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 occurr**in**g

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

p**in**econe, 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 | W**in**ter 2013

© 2012-2013 Orig**in**s, 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** Orig**in**s. The publisher, editor, contributors, and related parties assumes no responsibility**of** loss,

**in**jury or **in**convenience **of** any person, organization, or party that uses **the** **in**formation or resources provided with**in**

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 learn**in**g

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

Ma**the**matics 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** **In**terest

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 W**in**ter Solstice to you all! Personally, I wish I could

spend this fantastic day at an ancient site and observe **the**

sun set **in** an extraord**in**ary 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 ma**the**matical 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 entw**in**ed with be**in**g 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 go**in**g to explore **the** history **of** numbers

along with systems used to perform math. We’re go**in**g to

tackle **the** mystery **of** why we have to learn it. Spoiler alert:

you use it more **of**ten than you th**in**k (and most **of** **the** time

don’t even know it). Plus, we’re travel**in**g **the** world to some

**of** **the** most spectacular sites that were built (ma**the**matically)

for astronomy phenomena, also known as archaeoastronomy.

As humans, we’ve tried to understand math by creat**in**g

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 **the**y manifest

**in** nature **in** “Terrae Fracti” by Morgan V. Courage. Also,

when you’re ready **of** course, we’ve **in**cluded some fractal

generators you can use at home to make your own fractal

creations. We would love to see **the**m and show **the** world

through our site if you decide to share.

F**in**ally, Orig**in**s would like to beg**in** award**in**g Research

Grants so new explorations can start, **the** results shared

with **the** world. Jo**in** us Virtual Traveler with just $1!

Wish**in**g you all **the** happiest **of** holidays,

Melanie E Magdalena, Editor-**in**-Chief

editor@knowyourorig**in**s.org

www.knowyourorig**in**s.org

STAFF

MELANIE E MAGDALENA

Editor-**in**-Chief &

Creative Designer

The Founder **of** Orig**in**s and

BermudaQuest.

MARGARET SMITH

Copy Editor

Anthropology undergraduate

focus**in**g on Japanese studies for

her career **in** archaeology.

ETHAN KELLOGG

Graphics

Deranged **in**ternet hermit who

spends his time read**in**g fr**in**ge

ma**the**matics and contemplat**in**g

‘The Truth.’

ALEX VOSBURGH

Market**in**g & Public Relations

**Our** newest recruit eager to take

on challenges and explore **the**

scientific world.

FIDEL JUNCO

Director **of** Donor Relations

Specialist **in** mar**in**e animals and

o**the**r exotic reptiles, birds, and

amphibians.

CONTRIBUTORS

DAVID BJORKLUND

Athlete and biology

undergraduate m**in**or**in**g **in** history.

VINCENT BROWN

V**in**tuitive small bus**in**ess promoter.

MORGAN V COURAGE

Word architect and

mathmatician.

KAREN MEZA CHERIT

Undergraduate study**in**g

Bus**in**ess 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 extraord**in**ary creatures, as unique as snowflakes is **the** aye-aye. Malagasy

superstitious legend pa**in**ts **the** aye-aye as a Grim Reaper: if it po**in**ts at you with an elongated

middle f**in**ger you are marked for death unless you slaughter **the** defenseless animal. With a

swivel**in**g, th**in**, and long middle f**in**ger, 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 ra**in**forest.

Their bodies are covered **in** a thick coat

rang**in**g from brown to slate grey with white flecks,

lighter at **the** hair tips. Yellow-orange eyes are

accentuated by **the**ir pale face (compared to

**the** rest **of** **the**ir body) with large, lea**the**ry ears.

Unlike o**the**r lemurs, aye-ayes do not face **the**

issue **of** **the**ir teeth wear**in**g from nut and wood

gnaw**in**g: **the**ir **in**cisors are ever-grow**in**g.

The largest nocturnal lemur is well-adapted for

forag**in**g with its th**in** and elongated f**in**gers. The

middle, or third digit, is so th**in** it appears to hardly

be sk**in** and bones. Perfect for scoop**in**g pulp from

fruits and tapp**in**g branches to f**in**d cavities full **of**

**in**sects and larvae (**the** major part **of** its diet), **the**

extended third digit extracts prizes after **the** ayeaye’s

strong **in**cisors tear through whatever blocks

**the** master forager.

Human meddl**in**g has placed **the** aye-aye on **the**

**In**ternational Union for Conservation **of** Nature

(IUCN) Red List. People hunt **the**m **in** fear **of** **the**

“death omen” **the**ir middle f**in**ger **in**vokes; plus,

**the**ir habitat shr**in**ks with **the** expansion **of** human

settlements. This is not **the** first time **the** aye-aye

family has faced ext**in**ction. About 2,300 years ago,

when humans first arrived on **the** island, Madagascar

was home to a giant aye-aye weigh**in**g five

times more than today’s extant cous**in**.

Co**in**cidentally or not, **the** arrival **of** people marks

**the** island’s moment **in** history when **the** giant ayeaye

died out. Researchers have found **the** ext**in**ct

aye-aye’s teeth with holes drilled through ei**the**r

Orig**in**s Scientific Research Society

10 | ORIGINS

suggest**in**g **the** teeth were worn as pendants

or, accord**in**g to WIRED’s Matt Simon, islanders

provided giant aye-ayes with dental care.

Though endangered, **the** aye-aye can be saved

from purposeful slaughter**in**g (and possible

dental experimentation) if public programs **in**

Madagascar work with educat**in**g **the** people

about **the** lemur’s uniqueness.

Species come and go, but is it right for people

to be **the** only decid**in**g factor for who and

what lives on and is permanently removed

from Earth’s ecosystems? t

Learn more about aye-aye

conservation efforts regard**in**g

this near threatened

species with Durrell

“Sav**in**g Species from Ext**in**ction.”

www.durrell.org

AYE-AYE HAND SHOWING THE ELONGATED MIDDLE FINGER,

From **the** University **of** Copenhagen Zoological Museum. Photo by Dr. Mirko Junge.

www.knowyourorig**in**s.org

THE EARTH PYRAMID | 11

An artist’s impression **of** what **the** Earth Pyramid will look like.

