Haute Lumière

Commerce · III · MMXXVI · daylight

La Bourse  /  Volume III  /  Nº III.E1

For the Practitioner of Luminous Economics

Volume III — Money, Energy, Information · Extension I of III Nine movements, one circuit.

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THE PLATE

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THE LETTER

The eleven chapters you have just read take money seriously at a scale you may not have. They assume a treasury that can issue a note, a site with half-hourly metering, an auditor who returns calls, a credit committee to persuade, a covenant to negotiate, a board that can be asked to set a risk-tolerance parameter. You may have none of those. You may be one person with a laptop, or six people and a van, or a forty-member association whose treasurer is a volunteer with a spreadsheet.

Every one of those chapters, read from where you are sitting, has a paragraph in it that quietly assumes somebody down the corridor.

This chapter is Volume III re-cut for a person with no corridor, and it is not a simplification. The instruments are the same instruments — the indexed note of III.01, the second column of III.02, the clearing circuit of III.03, the levy of III.04, the decomposed rate of III.05, the indexed repayment of III.06, the four-column schedule of III.07, the retention run of III.08, the cheap rail of III.09, the layered reserve of III.10 and the incidence table of III.11. What changes is three things: the threshold below which each stops paying for its own paper, the order they are used in, and the budget, which we will hold under five thousand pounds and account for to the pound.

Five of the eleven do not work at your scale as written, and those five are said here, near the front, with the arithmetic attached. The other six work, and two of them pay in the first year without anybody's permission at all.

And one of them does something you have been told all your life that only a licensed bank can do. The Arithmetic movement computes exactly what it is and exactly what it costs to make it safe, and the answer is one percent of turnover.

— The Editors

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DISCOVERY

What is already working, at exactly your size

Begin with the record, and notice what these have in common: not one of them was built by an institution, and every one of them is still being run by people who could fit in a room.

A Bavarian association with about four hundred businesses and a stamp. The Chiemgauer has run the largest regional currency in Europe since 2003, and Chapter III.03 gives the figure that matters: its money turns over 7.00 times a year. Not two, not one — seven. The scheme publishes the clearest terms in the field, and the reason it can is that its entire financial design is three sentences long: paper loses value on a schedule, conversion back to euro costs five points, and two of those points run the system while three go to a local association the member chose when they joined. The operator is not a bank. It is an association with a list.

Sardinia's brokers, four of them at the start. Sardex was founded in 2010 by four people in Serramanna with no finance background. Chapter III.03 computes its velocity at 12.75 — the highest in the entire record, nine times Bristol's — and Chapter III.04 explains where that velocity came from, which was not software. It came from people telephoning members and introducing them. The circle is hand-woven, and hand-weaving is a thing a small organisation is uniquely good at.

A slate behind a bar, and a national utility running the same algorithm. Chapter III.04's plate is a village slate; its arithmetic is CLS settling over eight trillion dollars a day. Between them sits Slovenia's multilateral set-off, which has run as a public service since 1991 and clears 10 to 15 percent of participants' mutual obligations every round with no money moving. Hold that band. It is the floor under everything in this chapter, and it is a floor measured on a whole national population — the sparsest, least looped obligation graph anybody has ever put through this arithmetic.

A hundred thousand small merchants who put up a printed square of paper. Chapter III.09's UPI case is usually told as a story about a central bank. Read it instead as a story about the smallest party in the transaction: a merchant with a printed QR code accepted digital money at no cost whatsoever, and that decision required no terminal, no contract negotiation, no capital and nobody's approval. The cheapest instrument in Volume III is the one a person can adopt alone, on a Tuesday, for nothing.

A field with three more points of organic matter than the field next door. Chapter III.10's deepest case is agricultural and it has no institution in it at all: soil holding 56.0 millimetres of rainfall equivalent more than its neighbour, worth about 620 dollars a hectare in a dry year. On forty hectares that is 24,800 dollars of reserve, held by nobody, costing nothing, earning its keep the entire time it stands by. There is no corporate analogue to that. It is a reserve that only a practitioner can hold, because only a practitioner owns the thing it lives in.

One pattern, and it is what this chapter is built on. In every case the thing that travelled was a rule small enough for one person to hold — a stamp, a phone call, a set-off run, a square of paper, a cover crop. Not a balance sheet. Not a programme. The corporation of Chapter III.07 has to convert its intentions into documents because its people change; you have to do the same thing for the same reason, and you can do it this month.

