysis might take into ac-count that the bank offers some fraction of the ex-tracted revenue as interest to depositors. In that sce-nario some depositors will lose or gain total money-energy based on their ratio of nonbank money to bankdeposits.

growth, interest, temperature, etc.

“Anyone who believes exponential growthcan go on forever in a finite world is eithera madman or an economist.”

—Kenneth Boulding, economist

The prior model very carefully and deliberatelyavoided the issue of growth in the overall economyfor simplified analysis. For completeness an expand-ing economy will now be considered. Let Ti = pivirepresent the perfect gas law term nRT from eq. 2at different states. Then Ti is simply proportional toGDP, and

p1v1T1

=p2v2T2

(23)

Let the economy grow by the rate rT > 1 so thatT2 = rT · T1. Then

rT p1v1 = p2v2 (24)

For constant volume, e.g. no expansion in moneystock,

p2 = rT p1 (25)

i.e. an increase in pressure p2 per dollar. But sinceprices are proportional to 1/p this implies a decreasein any price in the economy, i.e. overall price defla-tion. This is a somewhat counterintuitive result byconventional wisdom: growth of the GDP results indeflation if money stock is held constant.

13

A major goal of modern monetary expansion poli-cies is price stability, in which in theory the moneystock is expanded to the degree of keeping prices‘stable’ or constant. From eq. 24 this occurs whenrT v1/v2 = 1 or when a quantity x of new dollars(v2 = v1 + x) are ‘created’ such that:

p1p2

=1rT

(v1 + xv1

)= 1 (26)

which, solving for x, occurs simply for

x = v1(rT − 1) (27)

Spending and circulating x new dollars will stabi-lize prices, but the key question is, who owns thosedollars? They may be either publicly-owned orprivately-owned. Cui bono caveat emptor. The is-sue of ownership ties into the question of how theeconomy enlarged. Presumably it is due to the in-creased work, productivity, or efficiency of all moneyholders. Therefore, fairly, all money holders shouldgain.

This is one embodiment of the principle of inter-est. If an economy grows then all money holders cangain that increased energy without risk or work. It ispossible to gain money in an economy without workvia other means such as speculation, but it inherentlyinvolves a risk-reward tradeoff. By the money-energyconservation principle, the only risk-free revenue pos-sible from an economy is via an increased GDP. Be-cause of boom and bust cycles, even that is subjectto fluctuation.

It is possible to have interest systems that are notdirectly tied to growth in the economy such as thecurrent framework, but they are necessarily equiva-lent to wealth redistribution systems!

Note that arguably any rational model of the econ-omy absolutely must consider the equilibrium state asone that does not involve growth. A century-and-a-half of the “dismal science” (or the history of moderncivilization) may be based on an evasion or defianceof that principle. It is quite possible that economics isbased on a mass collective rationalization in much thesame way that U.S. citizens subscribed to the visionof the “manifest destiny” during the era of expansionto the west. Relative to serious worldwide dangers of

environmental degradation (e.g. global warning, pol-lution, deforestation, etc.), at the dawn of the 21stcentury the rationalization is increasingly taking onthe signs of mass psychological delusions of grandeur.

mattress myth & other legends

A pivotal observation is crucial here. By the money-energy conservation principle, after a temperature in-crease, the money-energy that accrues to money hold-ers due to price deflation with constant money stockfrom eq. 25 is exactly equivalent to that representedby the x dollars of eq. 27! That is, no money expan-sion system is inherently necessary to distribute risk-free interest gains! It’s built into “invisible hand”supply-and-demand pressures on prices. It’s a simpleconsequence of the law of scarcity, or, scientificallyspeaking, an emergent property of the system.

This finding directly contradicts the supposedly en-lightened modern view of “putting money into thebank where it can earn interest instead of hidingit under a mattress.” If money stock is kept con-stant, all money holders effectively gain interest with-out keeping their money in banks based on increasedpurchasing power from a global economic tempera-ture increase. It’s also compatible with the use ofcommodity currency such as gold. The only-banks-can-do-it view is simply false mythology. The findingalso conflicts with the legend of deflation as synony-mous with economic catastrophe.

