The Hamlet Enigma

by

Elmar Manafov

The Tragical History of Hamlet, Prince of Denmark has puzzled the world for over four hundred years; the following work will attempt to prove that the text of Plato’s Phaedo is the intended key to its solution.

When Shakespeare’s Hamlet and Plato’s Phaedo are examined closely a common theme becomes evident, together with a particular sort of structure. Furthermore (and something that is particularly remarkable) the text of Hamlet reflects Phaedo line-by-line.  

Hamlet begins on a “platform” upon the fortification of Ellsinore, which the protagonist famously describes as a prison; Phaedo’s narrative also begins at the doors of a prison, where Socrates awaits his execution.

While the poisoned king returns as a ghost in the beginning of the play; in the dialogue, the philosopher is preparing to take poison, in order for his soul to transcend the physical and finite world into eternal existence. Note that for both Shakespeare and Plato the guard is present from the outset of both narratives, and this symbolism of the guard is only the first of many similarities which occur in the line-to-line juxtaposition of the two works.

In the opening scenes of both texts we are presented with transitions between the internal and external worlds; the spiritual freedom and the physical imprisonment; the microcosm and the macrocosm. We are being primed in the beginning of both works for a discussion on a central theme: that physical death results in the cyclical and perpetual rebirth of the human soul, which is thereby immortal.

The common theme of both Hamlet and Phaedo is a doctrine on the immortality (or the perpetual and infinite existence) of the soul and their structures follow the form of fractal self-similarity, whereby the complete whole (macrocosm) is encapsulated within a smaller constituent part (microcosm).

It is quite obvious when one contemplates on Shakespeare’s Hamlet and Plato’s Phaedo that both works are in large part devoted to the subject of the soul and its fate upon the death of the body.

In regard to Hamlet, one needs to merely consider the character of the old king’s ghost returning from the dead – which propagates the revenge cycle of the play, or the famous soliloquies of the protagonist, to recognize the role the soul and what happens to it after death, plays in this tragedy.

If examined closely, the correlation in Shakespeare's metaphor of the changing guard in the opening scene for the transition in the monarchy within the greater plot of Hamlet reminds us of Plato's famous references to “philosopher kings” whom Socrates calls “our guardians” in his Republic. 

Plato’s Phaedo - a 2,500-year-old dialogue (the oldest surviving philosophical texts on the nature of the soul) in which Socrates gives his final argument for the idea that the soul is immortal, remarkably parallels the theme and structure of Shakespeare’s tragedy.

Preliminary doubts about my hypothesis regarding the remarkable relationship between these two works may gradually dissolve upon a detailed and meticulous unfolding of the puzzle presented by a line-to-line juxtaposition of the two works.  

Although it isn’t obvious at first that either work is structured in any sophisticated and intricate manner, it is indeed true of both texts. The most general similarity in the structure of both works is that each, as a whole, is reflected within its opening scene and then, in turn, within the first line of each text. This unique sort of structure is known in geometry as fractal self-similarity and its implementation in the textual organization of Hamlet and Phaedo is not coincidental.        

The opening scene in Hamlet begins with an exchange between the guards, Bernardo and Francisco, each calling for the other to identify himself. First Bernardo asks “Who’s there?” and in response Francisco demands “Nay, answer me: stand, and unfold yourself.” In turn, the first word of Phaedo is «αὐτός» (yourself), in Echecrates’ opening line “Were you yourself, Phaedo, in the prison with Socrates on the day when he drank the poison?”

In a philosophic sense the concept of identity is inherently connected with the notion of the self (soul or psyche). It is clear that both authors considered it important from the outset to focus the reader’s attention on this ancient and ever-relevant form of philosophic inquiry regarding the nature of the human soul.

First the ontological "who's there?" contrasted with Phaedo's "were you yourself"; then the complimentary self-referential opposition of the words "unfold yourself" from Hamlet - establishing a mirrored dichotomy.

Then the existential triplet of birth, death and re-birth in (the implicit understanding that ‘the king is dead’) contrasted with Bernardo’s words in the third line "Long live the king" in Hamlet, together with the three references to Socrates' death in the third line of Phaedo "...his death...his last hours...he died by taking poison"

Followed in the fourth statement by reference to the time of death (metaphorically) in Francisco's compliment of Bernardo's punctuality with the words "you come most carefully upon your hour" and Socrates, who was put to death "not at the time, but long afterwards" in the corresponding line from Phaedo.

And again the fifth microcosmic statements of the two texts echo the dual symbolism of death and time, in Hamlet with the words: “Tis’ now struck twelve, get thee to bed Francisco” and in Phaedo, the symbolically loaded description of Theseus’ ship, as the reason for the delay in Socrates’ death, both emphasizing, once again, time or timing in regard to death.

