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--------------------- 2664 - MATH - secrets of the universe?
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- There is only one thing more confusing than the vast secrets of spirituality and that is the language of mathematics. And strangely enough, math and religion can sometimes come together.
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- For centuries humans have sought the great answers through the ancient art of geometry, out of the belief that all those weird triangles, cubes, and dodecahedrons might bring us a little bit closer to our creator
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- This ancient art of geometry played a major role in the beliefs, designs, and architecture of countless societies throughout history.
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- "Sacred geometry" is a broad umbrella term covering many studies, but it relates specifically to the belief that there are geometric patterns, shapes, and mathematical formulas that are central to life, creation, and the universe.
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- These patterns have seeped into every major religion, forming the blueprint for chapels, temples, and classic artwork. Followers of sacred geometry do believe that mathematics will help you get closer to God, Ein Sof, Brahma, or whichever divine figure you might believe in.
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- That's the basic idea, but what makes geometric shapes so divine?
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- Sacred geometry often centers on the belief that certain shapes in nature, due to their inherent perfection, hold the key to understanding the universe.
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- Deciphering the Code is the nautilus shell's distinctive spiral. See, the nautilus itself is a soft little creature in a big shell. As it matures, it creates bigger chambers for itself within that shell, each new chamber being exactly proportional to the smaller chambers from before.
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- Basically, the nautilus is the world's best engineer of such precise natural patterns.
Are they signs of an intelligent higher power inside this simple creature?
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- The “Fibonacci sequence“, a pattern wherein every number is the sum of the two preceding numbers. The sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, and so on. Fibonacci numbers pop up all throughout nature, whether in the number of spirals on a pinecone, an artichoke's flowers, or the pattern of leaves on a stem. Count the spirals on any pinecone in your yard.
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- The "golden ratio," which is the name for “1.618“, a number found when lots of division creates perfect symmetry. The golden ratio is found in countless ancient architectural feats, including the Great Pyramids.
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- Plato was one of the most influential thinkers in human history, and he taught the world all about the dangers of chaining people up in a cave and making them watch shadows. Not surprisingly, Plato's brilliant mind got delighted whenever someone mentioned mathematics, particularly geometry.
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- Over his academy was written "Let no one destitute of geometry enter my doors."
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- Plato theorized that the sensory world as we knew it was merely a flawed impression of divine reality. Plato tinkered with the ancient idea that the universe was constructed of five geometric shapes, each one symbolic of an element: earth, air, fire, water, and aether.
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- Plato didn't create these shapes, but people have come to call them the Platonic Solids. Plato's scientific approach, breaking down the universe's massiveness into smaller, identifiable parts, was way ahead of his time. Plato got sacred geometry started.
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- Archimedes was a highly intelligent Greek mathematician. His complex geometric designs of 13 shapes are called the Archimedean Solids. The difference between the Platonic solids and the Archimedean solids comes down to the level of complexity.
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- How was sacred geometry informed real world architecture, culture, and art?
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- Sacred geometry has played a major role in Islamic art and architecture since the eighth century, with the interiors of countless mosques, towers, and palaces being adorned with fascinatingly complex geometric shapes, all following a specific grid, using a ruler and a compass.
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- Muslim religious art is quite different from Christianity, where churches are usually decorated with literal figurative depictions of Christ, Mary, and the saints. The core beliefs of both religions are mostly the same, so why did their religious art go in such different directions?
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- Rather than use human images, Muslims employed dazzling abstract geometry as a form of religious expression, creating some of the most interesting religious artwork in the world.
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- There are still common geometric rules relating to the architectural designs of churches, steeples pointing toward God, and that most famous of all Christian icons, the cross. The perfection of geometry symbolizes the perfection of the divine, compared to man: order in chaos.
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- Hinduism is also done with the math, specifically fractal geometry, according to academic researchers from South Korea. Hinduism's sacred shape is a mandala, the intersection of a circle and a square, symbolizing the relationship between humankind and the divine.
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- Hindu temples have actually been planned, designed, and built with the mandala as their geometric center.