So the discovery question is not what should I build. It is: which of the eleven rules am I not yet keeping?

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THE ARITHMETIC

The thresholds, the forty-member circle, and where five instruments fail

First, the forty-member circle, because it is the question you actually came with.

Take an association of 40 members with a median annual turnover of £250,000 each. Set the two constraints Chapter III.03 specifies — a credit line of one part in a hundred of turnover, an acceptance undertaking of one part in ten:

  credit lines, M                          GBP   100,000
  acceptance backing                       GBP 1,000,000
  backing multiple                              10.00 x

Ten times backing, against Sardex's twenty. Now the running cost, and here the whole chapter forks. Run it standalone — half a broker fully loaded at £48,000 a year, ledger software at £1,800, an accountant's letter on the tax and policy treatment at £1,200 — and C is £27,000 a year. Bolt it on to a body that already employs somebody who answers the phone, and the marginal cost is the software and the letter: £3,000.

Chapter III.03's identity does the rest. V* = C / (M · f), at its own three percent fee test:

  V* standalone                                  9.00 turns/yr
  V* bolted on                                   1.00 turns/yr
  V* the 400-member circle of III.03             3.33 turns/yr
  the forty-member circle is harder by           2.70 x

Nine turns a year. Put that beside every velocity in the record and the verdict is immediate. Sardex, the best there has ever been, ran at 12.75 — it clears nine by 1.42 times. Chiemgauer's seven does not clear it at all: 0.78. Wörgl's 2.78, WIR's 2.58 and Bristol's 1.36 are not close. Read the cost ratio itself and the same fact arrives as money:

  scheme              V      c standalone   c bolted on
  ------------------------------------------------------
  Bristol Pound      1.36       19.85 %        2.21 %
  WIR (bound)        2.58       10.47 %        1.16 %
  Woergl 1932-33     2.78        9.71 %        1.08 %
  Chiemgauer         7.00        3.86 %        0.43 %
  Sardex 2015       12.75        2.12 %        0.24 %

The left-hand column is a scheme that fails its own fee test at every velocity anybody has ever achieved except one. The right-hand column clears it at every velocity in the record, Bristol's included. The difference between those two columns is not the currency, the software, the members or the town. It is whether the brokerage was already somebody's job.

Say the same thing as a carrying charge, which is the form Chapter III.03 shows is identical: d* = C/M is 27.00 percent a year standalone and 3.00 percent bolted on. Gesell's stamp, at the small scale, is not a monetary philosophy. It is a payroll decision wearing one.

Second, the second route, because a single route is not a finding.

Chapter III.04 reaches viability from an entirely different direction: not what the circle costs per unit turned over, but what the clearing is worth in interest members no longer owe anybody. At Chiemgauer's velocity the circuit turns over £700,000 a year. At the 38 percent netting efficiency III.04 assumes, and a practitioner's own 12.0 percent cost of capital:

  cash released                            GBP  266,000 /yr
  interest members no longer owe           GBP   31,920 /yr
  against C bolted on                           10.64 x
  breakeven netting efficiency, bolted on        3.57 %
  breakeven netting efficiency, standalone      32.14 %
  III.04's standalone circle needed             24.24 %

Three and a half percent. And Slovenia's national set-off — the sparsest real obligation graph in the record — clears 10 to 15. So the bolt-on circle is cleared by the worst case anybody has ever measured, by a factor of 2.80 at Slovenia's floor and 4.20 at its ceiling.

Two routes, no shared inputs beyond the turnover, one verdict: do not build a forty-member circle. Bolt one on to an organisation that already exists. That sentence is worth the evening.

Third, the levy, which is not optional and costs less than you think.

Chapter III.04's hardest finding is that a mutual credit circle is a bank read backwards at infinite leverage, and its repair is one percent of turnover. At forty members, with 40 percent of the lines drawn:

  net debits outstanding                   GBP   40,000
  levy at 1.0 % of turnover                GBP    7,000 /yr
  reserve ratio after one year                  17.50 %
  Basel leverage-floor equivalent          GBP    1,200   cleared in 0.171 yr
  13.0 per cent CET1 equivalent            GBP    5,200   cleared in 0.743 yr

Chapter III.04's circle took 0.44 and 1.89 years to reach the same two positions. Yours takes 0.171 and 0.743 — faster, and the reason is arithmetic rather than virtue: your debits are 5.71 percent of turnover against III.04's 14.55, so the levy's base is larger relative to what it has to cover. Replace the drawn-share assumption and that advantage moves. It is printed in the module for exactly that reason.

