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The Beast of Compounding You Might Not Have Noticed
By Marc Gauvin copyright (c) Jan 10^{th} 2020 All rights reserved
www.moneytransparency.com (MSTA) Revision 4 (Final)
An adventure of escaping the matrix and each coming into their own
Foreword
The purpose of this article is to provide and convey a simplified yet thoroughly illustrative mathematical model of the general nature and dynamic systemic effects of producers integrating into their costs of production percent commissions (e.g. for financial services) charged to them on the basis of the value of their production being transacted, as opposed to on the basis of any determinable calculation of the real value and costs of those services for which producers are being charged. These % commissions are typically charged by banks and lenders in general but not exclusively, government taxes have the same mathematical effect. Although this article does not attempt to represent any real life scale or breadth of actual amounts or scenarios, the scenarios presented do accurately represent the actual nature and consequences of common financial compounding as illustrated herein.
I dedicate this to Stuart B Weeks convenor of the Bretton Woods Monetary Institute and Festival www.brettonwoods.us, who has in the throws of composing the Concord Resolution nudged me into writing this to assist the readers of said resolution. And as always, my gratitude to the MSTA supporters and team who have taken the leap to see long before most, what others will also discover herein.
Introduction
Guess what! You are a worker! If you want to escape that, you either become a villain or a true hero. True heroes are actually workers too, but with the difference that they choose their job and accept the consequences. True heroes do not choose what knowledge to learn but learn all knowledge that is required of them, they overcome weakness with patience and resolve and defy defeat with grace.
“A coward dies a thousand times before his death, but the valiant taste of death but once. It seems to me most strange that men should fear, seeing that death, a necessary end, will come when it will come.” W. Shakespeare
Let’s now have an earnest look at the current machinery we have been born into whether rich or poor. Beginning with seeing how players serve, wittingly or unwittingly, undeclared masters.
Some use tricks none have contemplated or ventured to understand, or at least dare not admit to having done so, should what they do mark the eerie presence of untold mischief, malice or unconscionable evil. To live in a world free of such tricks, is not only possible but inevitable as truth always outruns error and deceit. The only question, is if in the process of the elimination of such deviance, souls can be spared in a state of wise innocence as opposed to one of inexorable culpability. Only such a prospect makes what we are about to undertake worthwhile. This is an adventure that begins by perusing our seemingly mundane, repetitive and boring practices that underlie our economy. But in doing so, we will soon begin to notice the trace of a strange beast, that is anything but boring, but rather surreal and ominous. A beast that while seemingly motionless, stirs everything it touches and everything it touches becomes an extension of it, lest what is touched by it be blessed by a true vision of it, the beast. During our adventure, we will apply all the necessary tools to arrive at a long awaited conclusion. A determination, that while it may seem to impact us considerably upon reaching it here, even jar us into a new sense of ourselves and our reality, whatever jolt it brings now, will seem little compared to all we will begin to see once we raise our gaze from these pages. It matters not whether we are poor, rich, famous or anonymous, beautiful, handsome or homely, talented or ordinary, this knowledge will transform us into what only can be recognised by those who share such knowledge fully and completely. To rise to this knowledge, is to become in this instant at least, integrally and wholly good, insightfully constructive and able to take on the responsibility of becoming a force for restoring all and everyone, beginning with our very selves.
The Battle Field and Horizon
In the world of this year 2020 “workers” still exist and in so far as they are able to do so, seek to “charge” for their value in “units” according to their “cost of living” (expenses, food, housing, utilities, clothing, tools and materials, schooling, medical, etc.) charged to them in those same “units”. Depending on a given worker’s demeanour and fortuitous circumstance, each fares better or worse.
All those things that make up our “cost of living”, are what we call material “goods and services” or simply “real wealth”, which is why they are included in what is called the “real economy”, without which we would all be pecking grains and worms from the ground like stray pigeons.
Workers are for the most part producers in that each contributes in one way or other to those “products” of “real wealth” that are “consumed” by “consumers” including all workers in the “real economy”. One peculiar type of worker, keeps track of all those units, that all use to represent the relative value of those things each of us produces and consumes. In our world of today, such a worker is called a “banker”, a term we will use to represent the collective of such workers as one entity, because as the Spanish say: “God creates them and then they choose to cluster together.” That is in general, what one bank does all banks do.
