Archive for the ‘Universo’ Category


“Most Relevant Generalities / Major Arcana” 🗝️:

The twenty-two cards of the Arcana Major. Tarot deck: Rider,Waite & Smith.

Introduction and Sketch of this Post:

This is the first post of  the series on “Tarot”. 

Firstly, in section 1), I´ll present an overview of the story of Tarot, its use for divination purposes, tarot spreads, cards´positions (upright or reversed), total number of cards, division into two categories: Major and Minor Arcana.

In the second section (2) of this post, I´ll assess in-depth the Major Arcana. 

For that purpose, I´ll use the classic Rider-Waite deck, illustrated by Pamela Colman-Smith, which has been continually printed since 1909. Hence, it is easy to find in Bookstores or online nowadays.

Let´s keep in mind that the Major Arcana cards are somehow related to Carl Jung’s archetypes. They are “patterns”, inherent part of the Collective Unconscious. These cards symbolise the process we go through in our lives, aiming to become a balanced and integrated person. 

With that being said, I´ll offer the meanings of the respective 22 cards comprising this group.

In both, the upright and reversed position. Worth noting that, when you shuffle the tarot cards, they often end up facing in different directions. So basically, each card can show up in an “upright” or a reversed” position.

To end, in the third (3) section, I´ll dig into the so-called “Fool´s Journey”. The Fool card is numbered zero, and if you look closely at the cards, in sequential order, starting with the Fool, you´ll notice that them seem to tell us a story. The story of our own evolution as persons, going through different stages, with their respective struggles and victories. Along this journey, we encounter challenges, face adversity, perform labours, meet people, make hard decisions and fight opposing forces. Each step of the way brings us closer to embrace the Wholeness of Ourselves and of the World. This “journey” is, in fact a cycle. And one could go through the same cycle many times in a lifetime. Or one could just fail to reach the end of the cycle. There is of course, an implied recurring element associated with Karma here. Maybe the “Fool´s Journey” could reach its finish line in another, next life. Or did so in a past life and now he is facing a new, different challenge.

►1) Tarot. Generalities:

Story and Purpose. Rider-Waite Deck: Spreads. Positions. Major and Minor Arcana:

I own this deck!: Tarot Rider Waite boxed-deck.

1.1.⇒♦ What is Tarot and how does a Tarot Reading work?: 

The Tarot is a pack of playing cards, used from the mid-15th century in various parts of Europe to play games such as Italian Tarocchini and French Tarot. In the late 18th century, it began to be used for divination.

In  this last sense, Tarot cards are commonly used to measure potential outcomes and evaluate influences surrounding a person, an event, or both. The technical term for tarot reading is Taromancy (divination through the use of tarot cards), which is a subsection of Cartomancy (divination through cards in general).

Tarot reading is not about predictions, but more about possible outcomes as well as examining influences related to the issue at hand. These could be influences which the subject might not even be aware of before the reading.A spread is the arrangement of cards dealt in a reading.

1.2 ⇒♦Spreads:

There are many types of spreads. Usually, the querent (receiver of the reading) asks a general question, or could just picture a situation in his mind. He can keep them to himself. You (person doing the reading) can then pull six cards, representing different aspects of your past, present and future situation. You can pull three cards, instead, where the first represents the past, the second represents the present, and the third represents the future. The three card spread is called The Three Fates. Also, we have the so-called Celtic- Spread Reading, which consists of ten cards representing a variety of things including any past and future influences, personal hopes, and conflicting influences. You can check out other spreads here

1.3 ⇒♦ Positions of the Cards: Upright or Reversed:

Cards can show up in two positions: Upright or Reversed.

The Upright position represents certain Idea or Situation.

But, what happens when the card shows up in a reversed or inverted position?.

a) If the card is reversed, the meaning is almost always considered to be the opposite of the one the card might reveal when it is upright.

Although this is the predominant criteria (and, hence, the one, I´ll stick to), there are still other ways of interpreting reversals.

b) One of them could be to say that they refer to the previous card (For example: If we have an inverted Strength card (8), it might actually be referring to The Chariot (7)).

c) Other way of interpreting reversals is to say that they represent blocked energies or resistance towards what the card represents. 

d) Finally, another way of doing reversals would be to say that it indicates an unconscious influence and, hence, that the querent is not aware of it. For example: If we pulled an inverted Sun, we might say that the querent lacks awareness towards this bright, joyful influence. Maybe because it is hidden, or perhaps because it has not fully developed yet. 

e) Another point to keep in mind: some people like to switch “gender” in those cards in which a female or male figure shows up. So, If we pulled Justice (with a Female figure) in an inverted position, we could assume that the characteristics of that card might be related to a Man in the querent´s life.

As I said above, I will provide the meaning of reversed cards as the opposite to which the card reveals in its upright position. But, when doing a reading you can include other interpretation criteria, too. 

1.4 ⇒♦ The Tarot Deck. Major and Minor Arcana:

A Tarot deck has 78 cards, consisting of two types of cards: Major and Minor Arcana.

The “Trump cards” (numbered 1 to 21) and the Fool (numbered 0) are called the Major Arcana, while the ten pip and four court cards in each suit are known as Minor Arcana.

•The Minor Arcana (Lesser Secrets) Consists of 56 cards, divided into four suits (Swords, Cups, Wands and Pentacles). Each suit has 14 cards: ten numbered cards and four court cards. The court cards are the King, Queen, Knight and Page/Jack, in each of the four tarot suits.

•The Major Arcana (Greater Secrets), consists of 22 cards, without suits: The Magician, The High Priestess, The Empress, The Emperor, The Hierophant, The Lovers, The Chariot, Strength, The Hermit, Wheel of Fortune, Justice, The Hanged Man, Death, Temperance, The Devil, The Tower, The Star, The Moon, The Sun, Judgement, The World, and The Fool. Cards from The Magician to The World are numbered in Roman numerals from I to XXI, while The Fool is the only unnumbered card, often placed at the beginning of the deck as 0.

I finally wanted to stress that when one lays out a spread or performs a reading and sees mostly Major Arcana cards,one can assume that the matter in question, and/or the querent’s life, is more profound in comparison to Minor Arcana cards. The Major Arcana are signposts to things, events, and people, that are meant to be taken more seriously and looked at more closely, in general, than the Minor Arcana cards will generally represent.

2) Major Arcana Cards (Rider-Waite Deck):

These are 22 cards of the Major Arcana and their respective meanings, in both the upright and reversed position.

⇒♦ 0. The Fool:

The Fool is shown at the beginning of his journey with unlimited potential. He has a bag holding off his staff and a bright sun rising up behind him.

The white rose in his left hand represents purity and innocence. He has a guardian in the little white dog warning him of danger as he approaches the edge of the cliff. The fool is unaware, as he is looking up.

The card represents beginnings, overly optimistic approaches and spontaneity. It also reminds us that, even if we are enjoying ourselves, there are always consequences facing our actions. 

•Upright: Living in the moment, feeling carefree or spontaneous, entering a new phase.
•Reversed: Being blocked, restricted.

⇒♦ I. The Magician:

When the Magician appears in a spread, it points to the talents, capabilities and resources at the querent’s disposal. It represents possibilities and the card shows that the querent has all the elements, as the four suits of the Minor Arcana (Swords, Wands, Pentacles and Cups) show up in the card. The magician is the creator of ideas and thoughts.


•Upright: Acting consciously, acknowledging your motivations. Feeling centered and committed. Being creative and energized.
•Reversed: Inability to act or react. Feeling drained. Losing focus or commitment.