A direct corollary to the above is that if GDPis increasing and prices are stable (and any inter-est payments are lower than the GDP increase) thenmoney holders are losing money-energy. By the ear-lier analogy of money as stock shares, it’s analogousto the idea of a company that has increased marketvalue but shareholders’ stock prices remain constant.Therefore the idea of maintaining price stability perse may be a specious economic doctrine!

Keynesian economic theory holds that prices andwages are “sticky,” especially downward, meaningthat they resist deflation. [17] This is one reason thatan allocation mechanism for the additional money xmay be justified. However, the problem is that sucha system is more readily manipulated to channel theincreased money-energy of the economy toward elitist

14

machinations that unfairly exclude money holders ingeneral.

But it seems plausible that deflation in prices oc-curs inversely to inflation in prices. It is known thatwage inflation increases slower than goods inflationso that the net effect to wage earners is diminishedpurchasing power. The inverse would be a decrease inwages that occurs slower than the decrease in prices,resulting in increased purchasing power. The finalconclusion is that the constant money stock systemis theoretically superior to the re-allocation methodbased on (a) guaranteed fairness and (b) lack of ne-cessity of a central administration system.

A closely related concept to stickiness of prices iselasticity. [17] Prices that are inelastic have associ-ated demand that is not affected by price changes.Elastic prices involve changes in demand at pricechanges. Elasticity is also a measure of “specific pricesensitivity to general inflation.” Elasticity is crucialbecause it suggests that in general inflation, somegoods, e.g. luxury items, inflate in price faster thanothers. Luxury items tend to have higher price elas-ticity.

The U.S. Consumer Price Index, CPI, measuresthe inflation of a market basket of goods purchasedby a “typical household.” However, by tracking onlya set of inelastic goods with prices that are not assensitive to inflation, the CPI may consistently un-derestimate true inflation rates. Such a misleadingor deficient indicator would be highly preferred byprivate bank owners in a privately-owned expansionsystem, because they would be able to extract moremoney-energy without detection by general moneyholders!

“optimal” expansion policy

Obviously, referring to the rate of increase of theeconomy as “interest” is not the concept generallyused in economics. The U.S. Federal Reserve deter-mines interest rates which are returns paid on govern-ment loans or bonds (“securities”) by taxpayers. Theremainder of the government deficit not covered viasales of the securities is that which must be financedvia money expansion. But this direct link means theFederal Reserve has strict control over the money ex-

d1

d2

r1 r2

secu

ritie

s de

man

d

�

interest rate

linear daexponential db

logistic dc

Figure 2: Three hypothetical scenarios da(r), db(r),dc(r) for increase in government securities demandby investors d1 → d2 from increasing interest rates inthe range r1 → r2.

pansion rate based on the interest rate selected. Totaldemand for (and therefore sales of) government secu-rities must vary based on interest rate according tosome relationship.

Fig. 2 gives three hypothetical scenarios for the in-crease in government securities demand by investorsover increasing interest rates. (The plot was gen-erated simply using mirror-symmetric versions ofeqs. 5.)

This mathematical relationship is the central pivotaround which monetary expansion policy is balanced.When the Federal Reserve “buys” government bonds,it involves inflationary money expansion and does notconform to the supply-demand curve(s) in the fig-ure. Government deficits could always be covered viahigher interest rates (and no expansion) if the FederalReserve chose that route.

The conclusion from the prior (simplistic) resultsis that the optimal monetary expansion policy fromthe point of view of money holders is always to in-crease interest rates up to 200% to meet budget short-falls, i.e. no privately-owned money expansion ever,assuming the budget outlay is not adjusted. Thosemoney holders will always end up paying less in totalmoney-energy than from privately-owned expansion.The 200% figure seems ridiculous, but really it shows

15

the absurdity of using privately-owned money expan-sion for any so-called “financing” whatsoever!

A strong case can be made that if the interestrate were managed and determined in this hypothet-ical way (the true free market embodiment), citizenswould begin to understand the true cost of publicly-owned government expansionary borrowing insteadof it being invisibly disguised in inflation. The infla-tion rate in a publicly-owned system probably variesalmost precisely according to interest rates in the hy-pothetical system! The inflation rate for a privately-owned system is even worse.