Workers operate within what are called value chains. Value chains represent links between workers that extract and distribute resources to those that manufacture and distribute products through to stores that deliver those products to final “consumers” i.e. everybody. Each link of a value chain accumulates the costs of all links that provide what they need, to which they add the value of their own contributions and then pass that sum to the next link, so on and so on successively throughout all links up to the final consumers.
In the vast majority of cases, the value each link charges to its corresponding value chain, is uniquely based on only its products and services, never that of any other products and/or services. Following, we provide a rudimentary example of a value chain that extracts wood to produce chairs for consumers:
1. Jack goes out into the woods and cuts trees for wood and charges 100 units for the wood.
2. George who builds chairs, gets the wood from Jack and builds five chairs, for which he charges 200 i.e. 100 for the wood to Jack and 100 for his efforts in building the chairs.
3. Mary who distributes many other things to stores gets the chairs from George and charges 250, 200 to George, 50 for her effort delivering the chairs to a store.
4. Marlene who has a store with many different things for sale gets the chairs from Mary and charges 300 for them, 250 to Mary and 50 for her efforts of storing and selling the chairs to consumers.
5. Jack, George, Mary and Marlene are all consumers too and each get one of the five chairs at 60 units each for a total of 300 units, with one chair left over for someone else, perhaps a worker from some other value chain.
This example doesn’t include any bank charges and so serves to illustrate the accumulation of real wealth brought together for a common end, from resource extraction up to final consumers of real wealth summarised as follows:
Value Chain Contributor 
Contribution 
Value Contributed 
Value Summed 
Jack 
Wood to Builder 
100 

George 
Chairs to Distributor 
100 
200 
Mary 
Distributor to Store 
50 
250 
Marlene 
Store to 5 Consumers 
50 
300 
Fig. 1 Real Wealth Transfer
For a total of 5 chairs at 60 units/chair).
Notice that the cost of each contribution of real wealth in the final consumer price is constant in the calculation of the final costs of the chairs? That is the value of Jack’s wood doesn’t change throughout, similarly the values of George’s, Mary’s and Marlene’s contributions are also constant.
Enter the Banker
Bankers offer services and record transactions for which they charge fees. This collective along with governments and a few others, are of a class that charges most everyone and for almost all if not all transactions that take place.
Now, assuming the banker in our example is like everyone else in terms of how they charge their value, i.e. according to the costs and measured value of the services they render, the following is what it would look like:
Let’s say that in our simplified but very illustrative mock value chain, to record/annotate any given transaction no matter the amount, a fair and generous fee is 10 units per transaction. Then, the banker fees to the whole value chain would be for 8 transactions in total (3 between producers and 5 to consumers).
Following is a summary of the cumulative cost of flat banker fees to our friendly value chain:
Value Chain Contributor 
Contribution 
Real Value 
Real Value Sum 
Transaction 
Transaction Cost 
Jack 
Wood to Builder 
100 
100 
10 
110 
George 
Chairs to Distributor 
100 
200 
10 
220 
Mary 
Distributor to Store 
50 
250 
10 
280 
Marlene 
Store to 5 Consumers 
50 
300 
50 
380 
Fig. 2 Real Wealth Transfer + Bank Service (flat fee)
For a total of 80 units in banking fees 26.66% of the 300 units of real wealth, raising the cost of the 5 chairs from 300 to 380 or from 60 to 76/chair. Right?
The Banker’s “divine/diabolic” inspiration
But, what happens if the banker convinces everyone against all reason, that each of those 300 units represent individual “products”, that the banker makes available to society, i.e. each unit bearing its own independent value? Such that, the more units used by society (i.e. the larger the sums), the more value the bank is actually providing the world! Thus, the banker so inspired (divinely or diabolically), ventures to test the waters by deciding to adopt a new regime of charging a percentage of the balances transacted, at say 10% per transaction.