If we consider Shakespeare’s changing of the guard within the context of James George Frasier’s pre-historic “kings of the wood” from the beginning of his seminal work The Golden Bough; or Robert Graves’ famous depictions of the “king of the waning year,”  or the king who rises and falls with the turn of Fortune’s Wheel alluded to by Hamlet in the second scene of the second act of the play (331^st line) then we get a clear picture of a cyclic birth, death and resurrection of the human soul described by Socrates in Phaedo (with the 331^st line of the dialogue being only one of numerous examples).  

Upon a close examination it becomes evident that the opening lines from both works reflect the major themes addressed in the two texts which correspond to the divisions of Hamlet into five acts of the first scene, five scenes of the first act, and the five acts of the entire play. Each of these correlations represent microcosms of corresponding discussions in the texts of Hamlet and Phaedo, which themselves exhibit line-to-line concurrence in the detailed juxtaposition of the two works. 

As will be illustrated shortly the concept of self-similar organization and the doctrine on the immortality of the soul are intimately related and are in fact co-dependant - and therein lies the core of this entire work - in the philosophical relationship between structure and substance, symbol and meaning or body and soul.

The ‘triangular’ relationship between this particular theme (on immortality of the soul), the unique structure of fractal self-similarity and methodology of cryptographic concealment has a historical context in which the dialogue of Plato’s Phaedo plays a central role.

This tradition spans back to the earliest written stories from ancient Babylon and Egypt; and the oral traditions which preceded them. Plato has been considered a bridge connecting philosophers with the secrets of those primordial stories for two and a half millennia.

The expression of the relationship between substance and structure in the symbolic form as body and soul belongs to this ancient tradition, a secret doctrine which has gone hand in hand with the methodology of cryptographic concealment as a means of hiding it from the masses, which unknowingly propagated this hidden knowledge in the form of symbolism encrypted into narrative, art and ritual thereby preserving it for future generations. The students of this tradition hold Socrates’ references to it, in the dialogue of Phaedo, as key evidence for the existence of these ancient Mysteries.

The process of cryptographic concealment plays an equally important and inseparable part in the relationship between self-similar organization and the doctrine on immortality of the soul, and is in fact their natural product as the very basis of symbolic language – the main tenant of philosophy in general and Plato’s teachings in particular (i.e. the doctrine on ideas and forms).

It is no coincidence that the 12^th line of Hamlet repeats the first line of the play “…who's there?” In lines 13 and 14 of Phaedo, the references to “listeners who are of the same mind” and “friends” are echoed in the references to “friends to this ground” “and liegemen to the Dane” in the 13^th and 14^th lines from Hamlet. Then again we have a resonance of “Who hath relieved you?” (16^th line from Hamlet) and in Phaedo “Who were present?” (17^th line)

What follows in both texts is a sort of “roll call” of dramatis personae, attributing particular care to separating “friends” from “strangers” amongst those present during these moments of transition. A changing of the guard - changing of the monarchy in the Danish kingdom - in Hamlet; while in Phaedo - a passing of a torch, a turning of the wheel in the history of philosophy.  

Phaedo soon reveals that Plato (the author) was not present at the death of Socrates, yet importance is being placed by Echecrates (in the first line of the dialogue) on Phaedo’s (the narrator’s) presence at the proceedings.

Plato's self-reference in Phaedo is certainly of great significance, even if presented in an unassuming fashion. This emphasis on the narrator’s physical presence at the scene of Socrates’ death, combined with the allusion to the author’s absence is intriguing because it presents an implicit contradiction to the importance of the “eye witness” account, and is arguably the first paradox of the dialogue and the discussion on the nature of the soul.

In lines 90 through 94 from both texts physical perception is contrasted with an idea of the “eye of the mind.” According to Socrates, while hearing, taste, touch, sight and smell are physical and common, the “eye of the mind” is an extraordinary property of introspective philosophic thought, or self-reflection. In Phaedo, Socrates describes the soul’s separation from the senses of the body, in Hamlet the reference is to the disembodied spirit of the dead king. In both texts, simultaneously, we are presented with a notion of a separation of body and soul - or death - as described by Socrates.

Liberation of the soul from corporeal bondage is discussed in the 96^th and 97^th lines of Phaedo. Meanwhile in Hamlet (lines 95-99) the prince is being informed of the old king’s ghost returning from the dead.

If we compare this dialogue from Hamlet with Socrates’ description in Phaedo of the human soul confined in the prison of the body, we find an intricate pattern of symbolic meaning reflected in the two texts, literally line-by-line.

While Shakespeare’s protagonist famously pronounces that the world is a prison (line 361 from Hamlet) Socrates insists that “the soul is only able to view existence through the bars of a prison” (in Phaedo’s 351^st line).

Particularly interesting is Socrates’ analogy in the dialogue for life and death as sleep and waking. Comparing these two opposite states and the cyclical transition between them to that of life and death, he comes to the conclusion that as death follows life, life is in turn generated from death.