Fourth — and this is the cut.

Chapter III.01 showed what a bank does when it lends. Two entries, one on each side, nothing moved:

  risk-weighted assets                     GBP   70,000
  capital the bank must hold               GBP    7,350
  money created per pound of capital            27.21 x

Seven thousand three hundred and fifty pounds of equity standing behind two hundred thousand pounds of new means of payment, in an economy where 97.19 percent of the money is somebody's bank deposit and 2.81 percent is notes and coin.

Now look at what your association's ledger does when a member goes into debit and another into credit. It writes the same two entries. A credit is created at the moment of a trade and destroyed at the moment of the matching trade, exactly as a deposit is created by a loan and extinguished by a repayment. The forty members have put £100,000 of spendable claims into the world, and nobody applied for a licence.

So ask the bank's question of the circle, and the honest answer is a refusal:

Money created per pound of capital: UNDEFINED. The circle holds no capital.

That refusal is the finding. It is Chapter III.04's leverage identity arriving at a kitchen table, and a module that answered zero or infinity here would be telling two opposite lies about the same fact. Then levy the one percent and ask again:

  capital after one year of the levy       GBP    7,000
  money created per pound of capital            14.29 x
  the licensed bank, on the same question       27.21 x
  the circle is more conservative by             1.90 x

One percent of turnover, levied for one year, leaves a forty-member association better capitalised against the money it creates than a licensed bank is against the money it creates. Not metaphorically — on the same ratio, computed the same way, at 14.29 against 27.21. The thing you were told requires a banking licence requires two columns and a discipline, and the discipline costs seven thousand pounds a year that stays inside the membership.

That is the single most valuable sentence in this chapter and it is also the reason the levy is not negotiable. Waive it in year one to attract members and you have reproduced, deliberately, the exact condition Chapter III.04 named as the thing between a commons and a loss.

Fifth, the thresholds — where five instruments stop paying for their paper.

The indexed regeneration note (III.01). The economics hold at any size: a real coupon of 2.25 percent on principal indexed at an expected 3.10 percent drift is an all-in 5.4197 percent against a nominal facility of 6.75, a spread of 1.3303 points. The paper does not scale. Drafting a note for a private placement costs about £12,000 once, and III.01's covenant requires a named annual verifier, call it £3,000 a year — £42,000 over a ten-year term.

  minimum principal                        GBP  315,730
  at a principal of                        GBP  100,000
    saving                                 GBP    1,330 /yr
    over the term                          GBP   13,303
    covers the cost                               0.317 x

Below £315,730 the note loses, and at a hundred thousand it recovers under a third of what it costs to exist. The substitute is one clause, not one instrument: write the contract price in a published index rather than issuing a security denominated in one. One hour of a solicitor, £280, and you have bought the same 1.3303 points of drift protection on whatever principal is outstanding. The clause is cheaper than the note by 150.0 times, and Chile has been proving since 1967 that an indexed unit of account needs no currency attached to it.

The kWh tranche (III.02). Here the surprise runs the other way. Chapter III.02's manufacturer has a 120.0 GWh site; a practitioner's whole load might be 300.0 MWh, a factor of 400.0. Scale the case down proportionally:

  saving at III.02's share of load               35.00 MWh/yr
  value at GBP 95.00/MWh                   GBP    3,325 /yr
  proportional facility                    GBP   10,000
  breakeven price, the worked case         GBP    76.19 /MWh
  breakeven price, the practitioner        GBP    76.19 /MWh

The breakeven price is scale-invariant. The paperwork is not. III.02 tells you to settle the embedded-derivative question with a technical accounting partner before the term sheet; one hour of one costs about £450, which is 0.0112 percent of the worked facility and 4.50 percent of yours — a ratio of 400.0, which is the scale factor itself, arriving as a bill. Do not build the tranche.

Take the discipline and leave the instrument. Half-hourly metering data costs about £360 a year and the saving covers it 9.24 times. And run III.02's exergy check on your own saving, because at your scale it decides whether the figure is real: weight the electricity at one and the 80 °C heat at its Carnot factor and 35.00 MWh becomes 23.3786 MWh of exergy. The flat joule overstates the tradeable saving by 49.71 percent, exactly as it does at a hundred and twenty gigawatt-hours.

