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🔗 Mathematics

In knot theory, Conway notation, invented by John Horton Conway, is a way of describing knots that makes many of their properties clear. It composes a knot using certain operations on tangles to construct it.

🔗 Mathematics

Hilbert's twenty-fourth problem is a mathematical problem that was not published as part of the list of 23 problems known as Hilbert's problems but was included in David Hilbert's original notes. The problem asks for a criterion of simplicity in mathematical proofs and the development of a proof theory with the power to prove that a given proof is the simplest possible.

The 24th problem was rediscovered by German historian Rüdiger Thiele in 2000, noting that Hilbert did not include the 24th problem in the lecture presenting Hilbert's problems or any published texts. Hilbert's friends and fellow mathematicians Adolf Hurwitz and Hermann Minkowski were closely involved in the project but did not have any knowledge of this problem.

This is the full text from Hilbert's notes given in Rüdiger Thiele's paper. The section was translated by Rüdiger Thiele.

The 24th problem in my Paris lecture was to be: Criteria of simplicity, or proof of the greatest simplicity of certain proofs. Develop a theory of the method of proof in mathematics in general. Under a given set of conditions there can be but one simplest proof. Quite generally, if there are two proofs for a theorem, you must keep going until you have derived each from the other, or until it becomes quite evident what variant conditions (and aids) have been used in the two proofs. Given two routes, it is not right to take either of these two or to look for a third; it is necessary to investigate the area lying between the two routes. Attempts at judging the simplicity of a proof are in my examination of syzygies and syzygies [Hilbert misspelled the word syzygies] between syzygies (see Hilbert 42, lectures XXXII–XXXIX). The use or the knowledge of a syzygy simplifies in an essential way a proof that a certain identity is true. Because any process of addition [is] an application of the commutative law of addition etc. [and because] this always corresponds to geometric theorems or logical conclusions, one can count these [processes], and, for instance, in proving certain theorems of elementary geometry (the Pythagoras theorem, [theorems] on remarkable points of triangles), one can very well decide which of the proofs is the simplest. [Author's note: Part of the last sentence is not only barely legible in Hilbert's notebook but also grammatically incorrect. Corrections and insertions that Hilbert made in this entry show that he wrote down the problem in haste.]

🔗 Philosophy 🔗 Skepticism 🔗 Philosophy/Logic 🔗 Psychology

Magical thinking is a term used in anthropology, philosophy and psychology, denoting the causal relationships between thoughts, actions and events. There are subtle differences in meaning between individual theorists as well as amongst fields of study.

In anthropology, it denotes the attribution of causality between entities grouped with one another (coincidence) or similar to one another.

In psychology, the entities between which a causal relation has to be posited are more strictly delineated; here it denotes the belief that one's thoughts by themselves can bring about effects in the world or that thinking something corresponds with doing it. In both cases, the belief can cause a person to experience fear, seemingly not rationally justifiable to an observer outside the belief system, of performing certain acts or having certain thoughts because of an assumed correlation between doing so and threatening calamities.

In psychiatry, magical thinking is a disorder of thought content; here it denotes the false belief that one's thoughts, actions, or words will cause or prevent a specific consequence in some way that defies commonly understood laws of causality.

🔗 Biography 🔗 Bangladesh 🔗 Architecture 🔗 Skyscrapers 🔗 Civil engineering 🔗 Chicago 🔗 Illinois

Fazlur Rahman Khan (Bengali: ফজলুর রহমান খান, Fozlur Rôhman Khan) (3 April 1929 – 27 March 1982) was a Bangladeshi-American structural engineer and architect, who initiated important structural systems for skyscrapers. Considered the "father of tubular designs" for high-rises, Khan was also a pioneer in computer-aided design (CAD). He was the structural engineer of the Sears Tower working with Architect Bruce Graham, since renamed Willis Tower, the tallest building in the world from 1973 until 1998, and the 100-story John Hancock Center.

Khan, more than any other individual, ushered in a renaissance in skyscraper construction during the second half of the 20th century. He has been called the "Einstein of structural engineering" and the "Greatest Structural Engineer of the 20th Century" for his innovative use of structural systems that remain fundamental to modern skyscraper design and construction. In his honor, the Council on Tall Buildings and Urban Habitat established the Fazlur Khan Lifetime Achievement Medal, as one of their CTBUH Skyscraper Awards.

Although best known for skyscrapers, Khan was also an active designer of other kinds of structures, including the Hajj airport terminal, the McMath–Pierce solar telescope, and several stadium structures.