In the opening lines of Phaedo (lines 5-7) the reason for the delay in Socrates’ execution is attributed to the delayed return of Theseus’ ship from its ceremonial voyage. In the corresponding lines from Hamlet, Francisco praises Bernardo’s punctuality in arriving at his post for the cyclical changing of the guard (line 6) to which Bernardo replies “'Tis now struck twelve; get thee to bed, Francisco” (line 7)

Even those who are loosely familiar with the tragedy of Hamlet and Plato’s Phaedo, can recognize in Hamlet’s famous soliloquy “to be or not to be” a reflection of Socrates’ discussions on the nature of life and death. Both express the idea that life and death are transitional states, and present death as an end to all the suffering of life. Although, Hamlet has his doubts, stating that death is “the undiscover'd country from whose bourn no traveler returns” (line 468) yet the appearance of the ghost supports Socrates’ notion:

“You want to have proven to you that the soul is imperishable and immortal, and you think that the philosopher who is confident in death has but a vain and foolish confidence, if he thinks that he will fare better than one who has led another sort of life, in the world below, unless he can prove this; and you say that the demonstration of the strength and divinity of the soul, and of her existence prior to our becoming men, does not necessarily imply her immortality. Granting that the soul is longlived, and has known and done much in a former state, still she is not on that account immortal; and her entrance into the human form may be a sort of disease which is the beginning of dissolution, and may at last, after the toils of life are over, end in that which is called death. And whether the soul enters into the body once only or many times, that, as you would say, makes no difference in the fears of individuals. For any man, who is not devoid of natural feeling, has reason to fear, if he has no knowledge or proof of the soul's immortality.”  (460^th line from Phaedo)       

In a book titled Dreaming Souls, Owen Flanagan examines Hamlet’s soliloquy, “possibly the most famous in all of English literature” and finds parallel between Hamlet’s anxiety regarding the afterlife and the dialogue in Plato’s Phaedo, stating that “the very same set of concerns arise in a conversation Socrates has with…Simmias and Cebes” Of course Flanagan has no reason to suspect the remarkably intricate relationship between the two works or the close proximity of these particular segments of the two texts in a line-to-line juxtaposition.

To return back to the notion of the “mind’s eye” According to Plato in the Republic, only “philosophers…are able to grasp the eternal and unchangeable (the soul or spirit)” This unique ability of reflective introspection is of paramount importance to understanding the intended meanings, inherent structure and the complex interaction between these two enigmatic works. The multidimensional meaning of the word reflection is the key to solving the mysteries of Hamlet and Phaedo.

If we were to hypothesize that Shakespeare designed Hamlet with a particular philosophic concept in mind - a concept described by Plato in the Phaedo, it would seem prudent to explore the historic origins of this conception.

To begin, let us turn to the five known Platonic arguments for the immortality of the soul. As Geoffrey W. Bromiley writes in The International Standard Bible Encyclopedia: “Immortality and Resurrection are inseparable ideas” and goes on to describe Plato’s contribution to their understanding as follows: 

“An essential ingredient of Orphic religion was belief in the essential divinity of the soul and in embodiment as the soul’s exile from its true heavenly home. Hence the celebrated Orphic pun soma sema, “the body is the tomb (of the soul).” This belief in the eternal survival of the soul gained intellectual respectability in the writings of Plato. According to Plato, in its rational or divine function the soul is preexistent and apparently eternal and has relations with both the phenomenal world and the unchanging ideal world. He adduces five arguments for the immortality of the rational soul: the argument from opposites (Phaedo 70c-72e) and the complementary argument from reminiscences (Phaedo 72e-77d); the argument from affinity (or from the simplicity of the soul) (Phaedo 78b-84b); the argument from “forms” (Phaedo 102a-107b) which he regards as the most conclusive proof; the argument from destructibility (Republic 608d-611a); the argument from motion (Phaedus 245c-246a). (p. 809)

Plato traced his conception of the world, including his ideas on the nature of the soul on that of Orpheus (a central figure of ancient Greek mystery religions) and Pythagoras (the man credited with being the first to use the word philosophy), and they in turn (according to many scholars) on the mythology of ancient Egyptian and Babylonian Mysteries.

Therefore, it seems clear that any analysis of Hamlet and Phaedo must be done against the backdrop of this ancient doctrine which has been cryptographically encoded into the narrative of myths for thousands of years. So let’s explore the general theme and structure of Hamlet and Phaedo in this proto-historical context.

