Issue 7: In the Name of Pi, Math in Our Lives

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.
F
IBO
Issue 7 | Winter 2013
© 2012-2013 Origins, founded by Melanie E Magdalena in association with BermudaQuest
Copyright: This work is licensed under a 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:
11
16
21
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
2+2=Fish
Yep, you read that right. The
answer can be 4, or Fish!
alex vosburgh
i
NAC C
ANDREW WEST | CC BY-NC-SA 2.0
22
DEPARTMENTS
6
9
41
42
55
Mathematics Through
The Ages
Arabic numbers are not alone!
Melanie e Magdalena &
David Bjorklund
Terrae Fracti
The Earth and our Bodies
in fractals.
morgan v courage
54
From the Editor
Creature Feature
Object of Interest
Sites to See
Review It
28
Tau-ists are never Pi-ous
Tau vs Pi: pick your constant.
ETHAN KELLOGG

6 | ORIGINS
ALEXEY KLJATOV | CC BY-NC 2.0
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.
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
editor@knowyourorigins.org
www.knowyourorigins.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.
The largest nocturnal lemur is well-adapted for
foraging with its thin and elongated fingers. The
middle, or third digit, is so thin it appears to hardly
be skin and bones. Perfect for scooping pulp from
fruits and tapping branches to find cavities full of
insects and larvae (the major part of its diet), the
extended third digit extracts prizes after the ayeaye’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, Madagascar
was home to a giant aye-aye weighing five
times more than today’s extant cousin.
Coincidentally or not, the arrival of people marks
the island’s moment in history when the giant ayeaye
died out. Researchers have found the extinct
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 & Vincent Brown
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?
Think BIG, Act 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
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.
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 participa-
Origins 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.
CONNECT WITH
EARTH PYRAMID
www.knowyourorigins.org

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.
Testing Ancient Techniques
and New Theories
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 Pyramid’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.
Generating Prosperity
from a National Investment
Several studies have been undertaken on the
costs of building a replica of the Great Pyramid in
One of the Earth Pyramid’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 Earth’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.
Platform for the World’s
Indigenous People
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.
Educating a New Generation
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
www.knowyourorigins.org

MATH
IN OUR LIVES
AND SOME EXAMPLES
OF HOW
YOU USE IT
(even if you don’t want to)
Margaret Smith

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.
OLGA LEDNICHEN KO | CC BY 2.0
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.
EGS | CC BY-SA 3.0
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
Alex 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
Mathematics
Through The Ages
Melanie E Magdalena & David Bjorklund
Fingers as Calculators
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 “digitus” 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.
Unary Tallies
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.
Chinese Rods
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.
Babylonian Powers of 60
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.
Ancient Egyptian
Numbers & Fractions
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.
Vigesimal Mayans
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.
Inca Quipus
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 Numerals
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).
Greek Attic System
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.
Senary
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.
Octal
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
“octal” 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.
Arabic
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
American Sign Language, Numbers 1-9.
www.knowyourorigins.org

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).
Binary
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!
Concluding
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
The Development of the
Fractal Concept
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:
z 4 + z 3 /(z-1) + z 2 /(z 3 + 4 z 2 + 5) + c
The formula for the Julia set is Z n+1
=Z n
2
+ 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
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.
www.knowyourorigins.org

Feliciano Guimarães | CC BY 2.0

32 | ORIGINS
MICHAEL LUX | CC BY-ND 2.0
www.knowyourorigins.org

Fractals in Nature
TERRAE FRACTI | 33
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.
Fractals are a natural
phenomenon in
everything seen and
unseen by the
unaided eye, ranging
from the spectacular
to the interesting.
The Miller School of Medicine at the University
of Miami is using fractal analysis
of the retina to determine the health of
the retina’s capillary network and provide
microvascular changes associated
with diseases such as stroke, hypertension
and diabetes. A Retinal Functional
Imager is used to scan the eyes’ capillaries
without the use of injecting a
dye to highlight the blood vessels to
produce clear images. These retinal
images are uploaded into a proprietary
software developed by Miller School
researchers to produce high-resolution,
non-invasive capillary perfusion maps
(nCPMs), which reveal more information
about small vessels. Fractal analysis
of the nCPMs may be more effective
to determine the health of the retina’s
capillary network with a natural descrip-
Origins Scientific Research Society

