The Fibonacci sequence is a naturally occurring pattern. The numerical patten is 0, 1, 1, 3, 5, 8, 13, 21, 34, 55, 89, 144, and so on. Look at an artichoke, a pinecone, or even a sunflower and you will see the golden spiral. Though Fibonacci did not actually discover the pattern it is named after him and admired by people who enjoy the fractal pattern in nature.
Issue 7 | Winter 2013 ÂŠ 2012-2013 Origins, founded by Melanie E Magdalena in association with BermudaQuest
Copyright: This work is licensed under aÂ Creative Commons Attribution-ShareAlike 3.0 Unported License. Permission of the authors is required for derivative works, compilations, and translations. Disclaimer: The views expressed in this publication are those of the authors and do not necessarily reflect the position or views of Origins. The publisher, editor, contributors, and related parties assumes no responsibilityof loss, injury or inconvenience of any person, organization, or party that uses the information or resources provided within this publication, website, or related products.
IN THIS ISSUE:
The Earth Pyramid
A global project that will unite ancient technology and modern voices for cultural preservation. s. ward & v. brown
Math In Our Lives
Why you are stuck learning algebra year after year and how you do use it! MARGARET Smith
Yep, you read that right. The answer can be 4, or Fish! alex vosburgh
Mathematics Through The Ages
Arabic numbers are not alone! Melanie e Magdalena & David Bjorklund
The Earth and our Bodies in fractals. morgan v courage
Tau-ists are never Pi-ous
Tau vs Pi: pick your constant. ETHAN KELLOGG
DEPARTMENTS 6 9 41 42 55
From the Editor Creature Feature Object of Interest Sites to See Review It
6 | ORIGINS
From the editor... Happy Winter Solstice to you all! Personally, I wish I could spend this fantastic day at an ancient site and observe the sun set in an extraordinary alignment with a structure built thousands of years ago. Throughout history math has been a component used for the advancement of civilization astronomically, architecturally, and scientifically to name a few. Today, our computers run on mathematical algorithms with zeros and ones. The present as we know it could not exist without the sworn enemy of most: math. So I say its entwined with being a human, but why do ALL of us have to learn math for our entire school lives? Calculators exist, plus smartphones! Apps can solve all the problems we do not want to calculate.
ALEXEY KLJATOV | CC BY-NC 2.0
In this issue, we’re going to explore the history of numbers along with systems used to perform math. We’re going to tackle the mystery of why we have to learn it. Spoiler alert: you use it more often than you think (and most of the time don’t even know it). Plus, we’re traveling the world to some of the most spectacular sites that were built (mathematically) for astronomy phenomena, also known as archaeoastronomy. As humans, we’ve tried to understand math by creating visualizations, such as numbers, so we can achieve a numerical goal. Nature uses math too. From the realm of fractals, explore what fractals are and how they manifest in nature in “Terrae Fracti” by Morgan V. Courage. Also, when you’re ready of course, we’ve included some fractal generators you can use at home to make your own fractal creations. We would love to see them and show the world through our site if you decide to share. Finally, Origins would like to begin awarding Research Grants so new explorations can start, the results shared with the world. Join us Virtual Traveler with just $1! Wishing you all the happiest of holidays, Melanie E Magdalena, Editor-in-Chief firstname.lastname@example.org
STAFF MELANIE E MAGDALENA Editor-in-Chief & Creative Designer The Founder of Origins and BermudaQuest. MARGARET SMITH Copy Editor Anthropology undergraduate focusing on Japanese studies for her career in archaeology. ETHAN KELLOGG Graphics Deranged internet hermit who spends his time reading fringe mathematics and contemplating ‘The Truth.’ ALEX VOSBURGH Marketing & Public Relations Our newest recruit eager to take on challenges and explore the scientific world. FIDEL JUNCO Director of Donor Relations Specialist in marine animals and other exotic reptiles, birds, and amphibians.
CONTRIBUTORS DAVID BJORKLUND Athlete and biology undergraduate minoring in history. VINCENT BROWN Vintuitive small business promoter. MORGAN V COURAGE Word architect and mathmatician. KAREN MEZA CHERIT Undergraduate studying Business Management at ITESM. STEVE WARD Director of Earth Pyramid.
SPONSOR ORIGINS TODAY http://myorig.in/1kr8wlG
CENZ | CC BY-NC-SA 2.0
Creature Feature Aye-Aye
Fidel Junco Madagascar's Grim Reaper
When it comes to extraordinary creatures, as unique as snowflakes is the aye-aye. Malagasy superstitious legend paints the aye-aye as a Grim Reaper: if it points at you with an elongated middle finger you are marked for death unless you slaughter the defenseless animal. With a swiveling, thin, and long middle finger, claw-like nails, squirrel-like bushy tail, and rat-like eyes and teeth, Daubentonia madagascariensis is by far one of the most unusual primates. It was first classified as a rodent! It’s a lemur.
Aye-ayes, endemic to Madagascar, appear in the northwest dry forests and in the east coast rainforest. Their bodies are covered in a thick coat ranging from brown to slate grey with white flecks, lighter at the hair tips. Yellow-orange eyes are accentuated by their pale face (compared to the rest of their body) with large, leathery ears. Unlike other lemurs, aye-ayes do not face the issue of their teeth wearing from nut and wood gnawing: their incisors are ever-growing.
aye’s strong incisors tear through whatever blocks the master forager.
Human meddling has placed the aye-aye on the International Union for Conservation of Nature (IUCN) Red List. People hunt them in fear of the “death omen” their middle finger invokes; plus, their habitat shrinks with the expansion of human settlements. This is not the first time the aye-aye family has faced extinction. About 2,300 years ago, when humans first arrived on the island, MadagasThe largest nocturnal lemur is well-adapted for car was home to a giant aye-aye weighing five foraging with its thin and elongated fingers. The times more than today’s extant cousin. middle, or third digit, is so thin it appears to hardly be skin and bones. Perfect for scooping pulp from Coincidentally or not, the arrival of people marks fruits and tapping branches to find cavities full of the island’s moment in history when the giant ayeinsects and larvae (the major part of its diet), the aye died out. Researchers have found the extinct extended third digit extracts prizes after the aye- aye-aye’s teeth with holes drilled through either Origins Scientific Research Society
10 | ORIGINS
suggesting the teeth were worn as pendants or, according to WIRED’s Matt Simon, islanders provided giant aye-ayes with dental care. Though endangered, the aye-aye can be saved from purposeful slaughtering (and possible dental experimentation) if public programs in Madagascar work with educating the people about the lemur’s uniqueness. Species come and go, but is it right for people to be the only deciding factor for who and what lives on and is permanently removed from Earth’s ecosystems? t
Learn more about aye-aye conservation efforts regarding this near threatened species with Durrell “Saving Species from Extinction.” www.durrell.org
AYE-AYE HAND SHOWING THE ELONGATED MIDDLE FINGER, From the University of Copenhagen Zoological Museum. Photo by Dr. Mirko Junge. www.knowyourorigins.org
THE EARTH PYRAMID | 11
An artist’s impression of what the Earth Pyramid will look like.