Let’s look and see how this plays out:
Value Chain Contributor 
Contribution 
Real Value 
Real Value Sum 
Transaction 
Transaction Cost 
Jack 
Wood to Builder 
100 
100 
10.00 
110.00 
George 
Chairs to Distributor 
100 
200 
21.00 
231.00 
Mar 
Distributor to Store 
50 
250 
28.10 
309.10 
Marlene 
Store to 5 Consumers 
50 
300 
35.91 
395.01 
Fig. 3 Real Wealth Transfer + Bank Service (10% Compounded)
For a total of 95.01 in banking fees generated to the banker, 31.67% over the cost of all the real wealth (i.e. 300 units). Thus raising the cost of the five chairs to 395.01 or 79.00/chair. Now representing a 15,01% increase in income to the banker compared to the case of charging a flat fee of 10 units/transaction.
But notice, all society has to show for all this is the exact same five chairs. Except for the bank, that by switching from charging passively in terms of the cost and merit of its own real service to charging dynamically in terms of the real wealth values of others, the bank so achieves a dynamically increasing return for their services on the basis of the value of other goods and services not their own, and for which they are not responsible at all. This means that in our example, the corresponding share to the bank of the final 5 chairs increases dynamically and as we will see, faster than the banker increases the cost of real wealth to everyone including the banker! Please ponder if this is true or not. Not sure? Maybe or maybe no? Well read on, the proof follows. I hope you take the time to learn what follows, if you need help with the basic math, contact any good engineer or engineering student, if the basic reminders and “tutorial notes” included herein prove insufficient.
Knowledge as a Weapon
First thing to notice from the above scenarios, is how the banker’s fee is obtained by virtue of multiplying by a percentage factor that in our example is 10%, the fixed sums of values corresponding to the instances of real goods or services, that are the objects of numerous transactions across a value chain and that the bank is not responsible for. The second thing to observe, is how the sums of the value assigned to those real goods and services by producers, are constants i.e. none of those values have any dynamic impact on the cost of final consumer products. The third and perhaps most important thing to remember, because it is conceptual and without it, NONE OF THIS WOULD BE HAPPENING!! Pause and think for a moment before continuing, remember the phrase above “...that each of those 300 units represent individual “products” that the banker makes available to society, each unit bearing its own independent value.” Remember that!
For greater simplicity, in illustrating the general principle at play, all we need is to examine the effect of any real object of value being subjected to a service with fees that are:
1. Not based on the measure of value of the service being rendered but on the value of the objects transacted for which the service is charged, i.e. a % commission, and;
2. Applied to several consecutive transactions, e.g. as in a value chain.
So, with that in mind and continuing with our mock example, but only focusing on the banker’s 10% charge over just the value of Jack’s wood, that we will represent as “W”, because it is a constant so no matter what we do to it, it will never change. That is, instead of writing 100 all the time we simply write W, that way we know it to be that hundred that corresponds to the value of Jack’s wood and not any other 100. Ok?
Jack´s wood is “W” = 100 units, a constant that will never change throughout.
(Tutorial note 1: Most will remember that percent (%) is simply “per hundred” represented by a % sign which corresponds to the number 1 divided by 100 i.e. 1/100 =0.01. So 10% is just 10 x 1/100 = 0.1. this is important to keep in mind for later.)
When we say the banker charges a fee of 10%, we are saying that it takes 10 for every 100 of something transacted. Now we know that the cost of Jack’s wood W = 100, and that for the bank to keep track of any transactions the bank wants 10 for every 100 transacted. So, the total cost of W plus 10% of W, can be written as follows:
Total Cost = W + 10% W
(Tutorial note 2: Now would be a good time to remember basic factoring. If you don’t, here is an easy refresher, if you have two numbers that you are adding together and that each share a common factor, you can take that common factor out to simplify the addition and turn what was a simple summation into a multiplication of two simpler terms, here is an easy example:
6+4 = 2 x (3+2) or 2(3+2) = to 2x5 = 10.
This will be important to remember for later. Also important is to remember that number 1 is the universal factor of all numbers and all numbers are a common factor of 1, for example 2 + 2 is equal to 2(1+1).)
