Chakras Scientific Description

7/29/2019 Chakras Scientific Description

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Anahata Nada -Uncreated SoundBy Mr. Roger Gould-King

AUM (The most sacred symbol in Hinduism)

INTRODUCTIONMr. Roger Gould-KingTotal silence is perfection. Silence is necessary for sound to exist, it is the aural canvasfor melodys brush in our three dimensional world. The sounds we know are producedby at least two elements the waves on a shore, wind in the trees, the blades of a


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bagpipe reed vibrating together, two lips, drum and drumstick, fingering a guitar stringand so on.

One of the koans of Zen asks, "What is the sound of one hand clapping?". This sound isknown in the Sanskrit tradition as "Anahata Nada," the "Unmade Sound". This means a

sound not made in the way we know of it is the "sound" of the universe, the primalsound of energy itself.

Ancient tradition says that the audible sound which most resembles this unmade soundis the sound of "AUM" (OM). ( Brahma Randhra: Brahma-aperture; opening in the crownof the head; "the tiniest of apertures, in which is the silent, primordial sound, which givesyou the impression that you are, but you really are not" (Nisargadatta)). According to theVedas, AUM is the most sacred of all words, out of which emanated the universe. Thesymbol of both the personal God and the Brahman or Absolute. AUM is regarded byHindus as the greatest mantra being of incalculable spiritual potency.

Aum is not, in itself, the un-struck sound, but leads one to it. The mantra is composed offour elements. Three are vocal sounds: A, U, and M, while the fourth element is thesilence which begins and ends the audible sound, the silence which supports it. Theobjective of intoning AUM is not only the mantra itself, but the experience of perceivingthe unmade sound that supports it. This is the same as seeking the space which"supports" the universe and its galaxies : the "emptiness" or nothingness of space isnecessary for the existence of everything seen and unseen.

Everything seen and unseen, heard and unheard, smelt and un-smelt, felt and unfelt,tasted and un-tasted, are manifestations of pure energy. This energy is the "container"for all things, and it is the seemingly elusive Source people have given numerous

names to God, Self, Brahman , Godhead. The Absolute, the Supreme Reality, theUltimate Reality, Truth or the Self of the Vedanta Philosophy are also usedinterchangeably for Brahman, and so on. Our interface with the material world isthrough our senses and the interpretation of these sensations with our minds ourthoughts. At a basic level, we tend to see things in their material form, not as energymanifested in many different ways. We categorise created forms with labels, namingthis form a rock, that a rose, the other water, another a human being, and yet others as"animals". What we seek is LOVE, but in applying labels to created forms, we end upwith:

A weed is a flower that has never been loved

There are about 50 definitions of the word "love" in an English dictionary, but not oneequates love to "God". In defining love in these many different ways, we define ourperception of everything, but if we become perfect Love ourselves, all apparentdifferences disappear and we see things as they really are. There is no such thing as"ugly" or "beautiful", for these are only descriptions we apply to describe our ownperceptions of things we havent yet seen as they see themselves in their own created


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form; we seek to be ekanta vasa [ekaant vaas]: free from mental concepts; "dwelling inmental solitude".

While classification appears to be useful as a means of physical identification in a three-dimensional world created in the mind, it is the major barrier to identifying oneself with

all created things that all came from the same Source, and this includes us. From thisSource we are born to don the garment of our bodies in order to experience this world,and in the death of the body we "return" to the Source which we in fact, never left : weare always part of this energy and it is only the manifestation of our present life formcoupled to the interference of our minds, which leads to the illusion that each one of usis a "separate" person.

This essay is not about suggesting some "path" for someone to follow, because a pathimplies distance, a distance separating oneself from the destination : Self, God,Brahman. To go on some religious path or other often turns out to be like someone onone of those exercise machine treadmills- one can walk forever and never get to the

desired destination because one never left it in the first place.

Chakras and the Natural Number series

Natural Number Series defined

Many years ago I was enthralled by the sight of a certain genus of flowering plant in aremote mountainous area, being pollinated by bees called by the plants by theiremission of a distinct humming sound. After recording the television documentary, Ichecked the frequency of the fundamental frequency generated by the plants and foundit to be 432 Hertz, or cycles per second. This prompted me to place small battery

powered sound generators in the flower beds on my farm where I kept bee hives, and todiscovering a whole new world of plant and bee intelligence.

