Category: Mathematics

The Fallacy of Airplane Mode Disabling the Global Positioning System Tracking of Smartphones

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Even when Airplane Mode is activated, the Apple iPhone still receives signals from the global positioning system because this apparatus is a passive, receive only system which does not rely upon a cellular connection, WiFi connection, and/or Bluetooth connection to function. The iPhone scans and listens for satellites orbiting the Earth and calculates its relative position based upon this timing data, which means the iPhone can still determine a users location even without an internet connection, however if this is not desirable by the end user, Location Services can be disabled which theoretically turns this function off. This information is true for most modern smartphones including Android, however not all (e.g. smartphones manufactured prior to 2010, minimalistic/budget conscious smartphone designs, smartphones with custom firmware and/or enterprise restrictions like those managed by corporate information technology teams or running custom read only memory etc.)

The Reason the Earth Becomes Colder When Closest to the Sun

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The Earth orbits the Sun in an elliptical path, meaning the distance between each body constantly fluctuates. Perihelion is the specific point in this orbit at which the Earth is closest to the Sun with this phenomena occurring near January 3rd annually. In contrast to this, aphelion, is when the Sun is at its farthest distance from the Earth, which occurs in July each year. Interestingly and counterintuitively, the Earth is coldest during its perihelion phase (when the sun is closest to the Earth) and warmest during aphelion (when the sun is furthest from the Earth). This paradox occurs because of the struggle between orbital distance and the 23.5 degree axial tilt of the Earth. Whilst the Earth is slightly closer to the Sun during the perihelion phase in early January, receiving 6% – 7% more solar energy than in July, the Northern Hemisphere is tilted away from the Sun which forces sunlight to strike the Earth’s ground at a more shallow angle, therefore spreading the light over a larger surface area and filtering it through more of the atmosphere. This reduction in heat overrides the slight shift of the Earth and Sun being closer or further away, as it is the tilt of the Earth, not the orbital proximity of the Sun which dictates both the 4 seasons as well as the perihelion/aphelion paradox. It should be noted, global temperatures peak in July because the Northern Hemisphere Continental Crust heats more rapidly than the Southern Hemispheres oceans

The Number of Gifts Santa Claus and the Elves Must Build and Deliver Each Christmas Eve

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Assuming Santa Claus delivers at least 1 gift to each child worldwide, this would equate to 2,100,000,000 (2.1 billion) gifts. With an average of 2.5 children per household worldwide, Claus would have to visit 840,000,000 (840 million) homes to accomplish this task. To finish this job in 24 hours (12 for each side of the world), Claus would need to visit 35,000,000 (35 million) homes per hour which would be 580,000 per minute, or nearly 10,000 every second! Because there are so many homes and so very many children, the elves of the North Pole face an equally grueling pace. Assuming each child receives 1 toy, and the build time is spread across 364 days, these elves would need to craft approximately 5,750,000 (5.75 million) toys per day. This would mean 240,000 toys per hour, 4,000 per minute, or nearly 70 every second without a work break for any of them. If the North Pole were to employ 100 elves, each would need to make 0.7 toys per second; and with a large company of 1000 elves, this value drops to 1 toy every 14 seconds which is more manageable; however with a massive company of 10,000 elves, each would only need to craft 1 toy every 2.5 minutes which would be much more probable for a workforce to achieve; if however the North Pole were capable of managing a city sized work force of 100,000 elves, each elf would need only to craft a single toy every 24 minutes which is a pace that a human powered North Pole, theoretically could handle. With that being said, mythologically speaking elves are immortal, or at the very least ageless, and they do possess arcane magic and clandestine knowledge which must be kept in mind when calculating what is theoretically possible

The Fallacy of Snowflakes Being Perfectly Symmetrical

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The 6 sided geometric symmetry observed within snowflakes is governed by the rigid molecular structure of hexagonal ice, which is the only crystalline form water can adopt within the Earth’s atmosphere, and the reason snowflakes always have 6 dendrites (points) like a hexagon. It is a common misconception that all snow crystals (snowflakes) exhibit perfect symmetry, as most often they do not possess this characteristic. It is true in the sense that at the microscopic molecular scale, snow crystals form perfectly, but it is untrue because at the macro, real world scale, anomalies virtually always form. This occurs because as the snow crystal becomes larger, water molecules no longer attach to develop and maintain a uniform orientation. Additionally, as the snow crystal grows and expands, factors of the ambient environment begin to influence it (e.g. effects of humidity and temperature etc.) causing the snow crystal to grow one way whilst in one position of a cloud and then grow in a completely different orientation once having been forcibly moved to a different spot within that same cloud. Because of this, it is rare but still possible to find a perfectly symmetrical snowflake. This explains why despite the complex and random nature of snow crystal growth, all 6 arms must align in every case and grow along the same 6 fixed 60 degree axes. If this does not occur, the snow crystal would violate the fundamental laws of energy minimization (to become most stable) dictated by the hydrogen bond lattice (framework connecting atoms within water), which would cause the structure of the snow crystal to become thermodynamically unstable and therefore highly prone to fracture