⇒♦ II. The High Priestess:

The High Priestess card shows her seated between two pillars marked B and J, which stand for Boaz  and Jachin respectively (You can find these names in the First Books of Kings). Furthermore, these letters are inscribed upon the pillars of the Salomon Temple, associated with Wisdom. There is a cloth behind her depicting pomegranates, a symbol of death and the afterlife in Greek Mythology. The High Priestess is the keeper of secret knowledge, as the crystal ball on her head shows. There is a crescent moon beneath her feet, which might represent that the opportunities could increase. She is holding a book, the Tora, the Jewish sacred book. 

•Upright: Withdrawing. Being passive or calm. Seeking guidance from within. Understanding the potential and possibilities. Looking beyond the obvious.
•Reversed: Inability to find your inner voice or to look beyond.

⇒♦ III. The Empress:

The Empress depicts a woman seating in a field. She represents fertility, being a sort of Mother figure. She is surrounded by flowers and plants. There is also a heart-shaped rock with a Venus symbol on it. As we know, this symbol stands for Women.

•Upright: Nourishing life. Nurturing and caring for others. Abundance. Experiencing the senses (pleasure, beauty, etc). Feeling connected to Nature.
•Reversed: Focusing on oneself without caring for other people. Scarcity. Inhibition. Closure.

⇒♦ IV. The Emperor:

The figure in this card depicts stability, structure, power and protection. He is related to Aries, in the Horoscope. 

•Upright: Father figure. Setting directions, laws rules or boundaries. Applying reason. Creating order. Exerting control.
•Reversed: Chaos. Lack of control and order.

⇒♦ V. The Hierophant:

He is a  High Priest. Sits upon his throne as to other men kneel before him. He is a man who shares rituals, he is a leader of a flock/group, not of individuals. He represents alliances, goodness, comfort and traditional values. The Hierophant is associated with Taurus, in the Zodiac.

•Upright: Education, becoming informed. Having a belief system. Following the rules, staying within conventional bounds.
•Reversed: Being heterodox, rebel. Not sticking to traditional values. Acting crazily.

⇒♦ VI. The Lovers:

This card shows temptation, represented by the snake on the tree. We can also see two human beings, male and female,  and a spirit with open hands above them, a brilliant sun. The card is not about two people however as it is about one: the person who experiences love. It refers to falling in love with someone or … Something. This card is associated with Gemini, in the Zodiac.

•Upright: Love. Marriage or partnership. Establishing bonds. Staying true to yourself. Determining values. Facing a moral choice.
•Reversed: Loneliness. Loss in relationships. Rejection. Sticking to others´opinions or values.

⇒♦ VII. The Chariot:

It represents labour and power. There are two sphinxes. Their colors are reversed, pretty much like a Yin-Yang symbol. The driver has a Sun on his head. We can see rising and falling moons close to his neck. The complementary nature of these two opposite natures tend to echo the sphinxes pointing out to Balance.  The Chariot is related to Cancer, in the Horoscope.

•Upright: Victory, reaching goals. Being determined and focussed. Feeling self-confident. Mastering emotions. Self control, discipline.
•Reversed: Putting other´s first. Resignation. Lack of determination or focus. Low self-esteem. Defeat. Confusion.

⇒♦ VIII. Strength: 

The card shows a maiden taming a lion, not with physical strength, but with strenght of character: understanding, compassion. This is symbolic of resourcefulness, of softening the power we have to control others. The card shows that harmony has been achieved as the lion seems to be happy as the woman caresses him and his tail is tucked between his legs, in a submissive attitude.  The woman has a symbol of infinite, as it appears in the card of the Magician. This represents endless possibilities. The card stresses that our strengths are much more than our physical abilities. This card is related to Leo, in the Horoscope.

•Upright: Strenght and power. Refusing to get angry, maintaining composure. Caring about others, compassion. Forgiveness. Persuasion, being able to influence.
•Reversed: Hard Control. Weariness. 

⇒♦ IX. The Hermit:

The card depicts an old man, alone, leading his way through the darkness by a light, which, is actually a little shining star. The Hermit represents knowledge, inner peace and understanding of his life. The card represents solitude, withdrawal, careful thought, ruminations.

The Hermit could represent a need to be alone in order to sort out things… Or a person in the querent´s life. The Hermit is associated to Virgo, in the Horoscope.

•Upright: Being introspective, looking for answers within. Withdrawing from the world. Loneliness.
•Reversed: Involvement with the world. Being with others.

⇒♦ X. Wheel of Fortune: 

We can see the letters T, A , R and O which stand for Tarot, as it its spelt. This represents endless circles. In the inner, little circle, we can see the signs for the four key elements in Alchemy: Mercury, Salt, Sulfur and Water. The Egyptian God Anubis, (painted in red) is holding the Wheel on his back. Anubis looked like a dog and was a Psychopomp and Ruler of the Underworld. Upon the wheel we can see a Sphinx, keeping the balance of the wheel itself.  There is a snake on the left of the card. Some say this snake is Typhon, a monster from Greek Mythology, representing Earth. On the four corners of the card yellow, winged creatures are reading books. This could reference the Book of Revelations. The creatures resemble a lion, a calf,  a human being and an eagle. The wheel is a circle, but carrying with it the past experiences. It represents completion, also Fate, sudden good luck, transitions and changes.

•Upright: Feeling a sense of destiny. Uncovering patterns and cycles. Turning point: altering the present course. Speed. Change.
•Reversed: Slow pace. Blocked change, no movement.

⇒♦ XI. Justice: 

The card depicts a King seated between two pillars. He has a sword in one hand and a scales of Justice in the other. It represents balance, a middle ground. This card could also be literal suggesting a Court proceeding, a conflict or the involvement of Authority to resolve a dispute. Justice is associated with Libra in the Horoscope. 

•Upright: Fairness, justice. Honesty. Responsibility. Acknowledging the truth. Accepting the consequences of your actions.
•Reversed: Avoiding the truth, disavowing your role. Shirking responsibility.

⇒♦ XII. The Hanged Man:

The card depicts a man suspended by his legs upside down from a tree. His leg is bent and his face is peaceful. There is no indication of suffering. A corona is around his head indicating wisdom. The hanged man indicates a change of perspective, swaying between different possibilities, an inability to make a decision. It is a time of internal focus , introspection and self-discovery. 

Being hung by one leg was traditionally a punishment for traitors. In that sense, what the hanged man sees as right is upside down to those who have passed judgement upon him. 


Upright: Waiting. Letting go. Accepting what is. Overturning priorities. 
•Reversed: Inability to let go. Control. Self-assertion. Struggle.

⇒♦ XIII. Death:

The Death card depicts a skeleton in dark armor,  a grim reaper upon horseback. Before him, a Priest offers prayers, a man lays dead, a young looks on with curiosity as an older child turns away in fear. Overall, we can see the range of emotions that people experience. In the Reaper´s hand there is a black flag. This card is a symbol of change, part of the cycle of death and rebirth. This card is associated with Scorpio, in the Zodiac.

•Upright: Endings. Putting the past behind you. Change or transition. Accepting the inevitable. Cutting out what isn’t necessary.
•Reversed: Beginnings. Fresh start.

⇒♦ XIV. Temperance:

The card depicts an archangel at the edge of a riverbank. One foot on land, the other in water.  He pours water from one cup into another. The card is about balance. It suggest finding compromise or agreement as well as reminder to maintain moderation. This card is associated with Sagittarius, in the Horoscope.

