Hard cash accounting

HARD CASH ACCOUNTING

© North Delta College 2015

Mathema'cs applied to Business Theory 1

NON-‐COMMUTATIVE STRUCTURES IN MODERN FINANCE

INTRODUCTION

We will in this presentaAon introduce a new AccounAng concept: Hard Cash.

Hard Cash is to Cash what Cash is to other types of Assets. The UlAmate form of Wealth.

To define these noAons properly we will spend some Ame with modern

mathemaAcal ideas such as non-‐commutaAvity coming from Group theory and show how they apply in the Financial realm.

This will naturally lead us to our key concepts.


SUMMARY


PART 1: THE EXISTING PARADIGM A) MathemaAcians versus Society at large B) US Dollars: The UlAmate commutaAve currency C) The Paradigm D) Why we disagree with the Paradigm PART 2: WHAT DO WE MEAN BY NON-‐COMMUTATIVE STRUCTURE? A) Examples of non-‐commutaAvity B) Formal definiAon C) Everyday life is non-‐commutaAve PART 3: INTRODUCTION TO GROUP THEORY A) Non-‐commutaAvity and Group theory B) Group theory in MathemaAcs C) What is Group theory? PART 4: HARD CASH ACCOUNTING A) What is Hard Cash? B) Why is Cash non-‐commutaAve? C) Hard Cash living FINAL STATEMENT

PART 1: THE EXISTING PARADIGM

The web of structures behind modern finance is sAll at its very core nothing more than playground mathemaAcs. On the other hand, modern mathemaAcs uses very subtle formalism that would leave the financier or the layman in total bewilderment if they were aware of them. We will show in this presentaAon why the Society at large has to bridge some of the gaps they have with mathemaAcians and how modern Maths can help us understand new financial concepts.


MathemaAcians versus Society at large

MathemaAcs Finance Layman

Abstract Structures

Elementary Algebra

Common Sense

Figure 1: MathemaAcs versus Society

US Dollars: The UlAmate commutaAve currency

The illusion that Cash and accounAng are commutaAve might come from the fact that the green currency, the US Dollar has become universally the unique reference

for monetary trade.

The fact that: 1) It can be used anywhere

2) Be used interchangeably whether under its physical bank notes aspects or its more digital avatars

3) And nothing in the physical aspect of the currency can hint at disconAnuiAes, ruptures or upheavals between the currency and what can be purchased through it.



Figure 2: US Dollar – The Universal Currency


The Paradigm

The most fundamental assumpAon of the current financial world is that the inner-‐structures of cash transacAons and the banking system at large follow very smooth, easy to understand, commutaAve pa`erns. That no financier or accountant needs to study higher mathemaAcs in order to understand financial flows. That one Ames ten pounds is equal to ten Ames one pound. In other words, 1x10 = 10x1. (MathemaAcal definiAon of CommutaAvity).


1 x 10 = 10 x 1 Figure 3: CommutaAvity of Cash – the ExisAng Paradigm

Why do we challenge such a basic assumpAon?

Our firm belief is that the workings of currencies in any country when dealing with cash is not commutaAve. That for accounAng transacAons:

1x10 is not necessarily equal to 10x1.

This shocking truth will be demonstrated in part 4 of this presentaAon.

The Algebra behind Cash is far more complex than the one dictated by using real numbers.


Why we disagree with the Paradigm


Cash Management

ExisAng Paradigm

Our Model

Real Numbers

Non commutaAve Structures

Figure 4: Our model

Examples of non-‐commutaAvity

What do we mean by non-‐commutaAve? Let us take the example of heaAng some baked beans. In order to accomplish this task one needs first to open the An of baked beans and then pour it in a pan. You cannot do it the reverse way. Try pouring the beans in a pan before opening the An and you will see where you will reach. The 2 operaAons, opening the An and pouring in a pan have to be performed in a definite order. Hence they do not commute.


PART 2: WHAT DO WE MEAN BY NON-‐COMMUTATIVE

STRUCTURE?

Figure 5: An Example – HeaAng Baked Beans

Formal definiAon

Now the formal definiAon of non-‐commutaAvity. A process is commutaAve if when one splits its component tasks into operaAon A and operaAon B, it doesn’t ma`er if operaAon A is done before or aeer operaAon B. Non CommutaAvity on the contrary says it does ma`er: Performing A before B is not the same as performing B before A. As we will see daily life is non-‐commutaAve.



STRUCTURE?

Time

OperaAon A OperaAon B

OperaAon B OperaAon A

Outcome X

Outcome Y X ≠ Y

Figure 6: Non-‐CommutaAvity DefiniAon

Everyday life is non-‐commutaAve

The processes of daily life are most of the Ame non-‐commutaAve. The order in which ones performs tasks does ma`er. Breaking a bo`le of wine and drinking it has to be performed in that order only. Washing your hands and opening the tap has to be performed in the reverse way in order to be effecAve. These are Non-‐CommutaAve processes. On the other hand, switching the light on and entering the room can in theory be done in any order and is therefore part of a commutaAve process.



STRUCTURE?