🔗 Internet 🔗 Computing

This is a list of Hypertext Transfer Protocol (HTTP) response status codes. Status codes are issued by a server in response to a client's request made to the server. It includes codes from IETF Request for Comments (RFCs), other specifications, and some additional codes used in some common applications of the HTTP. The first digit of the status code specifies one of five standard classes of responses. The message phrases shown are typical, but any human-readable alternative may be provided. Unless otherwise stated, the status code is part of the HTTP/1.1 standard (RFC 7231).

The Internet Assigned Numbers Authority (IANA) maintains the official registry of HTTP status codes.

All HTTP response status codes are separated into five classes or categories. The first digit of the status code defines the class of response, while the last two digits do not have any classifying or categorization role. There are five classes defined by the standard:

• 1xx informational response – the request was received, continuing process
• 2xx successful – the request was successfully received, understood, and accepted
• 3xx redirection – further action needs to be taken in order to complete the request
• 4xx client error – the request contains bad syntax or cannot be fulfilled
• 5xx server error – the server failed to fulfil an apparently valid request

🔗 United States 🔗 Law 🔗 Freedom of speech 🔗 United States/Massachusetts - Boston

"Banned in Boston" was a phrase employed from the late 19th century through the mid-20th century, to describe a literary work, song, motion picture, or play which had been prohibited from distribution or exhibition in Boston, Massachusetts. During this period, Boston officials had wide authority to ban works featuring "objectionable" content, and often banned works with sexual content or foul language. This even extended to the $5 bill from the 1896 "Educational" series of banknotes featuring allegorical figures which were partially nude.

🔗 United States 🔗 Finance & Investment

The Onion Futures Act is a United States law banning the trading of futures contracts on onions as well as "motion picture box office receipts".

In 1955, two onion traders, Sam Siegel and Vincent Kosuga, cornered the onion futures market on the Chicago Mercantile Exchange. The resulting regulatory actions led to the passing of the act on August 28, 1958. As of January 2020, it remains in effect.

🔗 Military history 🔗 Military history/North American military history 🔗 Military history/United States military history 🔗 Military history/Military science, technology, and theory 🔗 Military history/Weaponry 🔗 Physics

The hafnium controversy is a debate over the possibility of 'triggering' rapid energy releases, via gamma ray emission, from a nuclear isomer of hafnium, ^178m2Hf. The energy release is potentially 5 orders of magnitude (100,000 times) more energetic than a chemical reaction, but 2 orders of magnitude less than a nuclear fission reaction. In 1998, a group led by Carl Collins of the University of Texas at Dallas reported having successfully initiated such a trigger. Signal-to-noise ratios were small in those first experiments, and to date no other group has been able to duplicate these results. Peter Zimmerman described claims of weaponization potential as having been based on "very bad science".

🔗 Typography

Irony punctuation is any proposed form of notation used to denote irony or sarcasm in text. Written English lacks a standard way to mark irony, and several forms of punctuation have been proposed. Among the oldest and most frequently attested is the percontation point proposed by English printer Henry Denham in the 1580s, and the irony mark, used by Marcellin Jobard and French poet Alcanter de Brahm during the 19th century. Both marks take the form of a reversed question mark, "⸮".

Irony punctuation is primarily used to indicate that a sentence should be understood at a second level. A bracketed exclamation point or question mark as well as scare quotes are also occasionally used to express irony or sarcasm.

🔗 Alternative Views

The God helmet is an experimental apparatus originally called the Koren helmet (or Koren octopus) after its inventor Stanley Koren. It was developed by Koren and neuroscientist Michael Persinger to study creativity, religious experience and the effects of subtle stimulation of the temporal lobes. Reports by participants of a "sensed presence" while wearing the God helmet brought public attention and resulted in several TV documentaries. The device has been used in Persinger's research in the field of neurotheology, the study of the purported neural correlations of religion and spirituality. The apparatus, placed on the head of an experimental subject, generates very weak magnetic fields, that Persinger refers to as "complex". Like other neural stimulation with low-intensity magnetic fields, these fields are approximately as strong as those generated by a land line telephone handset or an ordinary hair dryer, but far weaker than that of an ordinary refrigerator magnet and approximately a million times weaker than transcranial magnetic stimulation.

Persinger reports that many subjects have reported "mystical experiences and altered states" while wearing the God Helmet. The foundations of his theory have been criticized in the scientific press. Anecdotal reports by journalists, academics and documentarists have been mixed and several effects reported by Persinger have not yet been independently replicated. One attempt at replication published in the scientific literature reported a failure to reproduce Persinger's effects and the authors proposed that the suggestibility of participants, improper blinding of participants or idiosyncratic methodology could explain Persinger's results. Persinger argues that the replication was technically flawed, but the researchers have stood by their replication. Only one group has published a direct replication of one God Helmet experiment. Other groups have reported no effects at all or have generated similar experiences by using sham helmets, or helmets that are not turned on, and have concluded that personality differences in the participants explain these unusual experiences.