Mathematical concepts applied to monetary systems in 20 slides

MATHEMATICAL CONCEPTS APPLIED TO MONETARY SYSTEMS

IN 20 SLIDES

© North Delta College 2015

Mathema'cs applied to Business Theory 1

INTRODUCTION

Name 4 key concepts in Physics: Time; Space; MaJer; Energy. Name 4 key concepts in Business Management: Money; Business OrganisaNons;

Time; Resources.

The 2 Flagship concepts of each are Energy (Physics) and Money (Business).

What we will show in this presentaNon is how these concepts belonging to 2 different spheres of knowledge interpenetrate each other. In parNcular, we will illustrate in these 20 slides how the core concepts of Physics can be interpreted

within Business OrganisaNons. And how Money is the Equivalent concept of Energy inside Business Management!!!


SUMMARY


Part I: FINANCIAL SPACES A) Structural DescripNon B) The AccounNng Meter

Part II: THE ACCOUNTING TRANSACTION PRINCIPLE A) DefiniNon B) The Universal Principle

Part III: A MONETARY SYSTEM SEEN AS A TOPOLOGICAL VEHICLE A) DefiniNon of Monetary System B) Why a Topological Vehicle?

Part IV: TRANSVERSE FLOW A) Money and Energy B) Transverse Flow C) Money, MaJer & The Tangible

Final Statement

PART 1: FINANCIAL SPACES

What is a Financial Space? It is the MathemaNcal DescripNon of a Business OrganisaNon where only the accounNng aspect of the organisaNon is kept. More precisely, we look only at the topological / structural aspect of the space. Looking at its general features. The most fundamental fact we want to encapsulate with this concept is that any topological model of Finance has to acknowledge 2 Transverse direcNons inside the space absolutely irreducible to each other. We call DirecNon 1: The Brick direcNon and DirecNon 2: The Conduct direcNon.


DefiniNon

Picture 2:

Picture 1:

2 Transverse direcNons

The sphere The plane A Torus

Bricks and Conducts

The Brick direcNon encapsulates the Physical constraints imposed on the Financial Space due to the existence of a Brick and Mortar organisaNon located in Space and Time and trying to make money.


Picture 3:

Picture 4:


This Brick dimension captures also the temporal aspect of the organisaNon from an accounNng standpoint. In the same layer, every brick of the layer is at accounNng Nme t = t0.

The Conduct direcNon are the spaces that the bricks have lee so that Energy can Flow in. Conducts are fundamentally transverse to Bricks.

Picture 5:

One layer of the brick dimension

Same Time-‐Stamp A conduct

Time T = 1

Time T = 2

Time T = 5


The AccounNng Meter

When the accountant wants to measure a given Financial Metric inside the organisaNon, the normal flow of accounNng Nme stops and the accountant comes at the JuncNon between Brick and Conduct and measures his Metric.

In fact the whole structure of the Financial Space looks a bit like the following:

Picture 6:


Picture 7:

Bricks

The Conduct’s DirecNon

The Measuring instrument

Time t = 1

Time t = 2

Time t = 3

The conduct where Energy Flows in

At each Nme T, an accounNng measure

Now let us leave Topology to study the MathemaNcal Structure behind any Financial TransacNon What is an AccounNng transacNon? 2 Monetary Systems are silng face to face with their openings ready to exchange money. Once the money has been exchanged. There is indeed an AccounNng transacNon. There is an Universal structure behind any transacNon that we cover in the next 2 slides.


DefiniNon

PART 2: THE ACCOUNTING TRANSACTION PRINCIPLE

Picture 8:

Picture 9:

Universal Principle

There are 3 players in this Game: Oscar; Mr. W; and Dr No At the beginning of the game, Oscar and Mr. W are silng on 2 parallel axis, not quite synchronic yet… Mr. W has to perform a task for Dr No. He can only perform it provided Oscar himself performs an acNon which has absolutely no link with the original task. Mathema'cs applied to Business Theory 8

Picture 10:

PART 2: THE ACCOUNTING TRANSACTION PRINCIPLE

Oscar

Mr. W

At the beginning of the transacNon, Oscar and Mr. W are facing each other on those axis, exactly at the same level.


Oscar does his trick. Mr. W performs his task. There is some movement on the axis. Oscar and Mr. W are moving in opposite direcNons. Mr. W has performed the task and is alive. Dr No got what he wanted. Oscar enriched himself.

Picture 11:

PART 2: THE ACCOUNTING TRANSACTION PRINCIPLE Universal Principle

Picture 12:

Oscar

Mr. W

Oscar

Mr. W

DefiniNon of Monetary System

Now back to Topology. Why did we introduce the concept of Financial Space earlier? The reason behind it, is because, if we look structurally to any Monetary System, they will look in their core shape as the Financial Space described in Part 1. Now, what do we mean by Monetary System? A Monetary System is any organised system trying to survive in an environment where the rule of the game is to make profit. These could be the bank balances and assets of an individual, a company, a government, a group of inter-‐linked organisaNons, or something more weird even …


PART 3: A MONETARY SYSTEM SEEN AS A TOPOLOGICAL VEHICLE

The Statement

The statement: A Monetary System can be seen as a Topological Vehicle. We will elaborate on this statement in the next 2 slides. But first, what does this vehicle structurally look like.