The Earth Pyramid

Creat**in**g a focal po**in**t for peace and environmental education

Steve Ward & V**in**cent Brown

**Our** modern world is bristl**in**g with technology,

celebrity, and all **the** trapp**in**gs **of** a wealthy society

but what about **the** future? We hear snippets

**of** **in**formation on **the** news about global warm**in**g,

melt**in**g ice caps, and dw**in**dl**in**g resources but

**the**se tend to be soon forgotten as life goes back

to “normal.” At what po**in**t do we start to look at

**the**se issues as a global community and start work**in**g

toge**the**r to try and come up with solutions?

Th**in**k BIG, Act BIG

The idea **of** creat**in**g a new pyramid to act as a focal

po**in**t 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 dr**in**k company Red Bull.

They have built **the**ir brand around extreme events

culm**in**at**in**g **in** **the** Red Bull Strata project. Gett**in**g

a man to jump out **of** a capsule from **the** edge **of**

space had an audience **of** Millions on **the** edge

**of** **the**ir seats and created an amaz**in**g platform

from which to promote **the**ir brand. The stunt had

noth**in**g to do with an energy dr**in**k but **the** **in**terest

it created was used to great effect.

Build**in**g a structure that hasn’t been attempted for

around 4,000 years will certa**in**ly create a platform

from which education could be presented. The

whole Earth Pyramid project from start to f**in**ish

is designed to engage and encourage participa-

Orig**in**s Scientific Research Society

12 | ORIGINS

**In**ternal 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 **the**y want to be remembered, and a family

box where **the** hopes, dreams, and op**in**ions **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 m**in**ds a chance to f**in**d solutions that move forward **in** peace and cooperation.

CONNECT WITH

EARTH PYRAMID

www.knowyourorig**in**s.org

THE EARTH PYRAMID | 13

tion from **the** **in**itial global vote to decide where

**the** structure should be built through **the** f**in**al

stages **of** fill**in**g **the** structure with contributions

from schools around **the** world.

Test**in**g Ancient Techniques

and New Theories

The construction process itself will be an amaz**in**g

mixture **of** new and ancient techniques designed

to showcase new susta**in**able technologies with**in**

**the** construction **in**dustry (geopolymer concretes

ETC) and answer some **of** **the** many questions

we have about ancient peoples and how **the**y

created **the**se amaz**in**g structures **of** **the** past.

How did **the** ancients build **the**se massive structures

with such precision that enabled **the**m to

rema**in** **in**tact for over four and a half thousand

years? The Great Pyramid **of** Egypt was built

with over two million stones weigh**in**g almost

three tons on average, many **of** **the** heaviest

be**in**g quarried almost a thousand kilometers

away. What sort **of** ma**the**matical knowledge is

required to achieve such a feat? Earth Pyramid’s

construction aims to answer such questions and

test some **of** **the** latest **the**ories.

Media **in**terest **in** **the** construction phase will

ensure that **the** platform for education will

rema**in** strong throughout **the** entire project

(expected to be ten years) and make it a great

focal po**in**t for gett**in**g children look**in**g at **the**

future **of** our planet.

Generat**in**g Prosperity

from a National **In**vestment

Several studies have been undertaken on **the**

costs **of** build**in**g a replica **of** **the** Great Pyramid **in**

One **of** **the** Earth Pyramid’s cas**in**g stones.

Orig**in**s Scientific Research Society

14 | ORIGINS

One **of** **the** Earth Pyramid time capsules.

modern times and as expected **the** numbers are

stagger**in**g. 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** fund**in**g. This **in**vestment will have a direct

impact **in** **the** country where it is built by creat**in**g

jobs dur**in**g **the** construction process and generat**in**g

**in**come through tourism that can be used to

tackle some **of** **the** issues raised dur**in**g **the** vot**in**g

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 with**in** **the** chosen country.

The o**the**r 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 fund**in**g **in** comparison and

**the** result is **the**y struggle to get **the**ir message

across to **the** public at **the** required scale to make

a difference. With many **of** **the**se issues start**in**g

to magnify with**in** **the** next fifty years, **the** world

needs to start plac**in**g more emphasis on **the**

education surround**in**g **the**m.

Platform for **the** World’s

**In**digenous People

The project will also create a platform that will

give a voice to those countries and **in**digenous

peoples who struggle to have **the**ir op**in**ions

heard. There are over 7,000 **in**digenous cultures

**in** **the** world, many **of** **the**m fac**in**g immense

challenges but very little press is ever given to

**the**ir voices. The same can be said for many **of**

**the** smaller nations on **the** planet. It is humbl**in**g

to th**in**k that some **of** **the**se 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 **the**se peoples is a

reflection on our future. It is important that we

notice NOW.

Educat**in**g a New Generation

There is a vast array **of** educational possibilities

surround**in**g **the** Earth Pyramid that will be

explored as **the** project progresses. This is an

immensely thought-provok**in**g venture that has

**the** possibility to create a real momentum for

empower**in**g a generation with **the** educational

tools needed for change. t

www.knowyourorig**in**s.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 someth**in**g we use **in** everyday life.

Don’t believe me? Well **the**n check out **the**se five examples.

OLGA LEDNICHEN KO | CC BY 2.0

SEAN MACENTEE | CC BY 2.0

18 | ORIGINS

1. Cook**in**g

Remember when we had to learn fractions **in** elementary school?

Then do you remember how us**in**g fractions suddenly got a lot

more complicated when we entered algebra? Well, believe it or

not, fractions have always been complicated (surprise!), especially

when cook**in**g a nice little meal for ourselves.

Let’s use bak**in**g cookies as an example. **In** a recipe, **the**re is a

bunch **of** **in**gredients like flour, sugar, chocolate chips, and eggs.

Now how could this possibly be math? **Math** is not food. Food is

food! However, cook**in**g 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** bak**in**g soda **in** order to make this batch **of**

cookies, but those numbers are not very appeal**in**g. So **in**stead,

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 mix**in**g bowl, we

actually count **the** improper fractions **in** order to make sure we

have **the** right amount.

2. Pump**in**g gas

Pump**in**g gas is simple, right? It doesn’t seem like we have to

do math every time we do it, especially s**in**ce we do it so **of**ten.

However, whe**the**r we like it or not, we are do**in**g math. Especially

when we see gas prices go up. There are two ma**in** ways people

get gas: ei**the**r fill**in**g up **the**ir tank fully, or gett**in**g 10-20 dollars

worth **in** order to get **the** 1/2 or 3/4 **of** a tank that **the**y want.

But how do **the**y know **the**y are gett**in**g **the** right amount **of** gas

needed? By sett**in**g 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 aga**in**!). 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 imag**in**ary gas tank.

