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(a)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=-=-=-=-=-=-=-=-=-=
