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🔗 Gödel's Loophole
Gödel's Loophole is a "inner contradiction" in the Constitution of the United States which Austrian-German-American logician, mathematician, and analytic philosopher Kurt Gödel claimed to have discovered in 1947. The flaw would have allowed the American democracy to be legally turned into a dictatorship. Gödel told his friend Oskar Morgenstern about the existence of the flaw and Morgenstern told Albert Einstein about it at the time, but Morgenstern, in his recollection of the incident in 1971, never mentioned the exact problem as Gödel saw it. This has led to speculation about the precise nature of what has come to be called "Gödel's Loophole". It has been called "one of the great unsolved problems of constitutional law."
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- "Gödel's Loophole" | 2025-08-06 | 21 Upvotes 11 Comments
- "Gödel's Loophole" | 2023-07-24 | 21 Upvotes 4 Comments
- "Gödel's Loophole" | 2023-04-05 | 12 Upvotes 2 Comments
- "Gödel's Loophole" | 2023-01-20 | 10 Upvotes 1 Comments
- "Gödel's Loophole" | 2021-03-25 | 131 Upvotes 130 Comments
🔗 Five Minute Rule
In computer science, the five-minute rule is a rule of thumb for deciding whether a data item should be kept in memory, or stored on disk and read back into memory when required. It was first formulated by Jim Gray and Gianfranco Putzolu in 1985, and then subsequently revised in 1997 and 2007 to reflect changes in the relative cost and performance of memory and persistent storage.
The rule is as follows:
The 5-minute random rule: cache randomly accessed disk pages that are re-used every 5 minutes or less.
Gray also issued a counterpart one-minute rule for sequential access:
The 1-minute rule: cache sequentially accessed disk pages that are re-used every 1 minute or less.
Although the 5-minute rule was invented in the realm of databases, it has also been applied elsewhere, for example, in Network File System cache capacity planning.
The original 5-minute rule was derived from the following cost-benefit computation:
- BreakEvenIntervalinSeconds = (PagesPerMBofRAM / AccessesPerSecondPerDisk) × (PricePerDiskDrive / PricePerMBofRAM)
Applying it to 2007 data yields approximately a 90-minutes interval for magnetic-disk-to-DRAM caching, 15 minutes for SSD-to-DRAM caching and 21⁄4 hours for disk-to-SSD caching. The disk-to-DRAM interval was thus a bit short of what Gray and Putzolu anticipated in 1987 as the "five-hour rule" was going to be in 2007 for RAM and disks.
According to calculations by NetApp engineer David Dale as reported in The Register, the figures for disc-to-DRAM caching in 2008 were as follows: "The 50KB page break-even was five minutes, the 4KB one was one hour and the 1KB one was five hours. There needed to be a 50-fold increase in page size to cache for break-even at five minutes." Regarding disk-to-SSD caching in 2010, the same source reported that "A 250KB page break even with SLC was five minutes, but five hours with a 4KB page size. It was five minutes with a 625KB page size with MLC flash and 13 hours with a 4KB MLC page size."
In 2000, Gray and Shenoy applied a similar calculation for web page caching and concluded that a browser should "cache web pages if there is any chance they will be re-referenced within their lifetime."
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- "Five Minute Rule" | 2015-10-06 | 51 Upvotes 12 Comments
🔗 The entire 1941 Japanese film Kanzashi can be watched on its Wikipedia page
Ornamental Hairpin (簪, Kanzashi) is a 1941 Japanese comedy-drama film written and directed by Hiroshi Shimizu. It is based on the short story Yottsu no yubune (四つの湯槽, lit. "The four bathtubs") by Masuji Ibuse.
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- "The entire 1941 Japanese film Kanzashi can be watched on its Wikipedia page" | 2025-05-02 | 13 Upvotes 1 Comments
🔗 Band-e Kaisar – “Caesar's dam”
The Band-e Kaisar (Persian: بند قیصر, "Caesar's dam"), Pol-e Kaisar ("Caesar's bridge"), Bridge of Valerian or Shadirwan was an ancient arch bridge in Shushtar, Iran, and the first in the country to combine it with a dam. Built by the Sassanids, using Roman prisoners of war as workforce, in the 3rd century AD on Sassanid order, it was also the most eastern example of Roman bridge design and Roman dam, lying deep in Persian territory. Its dual-purpose design exerted a profound influence on Iranian civil engineering and was instrumental in developing Sassanid water management techniques.
The approximately 500 m long overflow dam over the Karun, Iran's most effluent river, was the core structure of the Shushtar Historical Hydraulic System (سازههای آبی شوشتر) from which the city derived its agricultural productivity, and which has been designated by the UNESCO as Iran's 10th World Heritage Site in 2009. The arched superstructure carried across the important road between Pasargadae and the Sassanid capital Ctesiphon. Many times repaired in the Islamic period, the dam bridge remained in use until the late 19th century.
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- "Band-e Kaisar – “Caesar's dam”" | 2016-01-03 | 16 Upvotes 2 Comments
🔗 Stochastic Parrot
In machine learning, "stochastic parrot" is a term coined by Emily M. Bender in the 2021 artificial intelligence research paper "On the Dangers of Stochastic Parrots: Can Language Models Be Too Big?" by Bender, Timnit Gebru, Angelina McMillan-Major, and Margaret Mitchell. The term refers to "large language models that are impressive in their ability to generate realistic-sounding language but ultimately do not truly understand the meaning of the language they are processing."
