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

archgirl

Starting with elementary school until we finish high school, and still pushed on us in college, is math. Why do we spend so much time studying the subject if our "careers" don't necessarily use it? We're going to delve into mathematics and look at how we use it in our daily lives, both in the ancient past and in the present: the use of zero, the discovery of geometry, pyramids, astronomy, you name it!

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

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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

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SITES TO SEE | 45

STONEHENGE:ENGLAND

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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

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SITES TO SEE | 47

RUJM EL-HIRI:SYRIA

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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

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SITES TO SEE | 51

CHANKILLO:PERU

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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

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