That’s all f**in**e 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 f**in**d out. Solve for X, and we will

know exactly how much money to give **the** clerk to get **the** perfect

amount **of** gas us**in**g our convenient change jar kept **in** **the**

car. For those count**in**g at home, $2.50*11.25= $28.13. Bonus:

this is a great way to get rid **of** all your pennies.

www.knowyourorig**in**s.org

MATH IN OUR LIVES | 19

3. Road trips

Let’s go ahead and expand on this idea a bit fur**the**r. 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 **in**cludes

a pit stop **in** Las Vegas). But how much is our venture go**in**g

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, **the**n use that to f**in**d 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 go**in**g to cost $600.27, although I’m sure we can f**in**d a

quarter somewhere along **the** way.

4. How long will **the** drive take?

Algebra also pops up **in**to our life whenever we drive from place

to place, specifically when we want to figure out how long it will

take to get **the**re. That way, we can plan accord**in**gly. **In** order to

do this, we take **the** distance we are travel**in**g 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 driv**in**g 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 m**in**utes.

EGS | CC BY-SA 3.0

Orig**in**s Scientific Research Society

20 | ORIGINS

5. How long will it take to pay **of**f those pesky student loans?

Whe**the**r go**in**g on an epic road trip, head**in**g to college, or buy**in**g

a house, most people have to worry about **the** money it

will cost. Sometimes, this leads to tak**in**g out loans **in** order to

achieve that goal. Typically, we can put it **of**f as a future worry,

but we would all like to know when we no longer have to chop

**of**f part **of** our pay check **in** order to pay **the**m **of**f. Let’s imag**in**e

that while go**in**g 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 **the**se both paid back with**in** 5 years **of** graduat**in**g.

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

go**in**g to an accountant. The **in**terest is 2.5% for both loans, but

**the** unsubsidized loan accrued **in**terest while you were still **in**

school. That means **the** unsubsidized loan will have accumulated

**in**terest for 7 years, while **the** subsidized will have 5 years **of**

**in**terest added to it.

The simplified equation you use to calculate your **in**terest is:

3000*rt+2500*rt=X, where r=rate and t=time.

S**in**ce **the** time is different for each loan, it works out to

3000*(.025*7)+2500*(.025*5.5)=X.

**Math** it out and you f**in**d out that you end up ow**in**g an extra

$837.50. Add**in**g that to **the** orig**in**al 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 **of**f **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 pretend**in**g

it doesn’t exist, **the**re are lots **of** **in**stances where

do**in**g 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 **the**n. (Besides,

it comes on your smartphone. Use it like all your

o**the**r favorite apps!)

And, as always, remember to show your work. t

www.knowyourorig**in**s.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** bra**in**,

I stumbled upon a seem**in**gly magical **the**orem that I would like to pose to you all.

Because if you put your m**in**d to it, anyth**in**g 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 s**in**gular possessive pronoun, so it can be written that

our = 1

Hence, 4 = f*1 = f

Substitut**in**g, 4 = fish

And s**in**ce 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.

Orig**in**s Scientific Research Society

Ch**in**ese Bars from Katsuyo Sampo by Seki Kowa.

MATHEMATICS THROUGH THE AGES | 23

Ma**the**matics

Through The Ages

Melanie E Magdalena & David Bjorklund

F**in**gers as Calculators

F**in**gers are **the** oldest calculators! Early **in** life, we

naturally beg**in** count**in**g with our f**in**gers. Hav**in**g

ten f**in**gers makes Base 10 so common **in** number

systems. A s**in**gle symbol with**in** a number

is called a digit, which comes from “digitus” **the**

Lat**in** word for f**in**ger. 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.

Ma**the**matics **in** music has more to do with acoustics

than composition.

Unary Tallies

Tally marks are a simplistic form **of** count**in**g. We

tend to learn how to do this very young. L**in**es are

placed next to each o**the**r. Tally groups are separated

**in**to groups **of** five, **the** fifth l**in**e go**in**g diagonally

across **the** vertical four l**in**es. 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,

**the**n you have groups **of** ten (or five-tally pairs,

which two **of** equal ten), **the**n **the** same for hundreds

and so on. This system is considered unary:

one is represented by a s**in**gle symbol and **the**n

five or ten has a new symbol.

Ch**in**ese Rods

The first Ch**in**ese numerical system recognized

orig**in**ated 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 Ch**in**ese also used **the** number zero.

The f**in**ancial 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

count**in**g board divided **in**to rows and columns,

numbers were represented by rods **of** bamboo

or ivory. Rods were l**in**ed up us**in**g a positional

system **in** **the** rows and columns: **the** right-most

column would be units, followed tens, hundreds,

and so on. Ra**the**r than putt**in**g n**in**e 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 dist**in**guish between

**the** n**in**e numerical comb**in**ations was its

placement on **the** board.

Babylonian Powers **of** 60

A positional number system is one where numbers

are arranged **in**to 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, **the**n x3600, and so on.

They did not have a representation for zero. The

column position**in**g is **the** only way to dist**in**guish

Orig**in**s Scientific Research Society

24 | ORIGINS

1 and 60 was **the**ir position. If **the**re was a zero **in**

a number calculated, **the** column position had a

slanted symbol ra**the**r than a void. **In** total, **the**re

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 m**in**ute,

and 60 m**in**utes **in** an hour. Plus, 60 is used **in**

circles: 360 degrees makes a full circle, 60 m**in**utes

are **in** a degree, and 60 seconds **in** a m**in**ute.

Though clocks and circles use Base 60, **the**re is

no relation between angle m**in**utes and seconds

and time m**in**utes and seconds.

Ancient Egyptian

Numbers & Fractions

Ancient Egyptian numerology was written **in** hieroglyphs

with a Base 10 system (**the** equivalent

to how many f**in**gers you have). The number 1

was a l**in**e, a horseshoe shape was for 10, and a

coil or spiral was 100. A lotus, or water lily, was

used for represent**in**g 1,000, a f**in**ger for 10,000,

a tadpole for 100,000, and a million was **the** god

Heh. A circle was used for **in**f**in**ity. When multiply**in**g

numbers, **the** symbols show **the** f**in**al value

without a sign for zero. So if 7x3=21, 21 would be

written as two 10 symbols and a l**in**e 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 toge**the**r 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** f**in**gers

and toes. Dots represented units and l**in**es (or

bars) for **the** number five. Numbers were written

vertically with **the** lowest denom**in**ation on **the**

bottom. The first five (stacked) place values were

multiples **of** 20. Zero was **in**cluded, denoted with

www.knowyourorig**in**s.org

a “shell” symbol. To make th**in**gs “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.