•Upright: Showing moderation. Mitigating a harsh position. Harmony. Fostering cooperation and synthesis. Healing and flourishing.
•Reversed: Excesses. Disagreement, competition. Discord, lack of harmony.

⇒♦ XV. The Devil: 

The Devil in this card has horns, goat legs and  wings of a bat. He holds a torch in his left hand. Chained to his pedestal are a man and a woman, also with characteristics of the devil: horns and a tail, but interestingly, their chains are loose around their neck. They are capable of slipping them off. However, they choose to remain chained. The card represents addiction, vice or obsession, things to which we might choose to remain beholden. In relationships, this card could represent a  control and temptation. This card is related to Capricorn in the Zodiac.

•Upright: Being obsessed and unaware. Allowing yourself to be controlled. Being addicted. Overindulgence. Feeling hopeless.
•Reversed: Independence. Clarity. Hope and optimism. Release, freedom.

⇒♦ XVI. The Tower:

The Tower shows a tall tower pitched atop a mountain. Lightning strikes and flames burst from the building’s windows. People are leaping from the tower in desperation, wanting to flee such destruction and turmoil. 

The Tower signifies darkness and destruction on a physical scale. The Tower itself represents ambitions built on false premises. The card is associated with sudden, disruptive, rude awakening and destructive change.

•Upright: Sudden change, defeat, destruction. Erupting in anger. Letting everything go. Exposing what was hidden. Toppling from the heights
•Reversed: Victory, control. Staying together. Serenity. Calm.

⇒♦ XVII. The Star:

The card depicts a maiden  kneeling at the edge of a small pool. The woman holds two containers of water. She pours the water out to nourish the earth and to continue the cycle of fertility, 
The other container pours the water onto dry land in five rivulets, representing the five senses. The woman has one foot on the ground, representing her common sense, and the other foot in the water, representing her intuition. Behind her, shines one large star and seven smaller stars. All the stars have eight points, and eight represents Strength. 
The card entails illumination, guidance and renewal. It suggests nourishment and hope. The astrological sign of the Star is Aquarius.
•Upright: Regaining hope. Realizing an inner strength or truth. Wisdom. Being generous. Free-flowing love. Peace of mind. Calm.
•Reversed: Hopelessness, lack of faith, pessimism. Upheaval, Chaos.

⇒♦ XVIII. The Moon:

This card depicts two wolves howling at a Full Moon with a Crescent Moon inside.
The pool at the base of the card represents the subconscious mind and the crayfish that crawls out of the pool symbolises the early stages of consciousness unfolding.
The card suggests illusion, fear, anxiety. This might be a time of an emotional or mental trial and that the querent might not think clearly or could make questionable decisions as those inspired by the Lunacy of the Full Moon. The astrological sign of the Moon is Pisces.


Upright: Feeling fear. Deceiving yourself. Losing direction and purpose. 

Reversed: Being serene, untroubled, at peace. Enlightenment. 

⇒♦ XIX. The Sun: 

This is a joyful card.  The bright Sun is an image of optimism and fulfilment. The child in the card is happy. He is naked and this represents innocence and purity. The white horse upon which the child rides represents strength and purity of spirit. The horse is without a saddle and is controlled without the use of the hands.  The sunflowers in the background represent the fruitfulness of the spirit under the nourishment of the Sun.

•Upright: Understanding. Enlightenment. Believing in your worth. Greatness, shining brilliantly. Joy and enthusiasm.
•Reversed: Being tired or sad. Weariness, confusion.

⇒♦ XX. Judgement:

The Judgement card shows a number of naked men, women and children rising up from their graves, responding to the trumpet call of the Archangel Gabriel, a psychopomp, who hovers high above them.
The card represents absolution and rebirth. The card could suggest that this is a time of resurrection, of bringing back the Past, revisiting things and making peace with past situations that were long ago thought be to put to rest, in order to finally move forward. 

•Upright: Making a judgment. Making hard choices. Knowing what you must do. Making a fresh start. Releasing guilt. Forgiving yourself and others. Absolution.
•Reversed: Endings, feeling regretful and guilty.

⇒♦ XXI. The World:

The card depicts a woman surrounded by a wreath (symbol of Victory), holding two wands.

The figures in each of the four corners of the World card are the same figures that appear on the Wheel of Fortune. Interestingly, the World card is very much associated with the Wheel of Fortune, reflecting the cyclical progression of time and the human experience. 

The woman has one leg crossed over the other, just like the Hanged man. She is, in a sense, his opposite (i.e. the Hanged Man upright). As the Hanged Man looks inward, the woman in the World card looks outward. This card is a symbol of a completion and accomplishment. 

•Upright: experiencing wholeness and balance. Synthesis. Accomplishing your goals. Becoming involved. Feeling fulfilled.
•Reversed: Isolation, apathy, withdrawal. Lack of integration.

⇒♦Astrological Signs & Planets:

Which are their Equivalents in the Arcana Major?:

Here we have the Zodiac Signs and their respective cards in the Major Arcana:

💦Water Signs: Cancer: The Chariot Scorpio: DeathPiscis: The Moon.

🔥Fire Signs: Aries: The Emperor. Leo: StrengthSagittarius: Temperance.

💨Air Signs: Gemini: The LoversLibra: JusticeAquarius: The Star.

🌎Earth Signs: Taurus: The HierophantVirgo: The HermitCapricorn: The Devil.

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►3) The Fool´s Journey… Or the Fool´s Lifecycle:

The Fool (0) has no idea what will happen to him and sets out on his journey with only his hopes. At the start of his trip, the Fool is fresh, open and spontaneous. But he is also unaware of the hardships he will face as he travels this world.

On setting out, the Fool immediately encounters the Magician (I) and the High Priestess (II).
The Magician takes advantage of the opportunities the Fool has in himself and provides him with what he might find useful during his journey. The High Priestess provides the fertile ground in which creative events occur.

As he grows, he meets with the Empress (III). The Fool becomes more and more aware of his surroundings. Hence he comes to know Mother Earth, experiencing an awakening of his senses. The Emperor (IV) represents for the Fool a Father Figure and through him he learns about the importance of laws and rules.

III. The Empress. IV. The Emperor.

The Hierophant (V) teaches the Fool to acknowledge the value of the beliefs and traditions of his culture. The Fool learns to identify with a group and discovers a sense of belonging.

Eventually, the Fool experiences Love (VI). He wants to reach out and become half of a loving partnership. In the meantime, he also feels he need to decide upon his own beliefs.

The Fool becomes an adult, he has a strong identity and a certain mastery over himself. Through discipline and will-power, he has developed an inner control, which are characteristics of the Chariot (VII).

Over time, life presents the Fool with many challenges, some that cause them sorrow and disappointment. But he is resilient and strong. He develops Patience, Compassion and Tolerance, which are all attributes of Strength (VIII).

Sometime during his journey, the Fool begins to look inward, trying to understand his feelings and motivations. He seeks moments of solitude to find his own direction, in accordance with the Hermit card (IX).

After much soul-searching, the Fool begins to see how everything connects. The Cycles he and Nature go through remind him of a Wheel of Fortune (X). He believes in both the power of his freedom to choose and Fate. He faces changes, recognizing his destiny in the sequence of events that led him to certain turning points.

The Fool wonders about Justice (XI). He starts with himself and looks back over his life to trace his actions. He takes responsibility for his past actions so he can make amends and ensure a more honest course for the future.