All life used to live in synergy, and still strives to, despite the decimation of theenvironment by humankind. This interdependence establishes harmony on the physicaland spiritual planes, each life form being dependent on the other. The eradication of aspecies creates an irreplaceable void which nature tries to balance as best it can, butusually, this leads often to further extinction of other species because a fundamental linkin the material life form and spiritual chain has been destroyed.

The Natural Number series is formed by adding a succeeding number to the previous

root number, and is as follows :

0,1,1,2,3,5,8,13,21,34,55,89,144,233,377 and so on. In other words, 5+8=13,8+13=21, 21+13=34 etc. If one divides one number by another, one gets a ratio,89/144= 0.618, or, 144/89 = 1.618, and, 144/233=0.618.

This ratio, known variously as the golden section, golden mean or divine proportion, canbe found everywhere in nature. It is represented by a rectangle in which the width


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compared to the length, is in the same proportion as the length compared to the sum ofthe width and length; i.e. "the smaller is to the larger, as the larger is to the whole". Thissequence will be found in genetics and geometry, snail shells and in the growthformations of plants and other life forms, including the proportions of the human body.

2 Chakras of the Head

If one assigns the value of one to the distance between the chin and the crown of thehuman head, then 0.618 of this distance will be found to correspond exactly to thevarious locations of the head chakras.

2.1 Location of Head Chakras

In his exhaustive definitive work on the chakras according to the traditional Indianunderstanding, Layayoga - an Advanced Method of Concentration, Shyam SundarGoswami, citing many references, describes thirteen chakras altogether; the seven

standard chakras and six minor ones. The following lists the chakras according to the13-chakra model.

The location of these chakras is shown in the drawing.

3. The thirteen chakras

Chakra Location Petals Association Colour Tone

Sahasrara above head 1000 transcendent gold 486

Guru above head 12 transcendent silver

Nirvana crown 100 mind origin white


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Indu forehead 16 buddhi

Manas forehead 6 chitta

Ajna brow 2 manas violet 432

Talu/Lalana roof of mouth 12 or64

Vishuddha throat 16 space blue 405Anahata heart 12 air green 370

Hrit below heart 8

Manipura sternum base 10 fire yellow 324

Svadhistana below navel 6 water orange 288

Muladhara base of spine 4 earth red 270

The same method for determining the location of the headchakras, is used to locate those for the rest of the torso.This is illustrated in the diagram.

The physical location of each chakra is important in terms ofits response to vibrations, i.e. tones, colours and so on.

Top


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4 Determination of the pitches for each chakra note

The standard Western musical scale is based on an equally tempered (also calledthe 12-tone chromatic) scale. In this scale, an octave consists of 12 equallyspaced frequencies, each note being 2^1/12 (twelfth root of 2) from the previous

note, as shown in the following table for the A440 musical scale. Therefore, thetwelfth note is double the frequency of the first note.

MusicalNote

Frequency N Naturaltubelength

Equivalentdiatonic

Equation Hz Hz

A 440 440.00 432.00 432 397mm do

A# 440 x 2^1/12 466.16

B 440 x 2^2/12 493.88 484.90 486 353mm re

C 440 x 2^3/12 523.25 513.75

C# 440 x 2^4/12 554.37 544.29 540 318mm mi

D 440 x 2^5/12 587.33 576.65 576 298mm fa

D# 440 x 2^6/12 622.25

E 440 x 2^7/12 659.26 647.27 648 265mm sol

F 440 x 2^8/12 698.46

F# 440 x 2^9/12 739.99 726.53 740 232mm la

G440 x2^10/12

783.99

G#440 x2^11/12

830.61815.51

810 212mm ti

A2440 x

2^12/12

880.00864.00

do

The natural scale is the scale used by me for the chakras, and not the Westerndiatonic scale per se. A long time ago the Highland bagpipe and other traditionalinstruments had a fundamental "A" of 432Hz, but this was increased to 440Hzwith advent of the "standard" of 440, followed later by further increases in pitchto get pipe bands to perform with brass bands and orchestras. ThisWesternisation of folk instruments destroyed their inherent relationships withnatural phenomena, and consequent loss of spiritual synergy with nature.