In a book titled The Secret Teachings of All Ages, Manly P. Hall describes the basic evolution of this ancient tradition and Plato’s role in it as follows:   

“There are…but few mature minds in the world; and thus it was that the philosophic - religious doctrine of the pagans were divided to meet the needs of these two fundamental groups of human intellect – one philosophic, the other incapable of appreciating the deeper mysteries of life. To the discerning few were revealed the esoteric, or spiritual, teachings, while the unqualified many received only the literal, or exoteric, interpretations. In order to make simple the great truths of Nature and the abstract principles of natural law, the vital forces of the universe were personified, becoming the gods and goddesses of the ancient mythologies. While the ignorant multitudes brought their offering to the altars of Priapus and Pan (deities representing the procreative energies), the wise recognized in these marble statues only symbolic concretions of great abstract truths…These individuals were usually banded together, forming seclusive philosophic and religious schools. The more important of these groups were known as the Mysteries… Plato, an initiate of one of these sacred orders, was severely criticized because in his writing he revealed to the public many of the secret philosophic principles of the Mysteries.” (p. 40)

According to Hall as well as other scholars, most notably Charles François Dupuis, James Frazer, Jane Harrison, Robert Graves, Joseph Campbell and others, the tradition of expressing the universal relationship in nature between structure and substance in a form of a secret doctrine on the immortality of the soul is rooted in myths of early religions (e.g. Babylonian, Egyptian, Persian, Greek etc.) and flowered in the symbolic language of poetry and philosophy.

In a work which holds a special kinship to the current discussion, titled Hamlet’s Mill, the authors, Giorgio De Santillana and Hertha Von Dechend write the following: 

“Since it is an actual language, the idiom of myth brings with it the emergence of poetry…But, however vast the difference of poetical rank among the mythographers, the terminology as such had been coined long before poets, whose names are familiar to us, entered the stage…The main merit of this language has turned out to be its built-in ambiguity. Myth can be used as a vehicle for handing down solid knowledge independently from the degree of insight of the people who do the actual telling of stories, fables, etc. In ancient times, moreover, it allowed the members of the archaic “brain trust” to “talk shop” unaffected by the presence of laymen: the danger of giving something away was practically nil…Gilgamesh and his search for immortality was not unknown in times before the deciphering of cuneiform writing. This is the result of that particular merit of mythical terminology that it is handed down independently from the knowledge of the storyteller. (The obvious drawback of this technique is that the ambiguity persists; our contemporary experts are as quietly excluded from the dialogue as were the laymen of old.) Thus, even if one supposes that Plato was among the last who really understood the technical language, “the stories” remained alive, often enough in the true old wording.”  (Giorgio De Santillana and Hertha Von Dechend, Hamlet’s Mill, p. 312-213)

In the manner of Charles Francois Dupuis’ famous 1798 work Abrégé de l'origine de tous les cultes, the authors of Hamlet’s Mill describe an ancient system of astronomical knowledge of remarkable sophistication which has been concealed for millennia within the cryptographic symbolism of ancient myth. One of these stories which hides the secrets of apparent celestial motions and the mechanisms of time is the Scandinavian legend of Amlodhi, the originator of the universe and (according to De Santillana and Von Dechend) prototype of Shakespeare’s prince Hamlet.   

Incidentally the two names Shakespeare chooses to use for the two guards in the opening scene of the play, together  resemble the name of a character from Welsh mythology, a deified hero named Berndigeidfran (meaning Bran the Blessed) familiarly known simply as Bran. Compare the name Berndigeidfran to the names of the two guards in Hamlet, Bernardo and Francisco.

Bran is a legendary king of Britain, and a patron god of bards and poetry. A few other elements in Bran's story point to his potential relevance here in the present discussion of Hamlet. In Welsh mythology, it is told that Bran possessed a cauldron which brought dead soldiers to life. Consider therefore the ghost of a dead king, dressed as a soldier, returning from the dead.

Furthermore, the first line of Hamlet: “who’s there?” could also allude to a particularly ancient riddle of identifying a god by name.

Robert Graves in his book on the Historical Grammar of Poetic Myth or The White Goddess, writes that “the story of the guessing of Bran’s name is a familiar one to anthropologists. In ancient times, once a god’s name had been discovered, the enemies of his people could do destructive magic against them with it.” (p. 49)  

In The White Goddess, Graves examines the secret cryptographic language that prevails throughout the tradition of poetic composition. He discovers a common theme going back in history to the earliest known poems wherein bountiful information is elaborately encoded.

Robert Graves' preliminary description of this Theme matches the general plot of Hamlet exactly:

"The Theme, briefly, is the antique story, which falls into thirteen chapters and an epilogue, of the birth, life, death and resurrection of the God of the Waxing Year; the central chapters concern the God's losing battle with the God of the Waning Year for love of the capricious and all-powerful Threefold Goddess, their mother, bride and layer-out. The poet identifies himself with the God of the Waxing Year and his Muse with the Goddess; the rival is his blood-brother, his other self, his weird." (p. 24)

As the guards presented in the beginnings of both Hamlet and Phaedo, the secrets of the primordial poems analyzed by Graves were also protected by the characters of mythological guardians, such as Dog, Roebuck and Lapwing. These characters in the ancient stories served not only as symbols for the cryptographic nature of these poems but also as clues to their solutions, and the cauldron they were guarding was in essence a mirror, a standing pool of water being the earliest sources of reflection expressed in myth (most famously in the story of Narcissus).