Sooner or later, he faces an experience that seems too difficult to endure. This overwhelming challenge humbles him until he has no choice but to give up and let go. He feels his world has been turned upside-down. So he pauses free of pressures, like the Hanged Man (XII).

The Fool cuts out what no longer serves him, or what makes him feel bad about himself. Death (XIII) .. . and Rebirth. After al the changes, he is ready to start over.

The Fool realizes the balancing stability of Temperance (XIV) and its powerful effects. By experiencing the extremes, he has come to appreciate moderation.

But moderation doesn´t last forever and vices and excesses could prevail. The Fool confronts the Devil (XV) within himself, in the form of obsessions and addictions.

The Fool may only find release through the sudden change represented by the Tower (XVI). Sometimes only a monumental crisis can generate enough power to smash the walls of the Tower. Only the destruction of the tower will set him free.

After going through a harsh time, the Fool find serenity and calm. He looks up and sees his own Star (XVII), a reflection of his own inner Self, which replaces the negative energies of the Devil.

Woefully, he is still vulnerable to the illusions of the Moon (XVIII). The Fool’s joy is a feeling state. His positive emotions are not yet subject to mental clarity. In his dreamy condition, the Fool is susceptible to fantasy, distortion and a false picture of the truth.

However, the Sun (XIX) shines. It dispels the clouds of confusion and fear. It enlightens, so the Fool both feels and understands the goodness of the world.

The Fool´s false, ego-self has been shed and his true Self manifests. The Fool makes a deeper Judgement (XX) about his life. He forgives himself and others. He feels cleansed and absolved.

The Fool reenters the World (XXI), but this time with a more complete understanding. He has integrated all the disparate parts of himself and achieved wholeness and fulfillment.

XX. Judgement. XXI. The World.

Last, but not Least: Tarot, “Deepening Knowledge”:

🗣️Before waving Goodbye, I wanted to leave you a few recommendations, as to this topic. Check them out:

•Learn the meanings of all cards and other issues. (Playlist): Reading Tarot Cards by Goodie.

Free Tarot Readings on YouTube, according to your astrological sign. I´ll recommend you my favorite Tarotist over there, who (as such!) often uses the classic Rider Waite Tarot (Or variations of it). Keep in mind that we haven´t still  gotten into the Minor Arcana. But, we have already studied the Major Arcana. Look for your Zodiac sign, over here: Carol´s Universe. (Long, in-depth monthly reading & great knowledge of the cards).

•Poetry of the Tarot:  Deborah Gregory´s poems based on Tarot Cards are excellent!.

Thanks for reading!. My next post will focus on Minor Arcana. Stay Tuned if you want to learn more about Tarot. See you!. Aquileana💕. 

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“Greek Myths and Graffiti Murals”: “Collaboration With Resa McConaghy”⭐:


⇒About This Post. Abstract:

The following article is composed of two sections, each one of them including murals from Argentina and Canada, respectively. This post aims to analyze with a with a free, but still judiciously, well-founded criteria how certain mythological greek themes and characters might be recurrent, despite time and even against it.

As Resa and I found some graffitis which seemed to have mythological and even philosophical equivalents we decided we wanted to try to show those connections. Resa´s mural is from the University of Toronto (Toronto, Canada) whilst mine are from The Planetarium (Palermo, Buenos Aires, Argentina). With that being said, we just wanted to say that, after finding many similarities, we are quite pleased with the outcome. Both of, Resa and I believe the convergences are striking. And being so, they broaden and deepen the value of the immortal Ancient Greek Legacy.

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⇒Section I. Murals: The Planetarium:🇦🇷

The Galileo Galilei planetarium, commonly known as Planetario, is located in Parque Tres de Febrero in the Palermo district of Buenos Aires, Argentina. The building was officially opened to the public on April 5, 1968. It consists of a cylindrical framework with independent projectors for the Moon, the Sun and the visible planets (Mercury, Venus, Mars, Jupiter and Saturn) and two spheres in the extremes that project 8,900 stars, constellations and nebulas.
Nowadays the Planetarium is surrounded by a thin sheet metal with many murals on it. We´ll present here some of them, aiming to find mythological  and philosophical corollaries.
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⇒Eros and Psyche… And the Planetarium above them!:

This graffiti is quite the finding. It is based on an original painting “The abduction of Psyche” by William-Adolphe Bouguereau (1894). 
The artist included a Planetarium above the couple.
According to the greek myth Aphrodite was jealous due to men’s admiration for Psyche, so she asked her son, Eros, to poison men’ souls in order to kill off their desire for Psyche. But Eros fell in love with Psyche. Thus, against his mother´s wishes, he asked the west wind, Zephyr, to waft her to his palace.
They consummated their love that same night. But for that Eros had to make Psyche believe that he was an ugly beast, as the Oracle had told her parents that Psyche would marry an ugly beast whose face she would never be able to see. And apparently she firmly believed so!…
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⇒The Horned goat with human hands:

This mural with goat head and human hands might remind us of the constellation Capricornus .
Its name is Latin for “horned goat” or “goat horn” or “having horns like a goat’s”.
This constellation protected by Hestia, represents Pan, the god of the wild and shepherds. The myth tells us that, in order to escape Typhon, Pan cast himself into the river, making the lower part of his body look like a fish, and the rest a goat: Zeus, admiring his shrewdness, put this shape among the constellations .
However, in this mural, we lack of the sea elements… But the resemblance between hands and fins couldn´t go unnoticed, either way.
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⇒The Bull Surrounded by Snakes:

This mural seem to evoke the Great Greek Bull. It could be linked to the Minotaur.
According to the respective myth, after Pasiphae (the daughter of Helios, the Sun, by the eldest of the Oceanids Perse) become impregnated by a white bull, she gave birth to a sort of hybrid child, the bull-headed Minotaur.
Angered with his wife, Minos imprisoned the minotaur in the labyrinth of Crete in Knossos. Presumably, Minos was one of the three sons from the union of Europa and Zeus; when Zeus was in the form of a bull.

As to snakes, let´s remember the rod of Asclepius, God of Medicine and Apollo´s son. It symbolizes the healing arts by combining the serpent, which in shedding its skin is a symbol of rebirth and fertility. The Asclepius Wand, often confused with the Caduceus wand of Hermes, is the symbol of the medical profession.

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⇒Tiempo- Time:

The words on this mural mean: Time.
But what is exactly time. St Augustine of Hippo says in his “Confessions”: “What then is time? If no one asks me, I know what it is. If I wish to explain it to him who asks, I do not know”… Time is such an elusive concept, indeed!.
In Greek mythology, Chronos was the personification of time, not to be confused with Cronus, the Titan and father of Zeus.
The Greeks had two different words for time: Chronos refers to numeric or chronological time, while another word kairos refers to the more qualitative concept of the right or opportune moment. The figure of Chronos was typically portrayed as a wise old man with a long grey beard: Father Time.
Furthermore, the Horae or Hours were the goddesses of the seasons and the natural flow of time, generally portrayed as personifications of nature in its different seasonal aspects, and with the cycle of the seasons themselves symbolically described as the dance of the Horae.
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⇒Number 8. Toward Infinity… and beyond!:

This mural is certainly esoteric. The eyes, placed in circular shape, surround the central number eight (8).

Eight (8) is the Number of the perfection, the infinity. In mathematics the symbol of the infinity is represented by a 8 laid down.