**In**ca Quipus

The ancient South American civilization **of** **the**

**In**ca was highly developed with no writ**in**g system.

They used **the** quipu, a system **of** knotted

colored thread or str**in**g around th**in**ner str**in**gs.

The closer a knot was to a large cord, **the** greater

its value. Little is known about **the** quipu s**in**ce

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

**in**corporation **of** Greek letters **in**to ma**the**matics

as certa**in** 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** follow**in**g respectively: 1, 5, 10, 50, 100, 500,

1000. A l**in**e added above **the** symbol expanded

**the** values past 4,000. A l**in**e 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** pr**in**ciple 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, **the**n after

that everyth**in**g is a compound number **in**volv**in**g

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, orig**in**ally created

by **the** Phoenicians with 600 symbols, **the** Attic

system used a condensed version **of** 27 symbols.

Today only 24 are used. The purely ma**the**matical

symbols vau, koppa, and sampi became ext**in**ct.

Numbers 1-9, or **the** units, have **in**dividual symbols

from **the** alphabet; **the** tens (10, 20, 30…90)

also have **the**re own alphabet symbols; and f**in**ally

**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

**in**volved and enabled **the**m to count **in** **the** thousands.

S**in**ce **the** system lacked **the** need for zero,

if **the**re was no tens value **the**n a tens letter was

not needed!

To dist**in**guish between numbers and letters,

Greeks **of**ten 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, accord**in**g to Jo Edk**in**s is as

follows. Th**in**k **of** I as a f**in**ger, or one. Hundred

**in** Lat**in** is Centum (C) and we still use **the** word

“cent” **in** **the** context **of** 100 cents is a dollar. Lat**in**

for thousand is Mille (M), like millennium (a

thousand years are **in** a millennium). Five f**in**gers

equals five (obviously!) and if you were to connect

your thumb and p**in**ky 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 imag**in**ation:

If you cut **of**f 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 outl**in**es, 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 Gu**in**ea and **the** Proto-Uralic language are

suspected to have used Senary numerics. The

Orig**in**s Scientific Research Society

26 | ORIGINS

system has a lot to do with f**in**ger count**in**g. The

hand can have six positions: **the** fist and five extended

f**in**gers. The system is a bit complex, but

**the** punch l**in**e is you use one hand to represent

units and **the** o**the**r to represent sixes. This allows

you to count up to 55 **in** **the** Senary system, **the**

equivalent to 35 **in** **the** decimal system, ra**the**r

than only to ten!

Today, a Senary system can be observed on dice.

There are six faces to a die. You can ei**the**r 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

us**in**g **the** spaces between f**in**gers ra**the**r than **the**

f**in**gers **the**mselves. More recently, **in** 1801 James

Anderson criticized **the** metric system used by

**the** French. His solution was co**in****in**g **the** term

“octal” for a Base 8 system for recreational ma**the**matics,

primarily for weights and measurements

s**in**ce **the** English unit system was already mostly

octal.

The octal system today, or oct, is made from b**in**ary

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 programm**in**g

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** H**in**dus **in** **In**dia

**in**vented **the** H**in**du-Arabic number system. It

spread to **the** Middle East around **the** 9th century

CE and was used by Arab ma**the**maticians and

astronomers. Once it spread to Europe, people

adopted **the** system over **the** visible calculation

form, **the** abacus.

Count**in**g 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.knowyourorig**in**s.org

MATHEMATICS THROUGH THE AGES | 27

BRANDON GIESBRECHT & MELANIE E MAGDALENA | CC BY-SA 2.0

Calculation) which made him famous for spread**in**g

**the** numeral system **in** Europe. **In** his book, he

uses examples **of** his famous Fibonacci sequence

(which he did not discover, but noted).

B**in**ary

Computers do not count **the** way **the** rest **of** **the**

world does. With a two number system, or b**in**ary,

only **the** digits 0 and 1 are needed. The system

has existed prior to **the** **In**formation Era but

is was first documented as **the** modern system

by Leibniz **in** **the** 17th century. B**in**ary numbers

are usually longer than decimal numbers and

**the** str**in**gs **of** zeroes and ones grow to be even

longer when numbers get big. One million takes

twenty b**in**ary digits! For computers, one means

an electrical current is flow**in**g and zero means

that **the** current is switched **of**f. B**in**ary can also

be used to represent letters and symbols. Each

character is a comb**in**ation **of** eight digits. “A” is

0100 0001 and “a” is 0110 0001. If you want to try

out some b**in**ary convert**in**g, visit Roubaix **In**teractive’s

website!

Conclud**in**g

As we look back at all **of** **the**se different systems

**of** math we must realizethat without **the**se

ma**the**matical 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** ma**the**matics.

The **in**vention **of** currency also helped move society

from nomadic to agrarian which relied heavily

on count**in**g. Currency allowed for a standard

**of** trade which made it possible for transactions

to be made with ease. Zero became more prom**in**ent

because **of** its usefulness **in** represent**in**g

**the** absence **of** someth**in**g. **In** **the** 1900’s zero

became utilized **in** one **of** **the** most monumental

ma**the**matical system **of** our era, b**in**ary, which

led to **the** **in**ternet and **the**n to websites like Wikipedia,

Google, and now Orig**in**s. Imag**in**e what

our world might look like if we never came up

with **the**se ma**the**matical systems or **the** concept

**of** zero? t

Orig**in**s 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 def**in**itions, axioms, **the**orems, and postulates rema**in** unchanged today **in**

study and use **in** modern practical applications such as biochemical model**in**g, medical

imag**in**g, sequence alignment, and nanotechnology. Euclidean geometry def**in**es **in**teger

dimensions us**in**g **the** Pythagorean **the**orem, pi, and formulas for surface area and

volume. The Earth’s multi-dimensions cannot be conf**in**ed to classical geometry - l**in**es,

planes, and solids; it is fuzzy, dynamic, and chaotic **in** **the** complex numbers and fourth

dimension.

“**In** **the** whole **of** science, **the** whole **of** ma**the**matics,

smoothness was everyth**in**g. What I did was to open

up roughness for **in**vestigation.”