The natural scale proposed is calculated on the harmonization of any note with

the upper harmonics of the fundamental A=432. These "natural" frequencies willin turn harmonize with the relevant chakra centres in the body as heard by theears, and interpreted by the brain as sound.


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To hear what these notes actually sound like, the easiest thing to make is a set ofpitch pipes as illustrated. Any thin-walled tubing will do, such as bamboo or reed,or even metal curtain rod. Closing one end of such a pipe and blowing across theopen end will produce a note of a pitch determined by the length of the pipe. Thelengths of these pipes is given in the preceding table, calculated for sea level atstandard temperature.

To hear the sounds using your PC, use QBasics SOUND function to write asimple program to play the tones via your PC speaker e.g. SOUND 432,18.2 willsound A for 1 second.

5 Colours

Like sound, colours vibrate at specific frequencies, and therefore have theircorresponding sound equivalents. Blue for example, vibrates at about 749.999billion Hertz or cycles per second, and corresponds to the throat chakra andsound frequency of G. Red vibrates at half that of blue, and corresponds toMuladhara and C. Therefore sound and/or colours can be used in conjunctionwith specific chakras.

6 Smell, Taste and SensationThese three functions of the body all respond to vibrations. In meditation it isimportant to try to harmonise these three as well. Sitting in a very hot and humidroom, surrounded by foul smells and having a bitter taste in the mouth, are notconducive to meditation.

7 Brain functions

The electroencephalograph (AKA. EEG) is a machine that monitors brainwaveactivity. Laboratories have conducted many studies and experiments using thesetools to understand the four main brainwave patterns: BETA, ALPHA, THETA andDELTA.

Each frequency has a characteristic blueprint, and produces a distinctive state ofconsciousness. BETA waves (14 cycles per second and above) dominate thenormal waking state of consciousness when attention is directed towards theoutside world. ALPHA waves (8-13 cycles-per second) are present during


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dreaming and light meditation when the eyes are closed. THETA waves (4-7cycles per second) occur in sleep and are dominant in the higher state ofmediation.

In deep meditation and deep sleep, DELTA waves (0.5 to 3 cycles per second) are

experienced. Each of these brainwave frequencies serves an important function.The optimum level for deep no-thought is in the realm of THETA. When in THETA,the senses are withdrawn from the external world and focused on the inner one.DELTA waves enable a total disassociation from three-dimensional existence andprovide the most profound feelings of peace and it is in this state that all life is"connected" directly to Self"God".

In direct correlation, we see similar effects brought on by the constant andrhythmic drone of Tibetan Buddhist chants, which transport the monks and evenother listeners into realms of meditation. These chants are at 432Hz in frequency,above or below this fundamental by one octave 432 = 4.5 x 8 x 3 x 2 x 2.

Like sound waves, the brain has its own set of vibrations it uses to communicatewith itself and the rest of the body. EEG equipment distinguishes these waves bymeasuring the speed with which neurons fire in-cycles per second.

Beta waves range between 13-40 HZ. The beta state is associated with peakconcentration, heightened alertness and visual acuity. Nobel Prize Winner, SirFrancis Crick and other scientists believe that the 40HZ beta frequency may bekey to the act of cognition.

Alpha waves range between 7-12 HZ. This is a place of deep relaxation, but not

quite meditation. In Alpha, we begin to access the wealth of creativity that liesjust below our conscious awareness - it is the gateway, the entry point that leadsinto deeper states of consciousness.

Theta waves range between 4-7 HZ. Theta is one of the more elusive andextraordinary realms one can explore. It is also known as the twilight state whichwe normally only experience briefly as we rise from delta upon waking, or driftingoff to sleep. In theta we are in a waking dream, vivid imagery flashes before themind's eye and we are receptive to information beyond our normal consciousawareness.

