Cashlet Theory: Discovering the Nature of Accounting

Accounting is the “language of business”, which records how our society works from the monetary aspect. Just like mathematics and science, accounting is one of the subjects that help people understand the world. However, accounting is not explained in a way that can be easily understood even for very basic concepts such as debit and credit. This article introduces a novel concept of cashlet into accounting area enlightened by chemistry. Cashlet is defined as a basic accounting unit with a value of negative one in the same way that electron is in chemistry. By comparing accounting transaction with chemical reaction, the author finds out that an accounting transaction is actually a process of transferring cashlets from one account to another just in the same way of a chemical redox reaction that transfers electrons from one chemical species to another. The account that gives cashlets is credited, while the account that takes cashlets is debited. Graphs are introduced to visualize the process. In cashlet theory, credit always means positive or plus (+), while debit always means negative or minus (−). Philosophically, when people give, they get credits; when people take, they get debits. The same idea is true in accounting. This article discovers that the nature of accounting is a process of moving cashlets between accounts and a process of recombining accounts, which simplifies the accounting concepts and helps people better understand the world through accounting.

T.-K. Liu tablished in 1494 by Italian mathematician Luca Pacioli who was the first person to publish a work on the double-entry system of book-keeping [1]. In the double-entry accounting system, at least two accounting entries are required to record each financial transaction where every entry to an account requires a corresponding and opposite entry to a different account [2].
Double-entry bookkeeping is governed by the accounting equation: Assets = Liabilities + Equity.
At any time point, the equation should be true. Therefore, a change in one account must be matched with a change in another account. The terms debit and credit are used to record these opposite changes [2]. However, the usage of these terms in accounting is not the same with their everyday usage, sometimes even counter-intuitive, which makes accounting difficult for ordinary people to understand. Even worse, there is no consistency for an increase or a decrease of accounts by a debit or a credit post, which makes accounting even tougher. To break down these difficulties, I brought chemistry concepts to accounting.
Accounting equation is similar to chemical equation after several steps of transformation, and the knowledge of chemistry can be applied to accounting, which helps understand the nature of accounting from science perspective.
An accounting transaction is very similar to the chemical reaction named redox. Redox (short for reduction-oxidation reaction) is a chemical reaction where any such reaction involves both a reduction process and an opposite oxidation process simultaneously [3], which is similar to debit and credit posts of an accounting transaction. The electricity should be balanced to maintain a chemical equation in a similar way that the accounts should be balanced to maintain accounting equation.
In this article, I uncover the nature of accounting by comparing accounting equation with chemical equation and accounting transaction with chemical reaction. Using analogy, I introduce the concept of cashlet that is equivalent to electron in chemistry. I find out the nature of an accounting transaction is a process of transferring cashlets from one account to another, and the process can be visualized using graph theory. I discover that the nature of accounting is a process of moving cashlets and recombining accounts. Meanwhile, I introduce the concept of credit status, and simplify the terms "Debit" and "Credit", which makes accounting more accessible for ordinary people. In order to apply chemistry to accounting, I introduce a novel concept of cashlet which is equivalent to electron in chemistry. Cashlet is a basic accounting unit the value of which is always negative one (−1). The adjective form of cashlet is cashletic which is equivalent to electric. Cashlecity is equivalent to electricity. Chemical reaction is a process of moving electrons and recombination of atoms. The total electric charge of all atoms is always zero.

Comparison of Accounting Equation and Chemical Equation
Accounting transaction is the same thing: it's a process of moving cashlets and recombination of accounts. The total cashletic charge of all accounts is always zero.
In the new accounting equation ( 1) Business is always neutral, which means its cashletic charge is always 0.
2) The "+" sign between two accounts only means "AND", and between accounts there is only "AND" relationship (no minus relationship).
3) The calculation happens in the cashletic charge (or in the superscripts) of accounts.
4) The total cashletic charge of all accounts should be zero.
Based on the above prosperities, we can deduce lots of accounting equations. In this section, I introduce novel accounting concepts and novel accounting equation using analogy of chemical equation.