The Earth Pyramid
Creating a focal point for peace and environmental education Steve Ward & V incent B rown Our modern world is bristling with technology, celebrity, and all the trappings of a wealthy society but what about the future? We hear snippets of information on the news about global warming, melting ice caps, and dwindling resources but these tend to be soon forgotten as life goes back to “normal.” At what point do we start to look at these issues as a global community and start working together to try and come up with solutions?
people’s attention. An example of this was recently carried out by the energy drink company Red Bull. They have built their brand around extreme events culminating in the Red Bull Strata project. Getting a man to jump out of a capsule from the edge of space had an audience of Millions on the edge of their seats and created an amazing platform from which to promote their brand. The stunt had nothing to do with an energy drink but the interest it created was used to great effect.
T h i nk BIG, Ac t BIG The idea of creating a new pyramid to act as a focal point for peace and environmental education may seem to be a strange choice but in order to educate and promote your message you need to get
Building a structure that hasn’t been attempted for around 4,000 years will certainly create a platform from which education could be presented. The whole Earth Pyramid project from start to finish is designed to engage and encourage participaOrigins Scientific Research Society
12 | ORIGINS
Internal Chambers will hold time capsule boxes. Each country will be sent three time capsule boxes: a government box for its culture and achievements, a school box for children to discuss the future of the planet and how they want to be remembered, and a family box where the hopes, dreams, and opinions of families can be recorded for the future to remember. The global issues we face today will be saved for the future to learn from and give new minds a chance to find solutions that move forward in peace and cooperation.
C ON N EC T WITH EA R TH PYR A MID
THE EARTH PYRAMID | 13
tion from the initial global vote to decide where the structure should be built through the final stages of filling the structure with contributions from schools around the world. Te s ti ng An c ie n t Te c h n iqu e s a nd Ne w Th e o r ie s The construction process itself will be an amazing mixture of new and ancient techniques designed to showcase new sustainable technologies within the construction industry (geopolymer concretes ETC) and answer some of the many questions we have about ancient peoples and how they created these amazing structures of the past. How did the ancients build these massive structures with such precision that enabled them to remain intact for over four and a half thousand years? The Great Pyramid of Egypt was built
with over two million stones weighing almost three tons on average, many of the heaviest being quarried almost a thousand kilometers away. What sort of mathematical knowledge is required to achieve such a feat? Earth Pyramidâ€™s construction aims to answer such questions and test some of the latest theories. Media interest in the construction phase will ensure that the platform for education will remain strong throughout the entire project (expected to be ten years) and make it a great focal point for getting children looking at the future of our planet. G enerati ng Pros per i t y from a Nati onal I nves tme n t Several studies have been undertaken on the costs of building a replica of the Great Pyramid in
One of the Earth Pyramidâ€™s casing stones. Origins Scientific Research Society
14 | ORIGINS
One of the Earth Pyramid time capsules.
modern times and as expected the numbers are staggering. The Earth Pyramid at 50 meters high with a base length on 70 meters per side is still a large structure that will require a large amount of funding. This investment will have a direct impact in the country where it is built by creating jobs during the construction process and generating income through tourism that can be used to tackle some of the issues raised during the voting process. To put this in context, the Eiffel Tower in Paris generates over 3 billion Euros per annum through tourism. If the Earth Pyramid can generate even a fraction of this on an annual basis it will make a real difference to peace and environmental projects within the chosen country. The other consideration about the Earth Pyramid cost of production can be compared to money spent on war and conflicts, plus the exploitation of Earthâ€™s resources. Peace and environmental projects get very little funding in comparison and the result is they struggle to get their message across to the public at the required scale to make a difference. With many of these issues starting to magnify within the next fifty years, the world needs to start placing more emphasis on the education surrounding them. www.knowyourorigins.org
Pl atfor m for the Worl d â€™s I ndi genous Peopl e The project will also create a platform that will give a voice to those countries and indigenous peoples who struggle to have their opinions heard. There are over 7,000 indigenous cultures in the world, many of them facing immense challenges but very little press is ever given to their voices. The same can be said for many of the smaller nations on the planet. It is humbling to think that some of these nations, like Kiribati, Palau, Tuvalu, and the Maldives, may not exist over the next few decades due to the rapid rise in sea levels. The fate of all these peoples is a reflection on our future. It is important that we notice NOW. Educati ng a New G enera t i o n There is a vast array of educational possibilities surrounding the Earth Pyramid that will be explored as the project progresses. This is an immensely thought-provoking venture that has the possibility to create a real momentum for empowering a generation with the educational tools needed for change. t
MATH IN OUR LIVES
AND SOME EXAMPLES
OF HOW YOU USE IT
(even if you don’t want to) Margaret Smith
OLGA LEDNICHEN KO | CC BY 2.0
When we were younger, we used to always ask our teachers, “When will this ever help me in real life?” What we did not expect was that the subjects we learned in school would actually benefit our daily lives in the future. Little did we know, this would even happen in what most of us would consider the most difficult subject: math. And not just basic math, but even full blown algebra would become something we use in everyday life. Don’t believe me? Well then check out these five examples.
SEAN MACENTEE | CC BY 2.0
18 | ORIGINS
1. Cooking Remember when we had to learn fractions in elementary school? Then do you remember how using fractions suddenly got a lot more complicated when we entered algebra? Well, believe it or not, fractions have always been complicated (surprise!), especially when cooking a nice little meal for ourselves. Let’s use baking cookies as an example. In a recipe, there is a bunch of ingredients like flour, sugar, chocolate chips, and eggs. Now how could this possibly be math? Math is not food. Food is food! However, cooking is rarely done in whole numbers, but in fractions. For example, we need 8/3 cups of flour, 3/2 cups of sugar, and 5/3 tablespoons of baking soda in order to make this batch of cookies, but those numbers are not very appealing. So instead, what is typically written on the directions is 2 2/3 cups of flour, 1 1 /2 cups of sugar, and 1 2/3 tablespoons. Yet when we count out the amount we need to put in our handy dandy mixing bowl, we actually count the improper fractions in order to make sure we have the right amount. 2. Pumping gas Pumping gas is simple, right? It doesn’t seem like we have to do math every time we do it, especially since we do it so often. However, whether we like it or not, we are doing math. Especially when we see gas prices go up. There are two main ways people get gas: either filling up their tank fully, or getting 10-20 dollars worth in order to get the 1/2 or 3/4 of a tank that they want. But how do they know they are getting the right amount of gas needed? By setting up a simple algebraic equation. Let’s assume gas has miraculously dropped in price and is only $2.50 per gallon. We need to fill up our tank and take advantage of this! But how much do we need? We have a 15 gallon tank in our car, but we still have a quarter tank of gas. Now how do we figure out how much to get? First, we figure out the proportions; 3/4 equals X/15 (oh no, it’s fractions again!). Now 4 cannot be multiplied nicely in order to equal 15, but to save any headaches, the answer is 11 1/4 gallons (or 11.25 gallons) are needed to fill our imaginary gas tank. That’s all fine and dandy, but how much will this actually cost us? To answer that, we can use a simple algebraic equation ($2.50*11.25= X) in order to find out. Solve for X, and we will know exactly how much money to give the clerk to get the perfect amount of gas using our convenient change jar kept in the car. For those counting at home, $2.50*11.25= $28.13. Bonus: this is a great way to get rid of all your pennies. www.knowyourorigins.org
MATH IN OUR LIVES | 19
3. Road trips Let’s go ahead and expand on this idea a bit further. It’s time for a road trip! And to make this as awesome of a road trip possible, let’s start from Los Angeles, California and drive to New York City. That’s a round trip of 5600 miles (and that even includes a pit stop in Las Vegas). But how much is our venture going cost us? Well, let’s assume we wrangle ourselves a car with a 30 mile per gallon efficiency. Now we have to figure out how many gallons of gas our trip will take, then use that to find out how much it will cost us. The equation looks like this: cost = total miles/miles per gallon * gas price Well the gallons we will need to buy come out to about 187. Average gas price right now is around $3.21 a gallon. That means our trip is going to cost $600.27, although I’m sure we can find a quarter somewhere along the way. 4. How long will the drive take? Algebra also pops up into our life whenever we drive from place to place, specifically when we want to figure out how long it will take to get there. That way, we can plan accordingly. In order to do this, we take the distance we are traveling and divide it by the speed we would like to go. Let’s use our road trip idea as an example. We already know we’re driving 5600 miles, so let us assume our average speed is 60mph. We can use the handy equation of time = distance/speed. In our example, it works out to be 93 hours and 20 minutes.