The central theme of Hamlet is without a doubt ancient. The symbolic element of the divine guards or kings who serve as protectors of a sacred knowledge has accompanied this tradition from the earliest known sources. It is true of Babylonian Gilgamesh, Tammuz and Ishtar; Egyptian myths of Anubis, Horus, Isis and Osiris; and the Eleusinian myths of ancient Greece.

All these stories contain two general elements, the doctrine on immortality of the soul and the mechanisms of time or more precisely, timekeeping based of the apparent motions of celestial bodies. These are precisely the themes considered in Plato’s Phaedo and Timaeus.

It is no coincidence that the authors of Hamlet's Mill, connect the Scandinavian legend of Amlodhi with those of Gilgamesh and Osiris.

The general theme of fratricide and revenge by the son of the victimized king in Hamlet is identical to the Egyptian myth. After falling victim to his brother Typhon's deadly coffin-like trap, losing his life, wife and crown, his body hidden (as Hamlet hides Polonius' dead body which is being searched for in the fourth act of the play as Isis searches for Osiris' body in the myth), Osiris spirit returns from the dead to urge his son Horus to kill Typhon, much as Claudius is killed by prince Hamlet in vengeance for his father.

The secrets of cosmic motions and the mechanisms of time is not the extent of the secret knowledge encrypted into the symbolism of ancient myths but only a complimentary part of a larger doctrine on the immortality of the soul as a continuous cycle of death and rebirth, known as transmigration or metempsychosis.

As previously noted, in the opening lines of Hamlet, Francisco complements Bernardo on his punctuality, while simultaneously in the corresponding lines from Phaedo the delay in Socrates’ execution is described. In the following line from Hamlet, Bernardo responds “'Tis now struck twelve; get thee to bed, Francisco” while Phaedo, in the corresponding line of the dialogue describes Theseus’ ship as the reason for the delay in Socrates’ death.

At first glance the words “bed” and “ship” seem unrelated, however symbolically the two concepts have a close association with death as “deathbeds” and “burial ships.” 

Historically relevant to the setting of the Danish tragedy, is the traditional Norse burial at sea, in which a body of a king (or chieftain) is set afloat aboard a funerary barge sometimes called a ‘boat grave’. These ceremonial ships were not limited to actual sea worthy vessels but were also constructed as monuments on land as ‘stone ships.’ These served as lasting representations of historic funerals of kings, and have been discovered by archeologists across northern Europe and the British isles. The dead were often laid in a boat; afterwards, stone and dirt were usually laid on top of the remains in order to create a tumulus. Numerous tumuli honoring kings and chieftains have been discovered in Denmark.

The Norsemen were not the only people to have extolled the boat funeral on their leaders, the Egyptian pharos departed this world in a very similar manner as well. A most famous archeological example of such a funeral boat is the Khufu ship discovered at the foot of the Great Pyramid of Giza.

The changing of the guard at midnight in the beginning of Hamlet (which coincides with the ghost's appearances in the play) symbolizes the changing of kings in the greater plot of the tragedy (the revenge cycle propagated by the return of king Hamlet's ghost to urge his son's retribution for his own murder and usurpation of the throne). The shift change of the guards is thereby the first representation of time as the perpetual cycle of life death and rebirth and corresponds to the discussion in the beginning of Phaedo on the ceremonial coronation and voyage of Theseus' ship as the cause for the delay in Socrates' death.

Theseus' ship represents an important symbol in the history of philosophy, a symbol associated with an ancient paradox of identity (essence or soul) and its persistence through time. The ship mentioned by Phaedo is believed to be quintessentially the very same vessel in which Theseus himself sailed on his mythic journey. Or was it the same ship?

We therefore must ask, as Echercrates asks in the seventh line of Phaedo: "What is this ship?" 

Consider Plutarch's description of the ancient paradox associated with this holy vessel:

“The ship wherein Theseus and the youth of Athens returned had thirty oars, and was preserved by the Athenians down even to the time of Demetrius Phalereus, for they took away the old planks as they decayed, putting in new and stronger timber in their place, insomuch that this ship became a standing example among the philosophers, for the logical question of things that grow; one side holding that the ship remained the same, and the other contending that it was not the same.” (Plutarch, Life of Theseus)   

The paradox at the heart of the story about Theseus' ship has been well known throughout the history of philosophy, it has taken on many forms such as Hariclitus' famous words: "Upon those who step into the same rivers, different and again different waters flow" - more familiar as Plato's paraphrasing: "Hariclitus...says that everything moves on and that nothing is at rest; and, comparing existing things to the flow of a river, he says that you could not step into the same river twice."

