The Golden Ratio:

From Physics to the Human Brain, Behavior,

Esthetics and Ethics

Ramzi Suleiman

University of Haifa

Visiting Professor at the VU

Home Page: http://suleiman.haifa.ac.il

Paper presented at the Department of Social and Organizational Psychology

Free University of Amsterdam, May 23 2013

http://suleiman.hhaifa.ac.il/

An Alternative Title:

𝒙𝟐 + 𝒙 = 1

But First We need to get acquainted with the Golden Ratio, known also as the Golden Section, and the Divine Ratio.

It is the irrational number: φ = 𝟓−𝟏

𝟐 ≈ 0.618

and its twin: Φ = 𝟓+𝟏

𝟐 ≈ 1.618

It is the only number that satisfies:

x + 1 = 𝟏

𝒙 (or 𝒙𝟐 + x = 1)

x + 1 ≈ 0.618 + 1 = 1.618

1

𝑥=

1

0.618 ≈ 1.618

a

b

𝑎

𝑏 ≈0.618

𝑏

𝑎 ≈ 1.618

The Golden Ratio and the Fibonacci Numbers

Definition

The Golden Ratio ϕ, is defined as limn→ ∞𝑓𝑛

𝑓𝑛+1,

where fn is the nth term of the Fibonacci Series:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, …. in which each term is equal to the sum of the two preceding terms

𝒇𝒏 = 𝒇𝒏−𝟏 + 𝒇𝒏−𝟐

The golden ratio has fascinated intellectuals of diverse interests for at least 2,400 years.

“It is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics” Source: Livio M., (2002)The Golden Ratio: The Story of Phi, The World's Most Astonishing Number

The Golden Ratio is a significant number, not only due to its unique mathematical properties, but also due to its significant role in science and technology, starting from physics, to life science,

to humans' perception, cognition and emotion, to

social sciences, particularly the study of humans'

socio-economic behavior, values and religious

convictions

A shall say a very little about its appearance in Life Forms, Geometry, Art, Architecture and Design

Economics

Physics

Human Brain

Ethics

Music

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Golden Ratio in Life Forms

The Golden Ratio and the Fibonacci Series (which

converges to the Golden Ratio), play a key role in life

form by determining the structure of plants and

animals (Hammel, 1987; Klar, Nature, 2002),

including the the human body (Livio, 2002), human

DNA, and more ….

Golden Ratio in Life Forms

34 = 𝑓9

Golden Ratio in Geometry

Golden Ratio in Art

Golden Ratio in

Architecture

The CN Tower in Toronto, the tallest tower

and freestanding structure in the world,

contains the Golden Ratio in its design.

The ratio of observation deck at 342

meters to the total height of 553.33 is

0.618 or phi, the reciprocal of Phi!

The Great Pyramid of Giza

Golden Ratio in Design

Rectangular shapes with width to length

ratio of ≈ 0.618 are widely used in the

design of TVs, computer screens, and credit

cards, due to feelings of pleasantness and

harmony that the Golden Ratio is believed

to induce (Livio, 2002; Olsen, 2006; Pittard,

Ewing & Jevons, 2007).

Golden Ratio in Design

http://www.google.com/url?sa=i&rct=j&q=&esrc=s&frm=1&source=images&cd=&cad=rja&docid=Qw-e6Wgb3T5pwM&tbnid=DrwePtP2UuqQnM:&ved=0CAUQjRw&url=http://www.dukechronicle.com/articles/2013/02/26/golden-ratio-gives-sports-car-natural-appeal&ei=j7SJUbPXGKmw0QXo2IH4Dg&bvm=bv.46226182,d.d2k&psig=AFQjCNG9zzrqVmey5mZkiPXrbPBAuwU38g&ust=1368065474348790

Golden Ratio in Physics

Golden Ratio In Experimental Physics Chains of cobalt niobate become critically quantum at energies equaling the Golden Ratio

Source: You Tube Source: Coldea et al., Science, 2010

V – relative velocity

The Golden Ratio in Theoretical Physics Suleiman, R. The Dark Side Revealed: A Complete Relativity Theory Predicts the

Content of the Universe. Forthcoming in Progress in Physics, Vol. 3 July, 2013

m0

v

Picture recently taken at the Israeli Academy of Sciences in Jerusalem.