The Pythagoreans believed that number 8 was the symbol of love and friendship, prudence and rational thinking. . It was the Pythagoreans who held that there are in man eight organs of knowledge; sense, fantasy, art, opinion, prudence, science, wisdom, and mind.

The person who actually introduced the infinity symbol was John Wallis, in 1655. This symbol is sometimes called the Lemniscate. It presumably evolved from the Etruscan numeral for 1000, which looked like this: CIƆ. There is another theory that he actually derived the infinity symbol from omega (ω), the last letter of the Greek alphabet. 


The ouroboros symbol, showing a a snake twisted into a horizontal figure eight (8) and biting its own tail, is also said to be a most plausible basis for the infinity symbol because it is a fitting depiction of endlessness.

As to the eyes in this mural, we could think of the Eye of Providence Symbol (which appears in the USA dollar bill). It represents the eye of God, the singular divine power that has created the entire universe. The eye is most times enclosed in a triangle. At times, the Eye is also depicted as surrounded by clouds or bursts of light. Both of these images are representative of holiness and divine glory and so, here too, the symbol signifies that the Almighty is keeping a watchful eye on His creation.

The Eye of Providence Symbol.

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⇒Section II. Murals: University of Toronto: 🇨🇦

The University of Toronto is a public research university in Toronto, Ontario, Canada on the grounds that surround Queen’s Park. It was founded by royal charter in 1827 as King’s College. It comprises twelve colleges, each with substantial autonomy on financial and institutional affairs.
The mural in question is in an underpass that runs from Hart House Circle under Queen’s Park Crescent West to Wellesley Street. Resa came across this mural as she walked under Queen’s Park Crescent. She went by Hart House and exited using the King’s Park Circle. In the slide show below you can see some photographs of the location and buildings. The mural comes soon after!. 
About Resa Mc Conaghy:
Resa is a canadian artist, costume designer and author. 
She hosts two blogs: Graffiti Lux and Murals and Art Gowns.
You can find her version of this post here. Furthermore, Resa has written a book, “Nine Black Lives, available on Amazon. Find Resa on Twitter, too!.
(Disclaimer: All murals photographs and photographs from University of Toronto were taken by Resa and featured on her blog Graffiti Lux and Murals. © Resa McConaghy. 2017). Please check out Resa´s post regarding this collaboration here.
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⇒Damarchus / Lycanthropeis or Werewolf Man-Wolf:

This graffiti could be linked to the Werewolf Man-wolf, or Lycanthropeis. Meaning, a mythological human with the ability to shapeshift into a wolf, either purposely or after being placed under a curse or affliction.
A few references to men changing into wolves are found in Ancient Greek literature and mythology.
For instance, Herodotus, wrote that the Neuri, a tribe he places to the north-east of Scythia, were all transformed into wolves once every year for several days, and then changed back to their human shape. 
Furthermore, we have the story of Damarchus. He was a victorious Olympic boxer from Parrhasia (Arcadia) who is said to have changed his shape into that of a wolf at the festival of Lycaea, only to become a man again after ten years. The festival of Lycaea involved human sacrifice to Zeus. A young boy was killed and then consumed by one of the participants, in this case by Damarchus, and as a result Zeus would transform the cannibal into a wolf.
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On the Left: A man wearing a wolf-skin. Attic red-figure vase, c. 460 BC. On the Right: Zeus turning Lycaon into a wolf, engraving by Hendrik Goltzius. 16th century.

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⇒The Woman With an Extra Hand:

Following the hindu mythology pattern, according to which goddesses have many hands, we could conclude that having more than two hands is a mark of Divinity. Humans have two arms, so someone with multiple becomes special and out of the league. More hands at times also represents more strength.The multiplicity of hands also emphasizes the power and ability to perform several acts at the same time. 

As to number three, it represents the Holy Trinity. From a philosophical perspective, number  three is symbolic of the reconciliation of opposites, as with Hegel‘s dialectic: “thesis + antithesis = synthesis”.
Besides, it is both a lunar and a solar number.
The moon has three major phases – the two crescents and the full moon, while the sun has three primary points in its existence: the low winter solstice; the high summer solstice, and the two equinoxes of March and September.

⇒The Kholkikos Drakon or Colchian Dragon:

The Kholkikos Drakon or (Colchian Dragon) was the ever awake serpent that guarded the Golden Fleece in a grove sacred to Ares in Kolkhis. When the Argonauts came to aquire the Fleece, they had to get past it. There are two theories as towards how they past the Drakon, either Medea put the monster to sleep so Jason could grab the fleece while it slumbered or Jason slew it. There is also a belief that the monster swallowed Jason and then regurgitated him thanks to the power of Medea, so that Jason could then slay the beast. Different cultural traditions have portrayed dragons with reptilian or serpentine traits so that it may seem to resemble cobras, crocodiles or lizards. The word ‘dragon’ traces its origin in the Greek word ‘drakon’ that means a huge serpent or a giant sea fish.
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⇒Apollo (AKA previously Helios) and his Chariot:

Before Artemis became goddess of the moon, the Titaness Selene owned the Moon chariot, which she drove across the sky at night. Soon after, Artemis was the legatee of the carriage. In the same way, Apollo received the Chariot of the Sun, once Helios became identified with him.
Helios (Apollo), the Sun god, drives his chariot across the sky each day while Selene (Artemis) is also said to drive across the heavens. And, while the sun chariot has four horses, Selene´s (Artemis´) usually has two, described as “snow-white” by Ovid. 

As to the horse symbolism, it is often known as a solar symbol. Sometimes, horses are related to the sun, moon, and water. It acts as the mediator between Earth and Heaven. Horse symbolizes power, grace, beauty, nobility, strength, and freedom.

The woman looking at Apollo (former Helios) could be his twin sister, Artemis (Former Selene). Artemis was the Goddess of Hunting and of  Goddess of the Moon. In classical times, Selene was often identified with Artemis, much as her brother, Helios, was identified with Apollo. Both Selene and Artemis were also associated with Hecate, and all three were regarded as Lunar Goddesses, although only Selene was considered a personification of the moon itself.

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Caos: “A Propósito de La Teoría General de Sistemas”:

Entre el año de 1950 y 1968; se desarrolló  una teoría interdisciplinaria con los trabajos de Ludwing Von Bertalanffy. Bertalanffy criticaba la visión del mundo fraccionada en diferentes áreas de conocimiento. Éstas son divisiones arbitrarias que presentan fronteras sólidamente definidas, dado que la naturaleza  no está dividida.

La teoría general de los sistemas afirma que las propiedades de los sistemas no pueden describirse significativamente en término de sus elementos separados. La comprensión de los sistemas sólo ocurre cuando se estudian globalmente, involucrando todas las interdependencias de sus parte. 

Las sucesivas especializaciones de las ciencias obligan a la creación de nuevas palabras, estas se acumulan durante sucesivas especializaciones, llegando a formar casi un verdadero lenguaje que sólo es manejado por los especialistas. De esta forma surgen problemas al tratarse de proyectos interdisciplinarios, ya que los participantes del proyecto son especialistas de diferentes ramas de la ciencia  y cada uno de ellos maneja una semántica diferente a los demás. La Teoría de los Sistemas, para solucionar estos inconvenientes, pretende introducir una metodología integradora para el tratamiento de problemas científicos.

La   Teoría General de Sistemas se fundamenta en tres premisas, a saber: 

A. Los sistemas existen dentro de sistemas. Las moléculas existen dentro de células, las células dentro de tejidos , los tejidos dentro de órganos, los órganos dentro de un organismo y así sucesivamente.