The fair-value restatement (III.07). Chapter III.07 computed its own threshold honestly and it is large: the gross annual cost of carrying a restatement is £39,660, and against a 0.35 percent margin step-down it does not pay until the balance sheet carries £11,331,429 of debt. On the verified-stock step-down of 0.65 percent the breakeven facility is £3,076,923 at a gross verification cost of £20,000, and £1,153,846 if the valuation was being commissioned anyway and only the roll-forward is incremental at £7,500 — a factor of 2.67 between the two questions. Nearly every practitioner is below all three numbers.

What is not above any threshold at all is the four-column physical schedule: opening stock, additions, reductions, revaluation, counted in the unit the thing comes in. Eight of your own hours, £360, and it is the half of III.07 that carries the whole argument. Keep the money column empty where no exchange value exists, exactly as III.07's routing rules require, and the zero is a finding you have made rather than a job you skipped.

The node (III.06). If you have read Chapter III.06 and thought about lending into your own network, its arithmetic has already refuted you. A hundred and fifty stable relationships, thirty percent of them plausible borrowers, is 45.0 people:

  book at USD 2,000 a ticket               USD   90,000
  gross margin at 6 %                      USD    5,400 /yr
  servicing at USD 40 a facility           USD    1,800 /yr
  net to the node                          USD    3,600 /yr

Three thousand six hundred dollars a year is not a job, and no amount of enthusiasm converts it into one. What the same chapter does hand you is the line that explains your whole competitive position: a relationship officer cannot assess below a 33,333 dollar ticket and a neighbour can assess at 444 — a ratio of 75.0. You are the neighbour. Your advantage is not capital and never was; it is that your cost of knowing whether somebody is good for it is about two hours, and an institution's is three thousand dollars.

Sixth, the honest negatives, and there are four.

The standalone forty-member circle will not happen. Nine turns a year is a velocity one scheme in the history of the field has ever reached, and it reached it with about three thousand members and about fifty staff doing nothing but introductions. A founder who builds it standalone will spend four years discovering a number that was available on the first afternoon.

Do not issue a town pound. Of the 8 sterling local currencies of the transition wave, 6 have closed. Chapter III.03's Kaplan–Meier estimate puts the half-life at 9.0 years and the implied flat hazard at 7.70 percent — one closure every 12.98 scheme-years. The design that fails is precisely the one a practitioner reaches for first: a voucher sold for national money, to consumers, spent at a short list of shops, at a velocity of 1.36.

You cannot fund a circle alone, and Chapter III.04 says by how much. One firm of that chapter's size clearing its own payables saves £21,067 of interest a year against a circle costing £96,000 — a ratio of 0.22, and it takes 4.56 such firms to carry one. Join. Do not build.

And the thing you will be tempted to call an achievement is the one to distrust. Chapter III.11's water table is the warning: the poorest quintile pays 3.93 times per litre what the richest pays, under a policy everybody in the room believed was protective. A practitioner's scheme with no incidence table is in exactly that position, and the table costs an afternoon.

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DREAM

What becomes ordinary

Describe it in the present tense, because a dream in the future tense is a wish.

The association you belong to clears. Not as a campaign — as a member service, the way it already runs an insurance panel. The secretary who used to answer the phone about membership renewals now spends four hours a week introducing members who could trade and do not yet, and that is the whole of the operating cost. The monthly page carries five numbers: the stock outstanding, the turnover, the velocity, the cost, and their quotient. Everybody in the membership can read them, and the quotient is under half a percent.

The levy is boring and nobody argues about it. One percent of turnover, from the first transaction, into a fund that belongs to the members and is published every month against the debits outstanding. In the second year somebody works out that the fund puts the association in a better capital position against the credit it creates than the bank down the road is against the credit it creates, and this produces a short silence and then a good conversation.

Your contracts are written in a published index and you no longer renegotiate them every eighteen months. The clause is two sentences and your solicitor wrote it once. A customer who signed three years ago is still paying what they agreed to pay, in the sense that both of you meant, and neither of you has had to raise it.