A more mathematically rigorous treatment wouldrequire taking into account the “term structure of in-terest rates,” i.e. long-term vs. short-term rates, andthe exact speed of the inflation and government vs.private spending, but similar results are to be ex-pected. Whereas publicly-owned expansion has niceproperties as described, privately-owned expansion issimply scientifically and mathematically vacuous inany variation!

advanced verisimilitude

The prior models are easily criticized and should notbe taken too seriously, particularly the limit cases.The formulas for energy in particular are merelyrough analogies. They do not have major verisimil-itude but neither are they merely ‘toy’ models—primitive, but not crude. What is interesting aboutthem is how the mathematics can reflect the variousassertions (some obviously approaching hyperbole)made by various purely prose-oriented writers on theextreme implications of money expansion mechanics.There is new insight lurking in the framework; hope-fully future econophysicists can use this platform toseize them rapidly.

More sophisticated models are immediately avail-able from thermodynamical theory and are readilyutilized. A brief sketch of natural refinements will bemade here. In thermodynamics the general equationfor work based on pressure and volume changes is

W 21 =∫ 2

1

p dv (28)

For a polytropic process, also reversable, meaningroughly that there is no frictional dissipation, p vn isconstant, i.e.

p1vn1 = p2v

n2 (29)

The exponent n may range anywhere from −∞to ∞. n = 1 gives Boyle’s law. For n 6= 1,

W 21 =p2v2 − p1v1

1− n(30)

For n = 1 (isothermal perfect gas process),

W 21 = p1v1 lnv2v1

= p1v1 lnp1p2

(31)

The logarithmic dependency in this formula mighthave some relation to formulas for measuring “marketimpact” from buying or selling stock investigated byFarmer. [20]

If the pressure remains constant then

W 21 = p(v2 − v1) (32)

A constant pressure process is called isobaric. Theprior sections used this formula for work as a veryrough approximation for calculating energy changeswith x = ∆v and rough estimates for p (using thelimit cases).

The overall energy of the system remains constantwith a constant GDP. However, the isothermal casen = 1 applies only for perfect gases. n 6= 1 can beused to model a perfect gas and nonisothermal con-ditions, or a general polytropic process. n is also thenatural measure of the pressure decay rate mentionedearlier. The exact value of n would ideally be deter-mined from empirical data. Maybe there is some rulesuch as n→ 1 as the economy gets larger.

A more refined model can naturally use W 21 asa measure of the total energy associated with amoney redenomination. Note that by conservation ofmoney-energy, no money-energy is expended by a re-denomination; W 21 represents the maximum money-energy re-allocated or seizable via money expansiondepending on ownership. For constant temperature(no energy via increased temperature), a fraction ofthis energy is available to the government (providingpublic services financed by taxpayers), the remainder

16

is allocated to the private bank. A simple approachwould be to set x = y + z where y is dollars gained bygovernment, and z is dollars gained by private banks.z > 0 would be defined as “unfair.”

The above model is somewhat awkward in that theenergy calculation splits into two separate formula-tions depending on n = 1 or n 6= 1. To escape this,one alternative is a simple variation that uses a pa-rameter 0 ≤ m ≤ 1 to represent the continuum ofpressure available at different times during the ex-pansion process. Then

pm = p2 +m(p1 − p2) (33)

So pm = p1 for m = 1 and pm = p2 for m = 0. Themoney-energy associated with x dollars at differenttimes in the pressure decay process becomes simplyx · pm. Spenders obtain energy with different efficien-cies m1 > m2 > m3 depending at what point andtime in the process they spend the money. m canalso be related to the earlier pressure decay curves ofeqs. 5.

Another improvement in fidelity would break upexisting owned assets, say v1 = va + vb + vc whereva is assets owned by the government, vb by citizensand taxpayers, and vc private banks. vc could befurther split into domestic vs. foreign ownership. Theexpansion has variable allocation to the government,money holders (interest), and private banks, i.e. x =xa + xb + xc.

The general model would be very careful with theenergy analysis. Basically, additional energy out-side of overt capital flow is available from either in-creased temperature (GDP) or currency redenomina-tion. The analysis determines how much of this en-ergy goes into government services, how much goesto money holders via interest or money deflation, andhow much goes to private banks.

All of these equations can be easily converted todifferential form for extended computational simula-tions:

pt+1 = f1(pt)vt+1 = f2(vt) etc.

electronics analogy

“The greatest shortcoming of the humanrace is our inability to understand the ex-ponential function.”

