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🔗 Music theory 🔗 Tunings, Temperaments, and Scales

In music theory, the circle of fifths (or circle of fourths) is the relationship among the 12 tones of the chromatic scale, their corresponding key signatures, and the associated major and minor keys. More specifically, it is a geometrical representation of relationships among the 12 pitch classes of the chromatic scale in pitch class space.

🔗 Computer science

In computer science, Linda is a model of coordination and communication among several parallel processes operating upon objects stored in and retrieved from shared, virtual, associative memory. It was developed by Sudhir Ahuja at AT&T Bell Laboratories in collaboration with David Gelernter and Nicholas Carriero at Yale University in 1986.

🔗 Biography 🔗 Mathematics 🔗 Statistics 🔗 Systems 🔗 Biography/science and academia 🔗 Systems/Visualization 🔗 Graphic design

Edward Rolf Tufte (; born March 14, 1942) is an American statistician and professor emeritus of political science, statistics, and computer science at Yale University. He is noted for his writings on information design and as a pioneer in the field of data visualization.

🔗 Biography 🔗 California 🔗 California/San Francisco Bay Area 🔗 Finance & Investment 🔗 Business

Ronald Crawford Conway (born March 9, 1951) is an American angel investor and philanthropist, often described as one of Silicon Valley's "super angels". Conway is recognized as a strong networker.

🔗 Astronomy 🔗 Time 🔗 Holidays 🔗 Festivals

The winter solstice, hiemal solstice or hibernal solstice, also known as midwinter, occurs when one of the Earth's poles has its maximum tilt away from the Sun. It happens twice yearly, once in each hemisphere (Northern and Southern). For that hemisphere, the winter solstice is the day with the shortest period of daylight and longest night of the year, when the Sun is at its lowest daily maximum elevation in the sky. At the pole, there is continuous darkness or twilight around the winter solstice. Its opposite is the summer solstice.

The winter solstice occurs during the hemisphere's winter. In the Northern Hemisphere, this is the December solstice (usually 21 or 22 December) and in the Southern Hemisphere, this is the June solstice (usually 20 or 21 June). Although the winter solstice itself lasts only a moment, the term sometimes refers to the day on which it occurs. Other names are "midwinter", the "extreme of winter" (Dongzhi), or the "shortest day". Traditionally, in many temperate regions, the winter solstice is seen as the middle of winter, but today in some countries and calendars, it is seen as the beginning of winter. In meteorology, winter is reckoned as beginning about three weeks before the winter solstice.

Since prehistory, the winter solstice has been seen as a significant time of year in many cultures, and has been marked by festivals and rituals. It marked the symbolic death and rebirth of the Sun. The seasonal significance of the winter solstice is in the reversal of the gradual lengthening of nights and shortening of days.

🔗 Spaceflight 🔗 China

PAS-22, previously known as AsiaSat 3 and then HGS-1, was a geosynchronous communications satellite, which was salvaged from an unusable geosynchronous transfer orbit by means of the Moon's gravity.

🔗 Mathematics 🔗 Physics

Shor's algorithm is a polynomial-time quantum computer algorithm for integer factorization. Informally, it solves the following problem: Given an integer ${\displaystyle N}$, find its prime factors. It was invented in 1994 by the American mathematician Peter Shor.

On a quantum computer, to factor an integer ${\displaystyle N}$, Shor's algorithm runs in polynomial time (the time taken is polynomial in ${\displaystyle \log N}$, the size of the integer given as input). Specifically, it takes quantum gates of order ${\displaystyle O\!\left((\log N)^{2}(\log \log N)(\log \log \log N)\right)}$ using fast multiplication, thus demonstrating that the integer-factorization problem can be efficiently solved on a quantum computer and is consequently in the complexity class BQP. This is almost exponentially faster than the most efficient known classical factoring algorithm, the general number field sieve, which works in sub-exponential time — ${\displaystyle O\!\left(e^{1.9(\log N)^{1/3}(\log \log N)^{2/3}}\right)}$. The efficiency of Shor's algorithm is due to the efficiency of the quantum Fourier transform, and modular exponentiation by repeated squarings.

If a quantum computer with a sufficient number of qubits could operate without succumbing to quantum noise and other quantum-decoherence phenomena, then Shor's algorithm could be used to break public-key cryptography schemes, such as the widely used RSA scheme. RSA is based on the assumption that factoring large integers is computationally intractable. As far as is known, this assumption is valid for classical (non-quantum) computers; no classical algorithm is known that can factor integers in polynomial time. However, Shor's algorithm shows that factoring integers is efficient on an ideal quantum computer, so it may be feasible to defeat RSA by constructing a large quantum computer. It was also a powerful motivator for the design and construction of quantum computers, and for the study of new quantum-computer algorithms. It has also facilitated research on new cryptosystems that are secure from quantum computers, collectively called post-quantum cryptography.

In 2001, Shor's algorithm was demonstrated by a group at IBM, who factored ${\displaystyle 15}$ into ${\displaystyle 3\times 5}$, using an NMR implementation of a quantum computer with ${\displaystyle 7}$ qubits. After IBM's implementation, two independent groups implemented Shor's algorithm using photonic qubits, emphasizing that multi-qubit entanglement was observed when running the Shor's algorithm circuits. In 2012, the factorization of ${\displaystyle 15}$ was performed with solid-state qubits. Also, in 2012, the factorization of ${\displaystyle 21}$ was achieved, setting the record for the largest integer factored with Shor's algorithm.

🔗 Philosophy 🔗 Philosophy/Ancient philosophy 🔗 Philosophy/Ethics

The Tetrapharmakos (τετραφάρμακος) "four-part remedy" is a summary of the first four of the Κύριαι Δόξαι (Kuriai Doxai, the forty Epicurean Principal Doctrines given by Diogenes Laërtius in his Life of Epicurus) in Epicureanism, a recipe for leading the happiest possible life. They are recommendations to avoid anxiety or existential dread.

The "tetrapharmakos" was originally a compound of four drugs (wax, tallow, pitch and resin); the word has been used metaphorically by Roman-era Epicureans. to refer to the four remedies for healing the soul.

🔗 Discworld

The technology depicted in Terry Pratchett's Discworld novels takes two forms: magical and mechanical. Nearly all technology early in the series is at least partially magical, but in more recent books, a form of industrial revolution takes place, with numerous purely mechanical inventions being introduced. In Thud! ancient 'devices' of undisclosed origin and great power were introduced; it is not clear whether these are magical, mechanical, both or neither. Time-travel technology, the exact nature of which is usually unclear, is used by the History Monks. Most Discworld technologies have real-world equivalents, in function if not form.