TURMEL: Mathematics of how Interest works GREENDOLLAR AND TIMEDOLLAR LETSYSTEM ENGINEERING The problem of debt is created within the banking system and therefore a thorough understanding of the banking system is helpful. The money system is the only mechanical system not under the jurisdiction of engineers. Control has been usurped by economists. All others systems improve, the only one controlled by economists is failing. It's time scientists regain control of this errant system from which come all the financial woes of the world. As an electrical engineer specialized in banking systems, I will endeavor to explain the inner workings of this mysterious system at every possible level and its effects on users and debt. Though this might sound daunting, I think I can present an easy way of handling subjects such as - plumbing analogy with pipes for flows of money - simple algebra - exponential functions - differential equations - Laplace transformations - control system circuitry FALLACIES The two Big Lies of Economics and Banking are that: 1) Banks lend their depositors' savings. 2) Interest rates fight inflation; Banks do not lend out their depositors' funds, they lend out brand new money. Interest does not fight inflation, it causes it. HOW BANKS CREATE MONEY The inner workings of the engineering design of the Canadian "fractional reserve" banking system are mysterious to many but no matter how complex the actual process of creating money is, it can accurately be simplified to "HAVING THE MONEY PLATES," whether they be plates for changing metal to coins, plates for changing paper to notes, or plates inside a bank's computer changing electrical blips to bank deposits on which checks may be written. Since changes in the money supply are regularly reported, money must enter the supply from a source and leave through sink. Our liquidity system has both a tap and a drain. Since the government borrows money itself, it does not have control of the tap. Who controls the tap and the drain of the money supply? The easiest way to model our system of financial liquidity is with plumbing. All banking systems have the same exterior connections to the economy. Draw two squares side by side each. Title the first a "Piggy Bank" and the second "Chartered Bank." For both, draw three arrows going in at the top labelled "Deposits," "Interest paid," "Loans paid." Draw three arrows coming out from the bottom labelled "Withdrawals," "Expenses," Loans made." In the Piggy Bank, draw a rectangle wide enough to accept all three input flows and all three output flows. Label it "Reservoir." PIGGY BANK Deposits Interest(paid) Loans Paid | | | | | | |------------|-------------|-------------|--------------| | | | | | | | | | | | |----|-------------|-------------|----| | | | | | | | | | | | RESERVOIR | | | | | | | | | | | |----|-------------|-------------|----| | | | | | | | | | | | |------------|-------------|-------------|--------------| | | | | | | Withdrawals Expenses Loans Made The interior plumbing of a piggy bank reservoir system shows that a deposit is first made into the reservoir and a loan is then taken out of the reservoir which causes no increase in money supply. Conversely, when a loan is paid, it goes into the reservoir and there is no decrease in the money supply. A reservoir piggy bank system does not affect the money supply because there is no tap and no drain. Though the Bank of Canada operates a tap and adds a small amount of "high-powered" money to the money supply, Graham Towers, a former Governor of the Bank of Canada, pointed out that "The banks do not lend out the money of their depositors. Each and every time a bank makes a loan, new bank credit is created, new deposits, brand new money." So a chartered bank has a tap and is not the pure reservoir system like a piggy bank model! In the Chartered Bank, draw a rectangle wide enough to accept only the first two input flows and first two output flows. Label it "Reservoir." Draw a circle above the "Loans Out" flow, put a positive sign within, and draw the line to the circle. Label it the "Tap." Draw a circle below the "Loans in" flow, put a negative sign within, and draw the line to the circle. Label it the Drain. FRACTIONAL RESERVE BANK Deposits Interest(in) Loan Payments | | | | | | |------------|-------------|--------------|-------------| | | | | | | | | |---|---| | | |----|-------------|----| | DRAIN | | | | | |-------| | | | | | | | RESERVOIR | | | | | | | | | |-------| | | |----|-------------|----| | TAP | | | | | |---|---| | | | | | | |------------|-------------|--------------|-------------| | | | | | | Withdrawals Bank Expenses Loans Out The interior plumbing of a chartered bank shows that the loans do not come out