This paradox is central to the discussion in Phaedo on the relationship between the soul and the body - the birth, life and death of the physical body; and the perpetual transmigration of the soul for eternity. This is precisely the sort of relationship shared between the ever-changing guards on duty, at midnight, in the beginning of Hamlet and the kings in the greater plot of the play contrasted by the ideal guard or ruler (or in Plato's language the form of a guardian or Philosopher-king) remains constant and can pass from one physical body to the other, as the role of the guard on duty passes from Francisco to Bernardo in the opening of Hamlet.

In ancient allegory Theseus' ship also represents time or more precisely a calendar. According to Robert Graves the seven virgin victims from each sex (also known as 'the twice seven') demanded for annual sacrifice by the minotaur in the famous myth "may have represented the seven Titans and Titanesses of the sun, moon, and five planets" (Robert Graves, The Greek Myths, 98.4) in other words they symbolize the days of the week (Robert Graves, The Greek Myths, 1.3, 43.4) The number of oars the ship had may have represented the thirty days of the ancient Greek lunar calendar (whereby each of the fifteen occupants, including Theseus, presumably operated two oars) while the two sets of youths (male and female) illustrate how the ancient Greeks divided the month into two halves in accordance with the waxing and waning phases of the moon cycle. The two boys who Theseus disguises as two girls may point to the two day discrepancy between a twenty-eight-day month (of a thirteen-month year) and a thirty day month (of a twelve-month year) of the ancient Greek calendar.

In the opening lines of Phaedo, Theseus' ship explicitly represents time in that it is given as the reason for the delay in Socrates' execution in response to Echecrates' inquiry into why the philosopher's death was postponed, precisely at the same time as Francisco complements Bernardo on his punctuality in the opening lines of Hamlet, to which Bernardo responds: "Tis now struck twelve, get thee to bed Francisco"

Consider the fourth scene of the first act from Hamlet where 'time' is emphasized in the context of punctuality in the ghost's appearance and disappearance. This scene from Hamlet corresponds to the discussion in Phaedo on the cyclical relationship between life and death being generated from each other as sleep and waking. As a result the general similarities expressed in the juxtaposition of the two works become abundantly clear: the universal mechanisms of time are being expressed symbolically as a self generating cycle of life and death or sleep and waking.

Time is similarly emphasized in the first scene of Hamlet when the ghost appears and disappears like clockwork, “upon the crowing of the cock”. In this scene Horatio and Marcellus attempt to question the ghost about its identity and origin, this occurs simultaneously as Simmias’ and Cebes’ inquire from Socrates about the nature of death, and the subsequent fate of the human soul. All four characters from the two texts express a need for a deeper knowledge about the world beyond the corporeal - that “undiscovered country.” 

In Phaedo, Socrates is willing to share his knowledge on the subject of death, but expresses his surprise that his listeners did not “understand” the explanations of their teacher Philolaus the Pythagorean (lines 35-37). In the corresponding lines from Hamlet, Horatio and Marcellus are surprised by the fact that the ghost misunderstands their attempts at communication (lines 34-39). While Socrates is willing to disclose the ancient secrets of the mysteries, the ghost of the dead king in Hamlet is “forbid to tell the secrets of [his] prison house” as he later confides to his son. 

In both cases, the inference may be made, that this sort of knowledge is reserved for the select few, those who are capable of understanding the language of philosophy, to see with the “eye of the mind” past the empirical world into the essence of things, in Socrates’ words, philosophers.  

The means of cryptographic concealment in the form of symbolism associated with the tradition of the secret doctrine on the immortality of the soul and the methodology of self-similar structuring have another common relation (in addition to Sacred Astronomy described in Hamlet’s Mill) it is a system of knowledge often referred to as Sacred Geometry, which serves as the mathematical framework for this ancient doctrine. At the heart of the doctrine on the immortality of the soul is the mathematics of infinite progression.

Mathematical conception of the infinite is often associated with incommensurable numbers such as √2, π (Pi) and φ (Phi), the seedlings of these mathematical concepts can (with fair amount of certainty) be placed in ancient Babylon and Egypt, which at the very least provided the medium in which this knowledge evolved (by way of Pythagoras and Plato) to the level of sophistication of Euclid, for example, the man who was born shortly after Plato’s death and according to some sources studied from his direct students and went on to write possibly the most influential work in the history of mathematics to date, The Elements which serves as the earliest surviving, mathematically derived definition for the incommensurable constant which Euclid called the “extreme and mean ratio” which in the 20^th century became represented as the symbol φ after a 5^th century BC sculptor Phidias, who used the Devine Proportion in his art, examples of which are in the statues of Parthenon and one of the seven wonders of the ancient world: the statue of Zeus at Olympia.