Comparison of Accounting Transactions and Chemical Reaction
Each accounting transaction involves at least two posts where one account is debited and the other is credited. These debit and credit should always happen together; they cannot occur independently. Accounting transaction is very similar to the chemical reaction of redox (short for reduction-oxidation reaction) where any such reaction involves both a reduction process and an opposite oxidation process simultaneously. These reduction and oxidation should always happen together; they cannot occur independently either. Here, I coin a term-crebitto abbreviate credit-debit transaction, which is equivalent to the term redox in chemistry.
Redox reactions involve the transfer of electrons between chemical species and the changes of oxidation state of chemical species. The chemical species from which the electrons are stripped is said to be oxidized, while the chemical species to which the electrons are added is said to be reduced. It can be explained in simple terms: Oxidation is the loss of electrons or an increase in oxidation state.
Reduction is the gain of electrons or a decrease in oxidation state.
The oxidation state, also known as the oxidation number, is an indicator of the degree of oxidation of a chemical species in a chemical compound. It can be positive, negative or zero. Similarly, I introduce the concept of credit state, which is an indicator of the degree of credit of an account in accounting. It can also be positive, negative or zero.
Using the analogy of redox reaction, we can describe accounting transaction as following: An accounting transaction involves the transfer of cashlets between accounts and the changes of credit state of accounts. The account from which cashlets are stripped is said to be credited, while the account to which the cashlets are added is said to be debited (or decredited). It can be explained in simple terms: Credit is the loss of cashlets or an increase in credit state.
Debit is the gain of cashlets or a decrease in credit state.
To be more intuitive, it can be explained in this way: When an account gives cashlets, it is credited.
When an account takes cashlets, it is debited.
When an account is credited, its credit state increases.
When an account is debited, its credit state decreases.
When an account's credit state increases, it must have been credited.
When an account's credit state decreases, it must have been debited.
The above statements are always true and there is no exceptions. Table 1 shows the comparison in details.
In chemistry, magnesium sulfide is formed by the reaction of sulfur (S) with magnesium (Mg) where magnesium (Mg) transfers two electrons to sulfur (S).
Conceptually, the reaction happens like: charge of all accounts. Therefore, the total cashletic charge of all accounts involved should be the same before and after each transaction. For current example, the total charge of Equipment and Cash account is 10,000− before transaction. After transaction, the total charge of the two accounts is still 10,000−. Only the distribution of cashlets among accounts is changed.

Expression of Accounting Transactions Using Graph Theory
To visualize how cashlets move between accounts during transactions, I introduce graph theory to accounting. In computer sciences, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects [4]. Objects are termed as nodes that are usually expressed by circles or ellipses in graphs, while relations are termed edges that are normally lines or arrows connecting two nodes. Accounting transactions can be easily expressed using graph theory. Accounts are nodes, while transactions are edges.
An edge always goes from one node to another denoting that cashlets moves from one account to another.
Let's look at an example. A new business gets investment of $10,000 in cash by issuing common stocks (Event I). First, we identify two accounts (Common Stock and Cash) that are involved. They have zero balance at the beginning ( Figure 1(a)). In second step, Common Stock account breaks down zero to +$10,000 and −$10,000 the sum of which is zero (Figure 1(b)). In the third step, cashlets (with a charge of −$10,000) move out of Common Stock account Figure 1(c)). Finally, Cash account receives the cashlets of −$10,000. Transaction is done (Figure 1(d)). For convenience of expression, we compress everything into one graph like Figure 1(e). The graph has the following properties: 1) At the beginning of time, each account (node) has zero balance.
2) For each transaction (edge), cashlets move from one account (node) to another account (node).
3) The account (node) that gives cashlets is credited, while the account (node) that receives cashlets is debited.
4) The credited amount is always denoted as positive, while the debited amount always negative. credit is also simplified: debit is nothing but a minus, while credit a plus.

Accounts
In cashlet theory, debit always decreases the credit state of accounts while credit always increases the credit state of accounts, no matter what types of accounts they are. However, business users may not be interested in credit state. Instead they are more interested in the absolute value of accounts. Therefore, we need to translate language of cashlet theory back to normal business language.
In cashlet theory, accounts can be categorized to three types: positive ac-

The Accounting Information System
An accounting information system (AIS) is a system that a business uses to collect, store, manage, process, retrieve and report its financial data so that it can be used by internal and external users. Nowadays computers are involved from data collecting to final reporting in modern business. However, the classic concepts of debit and credit complicate data processing for computers. In cashlet theory, debit always means minus while credit always means plus, and the relationship between any accounts is always "AND", which makes it easy for computers to process data.
For data collection in classic accounting, transactions are initially recorded in chronological order in journals before they are posted to ledgers. For each transaction, the journal shows debit and credit effects on specific accounts.
Therefore debit and credit are recorded in two separate columns. In cashlet theory, transactions are initially recorded in chronological order in a table that is then directly used as a source for any further data processing. Debit and credit are combined to one column called amount. Debit is always labeled as minus