Your energy has two columns, and the second one is exergy-weighted with the ambient temperature and the version date printed beside it. You know the hours your load actually falls in. When somebody proposes a retrofit you can say what the tradeable saving is rather than the flattering one, and the difference between those two figures is about half.

Your stocks are counted in the units they come in, once a year, by you, and confirmed by somebody who did not count them. The money column has empty rows in it and you can say in one sentence why each one is empty. When the price of the thing falls and the stock grows, you have a document that says both.

You are paid faster than you used to be, because you asked, and you asked with arithmetic rather than with feeling: here is what sixty days costs me, here is what ten days costs you, here is the discount that sits between our two costs of capital. Nobody was squeezed and it took one conversation.

And the payments line on your own statement has stopped being weather. You moved what could move to a rail that charges what the movement costs, the change took an afternoon, and the money it returns is larger than every subscription you pay put together.

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DESIGN

The order, and the money, to the pound

The order the instruments are actually used in. Not the order of the chapters — the order of dependency, each step producing the input the next one needs.

Steps one to four are the first ninety days and three of them are free. Steps five to eight are the second ninety. Steps nine to eleven need somebody else's member list, which is why they come last and why finding that list is the real work.

And the money. The whole apparatus, costed.

Three things about that table are worth saying out loud.

The apparatus is £4,720 and more than half of it is your own hours. There is no licence in it, no platform, no subscription and no consultant. It is one hour of a solicitor, a year of metering data, some software for a ledger, an accountant's letter, and about twenty-six hours of your own attention.

The larger line is not spent. The £7,000 levy is levied, it belongs to the members, and it is what converts the circle from a commons with no roof into something better capitalised than a bank. Against the circuit's first-year turnover the whole apparatus is 0.67 percent.

Two lines pay in year one, on their own, with nobody's permission. The payment migration returns £936 and the early-payment ask returns £1,860 — £2,796 a year between them, which is 0.59 times the apparatus and pays for the whole of it in 1.69 years. Everything else in the table is funded by those two.

Governance, in the four lines Chapter III.04 takes from Ostrom and the fifth this volume adds. Who may hold a debit and against whom. Debit lines set by the member's own in-network sales, recomputed monthly. One member, one vote, never one pound one vote. Warning, then a frozen line, then suspension — never straight to the extreme and never nothing. And then the fifth, which Ostrom's commons did not need because a pasture cannot be levered: the levy, its percentage, and the reserve ratio it is targeting, written into the constitution before the first trade.

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DESTINY

How it holds when you are ill, or bored, or busy

Three things keep this standing after the enthusiasm has gone, and they are the three the surviving schemes in the record all have.

The cost is somebody's existing job. This is the whole finding of the Arithmetic and it is the only structural protection available at this size. A circuit whose brokerage is a new hire has a c of 3.86 percent at Chiemgauer's velocity and dies in the first thin year; a circuit whose brokerage is four hours of a secretary who was already being paid has a c of 0.43 percent and survives one. Attach the work to a role that exists for another reason.

Velocity is somebody's number with their name against it. Turnover divided by stock, monthly, on the page. If nobody owns it, it drifts toward one, and at a velocity of one you are running Bristol's design without Bristol's grant.

The reserve is funded before it is needed. The temptation is always to waive the levy in year one. The circles that do are the circles that find out in year four that their loss absorber was a conversation.

Now the honest part. This fails when the templates are never reused, because a clause used once is a document rather than an instrument. It fails when the association's velocity is measured annually rather than monthly, because by the time an annual figure is low the year is gone. It fails when the practitioner reads Chapter III.06 and decides to become a lender, at which point the arithmetic has already said $3,600 a year before the first loan. It fails when the physical schedule migrates from beside the management accounts to the back of a brochure, and it does not come back. And it fails most often in the most ordinary way of all: the apparatus is treated as overhead and cut in a thin quarter, at which point the next contract costs £12,000 of drafting instead of £280 of clause, and the factor of 150.0 is paid back in full to nobody.

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DELIGHT

What it feels like

There is a particular pleasure in the first clearing run that closes.

A printer pays a joiner, the joiner pays a caterer, the caterer pays the printer, and the balances net to nothing — and every one of those three did work they would otherwise have turned down for want of cash. Nothing was created and nothing was lent. A constraint simply stopped applying, and you can see the exact moment it stopped on a page you printed yourself.