– Benoit Mandelbrot

The Development **of** **the**

Fractal Concept

Describ**in**g this cont**in**uous non-**in**teger dimension

and non-differentiable functions started to

formalize as recursion with Richard Dedek**in**d

(1888) and cont**in**ued with Giuseppe Peano’s five

axioms for positive **in**tegers (1891). Louis **Pi**erre

Joseph Fatou wrote his **the**sis on **in**tegration **of**

complex function **the**ory sett**in**g **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” focus**in**g 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 dur**in**g **the** generation

process and **the** value **of** Z0 varies. Each po**in**t **of**

**the** complex plane, **the** value **of** C, is associated

with a particular Julia set. This ma**the**matical

**in**genuity died with Julia until **the** advent **of**

comput**in**g mach**in**ery with **the** ability to visually

express **the** beauty and express **the** fourth

dimension.

**In** **the** 1960s, Benoit Mandelbrot, an IBM employee,

orig**in**ated **the** term fractal to solidify **the** past

one hundred years **of** ma**the**matical development

**in** endless self-similarity iterations **of** equations

describ**in**g roughness and irregularity on all

systems and life on Earth.

The famous Mandelbrot set is graphically represented

by someth**in**g 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** **in**itial

po**in**t **of** **the** iteration process. The po**in**ts **of** **the**

complex plane are separated **in**to two categories

and **the** color scheme is denoted by **the** value **of**

**the** po**in**t.

The formula’s start**in**g po**in**t is zero and generates

what may appear to be random and a somewhat

mean**in**gless set **of** numbers, but **the** graphic

portrayal shows **the** self-similar reclusiveness over

an **in**f**in**ite scale. The formula is a summary **of** **the**

fourth dimension — **the** real world that **in**cludes

an **in**f**in**ite set **of** fractal dimensions which lie **in**

**in**tervals between zero and **the** first dimension,

**the** first and second dimension and **the** second

and third dimension. Fractal geometry describes,

**in** algorithms, **the** non-**in**teger dimensions.

Fractal generators are computerized pa**in**t-bynumbers,

a stimulat**in**g comb**in**ation **of** math,

computations, and art.

www.knowyourorig**in**s.org

Feliciano Guimarães | CC BY 2.0

32 | ORIGINS

MICHAEL LUX | CC BY-ND 2.0

www.knowyourorig**in**s.org

Fractals **in** Nature

TERRAE FRACTI | 33

The branches **of** a deciduous tree stark aga**in**st

**the** w**in**ter 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 **in**tricate process **of** photosyn**the**sis

serves **the** purpose **of** respiration. The

leaves on branches absorb carbon dioxide from

**the** air and return oxygen **in**to **the** atmosphere.

Remarkably, a lung’s bronchiole tubes and arteries

resemble a self-repeat**in**g branch pattern whose

purpose **in** **the** body is also respiration. **In** reverse

to trees, **the** lungs brea**the** **in** oxygen and exhale

carbon dioxide. Almost as a reflection **in** **the** eyes

look**in**g at **the** trees or **in** a microscope at lung

tissue, this same tree pattern repeats **in** ret**in**al

blood vessels that provide oxygen to **the** eyes.

Fractals are a natural

phenomenon **in**

everyth**in**g seen and

unseen by **the**

unaided eye, rang**in**g

from **the** spectacular

to **the** **in**terest**in**g.

The Miller School **of** Medic**in**e at **the** University

**of** Miami is us**in**g fractal analysis

**of** **the** ret**in**a to determ**in**e **the** health **of**

**the** ret**in**a’s capillary network and provide

microvascular changes associated

with diseases such as stroke, hypertension

and diabetes. A Ret**in**al Functional

Imager is used to scan **the** eyes’ capillaries

without **the** use **of** **in**ject**in**g a

dye to highlight **the** blood vessels to

produce clear images. These ret**in**al

images are uploaded **in**to a proprietary

s**of**tware developed by Miller School

researchers to produce high-resolution,

non-**in**vasive capillary perfusion maps

(nCPMs), which reveal more **in**formation

about small vessels. Fractal analysis

**of** **the** nCPMs may be more effective

to determ**in**e **the** health **of** **the** ret**in**a’s

capillary network with a natural descrip-

Orig**in**s Scientific Research Society

TERRAE FRACTI | 35

tion **of** **the** complex branch**in**g structure.

The types **of** fractal analysis **in**clude box

count**in**g, lacunarity analysis, and multifractal

analysis. Differ**in**g from fractal

art, any **of** **the**se methods have fractal

generat**in**g s**of**tware that set **the** necessary

benchmark patterns needed to

assess **the** outputs. Box count**in**g breaks

**the** data set **in**to consecutive smaller

pieces, usually box-shaped, and analyzes

**the** pieces at each smaller scale by use

**of** algorithms that f**in**d **the** optimized

way **of** cutt**in**g a pattern to reveal **the**

scal**in**g factor. Lacunarity is a measure **of**

“gaps” **in** patterns. Difficult to perceive

or quantify, lacunarity is calculated with

computer aided methods such as box

count**in**g. A multifractal system needs a

cont**in**uous spectrum **of** components to

describe its dynamics. Datasets are extracted

from patterns and **the**n distorted

to generate a multifractal spectra that

illustrates how scal**in**g varies over **the**

entry dataset. Geophysics, stock market

time series, heartbeat dynamics and

natural lum**in**osity are all examples **of**

natural multifractal systems. Fractal

geometry is **the** math, or language, that

enables **the** description and understand**in**g

**of** nature, scientific concepts that

led and cont**in**u**in**g lead**in**g to breakthroughs

**in** biology, healthcare, and **the**

process **of** respiration.

Understand**in**g Fractals

If **the** po**in**t’s value is f**in**ite, it belongs to **the**

Mandelbrot set and is denoted **in** black. If **the**

po**in**t’s value is **in**f**in**ite, **the** color is denoted by

**the** program’s parameters to pa**in**t **the** po**in**t accord**in**g to a

rough measure **of** how fast **the** value approaches **in**f**in**ity.