Non-‐commutaAvity and Group theory

Non-‐commutaAvity was first introduced into MathemaAcs by Evariste Galois in the early 19th century when he discovered Group theory for the very first Ame. Groups were the first mathemaAcal objects where commutaAvity were not assumed. Groups exhibit the very first example of structures where someAmes operands do not commute.


PART 3: INTRODUCTION TO GROUP THEORY

1800 1900 2000 2100

Now: 2015 ApplicaAons

outside Maths

Development of the Theory Discovery

of Group Theory

Figure 7: History of MathemaAcs

Group theory in MathemaAcs

Group theory occupies a very special place in the mathemaAcal landscape. They were the first algebraic structure to be discovered and are the simplest example of such structures. Their applicability is almost universal, mostly in Physics. They exemplify the paradigm shie in MathemaAcs from numbers and computaAons to structures, pa`erns and conceptualisaAons. As such, they are a model of where every scienAfic endeavor is heading to. Mathema'cs applied to Business Theory 12

CEO


ComputaAons Concepts

MathemaAcal Research

Figure 8: EvoluAon of MathemaAcs

What is Group theory?

More pracAcally, what is Group theory? Groups are mathemaAcal objects where the consAtuent elements of the object are interlinked through an operaAon which obeys 3 basic laws. CommutaAvity is not pre-‐supposed in these 3 laws. If the operaAon is noted * and a and b are 2 consAtuent elements of the Group a*b is not necessarily equal to b*a. We will show in part 4 why Financial models can benefit from integraAng in their logic the facts that there exists processes where operands do not commute.



What is Hard Cash?


PART 4: HARD CASH ACCOUNTING

Let us now switch to Hard Cash. What do we exactly mean by such a concept? Hard Cash are those elements in the currency with the highest purchasing power. If Cash was commutaAve, This definiAon would be void. But we will show that Cash is not CommutaAve, and therefore this definiAon makes sense. More precisely, we have Hard Cash when we can maximise the following funcAon:

Purchasing power of the denominaAon / Value of the denominaAon

Figure 9: Cash and Hard Cash

What is Hard Cash?

What do we mean by purchasing power of the denominaAon? If you could only buy a cup of coffee with a unit value of the denominaAon you wouldn’t go very far. Therefore purchasing power comes with purchase of really valuable items to the eyes of the populaAon with regards to their income capability. Thus, a middle income individual in an emerging market would consider having Hard Cash in hand if with no more than 3 units of that denominaAon he could buy a TV or a mobile. Something he would really value intrinsically.



Figure 10: Buying items which are intrinsically worth

Why is Cash non-‐commutaAve?


Why does Hard Cash make sense? Because Cash is indeed non-‐commutaAve. One Ames 10 pounds is not equal to ten Ames 1 pound. Even if in theory it is true, in pracAce it is not. It is easier and more likely you will carry a ten pounder rather then 10 coins of 1 pound in your wallet. Moreover, the shopkeeper could in some instances refuse too much pe`y cash and ask for hard cash without naming it. Therefore, depending on what you buy, denominaAons do not necessarily follow laws of equal relevance.


Why is there a Max for Hard Cash?

An easy mistake at this stage would be to think the bigger the denominaAon, the harder it is. This is clearly wrong as there exists opAmum denominaAons depending on your monthly income. For example, a denominaAon could be too big for the given expense. Moreover, for a certain monthly income, there are targeted valuable purchases to be made which clearly restrict the Hard cash to a certain range of ideal denominaAons. (not too big, not too small).



DenominaAon

Purchasing Power / Value of DenominaAon

Hard Cash

Figure 11: Why Purchasing Power reaches a Max


Examples of Hard Cash

Let us give some examples.

In the UK, for an average income of £2,500 per month (a standard salary in 2015), a typical Hard Cash denominaAon would be the blue £20 note or the red £50 note.

In Dubai, for an average income of AED 8,000 ( a reasonable income by 2015 standards), a

typical Hard Cash denominaAon would be the red AED 100 note.

In both cases, few units of Hard Cash will give access to the middle class dream lifestyle, this middle class is precisely aspiring to.

è Good restaurants, technological gadgets, branded clothes, exciAng accessories

(watches, shoes etc…)


Hard Cash Living

Hard cash generates its own lifestyle which is the lifestyle of the future. Taking its source in the American dream, but exemplified more accurately in place like Dubai. A heavy spending middle class lifestyle, with branded products, shopping malls and no regrets. The whole Hard Cash concept and its subsequent lifestyle might seem shallow to an European intellectual, nevertheless it is THE lifestyle where all the emerging markets are converging to and in 20 years Ame, if the world passes through the economic storm there will be nothing else lee.



Figure 12: Dubai: The laboratory of the world to come

Final Statement

We have therefore shown in this presentaAon how proper usage of modern mathemaAcal concepts can enlighten very down to earth subjects. In parAcular, we extracted the noAon of non-‐commutaAvity from Group theory and applied it to a well known accounAng concept such as Cash. This led us to define Hard Cash. Hard Cash is the cash you have in hand that allows you to chase your dream material lifestyle. Although, theoreAcally a void concept, in pracAcal terms it is not. Once one becomes aware of its existence, one will soon realise that regarding Money and spending, sole Hard Cash gives you access to the Holy Grail.


FINAL STATEMENT

Hard cash accounting

Business

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