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🔗 Psychology 🔗 Linguistics 🔗 Linguistics/Applied Linguistics 🔗 Education

Cuisenaire rods are mathematics learning aids for students that provide an interactive, hands-on way to explore mathematics and learn mathematical concepts, such as the four basic arithmetical operations, working with fractions and finding divisors. In the early 1950s, Caleb Gattegno popularised this set of coloured number rods created by the Belgian primary school teacher Georges Cuisenaire (1891–1975), who called the rods réglettes.

According to Gattegno, "Georges Cuisenaire showed in the early 1950s that students who had been taught traditionally, and were rated ‘weak’, took huge strides when they shifted to using the material. They became 'very good' at traditional arithmetic when they were allowed to manipulate the rods."

🔗 Statistics

Nelson rules are a method in process control of determining if some measured variable is out of control (unpredictable versus consistent). Rules, for detecting "out-of-control" or non-random conditions were first postulated by Walter A. Shewhart in the 1920s. The Nelson rules were first published in the October 1984 issue of the Journal of Quality Technology in an article by Lloyd S Nelson.

The rules are applied to a control chart on which the magnitude of some variable is plotted against time. The rules are based on the mean value and the standard deviation of the samples.

The above eight rules apply to a chart of a variable value.

A second chart, the moving range chart, can also be used but only with rules 1, 2, 3 and 4. Such a chart plots a graph of the maximum value - minimum value of N adjacent points against the time sample of the range.

An example moving range: if N = 3 and values are 1, 3, 5, 3, 3, 2, 4, 5 then the sets of adjacent points are (1,3,5) (3,5,3) (5,3,3) (3,3,2) (3,2,4) (2,4,5) resulting in moving range values of (5-1) (5-3) (5-3) (3-2) (4-2) (5-2) = 4, 2, 2, 1, 2, 3.

Applying these rules indicates when a potential "out of control" situation has arisen. However, there will always be some false alerts and the more rules applied the more will occur. For some processes, it may be beneficial to omit one or more rules. Equally there may be some missing alerts where some specific "out of control" situation is not detected. Empirically, the detection accuracy is good.

🔗 Industrial design

In industrial design, preferred numbers (also called preferred values or preferred series) are standard guidelines for choosing exact product dimensions within a given set of constraints. Product developers must choose numerous lengths, distances, diameters, volumes, and other characteristic quantities. While all of these choices are constrained by considerations of functionality, usability, compatibility, safety or cost, there usually remains considerable leeway in the exact choice for many dimensions.

Preferred numbers serve two purposes:

1. Using them increases the probability of compatibility between objects designed at different times by different people. In other words, it is one tactic among many in standardization, whether within a company or within an industry, and it is usually desirable in industrial contexts (unless the goal is vendor lock-in or planned obsolescence)
2. They are chosen such that when a product is manufactured in many different sizes, these will end up roughly equally spaced on a logarithmic scale. They therefore help to minimize the number of different sizes that need to be manufactured or kept in stock.

Preferred numbers represent preferences of simple numbers (such as 1, 2, and 5) multiplied by the powers of a convenient basis, usually 10.

🔗 Economics 🔗 Philosophy 🔗 Philosophy/Logic

In economics, hyperbolic discounting is a time-inconsistent model of delay discounting. It is one of the cornerstones of behavioral economics and its brain-basis is actively being studied by neuroeconomics researchers.

The discounted utility approach states that intertemporal choices are no different from other choices, except that some consequences are delayed and hence must be anticipated and discounted (i.e., reweighted to take into account the delay).

Given two similar rewards, humans show a preference for one that arrives sooner rather than later. Humans are said to discount the value of the later reward, by a factor that increases with the length of the delay. In the financial world, this process is normally modeled in the form of exponential discounting, a time-consistent model of discounting. A large number of psychological studies have since demonstrated deviations in instinctive preference from the constant discount rate assumed in exponential discounting. Hyperbolic discounting is an alternative mathematical model that agrees more closely with these findings.