—Albert A. Bartlett, physicist

The science of “mechatronics” has been describedas a marriage of electrical and mechanical engineer-ing and computer science. A remarkable correspon-dence is noted in the field whereby mathematicalanalysis from one discipline can be mapped onto an-other. Holbert has compiled a convenient table sum-marizing these correspondences in [33], “Interdisci-plinary electrical analogies.” Electrical, mechanical,hydralic/acoustic, and thermal sciences all have sim-ilar laws for the basic physical entities of force, mass,energy, etc. This paper adds a new column for eco-nomics.

So under this correspondence, one could take acomplicated dynamical system from physics requir-ing analysis by Newton’s law. The physical setupor apparatus translates to a system of mathematicalequations. But there is a direct correspondence be-tween e.g. an electrical circuit that embodies exactlythe same properties and leads to an identical mathe-matical analysis. The established parallel is intuitive,extraordinary, and somewhat uncanny. For example,mapping mechanical to electrical:

force ⇔ currentvelocity ⇔ voltagefriction ⇔ resistance

mass/inertia ⇔ capacitance

For economics, the case for the electrical analogyis made in very sophisticated detail in [2]. Thesecorrespondences permit a systems analysis and mod-elling of a vast economic system, reduced to theo-retical equations. The electrical or circuit analogy isparticularly relevant in the computer age. This allcombines to serve as the strong underlying basis forthe new science of “blip mechanics” as a new engi-neering discipline.

In electronics, power is given by P = V I where Pis in watts, V is voltage in volts, and I is current inamperes (coulombs of charge per second). The energy

17

is given by the product of power and the timespan,V I ·∆t. But for the infinitesmal time period dt, thiscan be taken as the “instantaneous energy:”

Edt = V I dt (34)

Watts are joules per second, so this equation mea-sures joules. From the earlier equations (e.g. perfectgas law eq. 2), voltage V is analogous to pressurep and current times timespan I · dt to volume. Thequantity I ·dt as volume implies that dollars are anal-ogous to coulombs of charge. The system of a perfectgas in equilibrium with an internal energy is thereforeanalogous to a circuit in equilibrium being fed by avoltage source, e.g. a battery.

A brief example will be considered. In finance, thecompound interest formula can be given as a recur-rence relation At+1 = f(At),

At+1 =(

1 +r

k

)kAt = A0

(1 +

r

k

)kt(35)

where At is the capital at year t (initial capital A0),r is the interest rate per year, k is the number ofcompounding periods per year. But by an applicationof l’Hôpital’s rule (from elementary calculus) it canbe shown that as k →∞

limk→∞

At = A0 ert (36)

This is referred to as the “continuously com-pounded interest formula,” and the longer any com-pounding is in effect the closer it approaches the for-mula. It can also be used as an estimate of priceinflation given the inflation rate. Or conversely ifr < 0 it can measure the depreciation in value due toinflation.

In electronics the standard RC resistor-capacitorcircuit has similar exponential dynamics, analyzed intypical introductory references. [67] This is a circuitwith a battery with voltage V , R-ohm resistor, andC-farad capacitor all in simple series. The voltageover the resistor at time t is given by the formula

VR = V e−tRC (37)

The formula is giving the “inflation” that occursin the circuit when −1/RC = r. The resistor can

be thought of as the load. The capacitor accumu-lates charge over time. The voltage available to theload declines exponentially over time as the capacitorcharges. Recall that voltage is analogous to pressure,and prices are inversely proportional to pressure.

Current represents “dollar circulation.” The cur-rent and therefore instantaneous energy of the circuitfalls to zero as the capacitor charges and t→∞. Thecapacitor represents the mechanism of some entity(either public or private) that removes dollars fromcirculation in the economy. The asymptotic limit inthis model is a circulation deadlock or energy freeze.

So, this circuit gives one possible long-term dynam-ical solution for the earlier systems with decreasingpressures, pi > p2 > p3 > . . . > pf , approximatelyaccording to the recurrence relation (or differentialequation) associated with k = 1 and as t→∞

pt+1 · (1 + r) = pt. (38)

This example is simple yet important in how itexemplifies the depiction of inflation dynamics as aclosed energy system and analysis via engineeringprinciples. A key property of the science of “blip me-chanics,” somewhat in conflict with the conventionalwisdom of economics, is that inflation is not an in-explicable aspect of arbitrary mass psychology. Par-ticularly in a large scale economy, price inflation is aprecise, mathematical measure of the macroscopic en-ergy dynamics of a system which adheres to physicallaws.

recursive bite ’em ad infinitum

So, naturalists observe, a fleaHas smaller fleas that on him prey;And these have smaller still to bite ’em;And so proceed ad infinitum.