A Complete Theory of Relativity (CR) Suleiman, R., 2013

file://localhost/upload.wikimedia.org/wikipedia/en/9/90/Standard_conf.png

1. Every Thing is Relative . 2. all transfer of information from one frame of reference to another is carried by light or electromagnetic waves of equal velocity.

CR theory is based on two postulates:

The postulated complete relativism constitutes a profound departure

from the theories of Galileo-Newton and Einstein-Lorentz, since it "cuts

the universe loose with no anchor", neither a fixed, nonrelativistic,

spatial reference, as in Galileo-Newton's mechanics, nor a fixed

reference point on the velocities dimension (the velocity of light), as in

Einstein's mechanics.

file://localhost/upload.wikimedia.org/wikipedia/commons/a/a3/Buttersworth_James_E_Ship_In_A_Storm.jpg

REALITY IS IN THE EYES OF THE BEHOLDER AND HIS /HER TELESCOPE LENSE

Unlike Quantum Mechanics, my theory does not contradict Einstein’s view of “Local Realism”. However, I argue that what counts is not the local realism of things, but the relativistic information about them, as it is recorded by our measurement devices and processed by our senses and cognitive system. In the words of Einstein: what is behind the veil is the “OLD Guy’s” business.

It is YAHWAH’s not ours

The Kinetic Energy as a function of velocity:

E = ½ m0 𝒗𝟐

(𝟏−𝑉

𝑐)

(𝟏+𝑉

𝑐)

V – relative velocity

C – velocity of light

The Golden Ratio in Theoretical Physics

A Complete Relativity Theory (Suleiman, R. Progress in physics, vol. 3, 2013)

file://localhost/upload.wikimedia.org/wikipedia/en/9/90/Standard_conf.png

Denote 𝑉

𝑐 = β

To calculate the value β = βcr. which satisfies E =

Emax we derive β2(1− β)

(1+ β) with respect to β and equate

the derivative to zero.

This yields:

𝒅

𝒅𝜷 (β2

(𝟏− 𝜷)

(𝟏+ 𝜷)) = 2 β

(𝟏− 𝜷)

(𝟏+ 𝜷) + β2

[ 𝟏+ 𝜷 −𝟏 − 𝟏−𝜷 𝟏 ]

(𝟏+ 𝜷)𝟐

= 2 β𝟏−𝜷𝟐 − 𝜷

(𝟏+ 𝜷)𝟐 = 0.

for β ≠ 0 and we get:

β2 + β – 1 = 0

which yields:

β1. = φ = 𝟓−𝟏

𝟐 ≈ 0.618

β.2 = - (φ +1) = 𝟏

𝝋=

𝟓+𝟏

𝟐 ≈ 0.618

Golden Ratio In Theoretical Physics

Suleiman, R. (2013). The Dark Side Revealed: A Complete Relativity Theory Predicts the Content of the Universe. To appear in Progress in Physics, vol. 3.

The obtained energy term enables to derive plausible definitions of Dark Matter and Dark Energy and to predict their amount in the Universe with high precision

Content of the Universe

Source: NASA site

Prediction of the Content of the Universe

Golden Ratio in the Human Brain

Delta 1 (1.5 Hz) ; Delta 2 (2–3 Hz); Theta (6–8 Hz); Alpha (10 Hz); Beta1 (13–17 Hz); Beta2 (22–27 Hz); Gamma1 (30–50 Hz); Gamma2 (50–80 Hz)

The Number of Human Brain Waves is 8 – A Fibonacci Number

Source: Roopun A. K. et al . (2008). Frontiers in Neuroscience, 2(2), 145–154. 2008

It has been argued that the Fibonacci structure of our brain results in an optimal processing of perceptual information, and minimizes negative interference