B. Los sistemas son abiertos. Esta premisa es consecuencia de la anterior. Cada sistema que se examine, excepto el menor o el mayor, recibe y descarga algo en los otros sistemas, generalmente en los contiguos. Los sistemas abiertos se caracterizan por ser un proceso de intercambio infinito con su ambiente, constituido por los demás sistemas.

C. Las funciones de un sistema dependen de su estructura para los sistemas biológicos y mecánicos, esta afirmación es intuitiva. Los tejidos musculares, por ejemplo, se contraen porque están constituidos por una estructura celular que permite contracciones para funcionar.

En la teoría de Sistemas, el sistema es un conjunto organizado de cosas o partes interactuantes e interdependientes, que se relacionan formando un todo unitario y complejo.

El concepto de proceso es lo que transforma una entrada (input) en una salida (output). Las entradas (inputs) de los sistemas son los ingresos del sistema que pueden ser recursos materiales, recursos humanos o información.

Los sistemas consisten en totalidades, por lo tanto, son indivisibles. 

Poseen partes y componentes, en algunos de ellos sus fronteras o límites coinciden con discontinuidades entre estos y sus ambientes, pero corrientemente la demarcación de los límites queda en manos de un observador. En términos operacionales puede decirse que la frontera es aquella línea que separa al sistema de su entorno y que define lo que le pertenece y lo que fuera de él.

Cada sistema tiene algo interior y algo exterior así mismo lo que es externo al sistema, forma parte del ambiente y no al propio sistema. Los límites estan íntimamente vinculados con la cuestión del ambiente, lo podemos definir como la línea que forma un circulo alrededor de variables seleccionadas tal que existe un menor intercambio con el medio.

Cada sistema mantiene ciertas fronteras que especifican los elementos que quedan incluidos dentro del mismo, por eso dichos límites tienen por objetivo conservar la integración de los sistemas, evitar que los intercambios con el medio lo destruyan o entorpezcan su actividad.

Las salidas (outputs) de los sistemas son los resultados que se obtienen de procesar las entradas. Al igual que las entradas estas pueden adoptar la forma de productos, servicios  e información. Las mismas son el resultado del funcionamiento del sistema o, alternativamente, el propósito para el cual existe el sistema. Las relaciones son los enlaces que vinculan entre sí a los objetos o subsistemas que componen un sistema complejo.



En la transformación de entradas en salidas debemos saber siempre como se efectúa esa transformación. Con frecuencia el procesador puede ser diseñado por el administrador. En tal caso, este proceso se denomina “caja blanca”. No obstante, en la mayor parte de las situaciones no se conoce en sus detalles el proceso mediante el cual las entradas se transforman en salidas, porque esta transformación es demasiado compleja. Diferentes combinaciones de entradas o su combinación en diferentes órdenes de secuencia pueden originar diferentes situaciones de salida. En tal caso, la función del proceso se denomina una “caja negra”. 

En este último sentido,  la caja negra se utiliza para representar a los sistemas cuando no sabemos qué elementos o cosas componen al sistema o proceso, pero sabemos que a determinadas corresponden determinadas salidas y con ello podemos inducir el output, presumiendo que dados determinados estímulos, las variables  funcionarán en cierto sentido.

En términos generales, puede decirse que los aportes fundamentales de la teoría General de Sistemas son:

1) El Problema de la Caja Negra: Que emana de la incertidumbre de los complejos procesos del Sistema por los cuales entradas se transforman en salidas.

2) El Isomorfismo: Es decir, la identidad de la forma, la unidad de la materia (legado alquimista: un trozo de plomo puede transformarse en oro).

3)La Doble Vía para lograr la aceptación en los procesos: Valiéndose de dos tipos de equivalencias, a saber:

a) Equivalencias Translivéticas en los procesos (Por ejemplo, aplicación de principios de Derecho Internacional en un conflicto municipal: diferencia vertical de escalas).

b) Equivalencias Transdisciplinarias (Que surgen del traslado de aportes de una disciplina a otra).- 




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Caos: “A Propósito de la Teoría Matemática de Juegos”:


La teoría de juegos es un área de la matemática aplicada que utiliza modelos para estudiar interacciones en estructuras formalizadas de incentivos (los llamados “juegos”) y llevar a cabo procesos de decisión. Sus investigadores estudian las estrategias óptimas así como el comportamiento previsto y observado de individuos en juegos. Tipos de interacción aparentemente distintos pueden, en realidad, presentar estructura de incentivo similar y, por lo tanto, se puede representar mil veces conjuntamente un mismo juego.

La forma normal (o forma estratégica) de un juego es una matriz de pagos, que muestra los jugadores, las estrategias, y las recompensas. Cuando un juego se presenta en forma normal, se presupone que todos los jugadores actúan simultáneamente o, al menos, sin saber la elección que toma el otro. Si los jugadores tienen alguna información acerca de las elecciones de otros jugadores el juego se presenta habitualmente en la forma extensiva. También existe una forma normal reducida. Ésta combina estrategias asociadas con el mismo pago.

En el caso de los juegos con repetición, los que se juegan varias veces seguidas por los mismos jugadores, las estrategias pueden ser simples o reactivas, si la decisión depende del comportamiento que haya manifestado el contrincante en jugadas anteriores.

Hay dos clases de juegos que plantean una problemática muy diferente y requieren una forma de análisis distinta. Si los jugadores pueden comunicarse entre  ellos y negociar los resultados se tratará de juegos con transferencia de utilidad (también llamados juegos cooperativos), en los que la problemática se concentra en el análisis de las posibles coaliciones y su estabilidad. En los juegos sin transferencia de utilidad, (también llamados juegos no cooperativos) los jugadores no pueden llegar a acuerdos previos. Los modelos de juegos sin transferencia de utilidad, pueden ser de suma cero, cuando el aumento en las ganancias de un jugador implica una disminución por igual cuantía en las del otro (Ej: El go, el ajedrez), o de suma no nula, cuando la suma de las ganancias de los jugadores puede aumentar o disminuir en función de sus decisiones.

 La mayoría de los ejemplos reales en negocios y política, al igual que el dilema del prisionero, son juegos de suma no cero, porque algunos desenlaces tienen resultados netos mayores o menores que cero. Es decir, la ganancia de un jugador no necesariamente se corresponde con la pérdida de otro.

El premio Nobel de Economía en 1994, John Nash estableció un importante resultado en 1950 sobre la existencia de situaciones de equilibrio en el juego (equilibrio de Nash). Así, por definición, se dice de una combinación de estrategias (una por jugador) que está en equilibrio de Nash si ningún jugador puede aumentar sus ganancias por un cambio unilateral de estrategia. Así es bastante posible que en un equilibrio de Nash la situación se puede mejorar para todos por medio de un cambio simultáneo de estrategia por parte de varios jugadores. El equilibrio de Nash ocupa un lugar central en la teoría de juegos; constituye de alguna manera una condición mínima de racionalidad individual, ya que, si una combinación de estrategias no es un equilibrio de Nash, existe al menos un jugador que puede aumentar sus ganancias cambiando de estrategia.-




El Dilema del Prisionero (1950)

(A. W. Tucker 1905/1995).