—Jonathan Swift

A remarkable paradox emerges in the careful studyof the prior mathematics, very much reminiscent ofSchröedinger’s notorious is-it-alive-or-dead quantummechanical cat riddle (which many are not aware wasphrased mathematically in his original paper). Ear-lier x was defined as money loaned to the state in

18

excess of straight borrowing, i.e. the quantity of ex-pansion borrowing.

Consider that the model can be totally reformu-lated in a parallel way based on the earlier idea ofexpansion borrowing as a “double shortfall”. Letx simply refer to the budget deficit, the differencebetween funds spent by the government and totaltaxes collected. x then represents the amount offunds obtained from straight borrowing, and all themathematics is identical. Then the “reserve ratio”r = p2/p1 then represents the dilution of value ingovernment services provided to taxpayers due to theoverhead cost of repaying government borrowing, or,in a sense, the degree that the future has been mort-gaged to the present. There seems to be lurking hererecursive bite ’em ad infinitum, noted by some otherwriters, e.g. [2].

In fact, to take it to even further extremes, a po-litical libertarian in favor of a minimalist governmentmight take x to simply refer to all taxes. Then fromthat perspective the ratio r = p2/p1 represents the‘drain’ of government on ‘productive society’ ! (Fi-nally, the anarchist argues against the validity of ‘pro-ductive society’ !)

Apparently what the mathematics is really ad-dressing is the general theoretical concept of moneyspent without consent of money holders via moneysystem mechanics. x is the embezzlement, and r isthe resulting debasement. The government may notspend funds without consent of taxpayers. Borrow-ing requires the consent of future taxpayers. Privatebanks may not spend public funds. There dilutionimplies the consent of the public.

But if the government does it, why not privatebanks? The conclusion is that at the core of the prob-lem, banking and government contain two sides of onephenomenon. Both contain by nature some mecha-nisms, elements, and agendas capable of, and at timesapplying, money-energy extraction without consentof money holders via concealment within the moneysystem administration (i.e. embezzlement). Further-more, from kindergarten wisdom, “two wrongs do notmake a right.” So. . . is it alive, or is it dead? Howto stop it? The halting problem.

4 commentary: blip corruption

“One does not have to eat an entire appleto know it is rotten.”

—literary critic

Over centuries, many commentators and authoritieshave struggled to articulate these ideas using vocab-ulary that has been itself correspondingly debased!Many of their quotations will be re-examined in thisnew light over following sections. The process ofmoney expansion is typically called ‘creating money’and the pseudo-money pseudo-loaned by the pseudo-bank is typically referred to as “credit.” But alsowithin the literature, dire confusion or obfuscationreigns on the razor-sharp cui bono caveat emptordistinction set out here between publicly-owned vs.privately-owned expansion. As outlined, this intellec-tual error has potentially catastrophic consequences.The former case can be a legitimate means for collec-tion of government revenue. The latter stands cur-rently as unexposed embezzlement. The manufactur-ing of abstract credit is a means for real wealth ex-traction!

Banking authorities make a distinction between de-posits and loans in the same way they distinguishbetween “money” and “credit.” In the nonphysicalfractional reserve blip-based money system, the dis-tinction is invalid. Creation of credit is equivalent tothe creation of money. Whoever has or is given theauthority to create credit has the authority to extractwealth from the economy by that same mechanism.Moreover, there is no meaningful distinction betweenfractional reserve banking and money expansion.

The analogy of counterfeiting looms large asthe mathematics reveals. In many ways the onlydifference between illegal counterfeiting and legalprivately-owned money expansion is that gains by therecipient in the latter case are officially sanctioned,not indiscriminate, and limited based on the expan-sion rate. Therefore, paradoxically, privately-ownedmoney expansion is basically equivalent to ‘legalizedcounterfeiting,’ i.e. a surreptitious state-sanctionedplundering of money holder wealth by private bankers!Because it is an intrinsic oxymoron, however, thecounterfeiting analogy is awkward and unsatisfactory,

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and some other metaphor seems necessary.Perhaps the simplest explanation for this situation

is that new shares of the economy are issued, but theyare owned by private bankers at the expense of theownership of all other shareholders (i.e. money hold-ers, taxpayers, citizens). Via mere money manipula-tion the private bankers own a greater real share ofthe entire economy (e.g. GDP denominated in dol-lars).