According to hyperbolic discounting, valuations fall relatively rapidly for earlier delay periods (as in, from now to one week), but then fall more slowly for longer delay periods (for instance, more than a few days). For example, in an early study subjects said they would be indifferent between receiving $15 immediately or $30 after 3 months, $60 after 1 year, or $100 after 3 years. These indifferences reflect annual discount rates that declined from 277% to 139% to 63% as delays got longer. This contrasts with exponential discounting, in which valuation falls by a constant factor per unit delay and the discount rate stays the same.

The standard experiment used to reveal a test subject's hyperbolic discounting curve is to compare short-term preferences with long-term preferences. For instance: "Would you prefer a dollar today or three dollars tomorrow?" or "Would you prefer a dollar in one year or three dollars in one year and one day?" It has been claimed that a significant fraction of subjects will take the lesser amount today, but will gladly wait one extra day in a year in order to receive the higher amount instead. Individuals with such preferences are described as "present-biased".

The most important consequence of hyperbolic discounting is that it creates temporary preferences for small rewards that occur sooner over larger, later ones. Individuals using hyperbolic discounting reveal a strong tendency to make choices that are inconsistent over time – they make choices today that their future self would prefer not to have made, despite knowing the same information. This dynamic inconsistency happens because hyperbolas distort the relative value of options with a fixed difference in delays in proportion to how far the choice-maker is from those options.

🔗 Computing 🔗 Computer science

Ousterhout's dichotomy is computer scientist John Ousterhout's categorization that high-level programming languages tend to fall into two groups, each with distinct properties and uses: system programming languages and scripting languages – compare programming in the large and programming in the small. This distinction underlies the design of his language Tcl.

System programming languages (or applications languages) usually have the following properties:

• They are typed statically
• They support creating complex data structures
• Programs in them are compiled into machine code
• Programs in them are meant to operate largely independently of other programs

System programming languages tend to be used for components and applications with large amounts of internal functionality such as operating systems, database servers, and Web browsers. These applications typically employ complex algorithms and data structures and require high performance. Prototypical examples of system programming languages include C and Modula-2.

By contrast, scripting languages (or glue languages) tend to have the following properties:

• They are typed dynamically
• They have little or no provision for complex data structures
• Programs in them (scripts) are interpreted

Scripting languages tend to be used for applications where most of the functionality comes from other programs (often implemented in system programming languages); the scripts are used to glue together other programs or add additional layers of functionality on top of existing programs. Ousterhout claims that scripts tend to be short and are often written by less sophisticated programmers, so execution efficiency is less important than simplicity and ease of interaction with other programs. Common applications for scripting include Web page generation, report generation, graphical user interfaces, and system administration. Prototypical examples of scripting languages include AppleScript, C shell, DOS batch files, and Tcl.

🔗 Numbers 🔗 Linguistics 🔗 Malaysia

The long and short scales are two of several naming systems for integer powers of ten which use some of the same terms for different magnitudes.

For whole numbers smaller than 1,000,000,000 (10⁹), such as one thousand or one million, the two scales are identical. For larger numbers, starting with 10⁹, the two systems differ. For identical names, the long scale proceeds by powers of one million, whereas the short scale proceeds by powers of one thousand. For example, one billion is one thousand millions in the short scale, while it is one million millions in the long scale. The long scale system introduces new terms for the intervening values, typically replacing the word ending -ion with -iard.

🔗 Computing

OS-9 is a family of real-time, process-based, multitasking, multi-user operating systems, developed in the 1980s, originally by Microware Systems Corporation for the Motorola 6809 microprocessor. It was purchased by Radisys Corp in 2001, and was purchased again in 2013 by its current owner Microware LP.

The OS-9 family was popular for general-purpose computing and remains in use in commercial embedded systems and amongst hobbyists. Today, OS-9 is a product name used by both a Motorola 68000-series machine language OS and a portable (PowerPC, x86, ARM, MIPS, SH4, etc.) version written in C, originally known as OS-9000.