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- "Stochastic Parrot" | 2023-06-13 | 125 Upvotes 161 Comments
🔗 List of mathematical symbols
This is a list of mathematical symbols used in all branches of mathematics to express a formula or to represent a constant.
A mathematical concept is independent of the symbol chosen to represent it. For many of the symbols below, the symbol is usually synonymous with the corresponding concept (ultimately an arbitrary choice made as a result of the cumulative history of mathematics), but in some situations, a different convention may be used. For example, depending on context, the triple bar "≡" may represent congruence or a definition. However, in mathematical logic, numerical equality is sometimes represented by "≡" instead of "=", with the latter representing equality of well-formed formulas. In short, convention dictates the meaning.
Each symbol is shown both in HTML, whose display depends on the browser's access to an appropriate font installed on the particular device, and typeset as an image using TeX.
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- "List of mathematical symbols" | 2013-11-09 | 44 Upvotes 9 Comments
🔗 Charlieplexing
Charlieplexing (also known as tristate multiplexing, reduced pin-count LED multiplexing, complementary LED drive and crossplexing) is a technique for accessing a large number of LEDs, switches, micro-capacitors or other I/O entities, using very few tri-state logic wires from a microcontroller, these entities being wired as discrete components, x/y arrays, or woven in a diagonally intersecting pattern to form diagonal arrays.
The method uses the tri-state logic capabilities of microcontrollers in order to gain efficiency over traditional multiplexing, each I/O pin being capable, when required, of rapidly changing between the three states, logical 1, logical 0, and high impedance.
This enables these I/O entities (LEDs, switches etc.) to be connected between any two microcontroller I/Os - e.g. with 4 I/Os, each I/O can pair with 3 other I/Os, resulting in 6 unique pairings (1/2, 1/3, 1/4, 2/3, 2/4, 3/4). Only 4 pairings are possible with standard x/y multiplexing (1/3, 1/4, 2/3, 2/4). Also, due to the microcontroller's ability to reverse the polarity of the 6 I/O pairs, the number of LEDS (or diodes) that are uniquely addressable, can be doubled to 12 - adding LEDS 2/1, 3/1, 4/1, 3/2, 4/2 and 4/3.
Although it is more efficient in its use of I/O, a small amount of address manipulation is required when trying to fit Charlieplexing into a standard x/y array.
Other issues that affect standard multiplexing but are exacerbated by Charlieplexing are:
- consideration of current requirements and the forward voltages of the LEDs.
- a requirement to cycle through the in-use LEDs rapidly so that the persistence of the human eye perceives the display to be lit as a whole. Multiplexing can generally be seen by a strobing effect and skewing if the eye's focal point is moved past the display rapidly.
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- "Charlieplexing" | 2024-05-12 | 69 Upvotes 12 Comments
🔗 Magnetosome
Magnetosomes are membranous structures present in magnetotactic bacteria (MTB). They contain iron-rich magnetic particles that are enclosed within a lipid bilayer membrane. Each magnetosome can often contain 15 to 20 magnetite crystals that form a chain which acts like a compass needle to orient magnetotactic bacteria in geomagnetic fields, thereby simplifying their search for their preferred microaerophilic environments. Recent research has shown that magnetosomes are invaginations of the inner membrane and not freestanding vesicles. Magnetite-bearing magnetosomes have also been found in eukaryotic magnetotactic algae, with each cell containing several thousand crystals.
Overall, magnetosome crystals have high chemical purity, narrow size ranges, species-specific crystal morphologies and exhibit specific arrangements within the cell. These features indicate that the formation of magnetosomes is under precise biological control and is mediated biomineralization.
Magnetotactic bacteria usually mineralize either iron oxide magnetosomes, which contain crystals of magnetite (Fe3O4), or iron sulfide magnetosomes, which contain crystals of greigite (Fe3S4). Several other iron sulfide minerals have also been identified in iron sulfide magnetosomes—including mackinawite (tetragonal FeS) and a cubic FeS—which are thought to be precursors of Fe3S4. One type of magnetotactic bacterium present at the oxic-anoxic transition zone (OATZ) of the southern basin of the Pettaquamscutt River Estuary, Narragansett, Rhode Island, United States is known to produce both iron oxide and iron sulfide magnetosomes.
🔗 GOES 3 satellite
GOES-3, known as GOES-C before becoming operational, is an American geostationary weather and communications satellite. It was originally built for the National Oceanic and Atmospheric Administration as part of the Geostationary Operational Environmental Satellite system, and was launched in June 1978. It is positioned in geostationary orbit, from where it was initially used for weather forecasting in the United States. Since ceasing to function as a weather satellite in 1989, it has been used as a communications satellite, and has spent over thirty-eight years in operation. GOES-3 was decommissioned 29 June 2016 at the CSTARS facility in Miami, Florida.
GOES-3 was built by Ford Aerospace, and is based on the satellite bus developed for the SMS programme. At launch it had a mass of 627 kilograms (1,382 lb).
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- "GOES 3 satellite" | 2016-06-22 | 18 Upvotes 11 Comments
🔗 Planimeter
A planimeter, also known as a platometer, is a measuring instrument used to determine the area of an arbitrary two-dimensional shape.
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- "Planimeter" | 2015-04-26 | 14 Upvotes 1 Comments