Delta waves range between 0-4 HZ. Delta isassociated with deep sleep.

8 Practical applications


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>The foregoing sections detail briefly the physical aspects of intoning AUM as amantra to experience God, Self, Brahman , Godhead. The Absolute, the SupremeReality, the Ultimate Reality, Truth.

It is at the moment when the end of the mmm is reached and terminated, that the"Silence" which is God, Self, Brahman , Godhead. The Absolute, the Supreme

Reality, the Ultimate Reality, Truth, is experienced. Once this experience isattained, what one seeks has been identified as it were, and the destination ofones path has been reached.

Please note that the intonation of any mantra can be done mentally, that is, it isnot necessary to do so audibly.

From this point on, the objective is to attain a constant state of one-ness withSelf, perfect bliss. It is then that one knows (as opposed to beliefs) that all life andevery creature has a soul, that all things are sacred.

I offer these thoughts to you in humility and pray that you will find them ofinterest, and perhaps of use to you. I humbly offer this essay in the spirit ofkshama-prarthana and ask your forgiveness for the shortcomings and mistakes itmay contain.

Roger Gould-KingJohannesburgSouth AfricaJanuary 2002

__________________Top


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The Fibonacci Rectangles and Shell Spirals

The Fibonacci Rectangles and Shell SpiralsBy Ron KnottWe can make another picture showing the Fibonaccinumbers 1,1,2,3,5,8,13,21,.. if we start with two smallsquares of size 1 next to each other. On top of both ofthese draw a square of size 2 (=1+1).

We can now draw a new square - touching both a unitsquare and the latest square of side 2 - so having sides 3


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units long; and then another touching both the 2-squareand the 3-square (which has sides of 5 units). We cancontinue adding squares around the picture, each newsquare having a side which is as long as the sum of thelatest two square's sides. This set of rectangles whosesides are two successive Fibonacci numbers in length andwhich are composed of squares with sides which areFibonacci numbers, we will call the Fibonacci Rectangles

The next diagram shows that we can draw aspiral by putting together quarter circles, one ineach new square. This is a spiral (the FibonacciSpiral). A similar curve to this occurs in nature asthe shape of a snail shell or some sea shells.Whereas the Fibonacci Rectangles spiralincreases in size by a factor of Phi (1.618..) in a
http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/shell.gif


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quarter of a turn (i.e. a point a further quarter of aturn round the curve is 1.618... times as far fromthe centre, and this applies to all points on thecurve), the Nautilus spiral curve takes a wholeturn before points move a factor of 1.618... fromthe centre.These spiral shapes are called Equiangular orLogarithmic spirals.0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987Pine conesCan you see the two sets of spirals?How many are there in each set?


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(the lines are drawn connecting the centres ofeach segment of the pinecone):

Pine cones show the Fibonacci Spirals clearly.

Pine conesHere is another pine cone. It is not only smaller,but has a different spiral arrangement.Use the buttons to help count the numberof spirals in each direction] on this pinecone.Shows only the pinecone


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Shows the segment edges

Show the outline only


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Show one set of spiral

Show the other set of spirals


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Top


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Here is a picture of an ordinary cauliflower. Notehow it is almost a pentagon in outline. Lookingcarefully, you can see a centre point, where theflorets are smallest. Look again, and you will seethe florets are organized in spirals around thiscentre in both directions.

How many spirals are there in each direction?(lines are drawn between the florets):


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How many spirals are there in each direction?

Seed heads


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Fibonacci numbers can also be seen in thearrangement of seeds on flower heads. Thepicture here is Tim Stone's beautiful photographof a Coneflower, used here by kind permission ofTim. The part of the flower in the picture is about2 cm across. It is a member of the daisy family


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with the scientific name Echinacea purpura andnative to the Illinois prairie where he lives.You can see that the orange "petals" seem toform spirals curving both to the left and to theright. At the edge of the picture, if you countthose spiralling to the right as you go outwards,there are 55 spirals. A little further towards thecentre and you can count 34 spirals. How manyspirals go the other way at these places? Youwill see that the pair of numbers (counting spiralsin curving left and curving right) are neighboursin the Fibonacci series.