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- Geometry is part of the Jewish world as well. Geometric symbols are a key part of the ancient Jewish mystical tradition known as Kabbalah. Anyone who has studied Kabbalah can affirm that it's a fascinatingly complex belief system, loaded with symbolism. The point where geometry and Kabbalah intersect is within the "Tree of Life," a diagram central to Kabbalistic belief.
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- The Tree of Life is composed of ten geometric circles and 22 bars. It's a map of the sacred path between mankind the unknowable creator who lies beyond human comprehension.
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- The tree represents the multi-layered process of creation, and the endeavor to return to a more divine consciousness by climbing this tree, one branch at a time.
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- Da Vinci did have a lot of insane hidden meanings in his art, as all of his most famous works employ sacred geometry. Leonardo was really big on mathematics. One of the major guiding components in his art was that whole "golden ratio".
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- The number 1.618, which creates perfect geometric symmetry. Da Vinci wasn't the first person to discover this dazzling geometric miracle, but he did give it new prominence and inspired others to, as well. Da Vinci believed that true, natural beauty only came from drawing proportions that lined up with this ratio.
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- All of Da Vinci's most famous works pinpoint the golden ratio in Vitruvian Man, the Mona Lisa, The Last Supper, and Annunciation.
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- “Flower of Life” is totally different from the Tree of Life. This psychedelic arrangement of overlapping circles at least dates back to Ancient Egypt, where it was found within the Temple of Osiris.
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- This same geometric symbol can be found within Phoenician art in the ninth century B.C., so there's no question that it was important.
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- So sacred geometry has played a huge role in countless societies, religions, and movements, with its myriad of perfect shapes appearing in architecture, temples, mosques, churches, and art since the dawn of civilization.
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- POISSON'S DISTRIBUTION is an equation for predicting the future. Poisson's distribution lets scientists take a bunch of data, graph it, and predict future events based off that.
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- For example: we would like to know how much mail a person is going to get every day. If we measure how much mail you get over a time period, and then put that data into the distribution equation, we can predict how likely it is that you'll get three, four, five, or 80 messages on any given day in the future.
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- People have used this to predict the outcome of sports games or if random farms in Kansas will get hit by a space particle.
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- FIBONACCI SEQUENCE is probably one of the most famous set of numbers in the world, the Fibonacci sequence can be described by an equation. To find the next number in the sequence, add up the previous two. The sequence keeps going. It's straightforward but probably holds the keys to the universe.
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- We can use the Fibonacci Sequence to draw spirals and shapes, which show up in a whole lot of places. Flowers follow the Fibonacci Sequence. Big things do too: the shape of spiral galaxies follow the Fibonacci sequence, as do the shapes of tropical storms and hurricanes. Why does it show up everywhere?
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- TUPPER'S SELF-REFERENTIAL EQUATION looks like an absolute mess, but when run through a computer, it makes a very specific graph. Graphed equations can look like all sorts of things. When you plot Tupper's self-referential equation, the lines on the graph spell out the equation itself. If that's not mathematical sorcery, we don't know what is.
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- Using the technique that Tupper used, people have set up websites to let us spell out words with math.
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- BBP ALGORITHM. What's the 12,094,854,921th digit of pi? Picking out random digits of pi is an impossible task. The number goes on forever. A team of mathematicians came up with the BBP algorithm, an equation to find pi's random digits.
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- That property was totally accidental. The team first developed their equation simply to calculate pi more accurately but then realized they had a digit-extraction algorithm. An algorithm that lets mathematicians figure out the value of a certain digit of a long number without having to calculate the earlier digits.
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- Say we wanted to know the 100th digit of pi. Instead of having to memorize all the way up to that digit, we can just use the BBP algorithm to give us the number. We don't even need to know the 99th digit or the 101st digit.
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- That's a pretty amazing thing for an equation to do, especially since it came up accidentally. It does spit out the number in base 16 hexadecimal notation, so we have to convert it to our normal base 10 number system. Unless you can count in base 16.
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- RIEMANN ZETA FUNCTION for prime numbers. They are numbers that can only be divided by themselves or one. Some examples are 2, 3, 5, 7, and so on. This function is used to predict exactly where the prime numbers occur on the number line. They seem random, but equations like the Riemann zeta function might predict where we can find them.