In fact, it looks precisely like the Financial Spaces we described in Part 1.



Picture 13:

Picture 14:

Maths Real World The Concept

The MathemaNcal Object

The Real Thing IllustraNon

Example or Sub Class

Topological Vehicles

Financial Spaces Monetary Systems

Universality

Why do we use the Term Topological Vehicle?

First, because, this structure we exhibited (namely Financial Spaces), is absolutely Universal. All Monetary Systems, regardless of their object or purpose look like that.


CEO


Picture 15: Financial Spaces

Any Monetary System

Topological AbstracNon

Towards Maths

Stands on its own

Second, this structure, whether in the Maths world, or in its pracNcal realisaNons, stands on its own like a Topological Manifold in Geometry. Except it is not a Manifold.

It is far more subtle than that. As we will see in the next slides. Hence, Now, we will move to Part 4 of this presentaNon and go deeper into the Energy aspects of Monetary Systems. In parNcular, we will introduce the NoNon of Transverse Flow.



Picture 16:

Money and Energy


Einstein claims MaJer is Energy. We claim Money, ulNmately is Energy too, which crystallises from Nme to Nme into coins and notes. Business OrganisaNons, or more generally, any closed Monetary System lives also on Energy. The same as living organisms. They have Energy funcNons aJached to them linked to the flow of Money passing through them. We will in the following slides, describe in more detail the relaNonship between, Business OrganisaNons, their Energy levels and the flow of Money.

PART 4: TRANSVERSE FLOW

Picture 18:

Picture 17:

During an AccounNng TransacNon

Suppose you are at a counter, paying a transacNon, or at your bank, pulng some cash in.

Obviously, if you are using cash, there is a transfer of coins and notes between you and the person behind the counter. What we claim is that what is transferred is truly Energy and that the coins and notes are just an illusion.

è When Money goes from one Monetary System to another it loses its Materiality and regains its pure intangible form.



Picture 20:

Picture 19:

DefiniNon of Transverse Flow


The most amazing fact about Money and Business OrganisaNons is not how these organisaNons generate revenues. (These reasons could at the end be very fortuitous). But how they get funded. How does the funding circuit penetrate a Monetary System? We reach here the noNon of transverse flow. We have seen the 2 dimensions behind a Financial Space: Brick and Conduct. Money or Business Energy first finds a Conduct inside the organisaNon and then flows in, transversally to Brick which is the Space and Time component of the Business.


Picture 22:

Picture 21:

Monetary System Expenses

Funding Revenues

Object : Transverse Flow of Energy

PracNcal Example of Transverse Flow

To see graphically what happens Let us suppose a wooden construct made of 4 Layers. To hold it together, we need to hammer a nail down, right in the middle of each Layer, through each Layer. The nail is indeed transverse to all 4 Layers. When the carpenter hammers the nail down, there is a transverse flow of Energy going from the nail to the wooden construct…



Picture 24:

Picture 23:

Front View SecNonal View from one side Layer 4

Layer 1

The nail

Top View


Time-‐SecNons

If the Money coming from the Funding source is indeed a Transverse Flow of Energy across the Financial Space, why do I have the impression, then, that Money is something tangible. That I can hold in my hands. That is because, each Nme one uses an accounNng meter to measure Money, the accounNng Nme stops, and there is a cross secNon across the Financial Space, that we call a Time-‐secNon, and the monetary energy materialises and discreNses itself into coins and notes… The whole Financial space is only made of this: Transverse Flows of Monetary energy and Time-‐secNons.


Picture 26:

Picture 25:

Intangible Monetary Flow

Materialises and discreNses into

Coins and Notes: Physical Money

Transverse Flow Time-‐SecNons

Money, MaJer and the Tangible

Business at the accounNng level is therefore an interplay between, Money, MaJer and the duality Tangible/Intangible. The Financial Space can be seen as a vehicle standing on its own with transverse temporal secNons all laying one next to each other. The Monetary Energy then cuts through them in a Conduct where it flows transversally to the Time-‐SecNons.



Picture 27:

Transverse Flow

Transverse Flows and Time-‐SecNons

Time stopped at T = 1



Final Statement

Aeer a long journey through mathemaNcs, topology and money, it is Nme now to sum up in one page our findings.

Monetary systems have a very special topology made up of 2 transverse direcNons:

A transverse flow (The money flow) culng through Nme-‐secNons (The more physical layers of the organisaNon)

Some people may wonder how transversality can be discussed without pulng any metric. But for us transversality or orthogonality is a shape issue and pertains therefore to more

topological discussions and precedes irremediably any metric structure. Indeed, transversality precedes any noNon of size or distance in geometry. It might even precede MathemaNcs itself.

This Transverse flow is an Energy flow. Pure Energy. It is only when the accountant makes some Nme-‐secNon to measure how much money is in the system that this flow materialises

and discreNses itself into coins and notes which are money as we usually know it. Mathema'cs applied to Business Theory 20

FINAL STATEMENT

Mathematical concepts applied to monetary systems in 20 slides

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