The Reason WD-40 Was Developed

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The WD-40 formula was developed by 3 scientists who succeeded in their goal upon the 40th design attempt, with the name WD-40 being an acronym meaning “Water Displacement: 40th Formula”. WD-40 was created in 1953 by the Rocket Chemical Company located in San Diego, United States of America. The formula was originally researched and developed as a means to protect the outer skin and thin tanks (e.g. lightweight pressurized tanks which provide structural support when filled saving weight overall) of SM-65 Atlas intercontinental ballistic missiles from rust and corrosion during the manufacturing, handling, and storage process(es) of missile silos. This proprietary mixture resolved for the aerospace industry the need for a dependable water displacing solvent which prevented moisture and other related damage. Early use of WD-40 upon Atlas SM-65 missiles demonstrated the solutions superior effectiveness in comparison to analogs. This prompted a handful of employees to take canisters of WD-40 home which inadvertently inspired the projects founder, Norm Larsen, to package WD-40 in an aerosol form designed specifically for consumer use. WD-40 first appeared on store shelves in 1958 and developed applications in spacecraft maintenance, disaster recovery, and countless home and industrial tasks (eg. lubricating stuck hinges of seized doors, displacing moisture upon electrical contacts, loosening rusted and/or seized bolts etc.)

The Hottest Natural and Artificial Temperature in the Universe

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The hottest temperature ever measured and/or observed was within the Large Hadron Collider located on the border of Switzerland and France. When lead particles are smashed together within this particle accelerator, for a split second the temperature reaches 4,000,000,000,000 (4 trillion) degrees Celsius which is hotter than a supernova explosion, albeit the theoretical maximum possible temperature of the universe is believed to be 20 orders of magnitude greater. Contemporary models of physical cosmology postulate that the highest possible temperature is the Planck temperature, which has a value of 1.416785(71)×1032 kelvin. Temperatures above this are believed to be physically impossible because as particle energies become larger and larger, the gravitational forces between them inevitably become as strong as the other 3 fundamental forces which essentially boils and breaks down both the universe and space time. Outside of laboratory conditions however, the hottest naturally occurring place within the universe is the quasar 3C273 (the 273rd entry in the Third Cambridge Catalogue of Radio Sources), a blazing region surrounding a supermassive black hole approximately 2,400,000,000 (2.4 billion) light years away from the Earth, with matter within its accretion disk being measured at temperatures of approximately 10,000,000,000,000 (10 trillion) kelvin, making it far hotter than the core of any star, and 400,000x hotter than the core of the sun, rivaling the conditions of the universe right after the Big Bang

The Coldest Natural and Artificial Temperature in the Universe

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The coldest temperature ever measured and/or observed was within a controlled laboratory experiment in Germany; an experiment entitled “Time‑Domain Matter‑Wave Lens System for Atomic Clouds”. During this experiment, physicists cooled a cloud of rubidium atoms to 0.000000000038 (38 trillionths) of 1 degree above absolute zero which is -273.15 degrees Celsius, colder than the vacuum of space, slowing these atoms to a near motionless state for a very short period of time which created a fleeting state of matter existing closer to perfect stillness than anywhere or anything else within the universe. This experiment was the closest scientists have come to achieving complete absence of motion within a controlled setting. Contemporary models of physical cosmology postulate that the theoretical minimum possible temperature is absolute zero, which has a value of 0 kelvin. Temperatures below this are believed to be physically impossible because particle energies become so tiny that all molecular motion ceases to continue functioning, allowing quantum effects to dominate, and producing exotic states of matter (e.g. Bose-Einstein condensates in which matter behaves as a single quantum entity etc.). The coldest naturally occurring place within the universe is the Boomerang Nebula, a dying star cloud located approximately 5,000 light years away from the Earth. The Boomerang Nebula has been measured at 1 degree above absolute zero, making it even colder than the faint afterglow of the Big Bang itself, yet the Time‑Domain Matter‑Wave Lens System for Atomic Cloud experiment is 26,000,000,000x (26 billion) colder and closer to absolute zero than the Boomerang Nebula or any other naturally occurring region with low heat

