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Graham's number is an immense number that arises as an upper bound on the answer of a problem in the mathematical field of Ramsey theory. It is named after mathematician Ronald Graham, who used the number in conversations with popular science writer Martin Gardner as a simplified explanation of the upper bounds of the problem he was working on. In 1977, Gardner described the number in Scientific American, introducing it to the general public. At the time of its introduction, it was the largest specific positive integer ever to have been used in a published mathematical proof. The number was published in the 1980 Guinness Book of World Records, adding to its popular interest. Other specific integers (such as TREE(3)) known to be far larger than Graham's number have since appeared in many serious mathematical proofs, for example in connection with Harvey Friedman's various finite forms of Kruskal's theorem. Additionally, smaller upper bounds on the Ramsey theory problem from which Graham's number derived have since been proven to be valid.

Graham's number is much larger than many other large numbers such as Skewes' number and Moser's number, both of which are in turn much larger than a googolplex. As with these, it is so large that the observable universe is far too small to contain an ordinary digital representation of Graham's number, assuming that each digit occupies one Planck volume, possibly the smallest measurable space. But even the number of digits in this digital representation of Graham's number would itself be a number so large that its digital representation cannot be represented in the observable universe. Nor even can the number of digits of that number—and so forth, for a number of times far exceeding the total number of Planck volumes in the observable universe. Thus Graham's number cannot be expressed even by power towers of the form ${\displaystyle a^{b^{c^{\cdot ^{\cdot ^{\cdot }}}}}}$.

However, Graham's number can be explicitly given by computable recursive formulas using Knuth's up-arrow notation or equivalent, as was done by Graham. As there is a recursive formula to define it, it is much smaller than typical busy beaver numbers. Though too large to be computed in full, the sequence of digits of Graham's number can be computed explicitly through simple algorithms. The last 12 digits are ...262464195387. With Knuth's up-arrow notation, Graham's number is ${\displaystyle g_{64}}$, where

Reverse mathematics is a program in mathematical logic that seeks to determine which axioms are required to prove theorems of mathematics. Its defining method can briefly be described as "going backwards from the theorems to the axioms", in contrast to the ordinary mathematical practice of deriving theorems from axioms. It can be conceptualized as sculpting out necessary conditions from sufficient ones.

The reverse mathematics program was foreshadowed by results in set theory such as the classical theorem that the axiom of choice and Zorn's lemma are equivalent over ZF set theory. The goal of reverse mathematics, however, is to study possible axioms of ordinary theorems of mathematics rather than possible axioms for set theory.

Reverse mathematics is usually carried out using subsystems of second-order arithmetic, where many of its definitions and methods are inspired by previous work in constructive analysis and proof theory. The use of second-order arithmetic also allows many techniques from recursion theory to be employed; many results in reverse mathematics have corresponding results in computable analysis. Recently, higher-order reverse mathematics has been introduced, in which the focus is on subsystems of higher-order arithmetic, and the associated richer language.

The program was founded by Harvey Friedman (1975, 1976) and brought forward by Steve Simpson. A standard reference for the subject is (Simpson 2009), while an introduction for non-specialists is (Stillwell 2018). An introduction to higher-order reverse mathematics, and also the founding paper, is (Kohlenbach (2005)).

Project Orion was a study of a spacecraft intended to be directly propelled by a series of explosions of atomic bombs behind the craft (nuclear pulse propulsion). Early versions of this vehicle were proposed to take off from the ground (with significant associated nuclear fallout); later versions were presented for use only in space. Six non-nuclear tests were conducted using models. The project was eventually abandoned for multiple reasons such as the Partial Test Ban Treaty which banned nuclear explosions in space as well as concerns over nuclear fallout.

The idea of rocket propulsion by combustion of explosive substance was first proposed by Russian explosives expert Nikolai Kibalchich in 1881, and in 1891 similar ideas were developed independently by German engineer Hermann Ganswindt. Robert A. Heinlein mentions powering spaceships with nuclear bombs in his 1940 short story "Blowups Happen." Real life proposals of nuclear propulsion were first made by Stanislaw Ulam in 1946, and preliminary calculations were made by F. Reines and Ulam in a Los Alamos memorandum dated 1947. The actual project, initiated in 1958, was led by Ted Taylor at General Atomics and physicist Freeman Dyson, who at Taylor's request took a year away from the Institute for Advanced Study in Princeton to work on the project.

The Orion concept offered high thrust and high specific impulse, or propellant efficiency, at the same time. The unprecedented extreme power requirements for doing so would be met by nuclear explosions, of such power relative to the vehicle's mass as to be survived only by using external detonations without attempting to contain them in internal structures. As a qualitative comparison, traditional chemical rockets—such as the Saturn V that took the Apollo program to the Moon—produce high thrust with low specific impulse, whereas electric ion engines produce a small amount of thrust very efficiently. Orion would have offered performance greater than the most advanced conventional or nuclear rocket engines then under consideration. Supporters of Project Orion felt that it had potential for cheap interplanetary travel, but it lost political approval over concerns with fallout from its propulsion.

The Partial Test Ban Treaty of 1963 is generally acknowledged to have ended the project. However, from Project Longshot to Project Daedalus, Mini-Mag Orion, and other proposals which reach engineering analysis at the level of considering thermal power dissipation, the principle of external nuclear pulse propulsion to maximize survivable power has remained common among serious concepts for interstellar flight without external power beaming and for very high-performance interplanetary flight. Such later proposals have tended to modify the basic principle by envisioning equipment driving detonation of much smaller fission or fusion pellets, in contrast to Project Orion's larger nuclear pulse units (full nuclear bombs) based on less speculative technology.

