Bernoulli numberIn mathematics, the Bernoulli numbers Bn are a sequence of rational numbers which occur frequently in analysis. The Bernoulli numbers appear in (and can be defined by) the Taylor series expansions of the tangent and hyperbolic tangent functions, in Faulhaber's formula for the sum of m-th powers of the first n positive integers, in the Euler–Maclaurin formula, and in expressions for certain values of the Riemann zeta function. The values of the first 20 Bernoulli numbers are given in the adjacent table.
History of computing hardwareThe history of computing hardware covers the developments from early simple devices to aid calculation to modern day computers. The first aids to computation were purely mechanical devices which required the operator to set up the initial values of an elementary arithmetic operation, then manipulate the device to obtain the result. Later, computers represented numbers in a continuous form (e.g. distance along a scale, rotation of a shaft, or a voltage). Numbers could also be represented in the form of digits, automatically manipulated by a mechanism.
Lord ByronGeorge Gordon Byron, 6th Baron Byron (22 January 1788 – 19 April 1824) was an English romantic poet and peer. He was one of the leading figures of the Romantic movement, and has been regarded as among the greatest of English poets. Among his best-known works are the lengthy narratives Don Juan and ; many of his shorter lyrics in Hebrew Melodies also became popular. Lord Byron was educated at Trinity College, Cambridge, later travelling extensively across Europe to places such as Italy, where he lived for seven years in Venice, Ravenna, and Pisa after he was forced to flee England due to lynching threats.
Artificial intelligenceArtificial intelligence (AI) is the intelligence of machines or software, as opposed to the intelligence of human beings or animals. AI applications include advanced web search engines (e.g., Google Search), recommendation systems (used by YouTube, Amazon, and Netflix), understanding human speech (such as Siri and Alexa), self-driving cars (e.g., Waymo), generative or creative tools (ChatGPT and AI art), and competing at the highest level in strategic games (such as chess and Go).
SteampunkSteampunk is a subgenre of science fiction that incorporates retrofuturistic technology and aesthetics inspired by 19th-century industrial steam-powered machinery. Steampunk works are often set in an alternative history of the Victorian era or the American "Wild West", where steam power remains in mainstream use, or in a fantasy world that similarly employs steam power. Steampunk features anachronistic technologies or retrofuturistic inventions as people in the 19th century might have envisioned them — distinguishing it from Neo-Victorianism — and is likewise rooted in the era's perspective on fashion, culture, architectural style, and art.
ConsciousnessConsciousness, at its simplest, is awareness of internal and external existence. However, its nature has led to millennia of analyses, explanations and debates by philosophers, theologians, linguists, and scientists. Opinions differ about what exactly needs to be studied or even considered consciousness. In some explanations, it is synonymous with the mind, and at other times, an aspect of mind. In the past, it was one's "inner life", the world of introspection, of private thought, imagination and volition.
Difference engineA difference engine is an automatic mechanical calculator designed to tabulate polynomial functions. It was designed in the 1820s, and was first created by Charles Babbage. The name, the difference engine, is derived from the method of divided differences, a way to interpolate or tabulate functions by using a small set of polynomial co-efficients. Some of the most common mathematical functions used in engineering, science and navigation, are built from logarithmic and trigonometric functions, which can be approximated by polynomials, so a difference engine can compute many useful tables.