According to some sources Pythagoras and his disciples were familiar with the properties of these magic numbers, and one of them, Hippasus of Metapontum, made public the derivations of these so-called incommensurables. And according to one version of the story, his fellow Pythagoreans built him a tomb, unambiguously signifying that he was dead to them.

The unique properties of a constant known today as φ or the Devine Proportion (also referred to as the Golden Ratio, the Golden Mean and many other names), is closely related to the doctrine on the immortality of the soul and the structure of fractal self-similarity, however, due to the lack of direct evidence the extent to which it was known by the ancient Babylonians, Egyptians and even Pythagoras is highly controversial, but it is from this source, that some assert, Plato inherited this sacred knowledge in some form and indirectly passed it on to Euclid.

It is surmised by historians of mathematics from archeological finds that ancient Egyptian and Babylonian civilizations had sophisticated systems of multiplication and division, fractions, and even simple algebraic algorithms and calculus-like processes for solving complicated trigonometric problems, such as computing the mass of a truncated pyramid. All this is known of the ancient Egyptian mathematics primarily from a single scroll (Rhind Mathematical Papyrus) discovered by accident.

Unfortunately no such evidence exists for either civilization regarding the knowledge of Devine Proportion. But the absence of evidence is not the evidence of absence, and if it were not for the chance discovery of one, nearly 4,000 year old scroll, historians would have continued to think that the ancient Egyptians were only slightly more sophisticated in their understanding of mathematics than people who lived thousands of years earlier.

Archeological evidence is only slightly more prevalent for the mathematical knowledge in Mesopotamia during the Old Babylonian era (2000-1600 BCE), yet the discoveries of a few clay tablets have proven a remarkable sophistication in mathematic calculation. A single clay tablet (YBC 7289) shows that ancient Babylonians had algorithmic means to calculate the √2 correct to seven-digits and a chance discovery of another clay tablet (Plimpton 322) shows the Babylonians knew about the so-called Pythagorean triples.

In a fascinating book titled How Mathematics Happened, Peter 

Rudman writes:                    

“Babylonians knew the Pythagorean theorem at least one thousand years before Pythagoras, although Pythagoras may have been the first to prove it. In addition, the greatest Babylonian mathematical contribution, geometric algebra, is traditionally known as Pythagorean geometric algebra. This misplaced credit is simply because the mathematics attributed to Pythagoras has been studied for some twenty-five hundred years. It is only in the last one hundred years that Babylonian mathematical tablets have been unearthed and translated.” (Peter S. Rudman, How Mathematics Happened, p. 249)

Peter Rudman further states:

“Since the Babylonians did not have algebraic notation, how did they derive the “equations” their algorithms were evaluating? There is really only one possible answer; their “equations” were geometric diagrams. Such visualizations of geometric diagram is referred to as geometric algebra.” (Peter S. Rudman, How Mathematics Happened, p. 203)

It is not necessary for the present discussion to prove that the ancient Egyptian and Babylonian priests or Pythagoras (to whom not even the knowledge of the theorem named after him can be connected directly, the way it can to the Babylonians a thousand years earlier), or that Pythagoras’ followers or even Plato for that matter had the complete understanding of the mathematical principles of φ even to the extent and sophistication of Euclid’s understanding; but to merely hypothesize that the origins of this conception can be traced back to Plato then perhaps to Pythagoras and from him and his followers back to the two ancient civilizations which may have possessed only the most basic and rudimentary understanding of this mathematical phenomenon.  

My excursion into the depths of history, and mathematics may seem tedious and unnecessary to the reader. But I hasten to assure you that the role of Plato and his followers in the history of mathematics from ancient civilization to Euclid, and further on to Shakespeare’s time is an important consideration for any comprehensive analysis of Hamlet and Phaedo.

“In Pythagorean thought, immortality is conceived both in terms of the transmigration of souls (with the related notion of kinship between all living beings) and also in the possibility of purification and escape from the cycle of rebirth, from the bondage of bodily form. (It is this conception of the afterlife that is common to the Orphic and Pythagorean traditions.) This Pythagorean view of the soul is most systematically developed in Plato’s Phaedo…Plato is working with themes that are, in their origin, unmistakably Pythagorean. And it is primarily by way of…two dialogues, the Phaedo and the Timaeus, that Pythagorean ideas became such a powerful influence on the thought of later centuries, not only in antiquity but again in the Renaissance and beyond, down to our own time.” (Pythagoras and the Pythagoreans: A Brief History, Charles H. Kahn p. 4)

I propose that under the influence of this tradition we should examine Shakespeare’s Hamlet, which was formulated on the basis of an encoded doctrine on the immortality of the soul, which algorithmically encapsulates the conception of the universe with self-conception.

As Hamlet states:

“I could be bounded in a nutshell and count myself a king of infinite space”

Or

“A man may fish with the worm that hath eat of a king, and eat of the fish that hath fed of that worm.”