La enunciación clásica del dilema del prisionero es:

La policía arresta a dos sospechosos. No hay pruebas suficientes para condenarlos y, tras haberlos separado, los visita a cada uno y les ofrece el mismo trato. Si uno confiesa y su cómplice no, el cómplice será condenado a la pena total, diez años, y el primero será liberado. Si uno calla y el cómplice confiesa, el primero recibirá esa pena y será el cómplice quien salga libre. Si ambos confiesan, ambos serán condenados a seis años. Si ambos lo niegan, todo lo que podrán hacer será encerrarlos durante seis meses por un cargo menor. 

La aplicación de la estrategia maximizante conduce en este juego a un resultado subóptimo. Al no conocer la decisión del otro preso, la estrategia más segura es traicionar. Si ambos traicionan, el resultado para ambos es peor que si ambos hubieran elegido la lealtad. Este resultado es un punto de equilibrio de Nash. 



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 Caos: “Lanza los Dados de Nuevo, Sam”:


I) “Suerte y Probabilidad”:

Se llama suerte a la creencia en una organización de los sucesos afortunados y desafortunados. Es una forma de superstición interpretada de forma diferente por individuos diferentes.

Una aproximación racionalista a la suerte incluye la aplicación de las leyes de la probabilidad. El racionalista siente que la creencia en la suerte es el resultado de un razonamiento pobre o pensamiento ilusorio.

Para un racionalista, un creyente en la suerte comete la falacia lógica post hoc:

 > A ocurre (llevo mi camisa de la suerte) y entonces B ocurre (algo bueno) .

 > Por tanto, A causó B .

 En la visión racionalista del mundo, la probabilidad sólo está afectada por relaciones causales confirmadas estadísticamente. La probabilidad es la característica de un evento, que existen razones para creer que éste se realizará.

La probabilidad de que suceda un evento S  de un total de n casos posibles igualmente probables es igual a la razón entre el número de ocurrencias h de dicho evento (casos favorables) y el número total de casos posibles n.-



II) “La Falacia del Jugador”:


La falacia del jugador explica algunos problemas de razonamiento de las creencias comunes en la suerte. La misma implica negar la impredicibilidad de los sucesos aleatorios. La falacia del jugador es un falacia lógica por la que se cree erróneamente que los sucesos pasados afectan a los futuros en lo relativo a actividades aleatorias, como en muchos juegos de azar. Puede comprender las siguientes ideas equivocadas:

 > Un suceso aleatorio tiene más probabilidad de ocurrir porque no ha ocurrido durante cierto período.

 > Un suceso aleatorio tiene menos probabilidad de ocurrir porque no ha ocurrido durante cierto período.

La falacia del jugador puede ilustrarse considerando el lanzamiento repetido de una moneda.

Si ésta está equilibrada, las opciones de que salga cara son exactamente 0,5 (una de cada dos). Las opciones de que salgan dos caras seguidas es 0,5×0,5=0,25 (una de cada cuatro), las de obtener tres caras seguidas son 0,5×0,5×0,5=0,125 (una de cada ocho), y así sucesivamente.

 Razonar que es más probable que el próximo lanzamiento será cruz en vez de cara debido a los anteriores lanzamientos es la falacia… A veces los jugadores piensan: «Acabo de perder cuatro veces seguidas. Como la moneda está equilibrada y por tanto a la larga los resultados lo estarán también, si me limito a seguir jugando terminaré por recuperar mi dinero.». En ello reside el error.

 De alguna manera puede decirse que el lanzamiento de dados constituye en términos estadísticos un proceso de Márkov, esto es,  un fenómeno aleatorio dependiente del tiempo para el cual se cumple una propiedad específica: la propiedad de Márkov. En una descripción común, un proceso con la propiedad de Márkov, o sin memoria, es uno para el cual la probabilidad sobre el estado presente, futuro y pasado del sistema son independientes. Es decir cada lanzamiento del dado constituye un proceso discreto en que la evolución sólo depende del estado actual y no de los anteriores.-



III) “Bonustrack de Dados”:


Un juego de casino con dados muy popular es el CRAPS, para el cual es importante conocer las probabilidades de los distintos resultados en el lanzamiento de dos dados.

A continuación, van  un par de juegos de adivinación con dados.

1. Adivinar el Valor de Tres Dados: Pide a un espectador que, mientras tú estás de espaldas, lance tres dados. A continuación debe realizar las siguientes sencillas operaciones aritméticas:

> Multiplicar el resultado del primer dado por 2.

> Sumar 5 al resultado obtenido.

> Multiplicar por 5.

> Añadir el resultado del segundo dado.

> Multiplicar por 10.

> Añadir el resultado del tercer dado.

Pide ahora que te diga el resultado final. Si restas 250 a este número, obtendrás un número de tres cifras que corresponden a los valores obtenidos en los tres dados.

2. Adivinando con el Número 5: Entrega dos dados a un espectador y, contigo de espaldas, pídele que realice las siguientes operaciones: Lanzar uno de los dados, multiplicar por dos el valor obtenido, sumar 5 al resultado y multiplicar por 5. Lanzar el segundo dado y sumar el valor obtenido al resultado anterior. Una vez conocido el resultado, puedes adivinar los valores de los dados simplemente restando 25 al número indicado por el espectador.-


IV) “Good Luck/ Bonne Chance/ Buena Suerte”:

El Dato: Se estima que hay aproximadamente 10.000 tréboles de tres hojas por cada trébol de cuatro hojas.


V) “Superstition” / “Superstición” (Video):


VI) “Los Dados y Einstein, Bohr y Hawking”: 


Albert Einstein estaba particularmente en desacuerdo con las implicaciones de la mecánica cuántica. Durante muchos años, mantuvo un debate público con Niels Bohr acerca de cómo interpretar los resultados de ciertos experimentos de la física cuántica.

La mecánica cuántica describe un estado físico en terminos de probabilidades , al contrario de la mecánica clásica, que puede calcularlo de manera precisa. La velocidad y la trayectoria de un proyectil, son calculables con precisión según la mecánica clásica, sin embargo, para una partícula subatómica, según la mecánica cuántica, cuando más conocemos su posición, menos conocemos su cantidad de movimiento.

La idea que sólo pueden calcularse probabilidades y no puede tenerse una certeza absoluta, provocaba en Einstein un cierto disgusto, que se sintetiza en su famosa frase “Dios no juega a los dados” , a lo que Bohr respondió, “ Señor Einstein, ¡deje de decirle a Dios lo que debe hacer!”.

La mecánica cuántica funciona con una asombrosa precisión a pesar de su indeterminación. Bohr solía decirle a Einstein “usted no está pensando, sólo está siendo lógico”. Nos resistimos a aceptar al azar. Siempre pensamos que todo tiene una causa necesaria. 

Stephen Hawking se enroló en la crítica de Bohr a Einstein y de esta manera sostuvo: “Al parecer Einstein estaba doblemente equivocado cuando afirmó que Dios no juega a los dados. Los estudios sobre la emisión de partículas desde agujeros negros permiten sospechar que Dios no solamente juega a los dados, sino que, a veces, los echa donde nadie puede verlos”…


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 Pitágoras de Samos: “Hacia La Conquista de la Causa Primera”:

Pitágoras de Samos (570-480 a.C.).-



Es en el agua dijo Tales, es en el aire dijo Anaxímenes; no, es en el fuego el principio de todo lo que es dijo Heráclito. Está en  lo indeterminado dijo Anaximandro.  Pitágoras los corrigió: el principio es en el Número; la realidad es numérica y geométrica… Tuvieron que pasar 2500 años para que los compuestos computacionales de software empaquetado, pesado y comercializado le dieran la razón. El jonio era hijo de un mercader de Tiro y con aquel viajó aprendiendo de los ilustrados de Siria, luego se empapó en matemática y doctrinas religioso-filosóficas de Egipto y Babilonia y tuvo por maestros a Tales y Anaximandro de Mileto. Luego de viajes y peripecias Pitágoras fundó en Crotona (la calabria italiana) la Hermandad Pitagórica, secta elitista y perfeccionista del mundo antiguo. Entonces siendo todo Número el Número se expresaba en la aritmética, geometría, música y astronomía. Los pitagóricos impusieron la concepción de tetraktys sobre década: el 10 número perfecto reunía 1+2+3+4 formando un triángulo perfecto.  