The Role of Jewish Financiers Within Venice, Italy During the Renaissance and the Reason Christians Became Capable of Charging Interest Upon Loans

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During the Renaissance, Jews were tolerated in Venice, Italy because they could provide an invaluable service which Christian financiers and merchants were forbidden to do which was to charge interest upon a loan, a concept referred to as “usury”, derived from the Latin term “usura” which means “use” or “interest”. Christians considered charging interest to be a sin and therefore could not partake in this economic exchange. Unfortunately, the Catholic Church’s Medieval laws against usury acted as a major obstacle for the development of finance within Europe during this period. Jews were not technically permitted to lend capital with interest, but those who did relied upon a convenient clause found within the 23rd chapter of Deuteronomy of the Christian Bible which states that lending to a brother at interest was forbidden but that a stranger was a different matter all together. These Jewish lenders interpreted this scripture as a means to provide the ability to lend to Christians, as Christian’s were not considered brothers of the Jews in a religious context during this period, but they would still not be capable of lending finance to other fellow Jews, as these members of society were viewed as brothers regardless of familial ties. Eventually Christian’s were able to circumvent the prohibition of charging interest, primarily because of Giovanni di Bicci de’ Medici, one of the wealthiest entrepreneurs within Italy during the Renaissance. Medici was able to evade Christian usury legislation as Jewish bankers did because of a clever device of trade which made profit upon exchanging multiple currencies rather than interest rates alone. No “interest” paid to Medici meant no sin had been committed. Medici’s business model took a small commission for each currency conversion rendered, with the size of the loan directly impacting the commission of the person who lent it

The Mathematical Probability of Miracles

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Many would argue that miracles have a 1:1,000,000 (1 to 1 million) ratio, and others whom are more conservative would argue that miracles have a 1:1,000,000,000 (1 to 1 billion) ratio, meaning for every 1 miracle, 1,000,000,000 (1 billion) events occur without a miracle. 1 in 1,000,000,000 (1 billion) sounds astronomically high, as on the entire planet there are only 8,100,000,000 (8.1 billion) human beings, but if a person draws 6 cards from a standard deck of cards, whatever sequence they draw has a 1:14,000,000,000 (1 in 14 billion) chance of occurring. Because of this, one could argue that every hand of cards drawn is a miracle and not a random act of chance. This logic applies to all randomized items or numerical values (e.g. first 6 digits of a Social Insurance Number or last 6 digits of a phone number etc.). What humans refer to as a “miracle” is often merely a statistical anomaly, an event with low probability, but not impossibility, something which is guaranteed to occur given enough repetitions are made. The sheer volume of possible outcomes virtually guarantees that rare patterns will emerge eventually, not because they are miraculous, but because the mathematics demand it be so

The Reason Giants Cannot Physically Exist Upon Earth

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If volume and weight are both calculated as 1 unit, when a cube is made 1 x 1 x 1 when accounting for its length, width, and height, and 1 when accounting for its weight, the entire cube is in equal proportion; a concept referred to as a “unit cube” called as such because each of its dimensions (e.g. height, width, length etc.) are 1 unit in length. This changes however when doubling the cube in size and weight. When doubling the cube to 2 x 2 x 2 when accounting for its length, width, and height, the weight does not move in lockstep, because it becomes 8x (2 x 2 = 4 x 2 = 8). This fundamental mathematical principle referred to as the Square Cube Law, explains why as animals become bigger on land, life becomes exceedingly difficult because of the need to maintain and support the large weight associated with such large stature. As animals become more massive, the effect of gravity places an increasing role in their lives. The shape and form of the body is forced to change. Bones become more massive to scaffold their large bodies. This is why the largest animals on the planet are found within the Earth’s oceans as being within water is a way to circumvent this outcome and helps explain why as animals become larger upon land, life becomes exceedingly difficult because of the need to maintain an appropriate structure and weight associated with such large sizes. This principle also explains why the concept of a giant (e.g. mythology etc.) is physically problematic as if a human being were scaled up proportionally to twice their normal height, their volume and weight would increase 8x, whilst the strength of their bones and muscles would not scale at this same rate. The result would be a life form whose own mass would overwhelm its skeletal structure, making movement, balance, and even basic survival virtually impossible without some form of environmental and/or structural intervention and compensation