Orig**in**s Scientific Research Society

36 | ORIGINS

Physiologic Fractals

Blood is distributed throughout **the**

body **in** a fractal pattern. Researchers

are us**in**g ultrasound imag**in**g to measure

**the** fractal dimensions **of** blood

flow and derive ma**the**matical models

to detect cancerous cell formations

sooner than before. Accord**in**g to recent

studies, a healthy human heart does

not beat **in** a regular, l**in**ear rhythm, but

ra**the**r that is fluctuates **in** a dist**in**ctive

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

s**in**oatrial (SA) node, located **in** **the** back

wall **of** **the** right atrium, **in**itiates **the**

heartbeat. Cells with**in** **the** SA node,

known as **the** pacemaker cells, spontaneously

generates electrical discharge

at a rate **of** about one hundred spikes

per m**in**ute chang**in**g **the** electrical

charge from positive to negative and

back to positive. This **in**tr**in**sic rhythm is

strongly **in**fluenced by **the** autonomic

or **in**voluntary nerve. The vagus or

parasympa**the**tic nerve br**in**gs **the**

rest**in**g heart rate down to 60-80 beats

per m**in**ute and **the** sympa**the**tic nerves

speed up **the** heart rate. When **the**

heart is relaxed, **the** cells are electrically

polarized. The **in**terior **of** each cell

carries a negative charge and **the** exterior

environment is positive. Cells depolarize

as negative atoms pass through

**the** cell membrane, spark**in**g a cha**in**

reaction and **the** flow **of** electricity from

cell to cell with**in** **the** heart.

A heartbeat is caused from **the** action

potential generated by **the** SA node

spreads throughout **the** atria, depolariz**in**g

**the**m and caus**in**g 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.knowyourorig**in**s.org

38 | ORIGINS

BRIAN LEON | CC BY-ND 2.0

www.knowyourorig**in**s.org

apidly conduct **the** wave **of** depolarization throughout ventricles

caus**in**g contraction. The depolarization wave must travel unimpeded

and **in**tact through **the** heart so **the** chamber contractions are

coord**in**ated 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 **in**dependently

**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 result**in**g **in** a complete

loss **of** cardiac function caus**in**g 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**

cont**in**uos and successive heartbeats, known as an electrocardiogram

(ECG). Ventricle contraction sends out **the** most promi-nent

spike and **the** **in**terval 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** test**in**g equipment. Willem E**in**thoven (1903) **in**vented **the** first

practical ECG. **In** 1980, Boston’s Beth Israel Hospital (BIH) and **the**

Massachusetts **In**stitute **of** Technology (MIT) f**in**ished **the** MIT-BIH

Arrhythmia Rhythm Database conta**in****in**g 48 half-hour excerpts **of**

two channel ambulatory ECG record**in**gs for cl**in**ically significant

arrhythmias and **the** MIT-BIH Normal S**in**us Rhythm Database

conta**in****in**g 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** detect**in**g heart disease

early has shown a significant cl**in**ical advantage **in** us**in**g 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 S**in**us Rhythm

(NSR). The rhythms were taken from **the** MIT-BIH arrhythmia

database and a rescaled range method was used to determ**in**e **the**

specific range **of** fractal dimension for each disease and NSR.

Fractals **in** **the** Earth System

TERRAE FRACTI | 39

Lightn**in**g is an electrical current. Earth’s electrical balance is

ma**in**ta**in**ed by thunderstorms. A steady current **of** electrons flow

upwards from **the** Earth’s negatively charged surface **in**to **the**

positively charged atmosphere until lighten**in**g from thunder-

Orig**in**s Scientific Research Society

40 | ORIGINS

storms transfer **the** negative charges back to **the**

Earth. Lightn**in**g is generally negative; however,

on occasion, it is dangerously positive. An **in**visible

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 flow**in**g. A flash

is about twenty rapid return strokes, at 60,000

miles per second, back towards **the** cloud. Lightn**in**g

is visible when this process repeats itself

several times along **the** same path.

Each step goes **in** a slightly different direction

along that path creat**in**g **the** jagged pattern **in**

lighten**in**g. One typical lightn**in**g 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 dur**in**g this sudden **in**crease **in**

temperature result**in**g **in** a shockwave heard as

thunder.

Did You Know

From **the** space

station, fog fill**in**g

river valleys **in**

Ohio and

West Virg**in**ia

look like lightn**in**g.

ball **of** plasma **in** a strong magnetic field. This

lightn**in**g appears as a glow**in**g ball and has

been known to pass through walls or ceil**in**gs.

Dry lightn**in**g occurs without a thunderhead and

precipitation. Volcanic activity or wildfires create

pyrocumlus clouds from ash and debris creat**in**g

a hazardous cycle **of** fires.

Make Your Own Fractals

Download

Mandelbulber

Download

JWildfire

Download

Ultra Fractal 5

Send your fractal creations to Orig**in**s and have **the**m featured on our website!

This spectacular light show visible at any time

**of** day is a natural occurr**in**g fractal pattern and

has different shapes. Forked lightn**in**g has a

branch shape when two or more return strokes

follow slightly different paths. Ribbon lightn**in**g

is formed when str**in**g w**in**ds spread out **the**

plasma channel **of** **the** lightn**in**g strike. Bead lightn**in**g

occurs when small segments **of** lightn**in**g

rema**in** after **the** rest **of** **the** lightn**in**g disappears

leav**in**g spread out “beads” **of** light **in** **the** sky.

St. Elmo’s Fire, named after **the** patron sa**in**t **of**

sailors, is a blue to green colored light appear**in**g

around metal conductors **in** a high electrical

field. Metal bands on **the** tops **of** high masts **of**

sail**in**g ships, lightn**in**g conductors on tall

build**in**gs, airplanes, and even blades **of** grass

dur**in**g very strong thunderstorms produce this

phenomena. Ball lightn**in**g is perhaps a trapped

The most deadly is positive lightn**in**g, known as

bolts **of** blue, that form when positive strokes

form from **the** very top **of** a cloud and travel

longer distances giv**in**g **the**m 10x more power

than regular cloud to ground lightn**in**g. The sky

can be clear and **the**re is no warn**in**g when this

type **of** lightn**in**g 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 **the**m

**in** depth. We learn from Euclid how to th**in**k **in**

logic and build cities, roadways, and homes

with**in** **the**se dimensions but cannot see **the**

world’s roughness without describ**in**g **the** complexity.

t

www.knowyourorig**in**s.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** Rh**in**d 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** ma**the**maticians liv**in**g

sometime before 500 BC.

1600 AD

Coord**in**ate Geometry

Descartes merged algebra and

geometry toge**the**r by locat**in**g po**in**ts

on a plane with a pair **of** numbers after

observ**in**g a fly on **the** ceil**in**g.

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 l**in**es. Roger

Penrose created Penrose triangle and

made developments **in** physics and

cosmology.

1900 - Present

Fractal Geometry

Mandelbrot with **the** aide **of** comput**in**g

mach**in**ery devised **the** geometry **of**

rough surfaces.

