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🔗 Mathematics 🔗 Statistics

The secretary problem is a problem that demonstrates a scenario involving optimal stopping theory. The problem has been studied extensively in the fields of applied probability, statistics, and decision theory. It is also known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem.

The basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of ${\displaystyle n}$ rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator gains information sufficient to rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy (stopping rule) to maximize the probability of selecting the best applicant. If the decision can be deferred to the end, this can be solved by the simple maximum selection algorithm of tracking the running maximum (and who achieved it), and selecting the overall maximum at the end. The difficulty is that the decision must be made immediately.

The shortest rigorous proof known so far is provided by the odds algorithm (Bruss 2000). It implies that the optimal win probability is always at least ${\displaystyle 1/e}$ (where e is the base of the natural logarithm), and that the latter holds even in a much greater generality (2003). The optimal stopping rule prescribes always rejecting the first ${\displaystyle \sim n/e}$ applicants that are interviewed and then stopping at the first applicant who is better than every applicant interviewed so far (or continuing to the last applicant if this never occurs). Sometimes this strategy is called the ${\displaystyle 1/e}$ stopping rule, because the probability of stopping at the best applicant with this strategy is about ${\displaystyle 1/e}$ already for moderate values of ${\displaystyle n}$. One reason why the secretary problem has received so much attention is that the optimal policy for the problem (the stopping rule) is simple and selects the single best candidate about 37% of the time, irrespective of whether there are 100 or 100 million applicants.

🔗 Writing systems 🔗 Typography

The long s (ſ) is an archaic form of the lower case letter s. It replaced the single s, or the first s in a double s (e.g. "ſinfulneſs" for "sinfulness" and "ſucceſs" for "success"). The long s is the basis of the first half of the grapheme or the German alphabet ligature letter ß, which is known as the Eszett. The modern letterform is known as the short, terminal, or round s.

🔗 Transport 🔗 Sweden

Dagen H (H day), today usually called "Högertrafikomläggningen" ("The right-hand traffic diversion"), was the day on 3 September 1967, in which the traffic in Sweden switched from driving on the left-hand side of the road to the right. The "H" stands for "Högertrafik", the Swedish word for "right traffic". It was by far the largest logistical event in Sweden's history.

🔗 Computing

The Curta is a small mechanical calculator developed by Curt Herzstark. The Curta's design is a descendant of Gottfried Leibniz's Stepped Reckoner and Charles Thomas's Arithmometer, accumulating values on cogs, which are added or complemented by a stepped drum mechanism. It has an extremely compact design: a small cylinder that fits in the palm of the hand.

Curtas were considered the best portable calculators available until they were displaced by electronic calculators in the 1970s.

🔗 Television

TV detector vans are vans, which, according to the BBC, contain equipment that can detect the presence of television sets in use. The vans are operated by contractors working for the BBC, to enforce the television licensing system in the UK, the Channel Islands and on the Isle of Man. The veracity of their operation has been called into question in the media.

🔗 Germany 🔗 Law Enforcement 🔗 Typography

The FE-Schrift or Fälschungserschwerende Schrift (forgery-impeding typeface) is a sans serif typeface introduced for use on licence plates. Its monospaced letters and numbers are slightly disproportionate to prevent easy modification and to improve machine readability. It has been developed in Germany where it has been mandatory since November 2000.

The abbreviation "FE" is derived from the compound German adjective "fälschungserschwerend" combining the noun "Fälschung" (falsification) and the verb "erschweren" (to hinder). "Schrift" means font in German. Other countries have later introduced the same or a derived typeface for license plates taking advantage of the proven design for the FE-Schrift.

🔗 Computer Security 🔗 Computer Security/Computing 🔗 Microsoft Windows 🔗 Microsoft Windows/Computing 🔗 Cryptography 🔗 Cryptography/Computer science

_NSAKEY was a variable name discovered in an operating system from Microsoft in 1999. The variable contained a 1024-bit public key; such keys are used in cryptography for encryption and authentication. Due to the name it was speculated that the key was owned by the United States National Security Agency (the NSA) which would allow the intelligence agency to subvert any Windows user's security. Microsoft denied the speculation and said that the key's name came from the NSA being the technical review authority for U.S. cryptography export controls.

The key was discovered in a Windows NT 4 Service Pack 5 (which had been released unstripped of its symbolic debugging data) in August 1999 by Andrew D. Fernandes of Cryptonym Corporation.

🔗 Mathematics 🔗 Television 🔗 Statistics 🔗 Game theory 🔗 Television/Television game shows

The Monty Hall problem is a brain teaser, in the form of a probability puzzle, loosely based on the American television game show Let's Make a Deal and named after its original host, Monty Hall. The problem was originally posed (and solved) in a letter by Steve Selvin to the American Statistician in 1975 (Selvin 1975a), (Selvin 1975b). It became famous as a question from a reader's letter quoted in Marilyn vos Savant's "Ask Marilyn" column in Parade magazine in 1990 (vos Savant 1990a):

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

Vos Savant's response was that the contestant should switch to the other door (vos Savant 1990a). Under the standard assumptions, contestants who switch have a 2/3 chance of winning the car, while contestants who stick to their initial choice have only a 1/3 chance.

The given probabilities depend on specific assumptions about how the host and contestant choose their doors. A key insight is that, under these standard conditions, there is more information about doors 2 and 3 than was available at the beginning of the game when door 1 was chosen by the player: the host's deliberate action adds value to the door he did not choose to eliminate, but not to the one chosen by the contestant originally. Another insight is that switching doors is a different action than choosing between the two remaining doors at random, as the first action uses the previous information and the latter does not. Other possible behaviors than the one described can reveal different additional information, or none at all, and yield different probabilities. Yet another insight is that your chance of winning by switching doors is directly related to your chance of choosing the winning door in the first place: if you choose the correct door on your first try, then switching loses; if you choose a wrong door on your first try, then switching wins; your chance of choosing the correct door on your first try is 1/3, and the chance of choosing a wrong door is 2/3.

Many readers of vos Savant's column refused to believe switching is beneficial despite her explanation. After the problem appeared in Parade, approximately 10,000 readers, including nearly 1,000 with PhDs, wrote to the magazine, most of them claiming vos Savant was wrong (Tierney 1991). Even when given explanations, simulations, and formal mathematical proofs, many people still do not accept that switching is the best strategy (vos Savant 1991a). Paul Erdős, one of the most prolific mathematicians in history, remained unconvinced until he was shown a computer simulation demonstrating vos Savant’s predicted result (Vazsonyi 1999).

The problem is a paradox of the veridical type, because the correct choice (that one should switch doors) is so counterintuitive it can seem absurd, but is nevertheless demonstrably true. The Monty Hall problem is mathematically closely related to the earlier Three Prisoners problem and to the much older Bertrand's box paradox.

🔗 United States 🔗 United States/Washington - Seattle 🔗 United States/Washington

Capitol Hill's mystery soda machine was a Coke vending machine in Capitol Hill, Seattle, that was in operation since at least the early 1990s until its disappearance in 2018. It is unknown who stocked the machine.

🔗 Economics 🔗 Statistics 🔗 Business 🔗 Politics

Goodhart's law is an adage named after economist Charles Goodhart, which has been phrased by Marilyn Strathern as "When a measure becomes a target, it ceases to be a good measure." One way in which this can occur is individuals trying to anticipate the effect of a policy and then taking actions that alter its outcome.