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The same happens in many seed and flowerheads in nature. The reason seems to be thatthis arrangement forms an optimal packing of theseeds so that, no matter how large the seedhead, they are uniformly packed at any stage, allthe seeds being the same size, no crowding inthe centre and not too sparse at the edges.The spirals are patterns that the eye sees,"curvier" spirals appearing near the centre, flatter


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spirals (and more of them) appearing the fartherout we go.So the number of spirals we see, in eitherdirection, is different for larger flower heads thanfor small. On a large flower head, we see m orespirals further out than we do near the centre.The numbers of spirals in each direction are(almost always) neighbouring Fibonaccinumbers!Top


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Look at your own hand:You have ...

2 hands each of w hich has .5 fingers, each of which has ...3 parts separated by ...2 knuckles

Is this just a coincidence or not?????

However, if you measure the lengths of the bones in your finger (best seen by slightlybending the finger) does it look as if the ratio of the longest bone in a finger to the middlebone is Phi?What about the ratio of the middle bone to the shortest bone (at the end of the finger) -Phi again?


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Arrangements of the leavesAlso, many plants show the Fibonacci numbers in the arrangements ofthe leaves around their stems. If we look down on a plant, the leaves areoften arranged so that leaves above do not hide leaves below. Thismeans that each ge ts a good share o f the sunlight and catches the mostrain to channel down to the roots as it runs down the lea f to the stem.The computer generated ray-traced picture here is created by my brother,Brian.

Leaves per turnThe Fibonacci numbers occur when counting both the number of timeswe go around the stem, going from leaf to leaf, as well as counting theleaves we m eet until we encounter a leaf directly above the starting one.


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If we count in the other direction, we get a different number of turns forthe same number of leaves.

The number of turns in each direction and the number of leaves met arethree consecutive Fibonacci numbers!

For example, in the top plant in the picture above, we have 3 clockw iserotations before we meet a leaf directly above the first, passing 5 leaveson the way. If we go anti-clockwise, we need only 2 turns. Notice that 2, 3and 5 are consecutive Fibonacci numbers.For the lower plant in the picture, we have 5 clockw ise rotations passing 8leaves, or just 3 rotations in the anti-clockwise direction. This time 3, 5and 8 are consecutive numbers in the Fibonacci sequence.

We can write this as, for the top plant, 3/5 clockwise rotations per leaf ( or2/5 for the anticlockwise direction). For the second plant it is 5/8 of a turnper leaf (or 3/8).

Leaf arrangements of some common plantsThe above are computer-generated "plants", but you can see thesame thing on real plants. One estimate is that 90 percent of allplants exhibit this pattern of leaves involving the Fibonaccinumbers.Some common trees with their Fibonacci leaf arrangementnumbers are:1/2 elm, linden, lime, grasses1/3 beech, hazel, grasses, blackberry2/5 oak, cherry, apple, holly, plum, common groundsel


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3/8 poplar, rose, pear, willow5/13 pussy willow, almond where t/n means each leaf is t/n of a turn after thelast leaf or that there is there are t turns for n leaves.

Cactus's spines often show the same spirals as w e have already seen on pine cones,petals and leaf arrangements, but they are much more clearly visible. Charles Dills hasnoted that the Fibonacci numbers occur in Brom eliads.__________________To p


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In October 1982 there was a 10-planet alignment at whichpoint stock prices bottomed at the lower channel line whichis drawn across the 1942 and 1974 alignment/lows and thenthe Dow exploded through the "Magic 1000" barrier and thegreat bull market began that many believe continues to this day.In August 1987, with the "Harmonic Convergence" and afive-planet alignment, stock prices peaked along the uppertrendline running through the 1937 and 1962 peaks, thencrashed.

(see "The End O f The W orld" in 8/17 issue of Newsweek.)

In January 1991 stock prices hit a m ajor low with a 5-planetalignment and solar eclipse. This marked the deadline for Iraqto pull-out of Kuwait and the following day the Gulf War began.The Allies success triggered an sharp rally in stock prices thatcarried the DJIA through the 3000 barrier and since that timestock prices have not gone lower.