Object **of** **In**terest

The Abacus

Karen Meza Cherit

Consist**in**g **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 represent**in**g arithmetic

units. This tool is **the** first **of** its k**in**d known **of** and used by

man.

The abacus’ orig**in** is unknown, though it is assumed to be

Greek. Many o**the**rs say it was Ch**in**a. It is a precursor to **the**

era **of** modern comput**in**g, and did lead to **the** **in**vention **of**

**the** calculator.

Today, you can still f**in**d people us**in**g an abacus. Some places

where one may be sighted **in**clude Russia, **the** Middle East,

and Asia. t

How To Use

An Abacus!

OBJECT OF INTEREST | 41

ADELE & JUSTIN | CC BYNC 2.0

Orig**in**s Scientific Research Society

Astron

Buildi

Margaret Smith

All over **the** world **the** solstices and equ**in**oxes have proved **the**ir

importance **in** history over and over aga**in**. The w**in**ter solstice **in**

particular plays an important role by signally **the** beg**in**n**in**g **of**

w**in**ter to ready populations across **the** world for **the** cold that will

come. S**in**ce **the** w**in**ter 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

U

N

I

T

E

D

K

I

N

G

D

O

M

STONEHENGE

This past field season **the** excavations done by English Heritage have revealed even more

**in**formation on **the** structure **of** Stonehenge. These excavations po**in**t to Stonehenge as

be**in**g an important site not from only **the** structure itself, but because **of** **the** natural landscape

it was orig**in**ally on. Dur**in**g **the** end **of** **the** last glacial maximum, **the** beg**in**n**in**g **of** **the**

Holocene, **the** glaciers left ridges **in** **the** landscape **of** **the** Stonehenge site that po**in**t to both

**the** summer solstice and **the** w**in**ter solstice. Along **the**se ridges **the** Avenue was built, but

unfortunately **the** some it was destroyed when a modern road was built on top **of** it.

NEWGRANGE

Dur**in**g **the** w**in**ter solstice Newgrange is a well-known site for people to visit because one

**of** its passages illum**in**ates as **the** sun passes it that day. From a passage above **the** mound

**the**re is a ro**of** box or open**in**g where on **the** morn**in**g **of** a w**in**ter solstice a beam **of** light

enters. The light **the**n travels through **the** n**in**e meter passage to enter **the** **in**ner chamber. As

time passes throughout **the** morn**in**g **of** **the** w**in**ter solstice **the** entire passage and chamber

becomes illum**in**ated.

ANGELES MOSQUERA | CC BY-NC-SA 2.0

www.knowyourorig**in**s.org

SITES TO SEE | 45

STONEHENGE:ENGLAND

Orig**in**s Scientific Research Society

S

Y

R

I

A

RUJM EL-HIRI RINGS

This **in**terest**in**g 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 R**in**gs, however

scholars have agreed that **the**y most likely hold some sort **of** asrtroarchaeological

purpose. This unique build**in**g 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 n**in**e concentric r**in**gs depend**in**g on

which perspective you look at **the**m from. Not every r**in**g is complete, however and many

are connected by a series **of** spoke-like walls. These r**in**gs are also reach heights between

three to eight feet. **In** **the** center **of** **the**se r**in**gs lies a cairn.

It was noted that dur**in**g **the** summer solstice **the** entranceway **of** **the** center opens at

sunrise. There are also various notches **in** **the** walls that **in**dicate **the** tim**in**g **of** **the** spr**in**g and

fall equ**in**oxes. Ano**the**r astroarchaeological aspect **of** **the** walls with**in** **the** structure show

that **the**y may have po**in**ted to star ris**in**gs dur**in**g **the** time period **the**y were built, which

**in**dicates that **the**y could have been used to predict seasonal occurrences like **the** beg**in**n**in**g

**of** **the** ra**in**y or dry seasons.

ISREALTOURISM | CC BY-SA 2.0

www.knowyourorig**in**s.org

SITES TO SEE | 47

RUJM EL-HIRI:SYRIA

Orig**in**s Scientific Research Society

M

E

S

O

A

M

E

R

I

C

A

MONTE ALBAN

It was orig**in**ally proposed that this site’s architecture at Build**in**g J had astroarchaeological

significance because **the** stairway directly faces **the** vertical tube built **in**to Build**in**g P could

have been used to determ**in**e **the** day **of** solar zenith passage. This same sight l**in**e po**in**ts

to just above **the** nor**the**astern horizon where **the** star Capella would have first appeared

each year. There are also structures on build**in**g J which correspond with five **of** **the** twenty

five brightest stars **in** **the** sky with **in** a three to five degree error marg**in**. Recent research

however, has proposed that **the** build**in**g served a pr**in**ciple function as a calendar temple.

MAYAPAN

With**in** **the** ancient city Mayapan among **the** ru**in**s is an immense observatory. This circular

observatory **the** Mayan people used it to track **the** movements **of** Venus also known as **the**

morn**in**g and even**in**g star. This almost obsession with **the** planet Venus is thought to stem

from **the**ir 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 **in**to two semi

circles. Dur**in**g **the** Mayapan’s prime **the** observatory would have been covered **in** stucco

and pa**in**t. Ano**the**r prom**in**ent build**in**g **in** Mayapan is **the** Pyramid **of** Kukulcan. This pyramid

structure that looms over **the** central plaza **of** Mayapan has n**in**e tiers with a height **of** about

45 feet. With**in** **the** castle lies a room known as **the** room **of** frescoes with has multitudes **of**

impressively pa**in**ted murals.

MELANIE E MAGDALENA | CC BY-SA 3.0

www.knowyourorig**in**s.org

SITES TO SEE | 49

MAYAPAN OBSERVATORY:MEXICO

Orig**in**s Scientific Research Society

CHANKILLO

S

O

U

T

H

A

M

E

R

I

C

A

Chankillo is considered **the** earliest known solar observatory **in** **the** Americas, built around

400 BCE. Records from **the** 16th century give detailed accounts **of** this structure used **in**

practices **of** state regulated sun worship while **the** **In**ca Empire was still **in** power. With**in**

**the**se accounts **the**re are observations **of** towers be**in**g used to mark **the** sett**in**g and ris**in**g

positions **of** sun at certa**in** times **of** **the** year. This site also holds constructions that conta**in**

alignments with that cover **the** entire solar year. The thirteen stone pillars “sun pillars”,

whose purpose previously was unknown, are now considered to be mark**in**gs **of** time **in** **the**

solar year used **in** order to **in**dicate plant**in**g times and standardize seasonal observances.