S BYC C S|
Origins Scientific Research Society
20 | ORIGINS
5. How long will it take to pay off those pesky student loans? Whether going on an epic road trip, heading to college, or buying a house, most people have to worry about the money it will cost. Sometimes, this leads to taking out loans in order to achieve that goal. Typically, we can put it off as a future worry, but we would all like to know when we no longer have to chop off part of our pay check in order to pay them off. Let’s imagine that while going to school, you had to take out some loans in order to carry you through the last two years of school. You got a $3000 unsubsidized loan and a $2500 subsidized loan. You want to try to get these both paid back within 5 years of graduating. But, in order to do that, you first gotta figure out how much to pay. Let’s set up a complex algebraic equation so that we can skip going to an accountant. The interest is 2.5% for both loans, but the unsubsidized loan accrued interest while you were still in school. That means the unsubsidized loan will have accumulated interest for 7 years, while the subsidized will have 5 years of interest added to it. The simplified equation you use to calculate your interest is: 3000*rt+2500*rt=X, where r=rate and t=time. Since the time is different for each loan, it works out to 3000*(.025*7)+2500*(.025*5.5)=X. Math it out and you find out that you end up owing an extra $837.50. Adding that to the original borrowed amount means you owe $6337.50. Next, divide that by 60 (12 months * 5 years) and you get $105.63. That’s how much you need to pay every month to have the loans paid off in 5 years.
Despite some of our best efforts, math still manages to permeate our everyday lives. While most of the time we may be able to get away with pretending it doesn’t exist, there are lots of instances where doing just a little bit of math will save us a lot of hassle in the long run. So don’t be afraid to bust out a calculator every now and then. (Besides, it comes on your smartphone. Use it like all your other favorite apps!) And, as always, remember to show your work. t www.knowyourorigins.org
2+2 = FISH | 21 RINGO.COCO | CC BY-NC-SA 2.0
2+2 = Fish A lex Vosburgh
So in my travels down the avenues of the vast crevices of the brain, I stumbled upon a seemingly magical theorem that I would like to pose to you all. Because if you put your mind to it, anything is possible! 1 pie = full circle = 2 pi in radians 1 pie = 2 pi Divide by pi and you get e=2 2 = 2-ish To make this a bit more readable let’s divide by 2 and multiply by, let’s say f, and you get f = f-ish or fish (because I like fish) Now it is known that 4 = four But ‘our’ is a singular possessive pronoun, so it can be written that our = 1 Hence, 4 = f*1 = f Substituting, 4 = fish And since 2+2 = 4 it can be written that 2+2 = fish And that is why we show our work; because if you have a good reason, you will be amazed at what you can get away with. Now follow your dreams.
Origins Scientific Research Society
Chinese Bars from Katsuyo Sampo by Seki Kowa.
MATHEMATICS THROUGH THE AGES | 23
T h ro u g h T h e A g e s Melanie E Magdalena & D avid B jorklund F i ng e r s a s Ca lc u la to r s
Fingers are the oldest calculators! Early in life, we naturally begin counting with our fingers. Having ten fingers makes Base 10 so common in number systems. A single symbol within a number is called a digit, which comes from â€œdigitusâ€? the Latin word for finger. Numerals got creative over the years. On one hand it is possible to sign 1-9, tens, hundreds, and thousands! In musical acoustics, Confucius and Pythagoras regarded the small numbers 1, 2, 3, and 4 as the source of perfection in harmonics and rhythms. Mathematics in music has more to do with acoustics than composition. Un a r y Ta llie s Tally marks are a simplistic form of counting. We tend to learn how to do this very young. Lines are placed next to each other. Tally groups are separated into groups of five, the fifth line going diagonally across the vertical four lines. There is no positional system. You just add up in groups of five! A positional system can be used though. In the right hand column you have units from 1-9, then you have groups of ten (or five-tally pairs, which two of equal ten), then the same for hundreds and so on. This system is considered unary: one is represented by a single symbol and then five or ten has a new symbol. Ch in e se Ro d s The first Chinese numerical system recognized originated as far back as 1400 BCE. Numbers in
this standard system are written as words: different symbols were used for numbers 1 through 9 and the same goes for powers of ten. They were not written as a positional system. The number 153 would be written as one-hundred-five-tenthree. The Chinese also used the number zero. The financial system works in the extant same way but with different symbols. Rod numbers began around the 4th century BCE based on an early form of the abacus. Used on a counting board divided into rows and columns, numbers were represented by rods of bamboo or ivory. Rods were lined up using a positional system in the rows and columns: the right-most column would be units, followed tens, hundreds, and so on. Rather than putting nine rods in one box, a rod would be placed at right angles to represent five: this means that no box had more than five rods at one time. Also, a right angle rod would not be used until six; five was represented with five rods. The only way to distinguish between the nine numerical combinations was its placement on the board. Babyl oni an Power s of 6 0 A positional number system is one where numbers are arranged into columns. A Base 10 system, for example, starts with units in the right hand column, followed by tens, hundreds, thousands, and so on respectively to the left. For Babylonian numerics, the right column starts with units (ones and tens - each has a symbol), followed by x60 to the left, then x3600, and so on. They did not have a representation for zero. The column positioning is the only way to distinguish Origins Scientific Research Society
24 | ORIGINS