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- If you graph the function, all the places where the line hits zero can be connected by another line, one related to complex numbers. This property, called the “Riemann conjecture“, influences nearly everything. Researchers see it pop up randomly in quantum mechanics, number theory, and most importantly, figuring out where prime numbers will appear on the number line.
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- And yet the equation remains unproven. Researchers can find proofs for specific solutions, but nobody can find a general proof that works every time. It's such a big problem that mathematicians can win $1 million to solve it.
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- BEAUTY EQUATIONS: One of the best ways to predict the beauty of a person is using the Golden Ratio equation. The Ratio shows up all over nature, including in human faces. If a person's face matches the Golden Ratio more perfectly, then we like that person's face more. It's even possible to change pictures of faces to fit the Golden Ratio and make them even more beautiful. The Ratio holds the key to beauty.
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- SCHRÖDINGER EQUATION describes how quantum systems (like an electron or other particle) evolve over time. It totally revolutionized physics as we know it. It has some strange properties. It predicts something called “quantum tunneling“.
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- The quantum tunneling effect says that particles can do weird things, if they try to do it long enough. For example, a particle that couldn't travel through a solid wall would be able to, as long as it smashed itself against the wall long enough.
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- In our world of large things, that means if you kept running into an indestructible wall for an infinite amount of time, at some point, all of your particles would just jump through the wall. Fortunately, to do that would take longer than the age of the universe. That sounds absurd, but it's how the Sun works.
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- The equation also tells us that there are probably parallel universes hanging around.
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- CANTOR'S PROOF is one of the mind-blowing ideas in mathematics and it totally reinvented how we think of infinity. How big is infinity? In hard-core mathematics, it's not a useless question at all. In fact, it's super important.
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- Mathematician Georg Cantor investigated the idea of infinity, trying to figure out just how large infinity was. He developed the diagonal proof, to show that infinity has a size, and some infinities have different sizes than others.
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- That probably seems ridiculous, but it's mathematically sound. Cantor was able to show there were an infinite amount of natural numbers, which are whole numbers like 1,2,3,4, and so on.
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- He also showed there was an infinite amount of real numbers, which included all the decimal numbers between all the numbers. Here's the amazing part: the infinite amount of real numbers is bigger than the infinite amount of natural numbers. So there are different sizes of infinity, just like numbers are different!
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- EULER'S IDENTITY is considered by every mathematicians as the most beautiful equation in existence, Euler's identity is positively amazing and gives us some look into the interconnectedness of the whole universe. Richard Feynman called it "the most remarkable formula in mathematics."
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- The identity comes from the Euler's equation, which shows up for most students in undergraduate physics. People don't really think much about it. But when the “x” in the equation is set to “pi“, the equation equals zero.
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- With pi in the equation, it includes five of the most fundamental numbers in the universe: 1, 0, e, i (the imaginary root), and pi. Somehow, all five of those numbers are related to each other deep down in mathematics. The equation also has three of the most useful math operators (plus, times, exponentiation) and the relation =. Somehow, all the building blocks of mathematics ended up in the same equation.
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- Using these things, any civilization can build mathematics from the ground up, and it's all here in one little equation. If we were to leave one thing for our ancestors, should an apocalypse hit, it would be this identity, which would give them all the mathematical basis they need to rediscover everything we have.
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- P=NP: In computational mathematics, there are two types of problems: P problems and NP problems. P problems are a piece of cake for computers. NP problems are those that are not easy, unless we want to wait around 300 quintillion years to get the solution.
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- NP problems are weird though, because a computer can tell us that the answer to an NP problem is right if we show it a solution, it just can't get there easily on its own.
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- Here's an example of an NP problem: a salesman wants to visit 100 cities and still make it back home but only has 10,000 kilometers worth of gasoline. Can he make it to all the cities and back home with that gasoline? Think of all the different combinations of routes the salesman can take between all 100 cities, and its pretty easy to see that it would take a long time to figure out a solution because a computer would have to try every possible path.
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- But, if we gave a computer a path already solved, it could pretty easily figure out if the path worked. Just add up all the kilometers, and if its less than 10,000, and problem solved.
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- So what's the big deal? Well, in math-talk, P=NP says that there are no true NP problems. A computer can theoretically solve any complex problem. If somebody can prove that P=NP, they will make a sweet $1 million ... And completely revolutionize the world.