of the savings reservoir but come out of the tap of new money. When a chartered bank makes a loan, the amount of money in circulation goes up. When a loan is repaid, it goes down. In the textbook Economics by Lipsey, Sparks, Steiner, it states "The banking system as a whole can create deposit money." Therefore, the banks all have their very own tap, their very own set of electronic money plates. This power to refuse to turn on the tap for one businessman and foreclose while turning it on for another so that other can buy out the first businessman at auction is not fully appreciated. The injection of new money from their taps has been well hidden from the public view because the Bank Act insists that before any new money may be loaned into circulation, old money must be deposited into their reservoirs. It's just as if a casino were to insist on old chips being put into the safety deposit section before it would issue new chips. By merely matching new loans to deposits, this brilliant cover for the turning on of the tap misleads observers into falsely concluding that a chartered bank operates like a piggy bank. With a lawful reason to seek deposits before they can lend, there is no outward difference between chartered bank and a piggy bank. Yet, banks do not seek deposits to lend to other people. They seek them to lawfully turn on the tap. The famous "reserve ratio" of a "fractional reserve system" simply means that a fraction of all deposits is sent to the Bank of Canada's reservoir and the bank is then allowed to turn on the tap to match the deposits remaining in their reservoir. Banks create most of the money in circulation. To go step by step through the plumbing with a 10% reserve ratio, let the Bank of Canada turn on its tap and put $100 of "high-powered" new money into circulation: Depositing $100 into bank reservoirs turns on the tap for $90 more. These $90 end up deposited turning on the tap for $81 more. Depositing $81 into bank reservoirs turns on the tap for $72 more. Etc. until $10 into bank reservoirs turns on tap for $9 more. Etc. until $1 into bank reservoirs turns on tap for $.90 more. Etc. until the total deposits reaches a maximum of $1,000 with $900 newly created dollars added to the system by the chartered banks for every $100 issued by the Bank of Canada. This limit is the inverse of the reserve ration. A reserve ratio of 5% would generate total new money of 1/.05 = 20 times the initial high-powered Bank of Canada money. The demonstrates that the problem with the money system is that the amount of mass put into circulation is not a function of the production possible but of past savings of money. The major difference between a casino bank and a chartered bank is that the liquidity from a casino bank never suffers inflation while the liquidity from a chartered bank always suffers inflation. Since the hardware of a casino bank, chips of different colors and denominations, is functionally identical to the hardware of a chartered bank, computer credit pulses and coins or paper of different colors and denominations, inflation is not a hardware problem. It is a software problem. There is something wrong with the program which regulates how money is put into and taken out of circulation. There is nothing wrong with the hardware of our tap and drain system. It is the operators of the taps who are improperly restricting the flows. To fully appreciate our present predicament, consider a train- master in a wartime situation who, when he was ordered to ensure that an invading army did not capture the system in operating condition, burned all of the railroad tickets. Our failure to use our manpower, materials and tools because there are insufficient monetary tickets puts us in the same category as the invading army who failed to use the captured railway because they couldn't find any railway tickets. To get out of this silly predicament, public control of the money tap must be regained. HOW "MORT-GAGE" INTEREST CREATES A DEATH-GAMBLE The word "mort-gage" is derived from the French word "mort" meaning "death" and "gage" meaning "gamble". Bankers create the money supply when they make loans. Producers are forced to gamble by borrowing newly created Principal(P) to pay for production costs and then inflating their prices to earn back the Principal and Interest(P+I) in sales. Because total goods priced at (P+I) can never be sold when consumers only have P dollars available, a minimum amount of goods must remain unsold and a minimum number of producers must fail and suffer foreclosure. The economist Keynes likened the mort- gage death-gamble to the game of musical chairs. Just as there are insufficient chairs for all to survive the musical chairs death- gamble, so