The Mathematics Behind Why Rockets Can Escape The Gravitational Pull of the Earth

Konstantin-TsiolkovskyRobert Goddard’s liquid rocket never reached the 3 kilometer mark because of Tsiolkovsky’s Rocket Equation named after Soviet scientist Konstantin Tsiolkovsky (pronounced “con-stan-tyin tsel-kov-skee”). This equation states that as fuel increases for faster and further voyages, so too does the weight, becoming increasingly heavy as more and more fuel is added. Tsiolkovsky took into account the velocity of a rocket alongside its mass of payload, mass of fuel, and the mass of the rocket itself. The longer the engine burns, the more velocity the rocket will have, however longer burning means more fuel which adds weight and makes it more difficult to push upwards. To travel fast enough to deliver a rocket to space, most of the craft must be fuel. Scientists have battled with this question for decades and although mathematical constructs have been developed to explain the relationship between weight and thrust, no one has yet to develop an idea to get around this problem with currently available technologies. The equation developed to explain this limitation of space travel is △V^R = V^E x log^e (M^P + M^F + M^R / M^P + M^R). This effectively states that only a tiny portion of a rocket can be used to deliver payload, with notable cases being the Apollo missions which employed enormous rockets to carry just a few small astronauts and the things they needed into space. Tsiolkovsky theorized this in the beginning of the 20th century as his calculations demonstrated that kerosine wouldn’t be enough to go from the Earth to the moon with a single craft

The First Industrial Revolution, Second Industrial Revolution, and Impending Third Industrial Revolution

Third-Industrial-RevolutionIndustrial revolutions require 3 key components to occur, 3 defining technologies which emerge and converge to create the catalyst needed to usher in a new era of human achievement and progress. The first component is new methods of communication technologies to make communication more efficient and to manage economic and social life (e.g. video conferencing), the second is new sources of energy to more efficiently power economic and social life as well as governance (e.g. renewable energy technologies), and the third is new modes of mobility and logistics to more efficiently move economic and social life as well as governance (e.g. on demand ride sharing). The First Industrial Revolution was caused by the discovery of a new source of energy; coal. Coal powered the new communications medium, the steam powered press, and a new logistics structure via the locomotive railway. When these 3 technologies converged, much of the world (eg. the whole of Europe) changed seemingly overnight. As a direct consequence of the First Industrial Revolution, business models moved toward market capitalism and major city hubs began developing ushering in the modern world format. The Second Industrial Revolution occurred in the U.S. during the late 19th and early 20th century with the advent of the telephone in the late 19th century, and the advent of radio and television in the early and mid 20th century. At approximately the same time that the telephone and telecommunications networks were being developed, the U.S found a new source of energy which was oil in Texas, United States of America. Henry Ford compounded this discovery by producing a cost effective combustion engine, powered by oil which provided new logistics and mobility technology. The Second Industrial Revolution however is now fading away due to the impact it has had upon the Earth’s climate and humanity is now upon the precipice of a Third Industrial Revolution. The internet has become the new communication medium, millions of people are now adopting renewable energy (e.g. solar, wind, geothermal etc.) and it is predicted that when autonomous vehicles connect to smart roads, the last piece of this puzzle will be complete, thrusting humanity into its 3rd epic epoch

Super Mario’s Super Human Jumping Capabilty

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The Nintendo mascot Mario has a vertical jumping range of 11’5” within his own world which equates to 27’ upon Earth as Earth has a different gravitational pull than that of Mario’s world. Mario is capable of leaping 2.25x his own body height however his exact agreed upon height when converted to a real world measurement is unclear. Statues erected of Mario tend to be 4’10” – 5’1” in length and Nintendo has stated that Mario’s official height is in fact 5’1” however different video games portray Mario with a varying degree of physical characteristics (e.g. height, weight, speed etc.). Mario falls back down to the ground within 0.3 seconds of his take off which means that the gravitational pull of his fictional world is 8x stronger than the gravitational pull of Earth. If this world were physically real, Mario would need to have legs powerful enough to allow him to jump at a speed of 22.2 meters per second, an incredible feat of physical prowess as the average person standing upon the Earth is only able to jump at a rate of 2.24 meters per second, resulting in an almost 10x difference in terms of Mario’s physical capabilities to that of a typical human being