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- Theorists believe if somebody can prove that P=NP, they will also discover the key to breaking any encryption. Everything, from Gmail accounts to Swiss bank passwords would be open! Anybody who verifies P=NP had better hide, because we bet a lot of governments would want them dead.
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- FRIEDMANN EQUATIONS: Russian physicist Alexander Friedmann created these equations in the 1920s to explain how the universe was expanding. They show that the universe should expand. But when the equations came out, it looked like the universe wasn't expanding at all. Both sides of the equation were in balance. This is a totally unstable condition because The slightest imbalance would run to infinity.
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- Einstein freaked out about that and added a new term to the equation called the “cosmological constant“, a new variable to make the equations say that the universe is static. He didn't like the solution, so he broke the equation.
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- Soon after he came up with his "fudge factor," astronomers discovered that the universe is expanding. The Universe is not in balance. There was no need for a new variable. But that didn't solve the biggest mystery though: what was making the universe expand?
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- When astronomers started trying to figure it out, they couldn't see anything that would make the universe get bigger and bigger. Friedmann somehow predicted that the universe has a force that has eluded discovery for nearly a century. Eventually, astronomers just called it “dark energy“.
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- There's definitely something pushing the universe apart, but even today, nobody can figure out what that something is. It's a gigantic mystery, but the equations say that it has to exist. They show us the future of our universe will be dark energy pushing things apart.
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- They also imply that the universe might be shaped like a “saddle“.
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- RUSSELL'S PARADOX: Imagine a barber who has this sign on his store: "Do you shave yourself? If not, come in and I'll shave you! I shave anyone who does not shave himself, and no one else." Seems straightforward, but here's the question: does the barber shave himself?
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- If he does shave himself, then he shouldn't shave himself because he only shaves people who don't shave themselves. But then that means he has to shave himself, since the first statement means he doesn't shave himself.
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- But now he is contradicting the first statement. He both shaves himself and doesn't shave himself.
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- This isn't just a fun logic trick to play on our friends. The mathematical version of this paradox (which only uses variables and a mathematical object called a "set") is a profound statement, and totally revolutionized “set theory“.
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- It lead to some far-out theories like “Godel's Incompleteness theorem“, which says that any mathematical system will have problems that are impossible to solve, and the discovery of different sizes of infinity.
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- SPHERE EVERSION: Topology is the field that studies how shapes change as they're twisted and deformed, often in ways that can't happen in real life. For example: sphere eversion, which is turning a sphere inside out without making any tears, folds or creases on its surface.
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- That's impossible to do or even imagine in real life. How can you turn something inside out without tearing or folding it? With math!
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- Doing one of these eversions mathematically was impossible to prove for a long time. Now, topology people can do it all the time, especially since computers can crunch the equations for us.
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- Most people have a hard time thinking of applications of topology. The field shows up in really random places, from computer coding to chemistry and into the weird world of string theory, a physics theory to describe all of reality.
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- The cutting edge fields use topological techniques and mathematics. So who knows, maybe the sphere eversion will hold the secrets of the universe?
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- FUTURE PREDICTION EQUATION: Lots of mathematics revolve around predicting the future. For example: if we drop a ball from an airplane, how long will it take the hit the ground?
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- But some scientists want to predict more complex things. According to a group of neuroscientists at the University of Sussex, they may have found a way to predict incoming disasters, from massive problem like stock market crashes to individual tragedies like brain aneurysms. Turns out, those two situation follow similar mathematical trends, even though they're vastly different.
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- Their equation relies on the flow of information in complex systems and relies on a similar simulation to phase transitions, like what we see when water turns to ice.
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- According to their equation and computer simulations, by analyzing how information flows, we can predict when a "phase change" of fortune will happen, when normal events suddenly turn into a huge catastrophe. Like the corona virus that is attacking us right now.
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- It's a really complex idea and it could melt our brains. Thinking of the flow of events like the change from water to ice is super odd, but supposedly it works. Mathematicians can use it to predict when a future tragedy will happen and then take steps to prevent it.
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- Will we even believe the predictions? It is in the math. But, how many can understand it. Hopefully you learned a little math to think about.
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- March 12, 2020 2664
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