Hence the term “money stock” takes on new mean-ing! The tragic absurdity of the situation has reachedepic, international, worldwide proportions. All thecomplex economic theory, terminology, and mathe-matics could simply be dropped for the following ex-planation:

The government has delegated its responsi-bility of ensuring public monetary integrityto private bankers. But the arrangementhas devolved and degenerated to negligenceand abdication. Those bankers have re-neged on the implicit promise of providingmonetary integrity. Their system correctlymeticulously keeps track of ‘blip’ ownershipand its transfer except, via the delegatedownership and administration of the blip-system, and under the guise of specious,distorted, and flawed economic science, thebankers can arbitrarily create and own new‘blips’ !

What has occurred is an unequivocal corruption inthe integrity of the money. Money is a representationmeans for scarcity. Holders utilize it precisely forthat property. Any entity that can allocate scarcity-units without exerting economic work by definitionhas debased the scarcity-units relative to all otherholders—the units are not scarce for the embezzler.Somewhere along the line, the promise of integrityhas been trashed.

The holders of the scarcity-units determine the def-inition of economic work. Legitimate government ser-vices are included. The government is erected partlyto protect scarcity-unit ownership and regulate legaland illegal scarcity-unit transfer.

Privately-owned expansion is equivalent to siphon-ing or leeching of money-energy with dollar holders

“left out in the cold.”

scarcity integrity

“The price of liberty is eternal vigilance.”—Thomas Jefferson

“The buck stops here.”—Harry S. Truman

The terminology and mathematical vocabulary of theprevious sections gives a new framework for discus-sion of the different types of money. Evidently it’s acontinuum:

receipt money r = 1; the money is fully backed.

fractional money Fixed r < 1. The unbackedfraction 1− r may be either publicly-owned orprivately-owned.

fiat money Unfixed r < 1; r may arbitrarily fluctu-ate. Or r → 0.

Paper money, in contrast to commodity money, isrequired and a prerequisite for a fractional moneysystem, although a paper money system is not neces-sarily either receipt, fractional, or fiat. Paper moneyrepresents an abstraction away from directly trad-ing a scarce entity such as precious metals. Thisdivorce simplifies, but does not imply, debasementof its scarcity representation via money expansion—actual debasement is tied to administration. Elec-tronic money simply replaces paper with even moreconvenient ‘blips.’

What a fair and sound money system really re-quires is scarcity integrity. All systems devised so farcan be debased. However, debasement is not neces-sarily an intrinsic property of any of them. Clearly,a fair public money system must at the very mini-mum be either publicly-owned fractional, where thereis legislative control over r, or fully-backed, in whichcase ownership of the unbacked fraction is irrelevant(there is no unbacked fraction). Fiat currency is un-sound, but not in the sense that it will inevitablylead to total loss of value. Loss of value occurs atthe discretion of whoever can effectively manipulate

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r via scarcity-unit creation and ownership unilater-ally and clandestinely, concealed from other holders(i.e. without their consent).

As concluded, privately-owned fractional bankingis not a fair system because, in short, it facilitatesprivate confiscation of public property, representedby the public money. However, it is not necessarilyunsound in the sense that it is unstable or will alwayscollapse. Collapse occurs as r → 0. With negligent,malignant, greedy etc. administration, money movesthrough the “backing continuum” from full, to frac-tional, to fiat. But even private expansion ownerswould presumably seek to avoid r = 0. Privately-owned fractional banking can be quite sound.

Apparently, the unrecognized dichotomy of fairnessvs. soundness lies at the heart of much economic the-ory. One does not necessarily imply the other. It ap-pears another variation on the cui bono caveat emptorerror.

[32] quotes a bulletin of the Federal Reserve Bankof St. Louis:

Modern monetary systems have a fiatbase—literally money by decree—with de-pository institutions, acting as fiduciaries,creating obligations against themselves withthe fiat base acting in part as reserves. Thedecree appears on the currency notes: “Thisnote is legal tender for all debts, publicand private.” While no individual couldrefuse to accept such money for debt re-payment, exchange contracts could easily becomposed to thwart its use in everyday com-merce. However, a forceful explanation asto why money is accepted is that the fed-eral government requires it as payment fortax liabilities. Anticipation of the need toclear this debt creates a demand for the purefiat dollar.