Then the second one, which arrives later and is quieter. You are reading the monthly page and you notice that the levy fund has passed the number you wrote in the constitution eighteen months ago, and that the association is now standing behind the credit it creates more solidly than the bank on the corner stands behind the credit it creates. Nobody gave you permission for that. You did it with two columns and one percent.

And there is the smallest one, which is the one you will actually feel first. You open the merchant statement, find the line that used to make you hesitate for half a second before saying yes to a card for something small, and it is not there any more. You did not decide to stop hesitating. It simply became untrue.

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OPERATIONALIZE THIS

At the level of finance

The instrument: a bolt-on clearing facility inside an existing member organisation, at forty members, with a levy-funded reserve and a published cost ratio.

Not a new currency and not a new company. A clearing facility operated by a body that already has a member list, a subscription and somebody who answers the phone: a trade association, a chamber, a growers' cooperative, a federation of practices, a franchisor's network.

The terms.

The balance-sheet treatment. Credits receivable sit as trade receivables, credits payable as trade payables, netting within the circuit at the reporting date. The circle's unit is not a liability of the association — it is a bilateral trade obligation between members that the association nets, and the association's own balance sheet carries only the reserve fund and its working capital. One line in the accounting policies names the circuit and the settlement basis. Take this to the accountant in month one, with the £1,200 letter budgeted, not in year four.

The counterparty. The association itself is the netting agent and the only counterparty any member faces, and its obligation is limited to operating the ledger correctly. It guarantees nothing, and the first paragraph of the document says so. Hold the reserve at a credit union or cooperative bank — Chapter III.04's eighth principle, nesting, and also the cheapest credibility available.

The number that decides it, and it goes on the front page.

                annual operating cost
   V*  =  ------------------------------------
           credit lines outstanding  x  fee test

   worked:   3,000 / (100,000 x 0.03)  =  1.00 turns a year
   standalone, with a hired broker:            9.00 turns a year

And beside it, the same decision reached from the other direction, because a board will believe two routes and not one:

   breakeven netting efficiency  =  C / (turnover x members' cost of capital)

   worked:   3,000 / (700,000 x 0.12)  =  3.57 %
   Slovenia's national set-off clears        10 % to 15 %
   margin over the worst case in the record  2.80 x to 4.20 x

Above one turn a year this facility funds itself; below it, close it. Write that sentence into the constitution on day one. Having written it down in advance is what makes closing it a decision rather than a defeat, and it is the only sentence in the paper that will still matter in year three.

The first ninety days.

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APPRECIATIVE QUESTIONS

Twelve, for a room

Discovery — what is already working

1. Which two of the people in this room already buy from each other without anybody having introduced them — and how did that start?
2. Think of a time somebody here was paid late and it did not matter, because of who it was. What was holding that up, if it was not a contract?
3. Which association, chamber or cooperative do you already belong to that has a member list, a subscription and somebody who answers the phone?

Dream — what becomes possible

1. If a quarter of your trade with the people in this room settled without cash, what would you do first with the money that stopped being necessary?
2. Imagine your own monthly page carrying five numbers you would be proud to publish. What are the five?
3. If every recurring contract you write carried an index clause, which conversation would you never have to have again?

Design — what we build

1. Whose existing job could carry four hours a week of introductions — and what would make them want it?
2. What is the one stock in this practice you could count credibly this month, in a unit two people could count identically without conferring?
3. What is on your merchant statement that you have never argued with, and what would it take to find out by Friday?

Destiny — how it holds

1. If you were unavailable for three months, which of these eleven things would keep running — and what did you do that made that true?
2. What is the honest velocity below which this circle should close, and are you willing to write that number into the constitution today?
3. What would be the first sign that the levy had started being treated as a fee rather than as the members' own capital, and who would say so?

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Note on figures. Every figure in this chapter is computed in lib/verify/III_E1.py and prints with its inputs, its units and its source. Figures carried from chapters III.01 to III.11 are recomputed here rather than quoted, so that a reader checking this chapter need not open another module. The member count, the median member turnover, the brokerage cost, the drawn share, the practitioner's cost of capital, the hourly rates, the site load, the card volume and the merchant discount rate are stated assumptions, printed as such, and every threshold in the chapter moves when they are replaced. The question "money created per pound of capital" is answered for the circle with a refusal rather than a number, because the circle holds no capital and both a zero and an infinity would be lies about the same fact.