RMS
Richard Matthew Stallman (born March 16, 1953), commonly known by his initials RMS, is an American software developer and free software activist who launched the GNU Project in 1983 to create a Unix-compatible operating system composed entirely of free software, thereby founding a movement emphasizing users' freedoms to run, study, modify, and redistribute programs.[1][2] In 1985, Stallman established the Free Software Foundation (FSF) as a nonprofit to promote and fund free software development, serving as its president until 2019 and authoring the GNU General Public License (GPL), a copyleft license that mandates derivative works remain free.[2][1] He is the principal architect of influential GNU tools, including the Emacs text editor and the GNU Compiler Collection (GCC), which underpin much of modern computing infrastructure.[3] Stallman's early career at the MIT Artificial Intelligence Laboratory from 1971 to 1984 exposed him to a collaborative hacker culture that he later sought to preserve against proprietary software restrictions, leading to his rejection of non-free software as ethically incompatible with software freedom.[4] His philosophical writings, such as the GNU Manifesto, articulate a moral framework prioritizing freedom over mere practicality, influencing global licensing practices and debates on intellectual property in code.[1] Stallman received the 1999 MacArthur Fellowship for his contributions to computing ethics and continues advocating against software patents, digital restrictions management, and non-free drivers in operating systems.[4] Stallman has faced significant controversies, particularly regarding his personal views on topics like sexual consent and age-of-consent laws, which he has publicly argued should be lowered or abolished based on individual maturity rather than fixed ages, drawing accusations of promoting pedophilia from critics.[5] In 2019, he resigned from MIT after email comments questioning allegations against AI pioneer Marvin Minsky in the Jeffrey Epstein case, where Stallman suggested the accuser's participation was voluntary and challenged the terminology of "sexual assault" without coercion; these remarks, amplified by media outlets, prompted widespread backlash despite Stallman's defense that they aimed at precise language rather than exoneration.[6][7][8] He also stepped down from FSF leadership amid related pressure but rejoined its board in 2021 following community votes and his rebuttals emphasizing no evidence of personal misconduct.[9][10] These events highlight tensions between Stallman's unyielding commitment to logical precision and evolving social norms, with coverage often reflecting institutional biases toward conformity over substantive debate.[11]Science and mathematics
Root mean square
In mathematics and statistics, the root mean square (RMS), also termed the quadratic mean, quantifies the magnitude of a varying quantity by taking the square root of the arithmetic mean of the squares of its values. For a discrete set of n real numbers x_1, x_2, \dots, x_n, the RMS is given by\mathrm{RMS} = \sqrt{\frac{1}{n} \sum_{i=1}^n x_i^2}. [12] This formula arises from the need to average squared deviations without sign cancellation, emphasizing larger deviations due to the quadratic operation.[13] For continuous cases, such as a function f(t) over an interval [T_1, T_2], the RMS extends to
f_{\mathrm{RMS}} = \sqrt{\frac{1}{T_2 - T_1} \int_{T_1}^{T_2} [f(t)]^2 \, dt}, [12] or in probabilistic terms for a random variable X with probability density P(x),
\mathrm{RMS} = \sqrt{\frac{\int P(x) x^2 \, dx}{\int P(x) \, dx}} = \sqrt{\mathbb{E}[X^2]}. [12] Here, \mathbb{E}[X^2] = \mathrm{Var}(X) + (\mathbb{E}[X])^2, so the RMS equals the root-mean-square deviation when the mean is zero, linking it directly to variance as a measure of dispersion that includes the mean's contribution.[14] Key properties include the RMS being nonnegative and satisfying the quadratic mean-arithmetic mean inequality: RMS \geq arithmetic mean, with equality holding if and only if all values are identical.[12] As the power mean for exponent p=2, it generalizes other means and exceeds the arithmetic mean for non-constant sets, reflecting greater sensitivity to outliers.[12] In vector spaces, the RMS scales the Euclidean norm, serving as a foundational metric in functional analysis for L^2 spaces, where it defines inner product-induced magnitudes for signals or data sequences.[12] The concept traces to 19th-century developments in least squares and moments, formalized in statistical texts by the mid-20th century for broader analytical use.[12]