Got it? If so, do we have a summation of two numbers with a common factor in the total cost here?
Total Cost = W + 10%W.
Yes! W is a common factor of both terms, so we can factor it out
Total Cost = W(1+10%) or W(1+ 0.1)
This factoring out of the constant W, is important because it allows us to isolate the remaining critical factor in our case (1+10%) or (1+0.1). That, as you will learn next, is what is operated on to constantly grow the banker’s income faster than the growth of the cost of everything to everyone including the banker.
The critical factor (1+10%) alone, helps understand any singular summation of 10% to anything. For example, if you wanted to represent the cost of a car “C“ plus 10% you would write, C(1+10%).
But what about representing the cost of the second and third and the n^{th} transaction of W plus the accumulation of 10% fees over all previous links in a value chain? Well let’s see how we can do that:
Since we’re concerned with the total cost i.e. W + 10%W for several consecutive iterations, Lets call the whole thing “C_{subscript}”. Such that, C_{0 }represents the value before W is ever transacted, C_{1 }when W is first transacted, C_{2 } the second time and C_{n} the n^{th } time of any n number of times W is transacted.
The archer loads up with arrows
(Tutorial note 3. Now the last bit of math ammunition you need are “exponents”. Remember those? Exponents are superscripts that tell us how many times something appears as a factor in a multiplication of itself. For example 2^{1 }is simply 2 and 2^{2} = 2 x 2 = 4 and 2^{3} = 2 x 2 x 2 = 8. Notice how each unit increment of the exponent results in a doubling of the value expressed? Keep that in mind for every time you hear the word “exponential!!!”.)
One more amazing thing, what do you think 2^{0 } or 1,000,000^{0} are both equal to? Well, as it turns out, any number no matter how big or small raised to the power (exponent) of 0 is equal to just 1, so 2^{0 } = 1,000, 000^{0} = 1.)
With what we have covered so far, along with the tutorial notes, we should readily comprehend the following fully and perfectly:
The value of Jack’s wood “W = 100 before it is transacted is,
C_{0}_{ } = W(1 + 0.1)^{0} = 100.
(Remember, anything raised to the power of 0 is just 1, so (1 + 0.1)^{0} = 1, this just shows that our model works for the case 0 transactions.)
Now, Jack’s wood + banker’s 10 % for the first transaction (remember?) is,
C_{1}_{ } = W(1 + 0.1)^{1} = 110 .
And for the second, stop let’s think...., is it not C_{1} times the critical factor i.e. W(1 + 0.1)^{1}? Yes it is! So,
C_{2}_{ } = C_{1} x (1+0.1)
= W(1+0.1) (1+0.1)
= W(1+0.1)^{2} .
And for the general case of any n subsequent transactions of W,_{ }_{ }where the same critical factor is applied we have:
C_{n}_{ }= W(1+0.1)^{n}
Remember, that in this form i.e. with W factored out, we can look at the critical exponential factor (1+0.1)^{n} and study it on its own, separate from W the passive constant in all and any subsequent n transactions.
Hold on, we are getting closer to what all this means! We’re past the halfway point! The journey back is now longer and at least as perilous as continuing, more now hangs in the balance than ever before if we quit.
“A coward dies a thousand times before his death, but the valiant taste of death but once..”. “True heroes...choose not what knowledge to learn but learn all knowledge required, they overcome weakness with patience and resolve and defy defeat with grace...”.
The archer takes aim
Back to our quest! Now that we know that the compounding (exponential) factor that compounds 10% onto itself is,
(1+0.1)^{n}
Why do we care? Well, because we want to show how to calculate how the banker multiplies banker’s income faster than that same factor increases the cost of things for everyone including the banker.
Remember our number crunching where we showed how incorporating the bankers 10% in the cost passed on, raised the return to the bank by 15.01%? Well that increase gets bigger faster as the number of transactions (links in the value chain) of the constant W increases, Stick around and see!
Nowhere better to begin our exponential journey than with exponent 0!