By previous interpretation, “fiat base” might as wellbe called a “baseless base.” What the above amountsto, paraphrased: “wealth is denominated in blips andthose blips are legally, arbitrarily manipulated at cit-izens’, taxpayers’, and government’s expense for in-visible confiscation by faceless private bankers.” An-

other booklet entitled Modern Money Mechanics bythe Federal Reserve Bank of Chicago states:

In the U.S. neither paper currency nordeposits have value as commodities. Intrin-sically, a dollar bill is just a piece of paper.Deposits are merely book entries. Coins dohave some intrinsic value as metal, but gen-erally far less than their face amount.

What, then, makes these instruments—checks, paper money, and coins—acceptableat face value in payment of all debts andfor other monetary uses? Mainly, it is theconfidence people have that they will be ableto exchange such money for other financialassets and real goods and services wheneverthey choose to do so. This partly is a matterof law; currency has been designated “legaltender” by the government—that is, it mustbe accepted.

This reflects the perception of conventional wisdomthat money is backed by ‘confidence’ or ‘faith.’ Inreality the expectations over exchanging money forassets, goods and services are arguably a secondaryphenomenon. The confidence refers to the generalmoney holder’s expectation of an implicit promisethat blips will not be arbitrarily allocated—whichhas been exposed here and elsewhere as a monolithicfraud and sham. [32]

faith in blips

“One thing to realize about our fractionalreserve banking system is that, like a child’sgame of musical chairs, as long as the musicis playing, there are no losers.”

—Andrew Gause [27]

Many understandably fail to regard “faith in blips”as something to be taken very seriously. The re-duction of money to a total electronic abstractionand its consequences has been called “the death ofmoney” by Kurtzman. [39] But merely denominatingscarcity-units in terms of blips does not mean thatthose scarcity-units are meaningless or that they willbe arbitrarily manipulated! Blips have a total reality.

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Blips take the physical form of the vast accountingapparatus used to record, manage, and track them.Blip value is the mathematical property of energyderivable from the science of blip mechanics and nota mere psychological phenomenon. Blips are exactlyas real as the entire economy.

If wealth-owners wish to preserve their own as-sets against blind robbery, then they must understandthe basic engineering principles of sound blip-systemsand ensure their blip-system has the absolute high-est degree of integrity achievable and is free of cor-ruption—it is the imperative of citizens, taxpayers,and money holders to actively create one, and notpassively accept any shoddy or boobytrapped systemfoisted on them (bootytrapped?). They must be hy-pervigilant for the slightest signs of ‘leakage.’ Bugsin blip algorithms or implementations have the mostcatastrophic consequences imaginable—blip loss.

Evidently from history this task is in many waysfar more difficult than erecting a government—herculean, sisyphean, gordian, and pandoran (mas-sive, futilely repetitive, intractable, and insidious).It seems both government and banking are defectivelegacy systems and their functions need to be rewrit-ten and consolodated into a new blip-system!

The following statements were made during hear-ings of the House Committee on Banking and Cur-rency, September 30, 1941. [32] Members of the Fed-eral Reserve Board call themselves ‘Governors.’ Ec-cles was Chairman of the Federal Reserve Board atthe time.

Congressman Patman: “How did you getthe money to buy those two billion dol-lars worth of Government securities in1933?”

Governor Eccles: “We created it.”

Patman: “Out of what?”

Eccles: “Out of the right to issue creditmoney.”

Patman: “And there is nothing behind it, isthere, except our Government’s credit?”

Eccles: “That is what our money systemis. If there were no debts in our moneysystem, there wouldn’t be any money.”

Paraphrased, in a way that neither Eccles nor Pat-man would have understood at the time: after nation-wide economic dislocations that eventually escalatedinto a national congressional inquiry, almost certainlyensuing as direct consequences of the corrupt blip-system, Patman is asking Eccles if the blip-systemhas integrity. Eccles replies that no, the blip-systemhas no integrity, but that it is running smoothly andexactly how it was designed to operate. New blipscan be and were created arbitrarily and ownership as-signed to the private bank, and subsequently loanedto the government. The state is required to repaythose blips.