The Future of Body Modification

nanotechnology-dermal-implant

Near field communication, often abbreviated as “NFC” is the ability for wireless devices to communicate with eachother and has now made its way into the bodies of human beings with some opting to implant small subdermal microchips using a large gauge hypodermic syringe (e.g. 14 – 18 gauge) which is preloaded so that these individuals gain the ability to start their vehicle(s), open their home door locks, send contact information to another persons smartphone etc., wirelessly and without any intervention or effort upon the end user. This adaptation is referred to as “transhuman” as it goes beyond what the biological human body can do by introducing technology which cannot be evolved into existence. Devices have been developed for a number of different purposes (e.g. vibrating when pointed towards magnetic north turning the body into a compass or implanting a small chip containing tritium gas which glows beneath the skin but is radioactive and therefore not battery powered lasting indefinitely as tritium gas has a 12 year half-life etc.). In 2018, at the University of Colorado, Dr. Carson Bruns and his team developed a technology which allows for smart tattooing in that newly and highly specialized tattoo inks will be able to deliver new functions to the artistic medium of tattooing. The first design invented was a tattoo ink which is sensitive to ultraviolet light which allows it to lay invisible under typical lighting conditions and only appear as a blue hue once outside in the presense of sunlight or an artificial ultraviolet light source. This technology would be practical as well as esthetic as it would allow a person to know when they’ve had too much sun exposure while outside. Bruns’ team has also developed tattoo ink which changes color as the temperature of the body changes which again would be functional as well as artistic, acting as a thermometer to indicate when a person has had too much or too little exposure to cold or heat. Nanotechnology is used to engineer and design tattoo particles which have specialized properties and characteristics (e.g. thermal battery and/or storage mechanism). Real world applications could be spurred by this advent like the ability to keep the entire body at a comfortable temperature at all times, regardless of the environment, if the entire body was tattooed, either visibly with color or invisibly with translucent ink. Specially engineered tattooing can also have medical applications such as that of the distribution of a pharmacological medication or hormone which helps regulate biochemistry (e.g. insulin or neural catecholamines to control mood etc.). World militaries may find use with specially engineered tattoos as well, allowing skin to become more resilient to abrasions or epidermal damage. Specialized tattoo pigments are also tactile sensitive in that when touched, they have the ability to turn on or off as well as perform other functions (e.g. manipulate an options menu upon a screen or act as a controller for a game or software etc.). In 2018, billionaire futuristic Elon Musk unveiled Neuralink, a technology which he states provides the ability of “self-directed evolution”. Neuralink will be installed within the human body by using a specialized, robotic hypodermic syringe to inject an ultra thin mesh, referred to as “neuro lace”, into the neurocortex of the brain, to form a body of electrodes which are able to monitor and influence brain function. These microelectrodes will be able read and write onto neurons; a bi-directional information exchange. This will allow for the downloading and uploading of information to and from the internet, wirelessly. This technology will allow for thoughts to be sent between users in the same format that data is shared online during the modern day using peer to peer networking. This technology will also allow for the control of devices, remotely; in principle, telekinesis. Nanotechnology now provides scientists with the technology required to manufacture electronics small enough to become tattooed, which means that in the future, Neuralink will only require a small, cranial tattoo instead of a cranial implant

The Advent of Parallax Distance to Measure Immense Distances in Space

Hubble-Telescope-stars

Stellar parallax is a measurement technique developed by Friedrich Bessel to measure far away objects in deep space. The process of stellar parallax involves measuring an object from two separate vantage points hinging upon the fact that the object being observed will appear to move a lot more than objects further behind it (e.g. if an observer closes one eye and views their finger in front of a building, and then repeats this act with their second eye closed and the first eye open, the observers finger will appear as though it has moved much further left or right, relative to the other objects behind it). Because Bessel developed a method of calculation to take advantage of this phenomena, astronomers now have the ability to map grand distances with relative accuracy. Bessel worked out that if an observer took an image of a star when the Earth was at either side of its orbit around the sun, it would be possible to observe the star shifting in its position. By knowing how much a star shifts, it is possible to calculate the distance the star is from its observation point on Earth. Bessel surmised that the relatively close star 61 Cygni must be 100,000,000,000,000 (100 trillion) kilometers away from the Earth because of his parallax distance method. This technique unfortunately is severely limited as the diameter of the Earth’s orbit is only 300,000,000 (300 million) kilometers which means that the parallax method can only measure objects up to a factor of 1,000,000x (1 million) the Earths orbital rotation, allowing for a maximum distance of 300,000,000,000,000 (300 trillion) kilometers which is only a tiny fraction of the size of the Milky Way Galaxy or the universe as a whole

The Mathematical Inventions of Muhammad ibn Musa al-Khwarizmi

Muhammad-ibn-Musa-al-Khwarizmi

The mathematical concept of algorithms were developed by and subsequently named after Muhammad ibn Musa al-Khwarizmi (pronounced “moo-ham-mad ih-bin moo-sah al kwar-iz-me”), an Islamic scholar who lived during the 8th century. The concept of algorithms arrived in Europe in the 12th century and al-Khwarizmi’s name was translated to Latin which is where the term “algorithm” is derived. al-Khwarizmi also introduced the western world to the decimal system and introduced reduction and balancing methods (e.g. like and unlike terms) causing al-Khwarizmi to become referred to as the ”father and founder of algebra”. The term “algebra” is derived from the Arabic term “al-jabr” which means “reunion of broken parts”. al-Khwarizmi invented and used algebra to solve quadratic equations and it has been stated throughout history that the ideas that al-Khwarizmi developed, helped usher in the European Renaissance during the 14th, 15th, and 16th centuries

The End of the Universe and the Big Crunch Theory

big-crunch

The likelihood of a Big Crunch in which the universe expands to the point that it then collapses inward upon itself is not very probable as mathematical calculations demonstrate that there simply isn’t enough mass in the entire universe to be able to revert into into an enormous compaction. The idea of the universe folding in upon itself can be visualized by imagining a person throwing a ball in the air. The Earth has enough mass to bring a thrown ball back down to the ground but if thrown faster than the speed of escape velocity which is 11.186 kilometers per second, a thrown ball would never come back down, in fact, it would travel an infinite distance over an infinite timespan before the Earth mathematically had enough time and mass to pull the ball back to its starting position. The universe is represented by the Earth in that it acts as a force upon other objects and the ball represents all matter throughout the universe in this thought experiment

The Illusion of Fibonacci’s True Name

Fibonacci

Fibonacci’s name was created in 1838 by the Franco-Italian historian Guillaume Libri, and is short for “filius Bonacci” which means “son of Bonacci” in Italian. Fibonacci is also referred to as “Leonardo Bonacci”, “Leonardo of Pisa” where he was born, and “Leonardo Bigollo Pisano” which means “Leonardo, traveler from Pisa” in Italian, a name which Fibonacci actually used himself

The Physics of the Pac-Man Universe

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The game of Pac-Man allows players to exit the world on one side, and re-enter upon a completely different side without delay. Pac-Man’s universe appears to be a flat, two dimensional, rectangular shape, but in reality it must be cylindrical like a pipe, only with the 2 ends of the pipe touching, making Pac-Man’s universe actually in the shape of a donut