TERRAE FRACTI | 35
tion of the complex branching structure.
The types of fractal analysis include box
counting, lacunarity analysis, and multifractal
analysis. Differing from fractal
art, any of these methods have fractal
generating software that set the necessary
benchmark patterns needed to
assess the outputs. Box counting breaks
the data set into consecutive smaller
pieces, usually box-shaped, and analyzes
the pieces at each smaller scale by use
of algorithms that find the optimized
way of cutting a pattern to reveal the
scaling factor. Lacunarity is a measure of
“gaps” in patterns. Difficult to perceive
or quantify, lacunarity is calculated with
computer aided methods such as box
counting. A multifractal system needs a
continuous spectrum of components to
describe its dynamics. Datasets are extracted
from patterns and then distorted
to generate a multifractal spectra that
illustrates how scaling varies over the
entry dataset. Geophysics, stock market
time series, heartbeat dynamics and
natural luminosity are all examples of
natural multifractal systems. Fractal
geometry is the math, or language, that
enables the description and understanding
of nature, scientific concepts that
led and continuing leading to breakthroughs
in biology, healthcare, and the
process of respiration.
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

36 | ORIGINS
Physiologic Fractals
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

38 | ORIGINS
BRIAN LEON | CC BY-ND 2.0
www.knowyourorigins.org

apidly 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 Dimensions
in the Medical Practice
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.
Fractals in the Earth System
TERRAE FRACTI | 39
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 thunder-
Origins 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.
Did You Know
From the space
station, fog filling
river valleys in
Ohio and
West Virginia
look like lightning.
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
Download
JWildfire
Download
Ultra Fractal 5
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
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
www.knowyourorigins.org

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.
Babylonians
Clay tablets reveal Pythagorean relationships
in the Plimton 322 tablet, land
estimation, construction, and volume
measurements.
750-250 BC
Greeks
“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.
Object of Interest
The Abacus
Karen Meza Cherit
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!
OBJECT OF INTEREST | 41
ADELE & JUSTIN | CC BYNC 2.0
Origins Scientific Research Society

Astron
Buildi
Margaret Smith
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.
IAN BRITTON | CC BY-NC 2.0

omical
ngs

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STONEHENGE
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
www.knowyourorigins.org

SITES TO SEE | 45
STONEHENGE:ENGLAND
Origins Scientific Research Society

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RUJM EL-HIRI RINGS
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.
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
www.knowyourorigins.org

SITES TO SEE | 47
RUJM EL-HIRI:SYRIA
Origins Scientific Research Society

M
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MONTE ALBAN
It was originally proposed that this site’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 Mayapan’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
www.knowyourorigins.org

SITES TO SEE | 49
MAYAPAN OBSERVATORY:MEXICO
Origins Scientific Research Society

CHANKILLO
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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.
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
www.knowyourorigins.org

SITES TO SEE | 51
CHANKILLO:PERU
Origins Scientific Research Society

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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 spiral’s center
exactly between the fourth and fifth grooves.
Unfortunately, the stones were shifted and the
Sun Dagger no longer works. t
PLANET O TYLER | CC BY-NC-ND 2.0
MELANIE E MAGDALENA | CC BY-SA 3.0
www.knowyourorigins.org

SITES TO SEE | 53
FAJADA BUTTE:NEW MEXICO:UNITED STATES
Origins Scientific Research Society

54 | ORIGINS
Tau-ists are never Pi-ous
Ethan 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
www.knowyourorigins.org
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.

REVIEW IT | 55
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