The Golden ratio in Music

Processing Auditory Information

Human Taste for music

528 Hz

Famous musicians tuned their scale to match the C5 = 528 Hz.

http://en.wikipedia.org/wiki/John_Lennon

Examples of famous recordings in 528Hz

Meg White and Jack White at the 2007 Primavera Sound in Barcelona

"Seven Nation Army“ White Stripes

//upload.wikimedia.org/wikipedia/commons/9/92/Meg_&_Jack,_The_White_Stripes.jpghttp://en.wikipedia.org/wiki/White_Stripeshttp://en.wikipedia.org/wiki/White_Stripeshttp://en.wikipedia.org/wiki/White_Stripes

"Black or White“ Michael Jackson

http://en.wikipedia.org/wiki/File:Michael_Jackson_in_1988.jpg

"Imagine“ John Lennon

528love.com

528 is a simple number that is central to the “musical mathematical matrix of creation.” This LOVE vibration harmonically resonates in your heart inaudibly connecting your spiritual essence to the spiraling reality of heaven and earth. Even the parallel universes connect to the center of your heart by this LOVE channel broadcasting matter and energy according to the laws of physics. In fact, 528 is fundamental to these laws. This frequency, more than any other, epitomizes the unified field of musical metaphysics in the matrix of the spiraling fractal universe…….

65

40

24.5

15

10

7

2.5

1.5

BRAIN WAVES Hz

53.75 33.08 20.48 12.64 7.82 4.83 2.99 1.85 1 430 Hz

52.125 32.08 19.86 12.27 7.582 4.686 2.895 1.782 1.103 417 Hz

41.2 25.35 15.7 9.69 5.99 3.7 2.29 1.42 0.87

CHAKRA 9 FORK Hz

66 40.6 25.1 15.5 9.6 5.93 3.67 2.66 1.4 528 Hz

A hypothesis

0

10

20

30

40

50

60

70

0 20 40 60 80Brain Wave Frequency ( Hz)

𝑭𝒓

𝒆𝒒

𝒖𝒆

𝒏𝒄

𝒚

𝑭𝒊𝒃

𝒐𝒏

𝒂𝒄

𝒄𝒊

𝑵𝒖

𝒎𝒃

𝒆𝒓

𝒔

Superposition of Waves

The Golden ratio in Economics

Economic Harmony Theory (EHT)

Propositions: 1. Individuals are solely self-regarding players. 2. When making their decisions, individuals consider their payoffs relative to subjective reference points (SRPs), rather than their absolute payoffs. 3. A SRP can be social, when a player compares her payoff to the payoff(s) of another member or members in her group (e.g., a co-worker's salary), or non-social, when she compares her payoff with a neutral (non-social) reference point (e.g., her expected expenditure). 3. Individuals are aware of the norms of equality and equity, as they are practiced in their social group. 4. There exists a formal or informal sanctioning mechanism, by which sanctions are applied on deviants from the group's norms and rules.

EHT predicts behavior in a class of two, three and five person games, including two- and three-person Ultimatum Games and CPR Games.

The Standard Ultimatum Game The proposer makes an offer (x, 1-x), for herself and a designated recipient, respectively. The recipient responds by either accepting the offer, in which case both players receive their offered shares, or by rejecting the offer, in which case the two players receive nothing.

Game theory (SPE) predicts that the proposer should offer almost nothing. However: It is well documented that the modal and mean offers in the game are about 50% and 40%, respectively, and that offers of 20% or less are rejected with high probability

The question remains: Why do proposers offer on average of about 40% of the entire amount, and not, say, 45% or 55% or maybe 35%? Despite hundreds of studies on the ultimatum game, which replicate the 60/40-split result, the explanation of this finding remains elusive.