In June 1992 there was a 5-planet alignment with a solar eclipseat which point stock prices peaked and dropped off into October.Notably, this alignment coincided with the beginning of Westernintervention in the Yugoslavian civil war.

The last major peak in the stock market occurred at Dow 4000the upper trendline across the 1937, 1962 and 1987 p eaksin January of 1994 with a tight 7-planet alignment.The m arket corrected for about a ye ar after which the rallybegan which carried stock prices through Dow 5 000 lastNovember.

(see "Rare Planet Alignment Bodes A Bust For B oomingStock Market" in 1/12/94 issue of the W all St. Journal, P.B1.)

At the current juncture, the stock market is likely peaking abovea Supercycle upper trendline running through the 1937 peakand a 1 966 peak at D ow 1000 that coincided with a six-planet alignment.This peak


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comes with a five-planet alignment withthe new m oon a day prior to the March 20th Spring Equinox

Given how the current possible peak is connected by long-run trendlines, planetaryalignment turning points and, as is explained below, Fibonacci mathematicalrelationships, to the Elliott Wave Supercycle upswing in stock prices that startedfollowing the Great Depression of the 1930's, clearly the ingredients are in place for thisto be a Grand Supercycle or even Millenium Cycle turning point.

Now this is where things get interesting.

If you take the time span between the peak in Jan. of 1994and November/December of 1995 (when the Dow broke 5000in association with a major planetary alignment in Sagitarrius)and multiply it by the Fibonacci "Golden Ratio"of 1.6180339887498949, then you get the approximatetime span between the 1992 alignment/peak and thecurrent alignment/possible peak.

(The Fibonacci golden ratio is based upon simple numerology.Take any two numbers, e.g., 0 & 1, and add them together.Next, take the sum and add it to the larger of the two numbers,i.e., 1 + 1 = 2. Now add the new sum to the old sum, i.e.,2 + 1 = 3. A s you continue doing this you'll get a numericalseries like the following: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34...The further out you go in the series, the closer the ratio oftwo consecutive numbers comes to 1.6180339887498949(or, if you take the ratio of a number to the next higher number,0.618...).On a final note, if you create a new series based upon theexponential values of the golden ratio, i.e., 1.618034 tothe X power, you'll get a new Fibonacci series in whicheach number is the sum of the two previous numbers, e.g.,1.618 to the -1 plus 1.618 to the 0 equals0.618 + 1.00 = 1.618,and 1.618 is 1.618 to the 1st power.)


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Now, if you take the time span between the June 1992alignment/peak and the current possible alignment/peak andmultiply it by 1.618... (which is also 2.618, or 1.618 to the 2ndpower, times the length of time between the January 1994alignment/peak and the current possible alignment peak),then you get the time span from the 1991 alignment/price-lowand today.

If you keep doing this to the time periods between each ofthe alignment/Elliott Wave stock market turning points above,all the way to m ultiplying the time span between now and Jan.1994 by 1.618 to the 6th power to find the time span from the1962 peak to the present, then you uncover the co de of ElliottWaves and historical cycles. The correlation found bycomparing the lengths of time between the key planetaryalignment/stock market turning points noted above with exactFibonacci relationships is over 99.9 percent.

Now, to und erstand why this is so, you m ight note thatthe time span of plantery orbits in our solar system (i.e., thetime it takes for each planet to make one complete revolutionaround the sun), are related by Fibonacci relationships.

Specifically, given that the Earth takes one year to orbit thesun, the time that it takes Venus to orbit the sun is1.618 to the -1 years. The time it takes Mercury to orbitthe sun is approximately 1.618 to the -3 years. Mars is roughly1.618 years, the asteroid belt is roughly 1.618 to the 3rd years,Jupiter is approximately 1.618 to the 5th years, so on andso forth (note that Pluto does not fit).

Again, the correlation is around 99 percent (excluding Pluto).Given this property of the so lar system, the "astroharmonics"of when alignments will occur will be based upon Fibonaccirelationships. Thus, the time spans between planetaryalignments, which apparently affect turning points in


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mass m ood and w orld history, are related by Fibonacciproportions.