🔗 Internet 🔗 Computing 🔗 Brands 🔗 Microsoft 🔗 Home Living

The iLoo (short for Internet loo) was a cancelled Microsoft project to develop a Wi-Fi Internet-enabled portable toilet. The iLoo, which was to debut at British summer festivals, was described as being a portable toilet with wireless broadband Internet, an adjustable plasma screen, a membrane wireless keyboard, a six-channel speaker system, and toilet paper embossed with popular web site addresses. The iLoo was also to have an extra screen and keyboard on the outside, and was to be guarded. It was intended as the next in a series of successful initiatives by MSN UK which sought to introduce the internet in unusual locations, including MSN Street, MSN Park Bench and MSN Deckchair.

The project was announced by MSN UK on April 30, 2003, and was widely ridiculed before being declared a hoax by Microsoft on May 12. On May 13, another Microsoft press release stated that although the project had not been a hoax, it had been cancelled because it would do little to promote the MSN brand. There has since been speculation as to whether the project was cancelled for fear of being sued by Andrew Cubitt, who had invented the similarly named product "i-Loo". The iLoo was described as a public relations "debacle" by Online Journalism Review.

🔗 Mathematics

The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. Indeed, the reassembly process involves only moving the pieces around and rotating them without changing their shape. However, the pieces themselves are not "solids" in the usual sense, but infinite scatterings of points. The reconstruction can work with as few as five pieces.

A stronger form of the theorem implies that given any two "reasonable" solid objects (such as a small ball and a huge ball), the cut pieces of either one can be reassembled into the other. This is often stated informally as "a pea can be chopped up and reassembled into the Sun" and called the "pea and the Sun paradox".

The reason the Banach–Tarski theorem is called a paradox is that it contradicts basic geometric intuition. "Doubling the ball" by dividing it into parts and moving them around by rotations and translations, without any stretching, bending, or adding new points, seems to be impossible, since all these operations ought, intuitively speaking, to preserve the volume. The intuition that such operations preserve volumes is not mathematically absurd and it is even included in the formal definition of volumes. However, this is not applicable here because in this case it is impossible to define the volumes of the considered subsets. Reassembling them reproduces a volume, which happens to be different from the volume at the start.

Unlike most theorems in geometry, the proof of this result depends in a critical way on the choice of axioms for set theory. It can be proven using the axiom of choice, which allows for the construction of non-measurable sets, i.e., collections of points that do not have a volume in the ordinary sense, and whose construction requires an uncountable number of choices.

It was shown in 2005 that the pieces in the decomposition can be chosen in such a way that they can be moved continuously into place without running into one another.

🔗 Philosophy 🔗 Philosophy/Philosophical literature 🔗 Guild of Copy Editors

"The Unreality of Time" is the best-known philosophical work of the Cambridge idealist J. M. E. McTaggart (1866–1925). In the argument, first published as a journal article in Mind in 1908, McTaggart argues that time is unreal because our descriptions of time are either contradictory, circular, or insufficient. A slightly different version of the argument appeared in 1927 as one of the chapters in the second volume of McTaggart's greatest work, The Nature of Existence.

The argument for the unreality of time is popularly treated as a stand-alone argument that does not depend on any significant metaphysical principles (e.g. as argued by C. D. Broad 1933 and L. O. Mink 1960). R. D. Ingthorsson disputes this, and argues that the argument can only be understood as an attempt to draw out certain consequences of the metaphysical system that McTaggart presents in the first volume of The Nature of Existence (Ingthorsson 1998 & 2016).

It is helpful to consider the argument as consisting of three parts. In the first part, McTaggart offers a phenomenological analysis of the appearance of time, in terms of the now famous A- and B-series (see below for detail). In the second part, he argues that a conception of time as only forming a B-series but not an A-series is an inadequate conception of time because the B-series does not contain any notion of change. The A-series, on the other hand, appears to contain change and is thus more likely to be an adequate conception of time. In the third and final part, he argues that the conception of time forming an A-series is contradictory and thus nothing can be like an A-series. Since the A- and the B- series exhaust possible conceptions of how reality can be temporal, and neither is adequate, the conclusion McTaggart reaches is that reality is not temporal at all.