#DEB Double entry bookkeeping ([[Double Entry Bookkeeping|DEB]]) is a method of recording financial transactions that ensures accuracy and completeness in a company's financial records. It is based on the concept that every transaction has two aspects: a debit and a credit. For every debit entry made, there must be an equal and corresponding credit entry. Both [[Arthur Cayley]] and [[William Rowan Hamilton]] have studied or borrowed ideas in [[Double Entry Bookkeeping]], which I assert that it has significant influence to create the idea of [[Cayley-Hamilton theorem]]. The double entry system follows the accounting equation, which states that assets equal liabilities plus equity. This equation must always be in balance after each transaction is recorded. The system uses T-accounts to record these entries, with debits on the left side and credits on the right side. In double entry bookkeeping, each transaction affects at least two accounts. For example, when a company sells goods for cash, it would debit the cash account (increasing assets) and credit the sales account (increasing revenue). This ensures that both sides of the equation remain balanced. The advantages of double entry bookkeeping include: 1. Accuracy: By recording both debits and credits for each transaction, errors can be easily identified and corrected. 2. Completeness: Double entry ensures that all transactions are recorded, preventing any omission or misrepresentation of financial information. 3. Financial analysis: The system provides detailed records that can be used for analysis, such as preparing financial statements or calculating ratios. 4. Auditability: Double entry bookkeeping makes it easier for auditors to review and verify financial records. Overall, double entry bookkeeping serves as a foundational principle in modern accounting systems by providing a systematic way to record financial transactions accurately and maintain the integrity of financial information within an organization. # Arthur Cayley on DEB [[Arthur Cayley]] was a renowned mathematician in the 19th century and wrote a [[@PrinciplesBookkeepingDouble1894|booklet]] on double entry bookkeeping. However, double entry bookkeeping is a system of accounting that has been used for centuries. It was first documented by Italian mathematician [[Luca Pacioli]] in his book "Summa de Arithmetica, Geometria, Proportioni et Proportionalita" published in 1494. This book included detailed explanations of the double entry method and its benefits in recording financial transactions accurately. The connection bewteen Arthur Cayley's work on [[Double Entry Bookkeeping]] is further explained in this paper: [[@QuantumInformation|Quantum Information and Accounting Information]]. More over, it should be noted that Arthur Cayley being one of the progenitors of [[Group theory]], the following statement by [[David P. Ellerman]] is even stronger: ![[@ellermanMathematicsDoubleEntry1985#First Paragraph]] # Hamilton's Algebraic Couple and DEB [[Literature/People/William Rowan Hamilton|William Rowan Hamilton]] with a long title. It is called "[[@THEORYCONJUGATEFUNCTIONS|The Theory of Conjugate Functions|The Theory of Conjugate Functions or the Preliminary and Elementary Essay on Algebra as the Science of Pure Time]]". The later part of the title, on [[Algebra as the Science of Pure Time]], specifically talked about [[Algebraic Couples]], and therefore presented many examples to show that causally balanced data structures are crucial mechanisms to make reasoning work. David Ellerman also linked [[T-accounts]] to [[Literature/People/William Rowan Hamilton]]: ![[@ellermanMathematicsDoubleEntry1985#Mentioning Hamilton]] # Augustus De Morgan on DEB The famous logician, [[Augustus De Morgan]] also wrote a book [[@morganElementsArithmetic2022|Elements of Arithmetic]] which repeated mentioned [[Double Entry Bookkeeping]]. It would be clear in De Morgan's writing that [[arithmetic]] is inseparable from [[Logic]]. ## A Pedagogical Framing for DEB In [[GASing]] method, the way to relate physical concepts with numbers and paired or group action of pre-arithmetic students provides a process to help people become acquaint with numbers and quantities. This process is in fact richer than just [[Double Entry Bookkeeping]] but conceptually related. It also shows that [[arithmetic]] and [[Algebra|algebraic]] concepts should be taught with social and physical settings that relates to direct human experience at all temporal and spatial scales. # References ```dataview Table title as Title, authors as Authors where contains(subject, "Double Entry Bookkeeping") ```