To Mars by A-Bomb: The Secret History of Project Orion was a 2003 BBC documentary film about the project.

The Nebra sky disk is a bronze disk of around 30 centimeters (11 ³⁄₄ in) diameter and a weight of 2.2 kilograms (4.9 lb), having a blue-green patina and inlaid with gold symbols. These symbols are interpreted generally as the Sun or full moon, a lunar crescent, and stars (including a cluster of seven interpreted as the Pleiades). Two golden arcs along the sides, interpreted to mark the angle between the solstices, were added later. A final addition was another arc at the bottom surrounded with multiple strokes (of uncertain meaning, variously interpreted as a Solar Barge with numerous oars, the Milky Way, or a rainbow).

The disk is attributed to a site in present-day Germany near Nebra, Saxony-Anhalt, and dated by Archaeological association to c. 1600 BC. Researchers suggest the disk is an artifact of the Bronze Age Unetice culture.

The style in which the disk is executed was unlike any artistic style then known from the period, with the result that the object was initially suspected of being a forgery, but is now widely accepted as authentic.

The Nebra sky disk features the oldest concrete depiction of the cosmos yet known from anywhere in the world. In June 2013 it was included in the UNESCO Memory of the World Register and termed "one of the most important archaeological finds of the twentieth century."

Salter's duck, also known as the nodding duck or by its official name the Edinburgh duck, is a device that converts wave power into electricity. The wave impact induces rotation of gyroscopes located inside a pear-shaped "duck", and an electrical generator converts this rotation into electricity with an overall efficiency of up to 90%. The Salter's duck was invented by Stephen Salter in response to the oil shortage in the 1970s and was one of the earliest generator designs proposed to the Wave Energy programme in the United Kingdom. The funding for the project was cut off in the early 1980s after oil prices rebounded and the UK government moved away from alternative energy sources. As of May 2018 no wave-power devices have ever gone into large-scale production.

The Expert at the Card Table, originally titled Artifice, Ruse and Subterfuge at the Card Table: A Treatise on the Science and Art of Manipulating Cards, often referred to simply as Erdnase, is an extensive book on the art of sleight of hand published in 1902 by S. W. Erdnase, a pseudonymous author whose identity has remained a mystery for over a century. As a detailed manual of card sharps, the book is considered to be one of the most influential works on magic or conjuring with cards.

The Expert at the Card Table is the most famous, the most carefully studied book ever published on the art of manipulating cards at gaming tables."

The Dolgopolsky list is a word list compiled by Aharon Dolgopolsky in 1964. It lists the 15 lexical items that have the most semantic stability, i.e. they are the 15 words least likely to be replaced by other words as a language evolves. It was based on a study of 140 languages from across Eurasia.

The words, with the first being the most stable, are:

1. I/me
2. two/pair
3. you (singular, informal)
4. who/what
5. tongue
6. name
7. eye
8. heart
9. tooth
10. no/not
11. nail (finger-nail)
12. louse/nit
13. tear/teardrop
14. water
15. dead

The first item in the list, I/me, has been replaced in none of the 140 languages during their recorded history; the fifteenth, dead, has been replaced in 25% of the languages.

The twelfth item, louse/nit, is well kept in the North Caucasian languages, Dravidian and Turkic, but not in other proto-languages.

Implicate order and explicate order are ontological concepts for quantum theory coined by theoretical physicist David Bohm during the early 1980s. They are used to describe two different frameworks for understanding the same phenomenon or aspect of reality. In particular, the concepts were developed in order to explain the bizarre behavior of subatomic particles which quantum physics struggles to explain.

In Bohm's Wholeness and the Implicate Order, he used these notions to describe how the appearance of such phenomena might appear differently, or might be characterized by, varying principal factors, depending on contexts such as scales. The implicate (also referred to as the "enfolded") order is seen as a deeper and more fundamental order of reality. In contrast, the explicate or "unfolded" order include the abstractions that humans normally perceive. As he wrote,

In the enfolded [or implicate] order, space and time are no longer the dominant factors determining the relationships of dependence or independence of different elements. Rather, an entirely different sort of basic connection of elements is possible, from which our ordinary notions of space and time, along with those of separately existent material particles, are abstracted as forms derived from the deeper order. These ordinary notions in fact appear in what is called the "explicate" or "unfolded" order, which is a special and distinguished form contained within the general totality of all the implicate orders (Bohm 1980, p. xv).

The magic SysRq key is a key combination understood by the Linux kernel, which allows the user to perform various low-level commands regardless of the system's state. It is often used to recover from freezes, or to reboot a computer without corrupting the filesystem. Its effect is similar to the computer's hardware reset button (or power switch) but with many more options and much more control.

This key combination provides access to powerful features for software development and disaster recovery. In this sense, it can be considered a form of escape sequence. Principal among the offered commands are means to forcibly unmount file systems, kill processes, recover keyboard state, and write unwritten data to disk. With respect to these tasks, this feature serves as a tool of last resort.

The magic SysRq key cannot work under certain conditions, such as a kernel panic or a hardware failure preventing the kernel from running properly.

Below is a mostly comprehensive gallery of all images — illustrations, diagrams and animations — that I have created for Wikipedia over the years, some of which have been selected as featured pictures, or even picture of the day. As you'll probably notice, they're mostly related to physics and mathematics, which are my main areas of interest.

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