George Boole, in the 1840s, proposed that variables could represent more than just numbers. Boole’s work, published in “An Investigation of the Laws of Thought” (1854), introduced algebra with two values: 1 (true) and 0 (false). Instead of traditional algebraic operations, Boolean algebra uses AND, OR, and NOT, also known as conjunction, disjunction, and complement. …
Category Archives: History
Fechner-Weber
The Fechner-Weber law states that for a sensation’s intensity to increase in an arithmetic progression, the stimulus must increase in a geometric progression. This relation describes sensory perceptions and physical stimuli for hearing. Human hearing can detect noise so quiet that the eardrum moves less than an atom’s width, and noise 10 trillion times more …
Liouville and Numbers
In 1844, Joseph Liouville demonstrated that the decimal representations of certain numbers were infinitely long and lacked pattern. This idea, which suggests that numbers do not necessarily have an exact and finite value, was first proposed by Greek philosopher Zeno in the 5th century BCE. Zeno’s paradoxes are based on the infinite divisibility of space. …
On the Computer
Down the rabbit hole on digital calculations. Computers, as programmable tools, trace their origins to the 1800s. Joseph Jacquard’s loom, which used punched cards for pattern storage, indirectly influenced the field (1800s). C. Babbage, inspired by the loom, built the Difference Engine in 1822 for mathematical calculations and later designed the Analytical Engine, the first …
Complex Polynomials
The Fundamental Theorem of Algebra states that the field of complex numbers is algebraically closed, implying that every polynomial equation of degree n has n roots within the complex numbers, with at least one being a solution where the polynomial evaluates to zero. Historically, the theorem’s origin traces back to the conjectures by Albert Girard …
Personal Equation
1796, Maskelyne, Astronomer Royal of Britain, dismissed his assistant for what he believed to be persistent inaccuracies in the timing of observations, specifically delays of approximately half a second. This decision unknowingly set the stage for the development of an important concept in measurement science: the personal equation. Maskelyne’s published their mixed observational results. After …
Origins of Graph Theory
Graph theory emerged in the 18th century, connecting geometry with fields like topology and set theory. Leonhard Euler formulated graph theory during his time in Königsberg, now Kalingrad. His seminal work began with the 1736 paper, “The Seven Bridges of Königsberg.” Residents of Königsberg enjoyed crossing the city’s seven bridges in one outing – considered …
Revisiting \(e\) History
\(e\), defined by the limit \(\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n\) and approximating 2.71828, is characterized by its irrational and transcendental nature, indicating it cannot be depicted as a quotient of two integers nor as a solution to any non-trivial polynomial equation with rational coefficients. John Napier, a Scottish mathematician and theologian, significantly contributed to …
Binary’s Origin
Binary numbers were originally used for encryption and communication, a fact recognized as early as the 17th century by Francis Bacon. Bacon used the binary system for encoding the alphabet using strings of binary characters. This laid the framework for subsequent developments in coded communication, such as technologies like the telegraph (Samuel Morse), which relied …
In Florida by Professor Hofmann
Recently, one of the distinguished professors of English at University of Florida published a perspective of being in Florida in the time of academic turmoil. I wish I had the command of the English language like Professor Hofmann to express myself. Please see:https://www.lrb.co.uk/blog/2024/april/in-florida