This is all quite remarkable given how R.N. Elliott'stheoretical Elliot Wave fractal-based wave patternis characterized by Fibonacci relationships. Yet, hedidn't realize the connection between ElliottWave patterns and astroharmonics!__________________

Who was F ibonacci?

The "greatest European mathematicianof the middle ages", his full name was Leonardo of Pisa,or Leonardo P isano in Italian since he w as born in Pisa(Italy),the city with the famous Leaning Tower, about 1175 AD.

He called himself Fibonacci [pronounced fib-on-arch-ee orfee-bur-narch-ee] short for filius Bonacci which m eans son ofBonacci. Since Fibonacci in Latin is "filius Bonacci" andmeans "the son of Bonacci",

So Leonardo grew up with a North African education under theMoors and later travelled extensively around the Mediterraneancoast. He would have met with many merchants and learned oftheir systems of doing arithmetic. He soon realised the manyadvantages of the "Hindu-Arabic" system over all the others.D E Smith points out that another famous Italian - St Francis ofAssisi (a nearby Italian town) - was a lso alive at the same timeas Fibonacci: St Francis was born about 1182 (after Fibonacci's
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around 1175) and died in 1226 (before Fibonacci's deathcommonly assumed to be a round 1250).

[The portrait here is a link to the University of St And rew's sitewhich has m ore on Fibonacci himself, his life and works.]

Introducing the Decimal Numbersystem into Europe

He was one of the first people to introduce the Hindu-Arabicnumber system into Europe - the positional system we usetoday - based on ten digits with its decimal point and a sym bolfor zero:

1 2 3 4 5 6 7 8 9 . and 0

His book on how to do arithmetic in the decimal system, calledLiber abbaci (meaning Book of the Abacus or Book ofCalculating) completed in 1202 persuaded many Europeanmathematicians of his day to use this "new" system.

The book describes (in Latin) the rules we all now learn atelementary school for adding numbers, subtracting, multiplyingand dividing, together with many problems to illustrate the methods:

1 7 4 + 1 7 4 - 1 7 4 x2 8 2 8 2 8----- ----- -------2 0 2 1 4 6 3 4 8 0 +----- ----- 1 3 9 2-------

4 8 7 2-------

1 7 4 28is6 remainder 6

Let's first of all look at the Roman number system still in use
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in Europe at that time (1200) and see how awkward it was forarithmetic.

The Numerals are letters

The method in use in Europe untilthen used the Roman numerals:

I= 1,

V= 5,

X= 10,

L= 50,

C= 100,

D= 500 and

M= 1000

You can still see them used on foundation stones of old buildingsand on some clocks.

The Additive rule

For instance, 13 would be written as XIII or perhaps IIIXX. Thisis reflected in the Roman language of Latin where 23 is spokenas tres et viginti which translates as three and twenty.

Arithmetic was not easy in the Roman system:

CLXXIIII added to XXVIII is CCII

CLXXIIII less XXVIII is CXXXXVI

The Decimal Positional System

The system that Fibonacci introduced into Europe came from Indiaand Arabia and used the Arabic symbols 1, 2, 3, 4, 5, 6, 7, 8, 9 with,most importantly, a symbol for zero 0.With Roman numbers, 2003 could be written as MMIII or, just asclearly, it could be written as IIIMM - the order does not matter sincethe values of the letters are added to make the number in theoriginal (unabbreviated) system. With the abbreviated system ofIXmeaning 9, then the order did matter but it seems this sytem was not

often used in Roman times.In the "new system", the order does matter always since 23 is quitea different number to 32. Also, since the position of each digit isimportant, then we may need a zero to get the digits into theircorrect places (columns) eg 2003 which has no tens and nohundreds. (The Roman system would have just omitted the valuesnot used so had no need of "zero".)


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This decimal positional system, as we call it, uses the ten symbolsof Arabic origin and the "methods" used by Indian Hindumathematicians many years before they were imported into Europe.It has been commented that in India, the concept of nothing isimportant in its early religion and philosophy and so it was much

more natural to have a symbol for it than for the Latin (Roman) andGreek systems.================Related articles

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