1 and 60 was their position. If there was a zero in a number calculated, the column position had a slanted symbol rather than a void. In total, there are three symbols used for Babylonian numbers. Base 60 is still used today, not by Babylonians but in clocks! We have 60 seconds in a minute, and 60 minutes in an hour. Plus, 60 is used in circles: 360 degrees makes a full circle, 60 minutes are in a degree, and 60 seconds in a minute. Though clocks and circles use Base 60, there is no relation between angle minutes and seconds and time minutes and seconds. A nc ie n t E gy ptia n N umb e r s & Fra c tio n s Ancient Egyptian numerology was written in hieroglyphs with a Base 10 system (the equivalent to how many fingers you have). The number 1 was a line, a horseshoe shape was for 10, and a coil or spiral was 100. A lotus, or water lily, was used for representing 1,000, a finger for 10,000, a tadpole for 100,000, and a million was the god Heh. A circle was used for infinity. When multiplying numbers, the symbols show the final value without a sign for zero. So if 7x3=21, 21 would be written as two 10 symbols and a line for 1. Fractions worked differently. The god Horus had his eye gouged out and torn to pieces by his enemy Seth. The pieces of his eye were used as the basis for the ancient Egyptian fraction system: 1/2, 1/4, 1/8, 1/16, 1/32, and 1/64. These fractions were added together to reach a new value. One was equivalent to the entire eye. Now if you add up the fraction values, Horus’ eye only adds up to 63/64 - it was believed that the last 1/64 was made up of Thoth’s magic, the god who healed Horus. There was also no way to depict 1/3. V i g e sim a l Ma y a n s Mayan numerics used a Base 20 or vigesimal system, the equivalent to the number of fingers and toes. Dots represented units and lines (or bars) for the number five. Numbers were written vertically with the lowest denomination on the bottom. The first five (stacked) place values were multiples of 20. Zero was included, denoted with www.knowyourorigins.org
a “shell” symbol. To make things “more complicated,” numbers could also be represented graphically with hieroglyphs; some look like faces. Some Mayan groups used a Base 18 system for development of the calendar. Each month had 20 days and the year had 18 months. This created a 360 day calendar supplemented by five “bad luck days” at the end of the year to replicate the 365 day solar year. I nca Qui pus The ancient South American civilization of the Inca was highly developed with no writing system. They used the quipu, a system of knotted colored thread or string around thinner strings. The closer a knot was to a large cord, the greater its value. Little is known about the quipu since few survive in the archaeological record today. The manner in which knots were tied and colored may have been significant, but today that significance is shrouded in mystery.
MATHEMATICS THROUGH THE AGES | 25
incorporation of Greek letters into mathematics as certain constants (like pi), Classical Greece only had capital letters. Roman Numeral s The Roman numeral system uses seven symbols: I, V, X, L, C, D, M. Each symbol corresponds to the following respectively: 1, 5, 10, 50, 100, 500, 1000. A line added above the symbol expanded the values past 4,000. A line over V, for example, would be 5,000; each symbol after that would be 10,000, 50,000, 100,000, and 1 million respectively. The system is unary in principle but has a twist. If the value is beneath 5 (or V) it is subtracted and if it is greater it is added (4 is IV and 6 is VI). Numbers 1, 2, and 3 are I, II, and III, then after that everything is a compound number involving addition or subtraction. The number 3,647 would be written MMMDCXLVII (MMM-DC-XL-VII = 3,000-600-40-7, or 3,647).
G ree k Attic Sy ste m Based on the Greek alphabet, originally created by the Phoenicians with 600 symbols, the Attic system used a condensed version of 27 symbols. Today only 24 are used. The purely mathematical symbols vau, koppa, and sampi became extinct. Numbers 1-9, or the units, have individual symbols from the alphabet; the tens (10, 20, 30…90) also have there own alphabet symbols; and finally the hundreds (100, 200, 300…900) have alphabetical assignments. The symbol M represented 10,000 and multiples of this had symbols placed in front of it. A comma placed in front of the numerical sign was used to say zeroes were involved and enabled them to count in the thousands. Since the system lacked the need for zero, if there was no tens value then a tens letter was not needed! To distinguish between numbers and letters, Greeks often placed a mark by each letter, such as an “apostrophe” of sorts. Also, unlike the modern
A somewhat easy way to remember what the different letters mean, according to Jo Edkins is as follows. Think of I as a finger, or one. Hundred in Latin is Centum (C) and we still use the word “cent” in the context of 100 cents is a dollar. Latin for thousand is Mille (M), like millennium (a thousand years are in a millennium). Five fingers equals five (obviously!) and if you were to connect your thumb and pinky diagonally, it makes a V-shape. Do this with both hands and you have an X for 10 (two V’s make an X). If you were to chop the C for 100 in half, you get an L-like shape for 50. Now the last one needs your imagination: If you cut off half an M, you sort of get a D for 500. Let’s see if that helps you remember your Roman numerals! Today you see Roman numerals still used on clocks, as chapters in books and outlines, and as the copyright year shown at the end of British TV shows. Senar y Though not seen in many places, Senary is a Base 6 system. The Ndom language of Papua New Guinea and the Proto-Uralic language are suspected to have used Senary numerics. The Origins Scientific Research Society
26 | ORIGINS
system has a lot to do with finger counting. The hand can have six positions: the fist and five extended fingers. The system is a bit complex, but the punch line is you use one hand to represent units and the other to represent sixes. This allows you to count up to 55 in the Senary system, the equivalent to 35 in the decimal system, rather than only to ten! Today, a Senary system can be observed on dice. There are six faces to a die. You can either add up the values between dice or use the Senary technique to get higher values. Oc ta l Yuki (California) and Pamean (Mexico) languages have octal systems used by speakers who count using the spaces between fingers rather than the fingers themselves. More recently, in 1801 James Anderson criticized the metric system used by the French. His solution was coining the term â€œoctalâ€? for a Base 8 system for recreational mathematics, primarily for weights and measurements since the English unit system was already mostly octal. The octal system today, or oct, is made from binary digits in groups of three. To visualize this, replace the power of ten with the power of eight. The number 74 in the decimal system would be equal to 64+8+2, or 112. The only times you would see this might be some computer programming languages such as C or Perl. Octomatics (www.octomatics.org) is a visual calculation portal for the octal system. Ara b ic Around the 4th century BCE, the Hindus in India invented the Hindu-Arabic number system. It spread to the Middle East around the 9th century CE and was used by Arab mathematicians and astronomers. Once it spread to Europe, people adopted the system over the visible calculation form, the abacus. Counting with Arabic numbers was simpler. Fibonacci even wrote a book about Arabic number in the 13th century CE called Liber Abaci (Book of www.knowyourorigins.org
American Sign Language, Numbers 1-9.