Proposer

Responder

Social (S) Non-Social (N)

Social (S) (S, S) (S, N)

Non-Social (N) (N, S) (N, N)

Permissible SRP’s of Proposer and Responder

I demonstrate ETH solution of the UG

It makes sense to argue that from the point of view of the proposer, the amount that she could have received, had she retained the entire amount for herself, is most likely to be the preferred focal point to adhere to. Conversely, from the standpoint of the recipient comparison with the proposer’s portion is more probable than other comparisons.

Proposer

Responder

Social (S) Non-Social

(N)

Social (S) (S, S) (S, N)

Non-Social

(N)

(N, S) (N, N)

Permissible SRP’s of Proposer and Responder

Balance or Harmony is achieved if:

The amount kept by the proposer

The entire amount =

The amount received by the responder

The amount kept by the proposer

Or x

1 =

1− x

x

Which could be rewritten as: x2+x − 1 = 0.

Yielding :

x = −1± 12− 4.1.(−1)

2 = (-

5+1

2,

5−1

2 ) = - Φ , ϕ)

or approximately: - 1.618 and 0.618, respectively. For positive amounts, balance is achieved for a partition of about (0.62, 0.38) shares for the Proposer and Responder, respectively.

Empirical Tests

I tested the solution using two large-scale datasets: (1)Data from a Meta-analysis which integrated 37 studies

conducted in 25 different countries, representing different cultures and social-political systems (Oosterbeek, Sloof & Van de Kuilen, 2004)

(2)Data collected in a comprehensive study in 15 small communities, exhibiting a wide variety of economic and cultural conditions (Henrich et al., 2006).

A bargaining experiment in the village of Teci, on Yasawa Island, Fiji (Photo by Robert Boyd). Source: Henrich et al. Science, 312, 2006

nsignificant.

Distributions of offers, rejection rates and final payoffs in two large-scale studies

theory prediction 38.2% Prediction error ≈ 5.7%

theory prediction 38.2% Prediction error ≈ 3.3%

the concept of harmony between relative payoffs, could prove useful outside the laboratory for understanding, and possibly making policy recommendation for increasing organizations’ profit without sacrificing fairness in salary pay, or visa versa.

On the Applied Side

A straightforward application is to apply the concept of economic harmony for assessing the levels of harmony or disharmony in the distribution of salaries in a given organization. By modeling organizational structures as n-person games, it becomes possible to apply the theory in order to specify the conditions required for achieving harmony in the distribution of wages in the workplace, and consequently enhancing both profitability of the workplace and fairness in profit allocation.

An Example

The Golden ratio in Ethics

Love Thy Neighbor As You Love Thyself

Leviticus, 19:18

In Islam Prophet Mohammad, in his Hadith is quoted to say:

“No one could be considered a believer until he desires for his brother what he desires for himself”.

The New Testament mentions the principle in various chapters

In In Matthew 22:35-40, New King James Version, we are told: "Then one of them, a lawyer, asked Him a question, testing him, and saying, 'Teacher, which is the great commandment in the law?‘ Jesus said to him: 'You shall love the Lord your God with all Your heart, with all your soul, and with all your mind. This is the first and great commandment. And the second is like it: You shall love your neighbor as yourself. On these two commandments hang all the Law and the Prophets.”

love your neighbor as yourself In behavioral terms: Treat others as you treat yourself Which in symmetric situations means Equality While in asymmetric situations it means: Equity Thus the balance point derived in EHT based on rational considerations applies

Amount kept be self

Total Amount =

Amount received by other amount kept by self

Or:

x2+x = 1

Amount kept be self

Total Amount =

Amount received by other amount kept by self

Denote the amount kept by x and the amount transferred by 1-x The above equation becomes:

From my ethics paper with picture

Summary My talk is centered around a simple quadratic equation

𝑥2 + x =1

Physics

Β =𝑣

𝑐

Economics

Life Sciences

ϕ Ethics Aesthetics & the Arts

Music

Is it the hand of God?

I think not

At least this is what he said

when I forwarded the question to his Holiness

Towards An Integrative Theory of Everything

Thanks !

ϕ

http://www.youtube.com/watch?v=nBgQPSUTWVM&feature=player_embedded