Case Study
On January 2 nd , 2017, Stockholders invest $10,000 cash in a brand new company to be known as Laurens Corporation. On January 3 rd , the company borrows cash of $5000 by signing a 3-month, 12%, $5000 note payable. On January 4 th , the company uses $1000 cash to purchase equipment. On January 5 th , the company purchase $2000 inventory using cash, and buys another $1000 inventory on credit. On January 15 th , the company makes a sale of $3000 on credit. On January 25 th , it makes another sales of $5000 on credit. On January 27 th , the company pays $900 in cash for office rental. On January 30 th , the company receives $3000 cash for the sale of January 15 th . On the same day, it pays $4000 cash for employee salary, and it also finds out that the inventory is reduced by $2500. On the last of January, the company pays the $1000 to its vendor for the inventory purchased on January 4 th , and it also accrues $50 interest expense for notes payable.
All events are listed in Table 2.
Let's do a graphic analysis, an equation analysis and a debit-credit analysis before journalizing each transaction. The purpose of transaction analyses is first to identify the accounts and the types of accounts involved, and then to determine which account is debited and which is credited. The analysis of each transaction is illustrated in Figure 4.
We can visualize all transaction in one graph like Figure 5.
The journalized entries are showed in Table 3.
Using Pivot Table, we can easily calculate account balance for each account (Table 4).
We can also calculate the balance for each account category using Pivot Table   (Table 5).
From We can also prepare the Income Statement based on the above two Pivot Tables (Table 6).
Retain Earning = Net Income + Dividend. Since no Dividend was paid in January, Retain Earning is Net Income. We can prepare the balance sheet based on the above information (Table 7).

Discussion
In this work, I introduce two novel concepts-cashlet and credit state-to accounting enlightened by chemistry, and discover that the nature of accounting is a process of moving cashlets and recombination of accounts. I visualize accounting transactions using graphs, and simplify the concepts of debit and cre-        negative number (e.g. −$10,000) when it actually receives cash. This is because people do not differentiate cash from cashlet. Cash is real money, while cashlet is an accounting unit. In daily life, people use positive numbers to denote amount of cash, for examples "I owe you $10" or "I get $10". However, cashlet is only used in accounting, and it is always negatively charged, which agrees the concept that "money is root of all evil (negative)". When stakeholders invest $10,000 cash into a business, in real world the stakeholders give the real cash to the business owner. However in accounting, a Stakeholders' Equity account gives cashlets (not cash) to Cash account. Because cashlets are always negatively charged, the cash account gets a negative number whenever it receives cashlets. Remember any accounts can only give or receive cashlet(s) but not cash in accounting.
Most of accounting books use descriptive approach of natural language to present the double entry bookkeeping system, which works well for more than five centuries. But the approach requires significant human efforts to understand very basic concepts such as debit and credit, and it is not friendly to computers that operate with signed numbers illiterate of human concepts of debit or credit.
Mathematicians have noted that abstract algebra can be used to study double  gebraic Models for Accounting [5]. Instead of defining the required double entry accounting rules using descriptive approach, the authors took an abstract algebraic approach by defining a number of axioms that are used to structure down the whole accounting system including transactions and balances [5]. The authors put a lot of theory into accounting, which makes the discipline rigorous rather than descriptive as it used to be. Lots of axioms and abstract algebra concepts-such as balance vector, digraph, monoid, homomorphism, quotient group structure and so on-are introduced to accounting, which is good for mathematicians to further study the accounting systems, but may not be beneficial for accountants who have little knowledge of abstract algebra. The book used "−" sign to denote Debit and "+" sign to denote Credit, which is the same with this study. But the reasons why these signs are introduced are from very different perspectives: one from mathematics and the other from chemistry. The authors also used graphs where accounts are vertices and edges are transactions, which is similar to this study. However, the concept of cashlet or its equivalence was not introduced. And the purposes of using graphs of the two studies are different: By introducing cashlet, cashlet movement and graph theory, the cashlet theory provides full theoretical support for current practices of using signed numbers in accounting software. This theory is also easy for people including both accountants and computer scientists to understand. If it is widely accepted, the sign usage can be standardized, which will cause less confusing for all people. The graphs used in this theory may be helpful for accounting application development, because graph theory is a sound theory to be implemented in software development.
Cashlet theory can not only be applied to monetary accounting, but also to non-monetary accounting. With the emerging of new technologies and new forms of economic activities, this theory will be very useful. For example, the new economic form of Time Banking-the exchange of services using timebased currency-is not of a monetary system [12]. Using cashlet theory, the accounting for this new economic form become easier. The entity that provides services should be credited, while the one who receives services should be debited. Each of the transactions move cashlets from provider to receiver for cashletic accounting's point of view. In a broader sense, cashlet theory can be applied to any type of economic transactions that are quantifiable, not limiting to monetary transactions, which may be very helpful in economic research as well.

Conclusion
This article proposes a scientific theory for accounting: It first introduces a novel concept of cashlet-a basic accounting unit with negative charge-that is equivalent to electron in chemistry. It then deduces that an accounting transaction is a process of moving cashlets from one account to another, and that the total cashletic charges of all involved accounts should remain unchanged before and after transactions. The account that gives cashlets is credited, while the account that takes cashlets is debited. In this theory, credit always means positive or plus (+), while debit always means negative or minus (−). The article concludes that the nature of accounting is a process of moving cashlets between accounts which is known as debit-credit transactions, and a process of recombining accounts T.-K. Liu which are known as reconciliation in accounting. This article also helps people better understand the world in that accounting transactions and chemical reactions are the same in nature, and in that when you give you get credits when you take you get debits.