Q’ENQO

This structure refers to four **In**ca period rock complexes located east **of** Cusco. With**in**

Q’enqo Grande, **the** largest complex **in** **the** group, **the** focal po**in**t is an enormous carved

limestone outcrop. Astronomically, **the**se complexes served various proposes. **In** **the** limestone

outcrop **the**re are various caves, channels, bas**in**s, altars and, thrones many **of** which

l**in**e up with **the** seasonal passage **of** **the** sun. There are also two knobs on a small platform

next to a wall which are illum**in**ated dur**in**g **the** summer solstice. While **the**se knobs are

illum**in**ated **the**y cast a shadow on **the** floor that depicts a puma’s face. When **the** equ**in**oxes

occur **the**se knobs are also illum**in**ated, but **the**y 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 w**in**gs, curled up tails, and

wear**in**g rectangular helmets **of** sorts. **In** **the** center **of** **the** gate **the**re is a figure considered

to be **the** sun god with rays emitt**in**g 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.knowyourorig**in**s.org

SITES TO SEE | 51

CHANKILLO:PERU

Orig**in**s Scientific Research Society

S

O

U

T

H

W

E

S

T

CHACO CANYON

**In** New Mexico, at a site called Chaco Canyon

with a formation called Fajada Butte **the**re are

three slabs **of** sandstone that lean aga**in**st a

rock wall. These stone slabs form a shaded area

which **the** sun is able to illum**in**ate dur**in**g **the**

equ**in**oxes, **the** summer solstice, and **the** w**in**ter

solstice to create different patterns.

**In** this shaded area **the**re is a n**in**e grooved

spiral carved **in**to stone. Dur**in**g **the** summer

solstice **the** sunlight appears **in** **the** pattern

**of** dagger at **the** center **of** a spiral. The w**in**ter

solstice has **the** illum**in**ation **of** **the** sun placed

like daggers on ei**the**r side **of** **the** spiral. While

**the** equ**in**oxes are tak**in**g 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.knowyourorig**in**s.org

SITES TO SEE | 53

FAJADA BUTTE:NEW MEXICO:UNITED STATES

Orig**in**s Scientific Research Society

54 | ORIGINS

Tau-ists are never **Pi**-ous

Ethan Kellogg

There are some places on **the** **in**ternet that are

so dark and twisted, so bereft with unimag**in**able

horrors that to peer **in**to **the**m is to stare **in**to

untempered madness itself. I have stumbled

unto one such place. I have stared **in**to **the** deep,

and have come out forever changed. What terror

could cause such shock**in**g and disgust**in**g

turmoil? What’s **the** website that needs to be

blacklisted from everyth**in**g ever? It’s tauday.com

and I’m talk**in**g about **the** fr**in**ge 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 relat**in**g to

circles and **the**ir friends ellipses and spheres.

A = πr2 which is **the** formula we use to determ**in**e

**the** area **of** a circle is one such example. The Tau

Manifesto claims that us**in**g **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 **the**n take **the** result**in**g 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 us**in**g

www.knowyourorig**in**s.org

**the** radius **in**stead **of** **the** diameter, it’s basically

say**in**g **the** constant is 2π, with **the** numbers

show**in**g 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 look**in**g at **the** evidence presented, I was

conv**in**ced that my whole life up to that po**in**t

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, s**in** and

cos**in**e. Everyth**in**g made sense. That’s when I

realized that this had to be stopped. The website

could never see **the** light **of** day.

Imag**in**e **the** ramifications if this knowledge got

out and it was **the**n taught to our children folk.

I shudder to th**in**k. Trigonometry and geometry

would suddenly become easier for students to

understand, tutors and teachers would have less

work to do, who knows what o**the**r 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 expla**in**s **Pi** vs Tau us**in**g 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 **the**re and read

**the** truth for yourself, can you honestly say for

certa**in** that you wouldn’t jo**in** **the** Tauists? t

Is **Math** Real?

Hey! Before **the**y f**in**d me here, I need to spread **the** word. If you th**in**k that

was life shatter**in**g, just wait until you see this. Did you know that **the**re

are some people who th**in**k that math might not be real? You can go to

http://youtu.be/TbNymweHW4E and f**in**d out for yourself. Mike over at

PBS Idea Channel will make you question everyth**in**g 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** Santor**in**i, Greece, Nicholas Pedrosa

faces **the** job opportunity **of** a lifetime.

The possibility **of** discover**in**g **the** great

lost city keeps **the** reader turn**in**g to

**the** next page. Marcus Huxley, his boss,

has his team work**in**g at all hours at **the**

M**in**oan site with **the** dream **of** f**in**d**in**g an

o**the**rworldly 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

**the**ir similarity to **the** archaeologists

at **the** beach, and **the** **in**corporation **of**

modern identity **in**to ancient customs.

**In** **the** field **of** archaeology, **the**re are

always pr**of**essionals who will try and

warp **the** m**in**ds **of** **the**ir colleagues **in**to

see**in**g a site **the** way **the**y do. Unfortunately,

biases exist even though **the** field

is **in**tended to be objective. Travels **in**

Elysium does a fantastic job at show**in**g

**the** **in**ternal conflicts **in** archaeological

excavations while portray**in**g **the** mysticism

**of** island culture. It will have you

tumbl**in**g **of**f **the** cliff with Huxley out **of**

excitement. From murder to mystery,

mirages to reality Azuski has **in**cluded it

all.

From Melanie E Magdalena —

“I truly connected with Nicholas s**in**ce I

too must face arrogant superiors **in** **the**

field all **the** time. And I have to admit,

dur**in**g my own travels, it is entirely possible

to sit down at a site and start see**in**g

all those ancient people flash before your

eyes go**in**g about **the**ir 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 Publish**in**g

Plato’s metaphysical Atlantis mystery

plays out on an archaeological dig

on **the** island **of** Santor**in**i.

From **the** novel:

It was **the** chance **of** a lifetime. A dream job **in** **the**

sou**the**rn Aegean. Apprentice to **the** great archaeologist

Marcus Huxley, lift**in**g a golden civilisation

from **the** dead... Yet trad**in**g rural England for

**the** scarred volcanic island **of** Santor**in**i, 22-yearold

Nicholas Pedrosa is about to blunder **in**to an

ancient mystery that will threaten his liberty, his life,

even his most fundamental concepts **of** reality.

Orig**in**s Scientific Research Society