too, there is insufficient money for all to repay (P+I) and survive the mort-gage death-gamble. P < principle, I < Interest, i < Interest Rate, t < Time PERCENT ALGEBRA EXP. FUNC Production costs (principal) 100 P 1 Production prices (Debt) 100+i P+I exp(it) Purchasable Value 100 P 1 or ratio of money to prices ----- ----- ------- or survivors 100+i P+I exp(it) Unpurchasable value i I 1 or forced unemployment U= ----- ----- 1 - -------- or non-survivors 100+i P+I exp(it) For U=0, let i=0 I=0 i=0 or t=0 The odds of survival are always set by the interest rate(i). P/(P+I) survive, I/(P+I) do not. INFLATION The equation for the minimum inflation (J) we must suffer is the same as the equation for unemployment (U) because the fraction of the people foreclosed on is the fraction of collateral confiscated. Draw a large H and label the first left line as "$" and the right line "Collateral." Draw a small arrow up from the left axis. Label it "Shift A." Draw another arrow down from the right axis labelled "Shift B." Draw a line from the tip of the "Shift A" arrow to the base of the "Shift B" arrow and vice versa. Dollars Assets | | ________ | | |\ | | \ | Shift A | \ | | \ | | \ | ________ |__________\|________ |\ | | \ | | \ | Shift B | \ | | \ | | \| ________ | | | | | | Though we are led to believe that inflation is caused by an increase in the money chasing the goods (Shift A), actually, due to foreclosures, it is caused by a decrease in the collateral backing up the money (Shift B). Though both inflations shifts feel the same, the graph shows inflation is the direct function of interest, not the inverse exposing the Big Lie that interest fights inflation. Most people who have not studied economics, if asked whether interest fights or causes inflation, are quick to agree that a merchant must pass on increased interest costs in his prices and therefore it is evident that increased interest costs will result in increased prices. After a thorough brainwashing, economists have been convinced that increased interest costs will result in decreased prices as they constantly explain that "interest fights inflation." DIFFERENTIAL EQUATIONS The differential equation dB/dt = iB states that the increase or decrease of a bank balance (dB/dt), whether credit or debt, is equal to the interest rate (i) times the old balance (B). The solution to the differential equation is exp(it) where t = time. We can now examine the problem, not over one cycle with algebra, but over time with exponential functions. Exp(it) is a non-linear function, crooked. Draw an X axis labelled "Time" with units of 0, 1T, 2T, 3T.. Draw a Y axis labelled "$" with units of 0 to 16. At Y=1, draw a line to the right. At Y= -1, draw another to the right. At X=1T, make a point at Y=2 and Y=(-2). At X=2T, make a point at Y=4 and Y=(-4). At X=3T, make a point at Y=8 and Y=(-8). At X=4T, make a point at Y=16 and Y=(-16). Join the points. Label the curve going up +B*exp(it) and the curve going down as -B*exp(it). GRAPH#2 1600| B*exp(it) $1600 | $ 1400| $ | $ 1200| $ | $ 1000| $ | $ 800| $800 | $ 600| $ | $ 400| $400 | $ 200| $200 +B $-------------------------------------> time Yrs 0---------1---------2---------3---------4------- -$-------------------------------------> -200| -$200 -B | $ -400| -$400 | $ -600| $ | $ -800| -$800 | $ -1000| $ | $ -1200| $ | $ -1400| $ | -B*exp(it) $ -1600| -$1600 Consider that if two men are in a car accident and one owes the other money, if there there is no interest, the debt stays friendly, social and Christian like the two straignt lines for one owing -100 and the other being owed $100. The two straight lines from at +100 and -100 represent the growth of the debt and credit. Zero. If there is interest, the balances start to grow with time and double in time T, then again in time and again and again. Follow the $ curves to see how interest makes balances grow exponentially. For the record, the differential equation for inflation (J) can be described as: dJ^2/dt^2 + (i)dJ/dt = 0 or j'' + (i)j' = 0 LAPLACE TRANSFORMATIONS The Laplace transform of the balance B is 1/(s-i) where "s" is the Laplace constant. The moment the debt passes through the usury filter in banking system accounts, (1/(s-i)), it starts to grow. For the record, the Laplace transformation of the inflation (J) whose solution is (1-exp(-it)) is: 1 / s(s+i) CONTROL SYSTEMS With the Laplace transform, it is also possible to draw the electrical blueprint of a bank account in the usury banking system: |---------| | 1 | CONTROL SYSTEM FOR -------> ----- |---------> | s-i | |---------| |----------------| | Interest = 10% | |<---| Rate |<---------| | |----------------| | | | Old | |<-----------| Balance | | | + | + | | |------------| |------------| | Input + | Addition | + | Addition | New | ---------->| Node |------>| Node |---------------> |------------| |------------| Balance Draw two circles about two inches apart with a plus sign within both. These are addition nodes. Draw arrows from left to right right through both. Where all arrowheads touch a circle, draw a little plus sign. Label the left arrow "Input," the middle arrow "Total Input," and the right arrow "New Balance." Draw a small rectangle labelled "Interest Rate" above and between the two circles. Draw a line up to the right of the circles, an arrow to the rectangle, a line out stopping over the first circle and an arrow down to the first circle. Label the arrow "Interest." Draw another arrow to the left and down to the second circle but not through the rectangle. Label this arrow "Old Balance." This is the control system of the usury banking system. This blueprint of a usury bank account shows that added to any input is the feedback of the interest rate times the previous balance which can be positive or negative. This net amount is added to the previous balance to produce the new balance. This positive feedback makes the system unstable and the root of bad vibrations. Your $100 volt pulse is the input to the first addition node. Added to it is the interest voltage from the last balance which, to start, was 10% of zero. The new net $100 pulse enters the second addition node where it also is added to the old balance, still zero, to push the new balance up to $100 volts. Next year, with no new pulse at the input, added to this zero voltage is 10% interest, a pulse of 10 volts. The 10 volt pulse goes into the second addition node where it is added to the old balance, 100, to push the new balance to 110. Cycle after cycle with no new inputs, you have the exponential growth exp(it) which grows as the above series. It acts just like bringing a microphone up to a speaker. The sound from the speaker is picked up by the microphone and fed back to make the sound out of the speaker louder which is picked up and fed back to make it louder until you blow your speaker. Having an unstable positive feedback loop built into a system makes that system unstable. Negative feedback loops where the feedback from the previous balance is subtracted are very useful in stabilizing systems away from error but positive feedback always makes the error grow. A physical example of negative feedback, positive feedback and no feedback follows: If you have a bowl and you put a ball in it and then give the ball a little shove, it will travel up one side, gravity will bring it down and it will rock back and forth until it settles back to the middle. That's how engineers use negative feedback to bring back things which have been pushed out of normal operation back to normal. If you turn the bowl upside down and put the ball at the top, one small push and the gravity will make the ball fall faster and faster. That's unstable. If you put the ball on a platform and give it a push, without friction, it will just continue in rolling steady state. Both zero and negative feedback are acceptable while positive feedback is always unacceptably unstable. Engineers say that systems are stable if the pole of the system is in the left-hand plane or on the origin but unstable if the pole is in the right-hand plane. Knowing that the Laplace Transform of the system is 1/(s-i), the denominator is zero when s=+i and therefore, the pole is on the right-hand side of the origin, hence unstable. Eliminating the bad vibrations is as simple as making the interest feedback loop in the bank's computer programs zero and using only the simple interior circuit known as an "integrator." Currency systems presently using these simple "integrator" accounts are now known internationally as Greendollar systems of the Local Employment Trading System (LETS). We know that the LETSystem is an interest-free system and so we cut the positive feedback loop to get 1/(s-0). |---------| | 1 | CONTROL SYSTEM FOR -------> ----- |---------> | s | |---------| /\ \ |----------------| \ | Interest = 10% | \ |<---| Rate | | | |----------------| | | | Old | |<-----------| Balance | | Balance | + | + | | |------------| |------------| | Input + | Addition | + | Addition | | New ---------->| Node |------>| Node |---------------: |------------| |------------| Balance This leaves us with only the interior circuit: 1/s |---------| | 1 | CONTROL SYSTEM FOR -------> ----- |---------> | s | |---------| |<-----------| Old | | Balance | | |------------| | Input + | Addition | New | ---------->| Node |---------------> |------------| Balance This is the mathematical circuitry behind all interest-free systems and how