MATHEMATICS THROUGH THE AGES | 27 BRANDON GIESBRECHT & MELANIE E MAGDALENA | CC BY-SA 2.0
Calculation) which made him famous for spreading the numeral system in Europe. In his book, he uses examples of his famous Fibonacci sequence (which he did not discover, but noted). Bi nar y Computers do not count the way the rest of the world does. With a two number system, or binary, only the digits 0 and 1 are needed. The system has existed prior to the Information Era but is was first documented as the modern system by Leibniz in the 17th century. Binary numbers are usually longer than decimal numbers and the strings of zeroes and ones grow to be even longer when numbers get big. One million takes twenty binary digits! For computers, one means an electrical current is flowing and zero means that the current is switched off. Binary can also be used to represent letters and symbols. Each character is a combination of eight digits. “A” is 0100 0001 and “a” is 0110 0001. If you want to try out some binary converting, visit Roubaix Interactive’s website! Concl udi ng As we look back at all of these different systems of math we must realizethat without these mathematical systems many of our technological achievements would have stalled. Math is a pivotal part of construction. Large monuments like the Egyptian pyramids utilized a standardized system of measurement to achieve precision and accuracy. The Roman Coliseum would not have been possible without a system of mathematics. The invention of currency also helped move society from nomadic to agrarian which relied heavily on counting. Currency allowed for a standard of trade which made it possible for transactions to be made with ease. Zero became more prominent because of its usefulness in representing the absence of something. In the 1900’s zero became utilized in one of the most monumental mathematical system of our era, binary, which led to the internet and then to websites like Wikipedia, Google, and now Origins. Imagine what our world might look like if we never came up with these mathematical systems or the concept of zero? t Origins Scientific Research Society
BEATRICE TIBERI | CC BY-ND 2.0
terrae Fracti Morgan V Courage
30 | ORIGINS
Euclid’s Elements, first published in 300 BCE, is the most studied and edited book after the Bible. The definitions, axioms, theorems, and postulates remain unchanged today in study and use in modern practical applications such as biochemical modeling, medical imaging, sequence alignment, and nanotechnology. Euclidean geometry defines integer dimensions using the Pythagorean theorem, pi, and formulas for surface area and volume. The Earth’s multi-dimensions cannot be confined to classical geometry - lines, planes, and solids; it is fuzzy, dynamic, and chaotic in the complex numbers and fourth dimension.
“In the whole of science, the whole of mathematics, smoothness was everything. What I did was to open up roughness for investigation.” – Benoit Mandelbrot T he D eve lo pm e n t of th e F r a c ta l Co n c e pt Describing this continuous non-integer dimension and non-differentiable functions started to formalize as recursion with Richard Dedekind (1888) and continued with Giuseppe Peano’s five axioms for positive integers (1891). Louis Pierre Joseph Fatou wrote his thesis on integration of complex function theory setting the groundwork for iterations: the values and all nearby values behave similarly under repeated iterations of the function. Julia Gaston (1918) wrote “Mémoire sur l’itération des fonctions rationnalles” focusing on the iterative properties of a general expression: z4 + z3/(z-1) + z2/(z3 + 4 z2 + 5) + c The formula for the Julia set is Zn+1=Zn2 + C where C is always constant during the generation process and the value of Z0 varies. Each point of the complex plane, the value of C, is associated with a particular Julia set. This mathematical ingenuity died with Julia until the advent of computing machinery with the ability to visually express the beauty and express the fourth dimension. In the 1960s, Benoit Mandelbrot, an IBM employee, originated the term fractal to solidify the past www.knowyourorigins.org
one hundred years of mathematical development in endless self-similarity iterations of equations describing roughness and irregularity on all systems and life on Earth. The famous Mandelbrot set is graphically represented by something similar to a black beetle and is generated from an algorithm based on Julia’s recursive formula: Zn+1=Zn2 + C. Unlike the Julia set, C is migrated across the plane from the initial point of the iteration process. The points of the complex plane are separated into two categories and the color scheme is denoted by the value of the point. The formula’s starting point is zero and generates what may appear to be random and a somewhat meaningless set of numbers, but the graphic portrayal shows the self-similar reclusiveness over an infinite scale. The formula is a summary of the fourth dimension — the real world that includes an infinite set of fractal dimensions which lie in intervals between zero and the first dimension, the first and second dimension and the second and third dimension. Fractal geometry describes, in algorithms, the non-integer dimensions. Fractal generators are computerized paint-bynumbers, a stimulating combination of math, computations, and art.
Feliciano Guimar達es | CC BY 2.0
MICHAEL LUX | CC BY-ND 2.0
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TERRAE FRACTI | 33
Fractal s i n Nature The branches of a deciduous tree stark against the winter sky clearly show the natural fractural pattern: the repetition smaller copies of itself from the trunk to the tips of twigs. This structure with a seasonal and intricate process of photosynthesis serves the purpose of respiration. The leaves on branches absorb carbon dioxide from the air and return oxygen into the atmosphere. Remarkably, a lung’s bronchiole tubes and arteries resemble a self-repeating branch pattern whose purpose in the body is also respiration. In reverse to trees, the lungs breathe in oxygen and exhale carbon dioxide. Almost as a reflection in the eyes looking at the trees or in a microscope at lung tissue, this same tree pattern repeats in retinal blood vessels that provide oxygen to the eyes.
Fr a c ta l s a re a n a t u r a l phenomenon in eve r y t h i n g s e e n a n d unseen by the unaided eye, ranging f ro m t h e s p e c ta c u la r to t h e i n te re s t i n g . Th e M iller Sc h ool of M edic in e a t t he Uni ver sit y of M iami is u sin g f rac t a l a na l y s i s of t h e retin a to determin e th e he a l t h of th e retin a’s c apillar y n etwo rk a nd provide mic ro vasc u lar c h an ges a s s oc i a te d with diseases su c h as st ro ke, hy pe r te nsio n an d diabetes. A Retin al F unc t i ona l Imager is u sed to sc an th e e ye s ’ c a pillaries with o u t t h e u se of in j e c t i ng a dye to h igh ligh t t h e b lood ve s s e l s to p ro du c e c lear images. Th ese re t i na l images are u p loaded in to a propri e t a r y sof tware develo ped b y M ille r S c hool researc h er s to p ro du c e h igh -re s ol ut i on, n on -in vasive c apillar y p er fu s i on m a ps (n CPM s), wh ic h reveal more i nf orm a tion ab ou t small vessels. Frac ta l a na l y s i s of th e n CPM s may be mo re e f f e c t i ve to determin e th e h ealth of t he re t i na ’s c ap illar y n et wo rk wit h a n at u ra l d e s c ri pOrigins Scientific Research Society
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t io n of t h e c o mplex br anching s tr uc t u re. T h e t y p e s of f r actal analy s is include b ox c o u n t i n g , l a c unar ity analy s is , and mu lt if ra c t al an a l y s is . Differ ing from f rac t al a r t , an y of t h e s e m ethods have frac tal g e n e r a t i n g s of tw are that s et the n ec e ssa r y b e n c h mar k patterns needed to a s se s s t h e o u t puts . Box counting breaks t h e d at a s e t into cons ecutive s maller p iece s , u s u al l y box-s haped, and an alyz es t h e p i e c e s a t e ach s m aller s cale by u se of a l g o r i t h m s that find the opti miz ed wa y of c u t t i n g a pattern to reveal t h e sc a li n g f a c to r. L acunar ity is a m easu re of “g a p s ” i n pat terns . Difficult to perc eive o r q u a n t i f y, l a cunar ity is calculated wit h
c omp u ter aided meth o ds su ch a s box c ou n t in g. A mu ltif rac t al system ne e d s a c on tin u ou s spec t ru m of c omp one nt s to desc rib e its dyn amic s. D ataset s a re e xt rac ted from pattern s an d th en d i s tor te d to gen erate a mu ltif rac t al spe c t ra t ha t illu strates h ow sc alin g varies ove r t he en tr y dat aset . G eoph ysic s, stoc k m a rke t t ime series, h ear t beat dyn a m i c s a nd n atu ral lu min o sit y are all ex a m pl e s of n atu ral mu lt if rac t al systems . F ra c t a l geo metr y is th e mat h , o r lan gua g e , t ha t en ab les t h e desc ript ion an d u nd e r s t a nd in g of n atu re, sc ien tif ic c on ce pt s t ha t led an d c o n tin u in g leadin g to bre a kt h rou gh s in biology, h ealth c are , a nd t he pro c ess of respirat ion .