The debt is the blip-debt owed to the private Fed-eral Reserve bank by the U.S. government, i.e. citi-zens, taxpayers, and money holders. Eccles has suc-cinctly explained the process whereby all money is ul-timately based on blip-debt—to private bankers. AsSenator Barry Goldwater stated:

Most Americans have no real understandingof the operation of the international moneylenders. The accounts of the Federal Re-serve System have never been audited. Itoperates outside the control of Congress andmanipulates the credit of the United States.

Translation: the entire U.S. economy is denominatedin blips, the debasement of which its government haszero control over. By the design architecture, dic-tated by first-class users, the blip system is simply notaccountable to second-class users. The world’s “lastremaining superpower,” with the largest stockpile ofnuclear weapons, and the correspondingly most gar-gantuan and highest security military-industrial com-plex of all nations worldwide, has outsourced its blipmanagement! The blips stop somewhere else.

gold & Greenspan

“In truth, the gold standard is already abarbarous relic.”

—John Maynard Keynes

Complex treatises on gold as a money standard havebeen written and its role in finance will only be brieflyregarded here for completeness. For a representative

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view on its role, an excerpt from an unreknownedarticle by current Federal Reserve chairman AlanGreenspan is highly useful. The article (or the follow-ing quote from it) circulates among money reformistsand gold money advocates. Entitled “Gold and Eco-nomic Freedom,” it was published in 1967 in the bookCapitalism, the Unknown Ideal edited by Ayn Rand:[30]

The abandonment of the gold standardmade it possible for the welfare statists touse the banking system as a means to anunlimited expansion of credit. . . .

The law of supply and demand is notto be conned. As the supply of money (ofclaims) increases relative to the supply oftangible assets in the economy, prices musteventually rise. Thus the earnings savedby the productive members of society losevalue in terms of goods. When the econ-omy’s books are finally balanced, one findsthat this loss in value represents the goodspurchased by the government for welfare orother purposes. . . .

In the absence of the gold standard,there is no way to protect savings from con-fiscation through inflation. There is no safestore of value. If there were, the governmentwould have to make its holding illegal, aswas done in the case of gold. . . . The finan-cial policy of the welfare state requires thatthere be no way for the owners of wealth toprotect themselves.

This is the shabby secret of the welfarestatists’ tirades against gold. Deficit spend-ing is simply a scheme for the “hidden” con-fiscation of wealth. Gold stands in the wayof this insidious process. It stands as a pro-tector of property rights.

More on young Greenspan’s brush with Rand’s phi-losophy of Objectivism can be found in Bradford’sarticle, “Alan Greenspan: Deep Cover for Capital-ism?” [10] Or, the Randian libertarianism view ofmoney finds expression in her novel Atlas Shrugged[52] in which a secluded utopian society is foundedbased on a gold coin money system.

Greenspan’s article is very astute and incisive, suchas in how it focuses on the issue of consent by moneyholders, but it contains the same classic cui bonocaveat emptor error. Greenspan assumes the “wel-fare state” is the recipient of the revenue accruingfrom money expansion. The article also tends to mixup the fairness vs. soundness issue.

By the previous section, scarcity integrity is thetrue goal of a fair and sound monetary system.Greenspan’s argument phrased in this terminology isthat a gold standard implies scarcity integrity. Yet inthe same article he describes privately-owned moneyexpansion based on fractional reserves, backed by agold standard, as an accepted, conventional, and le-gitimate banking practice. But in that case there isnot necessarily a way for wealth-holders to protectthemselves from confiscation via dilution either, ex-cept, traditionally, government regulation! Alas, an-other case of recursive bite ’em ad infinitum, whichgold does not inevitably halt.

Greenspan does make the excellent point that ina free market of private fractional reserve banks,r will at least be subject to competitive pressuresbased on best interest rates offered. Unfortunately,there is nothing intrinsic about gold that ensuresthat bankers will not debase a receipt system—historically, oftentimes governments (taxpayers) havehad to refund losses to depositors due to collapsesfrom poor or greedy management. (A minor casecould be made that gold coins circulating in the econ-omy would serve as a check on private expansion.)

Gold money advocates, oftentimes a motley crew,have recently gained some traction by starting newcurrency systems admini