Greendollars work. Instead of an output which is exponential, crooked, we have an output which is linear, straight. Your $100 volt pulse is the input to the addition node. Added to it is old balance, starting at zero, to push the new balance up to $100 volts. Next year, with no new pulse at the input, and with interest voltage to add, the balance stays at $100 volts. If another deposit comes in, it's added to the old balance to create a new balance. A negative coming in will reduce the old balance. But the system is always in balance. Positives equal negatives. This analysis shows that unemployment and inflation must go to zero if the banks' computers, which are now permitted to charge both interest and service charges, are restricted to only the service charge. Note that the exponential derivation shows that there are two solutions to the mort-gage (death-gamble). The software solution is interest rate(i) = 0 by restricting the banks computers to a pure service charge and abolishing the interest charge. The hardware solution is time(t) = 0 by installing an instantaneous electronic cashless marketplace. GAME MODEL: SERVICE CHARGE VS. INTEREST In his book `The Theory of Games and Economic Behavior', John Von Neumann, one of this century's top mathematicians, stated that "important questions in economics arise in a more elementary fashion in the theory of games." In the business war for markets, the economy decides who sells their goods and who fails to. Models used by economists are flawed by guesses and approximations about what the economy will choose. The only way to perfectly model the economy is to use fair chance to pick the winners and losers. TO PLAY MORT-GAGE: The necessary game equipment for "mort-gage" is 1) a box to represent the market economy); 2) 3 types of tokens to represent food, shelter, and energy (the tokens can be mints, napkins, cutlery); 3) a fair chance mechanism like a coin, cards, dice, straws, etc.; 4) matches or tokens to represent currency. In the Interest Game, all owe the bank 11 for every 10 tokens they borrow and have to inflate their prices to repay both the principal and the interest. Step 1) Have all the players wishing to get into business pledge their watches to borrow 10 matches from the bank at an interest rate. Step 2) Have all players spend 10 matches into the market box in exchange for a token representing the product of the economy's labor. Step 3) Have pairs of players, those with similar tokens first, use chance to decide which will win a market share out of the box large enough to pay the principal and the interest necessary to survive the bank's demand. Step 4) When the market runs out of currency, let the bank seize the tokens and watches of the losers. Step 5) Record the percent of those knocked into unemployment and the collateral seized. In the Service Charge Game, all owe 11 for every 11 they borrow with the 11th paid immediately to the bank employees as a service charge. Step 1) Have all the players wishing to get into business pledge their watches to borrow 11 matches from the bank. Step 2) Have all players spend 11 matches into the market box in exchange for a product token, 10 for the services of those who produce the goods like on Interest Island, but also 1 for the services of the bank employees who facilitated the transactions. Follow Step 3), 4) and 5) and note that in the Service Charge Game, unlike in the Interest Game, everybody can sell all their goods because the 11th unit of money entered the market through the bank employees. The very subtle difference between systems is that in the Interest Game, the bank demands payment of money it did not create while in the Service Charge Game, the bank demands payment of money it did create. With exactly enough markets to match the prices of goods produced, there can be no foreclosures. I hope this analysis has helped clear up many of the formerly misrepresented and misunderstood aspects of the usury banking system as well as explain why usury has been condemned throughout history as the greatest crime against humanity. It's the only thing standing between mankind and abundant salvation. I welcome any questions on any aspects of how the banking systems engineering. -- John C. "The Engineer" Turmel, Leader, Abolitionist Party of Canada, 2918 Baseline Rd., Nepean, ON, K2H 7B7, Canada,Tel/Fax: 613-820-8656 All TURMEL topics cross-posted to newsgroup: can.politics -- =-GRAHAM-JOHN BULLERS=-=AB756@FREENET.TORONTO.ON.CA=-=ALT.2600.MODERATED-= Lord grant me the serenity to accept the things I cannot change.The courage to change the things I can.And the wisdom to hide the bodies of the people =-=-=-=-=-=-=-=-=I had to kill because they pissed me off=-=-=-=-=-=-=-=-=-=