Understanding Fractals If the point’s value is finite, it belongs to the Mandelbrot set and is denoted in black. If the point’s value is infinite, the color is denoted by the program’s parameters to paint the point according to a rough measure of how fast the value approaches infinity. Origins Scientific Research Society
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P hy s i o l o g ic Fra c ta ls Blood is distributed throughout the body in a fractal pattern. Researchers are using ultrasound imaging to measure the fractal dimensions of blood flow and derive mathematical models to detect cancerous cell formations sooner than before. According to recent studies, a healthy human heart does not beat in a regular, linear rhythm, but rather that is fluctuates in a distinctive fractal pattern. The heart has four chambers: two upper small chambers called the left and right atrium with two lower larger chambers called the left and right ventricle. The sinoatrial (SA) node, located in the back wall of the right atrium, initiates the heartbeat. Cells within the SA node, known as the pacemaker cells, spontaneously generates electrical discharge at a rate of about one hundred spikes per minute changing the electrical charge from positive to negative and back to positive. This intrinsic rhythm is strongly influenced by the autonomic or involuntary nerve. The vagus or parasympathetic nerve brings the resting heart rate down to 60-80 beats per minute and the sympathetic nerves speed up the heart rate. When the heart is relaxed, the cells are electrically polarized. The interior of each cell carries a negative charge and the exterior environment is positive. Cells depolarize as negative atoms pass through the cell membrane, sparking a chain reaction and the flow of electricity from cell to cell within the heart. A heartbeat is caused from the action potential generated by the SA node spreads throughout the atria, depolarizing them and causing contraction. The electrical impulse travels to the ventricles via the atrioventricular (AV) node, located in the wall between the atria, where specialized conduction pathways www.knowyourorigins.org
BRIAN LEON | CC BY-ND 2.0
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TERRAE FRACTI | 39
rapidly conduct the wave of depolarization throughout ventricles causing contraction. The depolarization wave must travel unimpeded and intact through the heart so the chamber contractions are coordinated to send blood efficiently to the lungs and the rest of the body. There are two types of fibrillation — an occurrence when the depolarization wave breaks up and the heart contracts in a totally disorganized way — atrial and ventricular. Atrial fibrillation is irregular and rapid contractions of the atria that work independently of the ventricles and are associated with around 10% loss of cardiac function. Ventricular fibrillation, similar to atrial, is the irregular contraction of the ventricles resulting in a complete loss of cardiac function causing death if not treated immediately. Fractal Di mens i ons i n the Medi cal Practi ce The electric fields generated by the depolarization and contraction of the atria and ventricles are detectable throughout the body. Placement of electrodes on the chest, ankles, and wrists record the continuos and successive heartbeats, known as an electrocardiogram (ECG). Ventricle contraction sends out the most promi-nent spike and the interval between the large spikes is the heartbeat. The first successful ECG in the 1800s on a test subject was attempted on a frog; however, the heart had to be exposed to the testing equipment. Willem Einthoven (1903) invented the first practical ECG. In 1980, Boston’s Beth Israel Hospital (BIH) and the Massachusetts Institute of Technology (MIT) finished the MIT-BIH Arrhythmia Rhythm Database containing 48 half-hour excerpts of two channel ambulatory ECG recordings for clinically significant arrhythmias and the MIT-BIH Normal Sinus Rhythm Database containing 18 excerpts of no significant arrhythmias. The World Health Organization (WHO) listed ischemic heart disease as the number one cause of death (2011) with seven million people. A recent research study in detecting heart disease early has shown a significant clinical advantage in using fractal analysis ECGs for three major heart diseases — Atrial Premature Beat (APB), Left Bundle Branch Block (LBBB), Premature Ventricular Contraction (PVC) — and the healthy heart Normal Sinus Rhythm (NSR). The rhythms were taken from the MIT-BIH arrhythmia database and a rescaled range method was used to determine the specific range of fractal dimension for each disease and NSR. Fractal s i n the Ear th Sys tem Lightning is an electrical current. Earth’s electrical balance is maintained by thunderstorms. A steady current of electrons flow upwards from the Earth’s negatively charged surface into the positively charged atmosphere until lightening from thunderOrigins Scientific Research Society
40 | ORIGINS
storms transfer the negative charges back to the Earth. Lightning is generally negative; however, on occasion, it is dangerously positive. An invisible channel of electrical charge, called a stepped leader, zigzags downward mostly in forked pattern segments to the ground and connects to an oppositely charged stepped leader and a powerful electrical current starts flowing. A flash is about twenty rapid return strokes, at 60,000 miles per second, back towards the cloud. Lightning is visible when this process repeats itself several times along the same path. Each step goes in a slightly different direction along that path creating the jagged pattern in lightening. One typical lightning flash alone carries around 500,000+ million Joules with temperatures between 20,000 and 30,000 degrees, far hotter than the surface of the sun. The air expands during this sudden increase in temperature resulting in a shockwave heard as thunder.
D i d Yo u K n o w
Fro m t h e s p a c e s ta t i o n , fo g f i ll i n g r i ve r va lle y s i n Ohio and West Virginia lo o k l i ke l i g h t n i n g . ball of plasma in a strong magnetic field. This lightning appears as a glowing ball and has been known to pass through walls or ceilings. Dry lightning occurs without a thunderhead and precipitation. Volcanic activity or wildfires create pyrocumlus clouds from ash and debris creating a hazardous cycle of fires.