So, for n = 0 (i.e. no transaction has taken place yet),
(1+0.1)^{n} = 1
Here the bank receives 0% because (1+0.1)^{0} = 1 and the difference of that result and 1 is 1  1 = 0% going to the bank! Neat how this shows how our model works even before anything has happened.
And for n = 1? (we’ve done this before the factor is simply itself (one times) )
(1+0.1)^{n }= 1.1,
so the difference of the result is 1.1  1 = 0.1 (i.e. 10%) going to the bank as income, as expected, right? Right!
And for n = 2 we have,
(1+0.1)^{n }= 1.21
with the difference of 1.21  1 = 0.21 (i.e. 21%) going to the bank as income, again as we demonstrated in our first brut force number crunching, so this too is as expected.
But do we see a pattern? Hmmm, sneaky beast eh?
And now, drum roll.... for n = 10! Let’s see (take out your calculator),
(1+0.1)^{n } = 2.59!
with the difference 2.59  1 = 1.59 (i.e. 159% yikes!!!) going to the bank as income! Let’s try that again 2.59 x 100 = 259 = (100 + 100 x 1.59) = (100 + 159) = 259. Yep it pans out! Amazing beast!
And for n = 20,
(1+0.1)^{n}^{ }= 6.73!!!
With a difference of 6.73  1= 5,73 (573%!!!) of units of income to the bank.
Getting the picture now? No matter what we charge for our REAL goods and services, by applying the notion that each unit of the numbers that represent those goods and services are products in and of themselves and thus have a unitary value if not cost, such that their use can be charged:
1. Not based on the measure of value of the service of providing the units, but on the value of the object being transacted measured by those units.
2. And applied over several subsequent transactions.
Then, it follows that no matter the cost of living, those who charge for their services on the above criteria, are guaranteed an increase in income that is equal to that increase in cost of living such that the proportion of wealth that corresponds to that increase grows correspondingly. All this without that income corresponding to their costs/value but rather to everyone else’s costs, that as we have well established are constants. And finally, that income being the cause of the increase to the system must necessarily be received before it the increase is incorporated .
Note also, how this compounding feeds back into subsequent value chain cycles thus the growth becomes a function of the cycles too.
The archer shoots at the heart of the beast, or?
Notice how if everyone tries to raise their cost of living, by increasing the initial nominal cost of their real value, nothing is solved, the same proportion is applied to the final distribution of real wealth (always in favour of the banker) because it is the result of multiplying with the percentage based compounding (critical) factor! Which is why we emphasised that W is a constant! That is, no matter how much or little people decide to charge for their constant value in units, the same growth rate takes place relentlessly, NOT as a function of the value of things but as a function of the critical factor we isolated. And reducing the banker’s percentages doesn’t stop the growth, i.e. any lesser percentage > 0 will do the same thing just slower. But all percentages have the same insane target, i.e. all aim to reach infinity over the number of transactions over time.
There you have it. With skilful stealth we have invaded the beast’s domain and even its den. We’ve seen its seemingly limitless tentacles reaching out every which direction up down and all around, even when it seems to be inanimate. Along the way we have armed ourselves with mastery of all the relevant knowledge to spot, observe, slay the beast and to lay down barriers so that no more can such a vile creature invade us robbing us of our wise innocence. Meanwhile, our world will, with exponential speed, restore itself replete with all the requisite strength, goodness, courage and genius that comes with true knowledge.
So, there are only two solutions, we either shoot the beast in the heart that which multiplies bankers income faster than that same factor increases the cost of things for everyone including the banker i.e. slay the compounding factor (1+0.1)^{n} so that no banker or anyone else for that matter e.g. Government will charge in terms of anything but the true value of the services they provide. But, to prevent this from happening again, all we have to do is correct this insane idea that every unit of a number can be rationally treated as a separate product as without this concept none of the compounding could ever take place!
OR! All this journey is mostly for nought and our arrows will keep being shot off target and in our frenzied panic, we will shoot more and more of them in all directions but upon the beast. Is that not what we are doing now, wittingly or unwittingly, maliciously or hopelessly?
“A coward dies a thousand times before his death, but the valiant taste of death but once. It seems to me most strange that men should fear, seeing that death, a necessary end, will come when it will come.”