La   tetrakty será el símbolo sagrado de los pitagóricos, un triángulo de cuatro hileras representando las dimensiones de la experiencia. 1 punto • 2 línea • • 3 plano • • • 4 sólido • • • •.  En el caso de la música simbolizaba las proporciones entre las notas empezando por la proporción 1:2 para la octava. Los experimentos de Pitágoras con el monocordio llevaron a un método de afinación con intervalos en razón de enteros conocido como la afinación pitagórica. La escala producida por esta afinación se llamó escala pitagórica diatónica y fue usada durante muchos años en el mundo occidental.  



Y el símbolo órfico que misteriosamente sigue hoy presente en diversos lugares poco comunes entre sí, la estrella de cinco puntas inscripta en un pentágono o pentalfa (estrella de cinco alfas) era la geometrización del número aúreo -luego llamado Phi en honor a Fidias y no a Pitágoras: la relación existente entre una diagonal y un lado del pentágono y que siempre es la misma: 1,6180339 la Razón Dorada. 




 Aportes: 1) Pitágoras inventó la palabra Filosofía como Amor por la Sabiduría.
2) Pitágoras inventó la palabra Matemática, es matemático todo aprendiz del Número que todo lo rige.
3)Pitágoras comenzó los estudios más primigenios de acústica y en su pentagrama se registran y matematizan los eventos del sonido en su relación con la amplitud (intensidad) en la coordenada Y sobre el transcurso del tiempo coordenada X. Todo esto 2000 años antes de Descartes y las coordenadas cartesianas. A su vez, ideó el famoso Teorema que lleva su nombre.
Limitaciones: Cuando los pitagóricos se toparon con el problema de los números  irracionales y su falta de orden sucumbieron. Dicho acontecimiento comenzó con la raíz cuadrada de 2 presente en el teorema que nos dice que la suma de los catetos al cuadrado resulta en el cuadrado de la hipotenusa. La raíz cuadrada de 2 o diagonal del cuadrado mostró los irracionales, un muy duro golpe para los pitagóricos del que nunca se repusieron, pi los golpeó y el número aúreo los golpeó. La tetraktys todoperfecta se topaba con imperfectos que no se podían delimitar…



Eluveitie: “Uis Elveti”:


Swiss Pagan/Folk Metal. Album: Spirit.

Lyrics: Gaulish/English:





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“Donald en el Mágico Mundo de las Matemáticas”:

(Cortometraje de Walt Disney, 1959. En Tres partes): 




Sinopsis del Cortometraje:

thumb_donald070305e.gif (34388 bytes)

Donald se introduce como un intrépido explorador en el país de las Matemáticas, en el que contempla sorprendido árboles con las raíces cuadradas, un río de números, un extraño animal con cuerpo de lápiz que recita los dígitos del número pi… Después, guiado por el narrador, el pato Donald viaja a la antigua Grecia para conocer a los Pitagóricos, creadores de la escala musical, y aprende las proporciones que se encuentran en la estrella de cinco puntas, proporciones que conducen al número áureo y al rectángulo perfecto. El pato Donald también descubre el empleo de la lógica matemática en el ajedrez, y la presencia de las matemáticas y de la geometría en los juegos y deportes. Así descubre el billar, en su modalidad de carambola a tres bandas, y el narrador le enseña cómo calcular el modo de obtener carambolas sencillas usando las marcas que aparecen en los bordes de la mesa de billar y sumando y restando números y fracciones simples. Por último el corto nos enseña a utilizar la imaginación, ese poder de nuestra mente mediante el cual podemos ver las figuras geométricas, la esfera, el cono, el paraboloide, el cilindro… que luego tendrán aplicación en la óptica, ingeniería, mecánica, astronomía… Esa misma imaginación nos ayudará a ir abriendo las infinitas puertas del conocimiento que todavía nos quedan por abrir.


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David Bohm: “Órdenes Implícitos y Explícitos”: 


David Bohm, antiguo colaborador de Einstein en Princeton, plantea los conceptos de “Orden Implicado y Orden Explicado” para intentar abrir una vía a la cuestión de la indeterminación espacio-temporal de la Mecánica Cuántica a la hora de explicar la posición de una partícula atómica: la dificultad para predecir la ubicación, en espacio y tiempo, de cualquier partícula atómica, dentro del modelo.

A diferencia de la Teoría Mecanicista de Newton, la Teoría Cuántica tiene tres características básicas:

1.- El movimiento es generalmente discontínuo en el sentido de que la acción está constituida por cuantos indivisibles (que implican también que un electrón, por ejemplo, pueda pasar de un estado a otro sin pasar por todos los estados intermedios).

2.- Las entidades, como los electrones, pueden mostrar propiedades diferentes (por ejemplo, como partícula, como onda, o como algo intermedio), dependiendo del entorno en el que existan y desde el que están sujetas a observación.

3.- Dos entidades, como los electrones, que se combinan al principio para formar una molécula y que después se separan, muestran una peculiar relación no local que puede describirse como una conexión no causal de elementos que están separados (como se demuestra en el experimento de Einstein, Podolsky y Rosen).”

Añade Bohm que estas leyes son, simplemente, estadísticas, y que no pueden predecir aisladamente los acontecimientos futuros individuales. Así, la mecánica clásica :

“… precisa de la causalidad estricta (o determinismo) y localidad. Por el contrario, la teoría cuántica precisa de discontinuidad, no de causalidad “

En el intento de explicar esta nueva “realidad descubierta”, Bohm postula una teoría en la que todo fenómeno tiene diversos niveles de expresión, de tal forma que la luz, por ejemplo, como es estudiada en óptica, responde a unas leyes que no son más que el Orden “Desplegado”, en las tres dimensiones conocidas, correspondiente a otros Ordenes “Implícitos” o “Plegados“. 

 Sin embargo, estos órdenes “plegados” son, en el modelo de Bohm, más reales que los “desplegados”, de tal forma que la explicación última no puede encontrarse en el fenómeno “desplegado” sino en un nivel operativo.

De hecho, una de las explicaciones más atrevida, dada por Eugene P. Wigner, premio Nobel de 1963, fue que el experimentador influía de forma inextricable en las observaciones en tanto que instrumento participante. ¿Cómo? ¡con su conciencia!: produciendo un “colapso” en la Función de Onda (“derrumbando” la función de onda), colapso que, teóricamente, el mecanismo cerebral es capaz de producir.

Estos órdenes se dice que están plegados unos dentro de otros y que están en íntima relación. Las variables de un orden más plegado respecto a otro representan una relación de tipo “no causal ni local”. Y estos órdenes no son abstracciones sino realidades “físicas” en el más amplio sentido del término (Bohm).-


David Joseph Bohm (1917/1992).-



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David Bohm: Niveles de Ser: “Aportes del Nuevo Paradigma Holográfico”:



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