Make Your Own Fractals Download Mandelbulber
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Send your fractal creations to Origins and have them featured on our website! This spectacular light show visible at any time of day is a natural occurring fractal pattern and has different shapes. Forked lightning has a branch shape when two or more return strokes follow slightly different paths. Ribbon lightning is formed when string winds spread out the plasma channel of the lightning strike. Bead lightning occurs when small segments of lightning remain after the rest of the lightning disappears leaving spread out “beads” of light in the sky. St. Elmo’s Fire, named after the patron saint of sailors, is a blue to green colored light appearing around metal conductors in a high electrical field. Metal bands on the tops of high masts of sailing ships, lightning conductors on tall buildings, airplanes, and even blades of grass during very strong thunderstorms produce this phenomena. Ball lightning is perhaps a trapped www.knowyourorigins.org
The most deadly is positive lightning, known as bolts of blue, that form when positive strokes form from the very top of a cloud and travel longer distances giving them 10x more power than regular cloud to ground lightning. The sky can be clear and there is no warning when this type of lightning will strike. _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ The tree of life can be a description of many branch patterns that have become visible with the study of fractal geometry to study them in depth. We learn from Euclid how to think in logic and build cities, roadways, and homes within these dimensions but cannot see the world’s roughness without describing the complexity. t
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A GEOMETRICAL TIMELINE (OR THE EVOLUTION OF GEOMETRY)
2000-500 BC Egyptians
Used geometry for survey, construction and tax collection. Pi is approximated in the Rhind Papyrus.
Object of Interest The Abacus Karen Meza Cherit
Clay tablets reveal Pythagorean relationships in the Plimton 322 tablet, land estimation, construction, and volume measurements.
750-250 BC Greeks
ADELE & JUSTIN | CC BYNC 2.0
“Let no one unversed in geometry enter here” was placed above entrance to Plato’s Academy. Euclid’s 13 books in Elements are written around 400 BC. Pythagoreans emerge: a secret society of mathematicians living sometime before 500 BC.
1600 AD Coordinate Geometry
Descartes merged algebra and geometry together by locating points on a plane with a pair of numbers after observing a fly on the ceiling.
1800 – 1900 Differential Geometry Gauss and Riemann devised geometries of curved surfaces.
1800 - Present Non-Euclidean Geometry
Bolyai and Lobachevsky devised geometries with no parallel lines. Roger Penrose created Penrose triangle and made developments in physics and cosmology.
1900 - Present Fractal Geometry
Mandelbrot with the aide of computing machinery devised the geometry of rough surfaces.
Consisting of a wooden box with parallel bars (made of wood, metal or plastic) that has small beads which move from sideto-side, the abacus was created for representing arithmetic units. This tool is the first of its kind known of and used by man. The abacus’ origin is unknown, though it is assumed to be Greek. Many others say it was China. It is a precursor to the era of modern computing, and did lead to the invention of the calculator. Today, you can still find people using an abacus. Some places where one may be sighted include Russia, the Middle East, and Asia. t
How To Use An Abacus! Origins Scientific Research Society
Astron Buildi Margaret Smith
IAN BRITTON | CC BY-NC 2.0
All over the world the solstices and equinoxes have proved their importance in history over and over again. The winter solstice in particular plays an important role by signally the beginning of winter to ready populations across the world for the cold that will come. Since the winter solstice is a time of the year that is very important to keep track of, people from various civilizations have built monumental architecture that can show the time of the year.
U N I T E D
This past field season the excavations done by English Heritage have revealed even more information on the structure of Stonehenge. These excavations point to Stonehenge as being an important site not from only the structure itself, but because of the natural landscape it was originally on. During the end of the last glacial maximum, the beginning of the Holocene, the glaciers left ridges in the landscape of the Stonehenge site that point to both the summer solstice and the winter solstice. Along these ridges the Avenue was built, but unfortunately the some it was destroyed when a modern road was built on top of it.
NEWGRANGE During the winter solstice Newgrange is a well-known site for people to visit because one of its passages illuminates as the sun passes it that day. From a passage above the mound there is a roof box or opening where on the morning of a winter solstice a beam of light enters. The light then travels through the nine meter passage to enter the inner chamber. As time passes throughout the morning of the winter solstice the entire passage and chamber becomes illuminated.
ANGELES MOSQUERA | CC BY-NC-SA 2.0
K I N G D O M
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STONEHENGE:ENGLAND Origins Scientific Research Society
RUJM EL-HIRI RINGS
S Y R I
It was noted that during the summer solstice the entranceway of the center opens at sunrise. There are also various notches in the walls that indicate the timing of the spring and fall equinoxes. Another astroarchaeological aspect of the walls within the structure show that they may have pointed to star risings during the time period they were built, which indicates that they could have been used to predict seasonal occurrences like the beginning of the rainy or dry seasons.
ISREALTOURISM | CC BY-SA 2.0
This interesting architectural work is located east of the Sea of Galilee in an area known as the Golan Hieghts. There is still a lot unknown about the Rujum el-Hiri Rings, however scholars have agreed that they most likely hold some sort of asrtroarchaeological purpose. This unique building was made some time between the late Chalcolithic and the Early Bronze Age and consists of about 40,000 tons of uncut volcanic rock. These basalt stones were placed to form somewhere between five to nine concentric rings depending on which perspective you look at them from. Not every ring is complete, however and many are connected by a series of spoke-like walls. These rings are also reach heights between three to eight feet. In the center of these rings lies a cairn.
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RUJM EL-HIRI:SYRIA Origins Scientific Research Society
MONTE ALBAN It was originally proposed that this siteâ€™s architecture at Building J had astroarchaeological significance because the stairway directly faces the vertical tube built into Building P could have been used to determine the day of solar zenith passage. This same sight line points to just above the northeastern horizon where the star Capella would have first appeared each year. There are also structures on building J which correspond with five of the twenty five brightest stars in the sky with in a three to five degree error margin. Recent research however, has proposed that the building served a principle function as a calendar temple.
MAYAPAN Within the ancient city Mayapan among the ruins is an immense observatory. This circular observatory the Mayan people used it to track the movements of Venus also known as the morning and evening star. This almost obsession with the planet Venus is thought to stem from their belief that the gods were able to pass through the celestial plane between the Earth and the Underworld. The observatory was built on top of base divided into two semi circles. During the Mayapanâ€™s prime the observatory would have been covered in stucco and paint. Another prominent building in Mayapan is the Pyramid of Kukulcan. This pyramid structure that looms over the central plaza of Mayapan has nine tiers with a height of about 45 feet. Within the castle lies a room known as the room of frescoes with has multitudes of impressively painted murals.
MELANIE E MAGDALENA | CC BY-SA 3.0
M E S O A M E R I C A
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MAYAPAN OBSERVATORY:MEXICO Origins Scientific Research Society
S O U T H
Q’ENQO This structure refers to four Inca period rock complexes located east of Cusco. Within Q’enqo Grande, the largest complex in the group, the focal point is an enormous carved limestone outcrop. Astronomically, these complexes served various proposes. In the limestone outcrop there are various caves, channels, basins, altars and, thrones many of which line up with the seasonal passage of the sun. There are also two knobs on a small platform next to a wall which are illuminated during the summer solstice. While these knobs are illuminated they cast a shadow on the floor that depicts a puma’s face. When the equinoxes occur these knobs are also illuminated, but they only depict half of a puma’s face.
TIWANAKU It is unknown how old the Sun Gate of Tiwanku is however, researchers believe it to be a least 14,000 years old. Located in the city known as Tiahuanaco this sun gate was carved out of one gigantic slab of stone. It is decorated with figures believed to have astrological significance. These figures resemble anthropomorphic figures with wings, curled up tails, and wearing rectangular helmets of sorts. In the center of the gate there is a figure considered to be the sun god with rays emitting all around him and a staff in each hand. It has been suggested that this gate was used in order to mark calendrical cycles.
ROB ROGOYSKI | CC BY-NC-ND 2.0
A M E R I C A
Chankillo is considered the earliest known solar observatory in the Americas, built around 400 BCE. Records from the 16th century give detailed accounts of this structure used in practices of state regulated sun worship while the Inca Empire was still in power. Within these accounts there are observations of towers being used to mark the setting and rising positions of sun at certain times of the year. This site also holds constructions that contain alignments with that cover the entire solar year. The thirteen stone pillars “sun pillars”, whose purpose previously was unknown, are now considered to be markings of time in the solar year used in order to indicate planting times and standardize seasonal observances.
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CHANKILLO:PERU Origins Scientific Research Society
CHACO CANYON In New Mexico, at a site called Chaco Canyon with a formation called Fajada Butte there are three slabs of sandstone that lean against a rock wall. These stone slabs form a shaded area which the sun is able to illuminate during the equinoxes, the summer solstice, and the winter solstice to create different patterns. In this shaded area there is a nine grooved spiral carved into stone. During the summer solstice the sunlight appears in the pattern of dagger at the center of a spiral. The winter solstice has the illumination of the sun placed like daggers on either side of the spiral. While the equinoxes are taking place the dagger appears slightly to the side of the spiralâ€™s center exactly between the fourth and fifth grooves.
MELANIE E MAGDALENA | CC BY-SA 3.0
Unfortunately, the stones were shifted and the Sun Dagger no longer works. t
PLANET O TYLER | CC BY-NC-ND 2.0
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FAJADA BUTTE:NEW MEXICO:UNITED STATES Origins Scientific Research Society
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Tau-ists are never Pi-ous E than Kellogg
There are some places on the internet that are so dark and twisted, so bereft with unimaginable horrors that to peer into them is to stare into untempered madness itself. I have stumbled unto one such place. I have stared into the deep, and have come out forever changed. What terror could cause such shocking and disgusting turmoil? What’s the website that needs to be blacklisted from everything ever? It’s tauday.com and I’m talking about the fringe math movement called the Tau Manifesto. Established June 28th, 2010, (Tau Day for the self proclaimed ‘Tauists’) the Tau Manifesto claims that the reverent symbol we use for the circle constant, π (or Pi), is wrong. The circle constant is of course the number we use when we have any equations relating to circles and their friends ellipses and spheres. A = πr2 which is the formula we use to determine the area of a circle is one such example. The Tau Manifesto claims that using Pi in in this equation, and almost all equations, mucks up the math and creates more trouble and problems than is needed. For you normal people, the circle constant sets Pi equal to the ratio of of a circle’s circumference to its diameter. When this is done, you get the beautiful number most people know, 3.1414159265 and so on and so forth. The math rebels, however, set the circle constant to the ratio of a circle’s circumference to its radius. They then take the resulting number, 6.28318530 etc. etc., and use the symbol τ (or Tau) to represent it. The more observant of you will notice that when you set the constant using
the radius instead of the diameter, it’s basically saying the constant is 2π, with the numbers showing that (6.28 is double 3.14). The Tauists claim that Tau is a more natural representation of the circle constant and says that almost all major formulae used in all of the hard scientists already use Tau, or at least a representation of Tau (2π). After looking at the evidence presented, I was convinced that my whole life up to that point had been a lie. The Manifesto have charts and graphs and formulae that use both Pi and Tau and the Tau charts made more sense! I suddenly realized the relation to circles, angles, sin and cosine. Everything made sense. That’s when I realized that this had to be stopped. The website could never see the light of day. Imagine the ramifications if this knowledge got out and it was then taught to our children folk. I shudder to think. Trigonometry and geometry would suddenly become easier for students to understand, tutors and teachers would have less work to do, who knows what other unfortunate, unforeseen consequences could arise. Do yourself a favor. Don’t go to tauday.com and don’t read the Tau Manifesto. Don’t listen to the music, or the nice presentation by Michael Hartl, or the video by Vi Hart that explains Pi vs Tau using pie. Don’t do it. Use Pi. Stay with what’s always been here. Why rock the boat? You probably don’t even use circles in your life. Perhaps more importantly though, if you do go there and read the truth for yourself, can you honestly say for certain that you wouldn’t join the Tauists? t
Is Math Real?
Hey! Before they find me here, I need to spread the word. If you think that was life shattering, just wait until you see this. Did you know that there are some people who think that math might not be real? You can go to http://youtu.be/TbNymweHW4E and find out for yourself. Mike over at PBS Idea Channel will make you question everything you thought you knew about math.
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Atlantis is one of the most explored myths of all time. The thrill of supernatural adventure never ceases. On the island of Santorini, Greece, Nicholas Pedrosa faces the job opportunity of a lifetime. The possibility of discovering the great lost city keeps the reader turning to the next page. Marcus Huxley, his boss, has his team working at all hours at the Minoan site with the dream of finding an otherworldly discovery. This novel entices the reader with vivid literary imagery. Descriptions of the Mediterranean sea as the breeze caresses the characters faces, the frescoes and their similarity to the archaeologists at the beach, and the incorporation of modern identity into ancient customs. In the field of archaeology, there are always professionals who will try and warp the minds of their colleagues into seeing a site the way they do. Unfortunately, biases exist even though the field is intended to be objective. Travels in Elysium does a fantastic job at showing the internal conflicts in archaeological excavations while portraying the mysticism of island culture. It will have you tumbling off the cliff with Huxley out of excitement. From murder to mystery, mirages to reality Azuski has included it all. From Melanie E Magdalena — “I truly connected with Nicholas since I too must face arrogant superiors in the field all the time. And I have to admit, during my own travels, it is entirely possible to sit down at a site and start seeing all those ancient people flash before your eyes going about their daily activities. It is creepy and fantastic at the same time. A thrill not everyone gets to have. A thrill I treasure.”
Travels in Elysium william azuski
Iridescent Publishing Plato’s metaphysical Atlantis mystery plays out on an archaeological dig on the island of Santorini. From the novel: It was the chance of a lifetime. A dream job in the southern Aegean. Apprentice to the great archaeologist Marcus Huxley, lifting a golden civilisation from the dead... Yet trading rural England for the scarred volcanic island of Santorini, 22-yearold Nicholas Pedrosa is about to blunder into an ancient mystery that will threaten his liberty, his life, even his most fundamental concepts of reality. Origins Scientific Research Society