To note in passing, Shakespeare mentions Pythagoras' doctrine on transmigration of souls in the Twelth Night:

“What is the opinion of Pythagoras concerning wild fowl?” asks a clown, to which Malvolio replyes, “That the soul of our grandam might haply inhabit a bird.” The Clown retorts, “What thinkest thou of his opinion?” to which Malvalio responds, “I think nobly of the soul, and no way approve his opinion.” the clown then says “Fare thee well. Remain thou still in darkness: thou shalt hold the opinion of Pythagoras ere I will allow of thy wits, and fear to kill a woodcock, lest thou dispossess the soul of thy grandam. Fare thee well.”

As Manly Hall writes in The Secret Teachings of All Ages:

“The philosophic ideals promulgated throughout the Shakespearian plays distinctly demonstrate their author to have been thoroughly familiar with certain doctrines and tenets…who but a Platonist…or a Pythagorean could have written The Tempest, Macbeth, Hamlet, or The Tragedy of Cymbeline?” (p. 165)

Consider the interpretation of Pythagorean concept of transmigration by James Luchte in a book titled Pythagoras and the Doctrine of Transmigration:

“Transmigration is a poetic topos which opens the space for a complex indication of existence amid a mnemotechnic shelter for a philosophical truth that seeks to be attuned to the All…within its ‘symbolic nexus,’ in this way, transmigration abides the fundamental meaning and specific regions of Pythagorean thought. It is a cathexis which articulates the myriad facets of inquiry, both esoteric, philosophy and poly-theology, and exoteric, mathematics, cosmology, cosmogony and musical theory. An attentive re-telling of the tale of transmigration, from this perspective, would reveal all that which is tacitly assumed by such a “primitive narrative”: conceptions of body, perspective, praxis, and of soul, souls, kinship, number, geometry and music. These many strands come together in the Pythagorean philosophical movement, articulated in its narrative, the unity of which abides an ethos of the bios, or way of life, which encompasses not only the various facets and aspects, but also the destiny of lived existence. The bios is rooted in the cycles of recurrence which is an even more primary ‘unity’. For the Pythagoreans, existence and eschatology are separated only by forgetfulness…Yet, despite the wide agreement of early modern and ancient commentators, Pythagoras’ religious and “mystical” preferences – his doctrine of immortality – are not taken seriously by Late Modern scholarship, and are never considered as intrinsically related, even in a symbolic sense, to his mathematical or scientific significance.” (James Luchte, Pythagoras And The Doctrine of Transmigration)

Due to the remarkable insight and intuition of professors Scott Olsen and Alexey Stakhov, we can surmise that the “crown jewel” of Platonic and Pythagorean thought is in fact the golden section - a harmonic ratio connecting the universe with the human soul. Olsen, in particular, argues that Plato’s Timaeus and Republic demonstrate that the "golden section" is the basis of his philosophy. In a book called The Golden Section: Nature's Greatest Secret, Dr. Olsen proves that the "golden section" is embodied in the most important ontological principles of Platonic and Pythagorean thought.

The geometric principles of the Devine Proportion were described by Plato in the Timaeus:

"For whenever in any three numbers, whether cube or square, there is a mean, which is to the last term what the first term is to it; and again, when the mean is to the first term as the last term is to the mean—then the mean becoming first and last, and the first and last both becoming means, they will all of them of necessity come to be the same, and having become the same with one another will be all one" (Plato, Timaeus, 31c - 32a)

The concept of φ is important to the current discussion of the common structure and theme of Hamlet and Phaedo, because the concept of Devine Proportion is precisely the context in which infinite progression (as in the example of the doctrine on immortality of the soul) can be expressed mathematically, geometrically and in turn structurally in the form of self-similar fractals.

The Devine Proportion is itself a product of self-similarity and it in turn produces self-similarity in such examples as the pentagon, pentagram and dodecahedron.  It is in fact the framework on which the doctrine on the immortality of the soul is constructed (for which only a very rudimentary conception of the Sacred Geometry is necessary, and no sophisticated mathematical understanding is needed) and conversely it is the secrets of this divine proportion which the doctrine on immortality of the soul may really be hiding. Which, of course, would account for the lack of evidence of its existence in the ancient world, while at the same time illuminates the vast abundance of (if not evidence then at least as possible) clues to the presence of this knowledge in a far more distant past than is allowed by the skepticism of the academic community. This is somewhat ironic, because this community of course originates from Plato’s Academy, the institution which first shed light on this secret tradition over two millennia ago.

It would be prudent to remember the sign which purportedly hung above the doors to Plato’s Academy: “let none ignorant of geometry enter.”

What the Pythagorean Mysteries had in common with those of ancient Egypt, Babylon, Persia, India and many others, was a secret religious doctrine which unified all knowledge. This included a sophisticated system of arithmetic, geometry and astronomy encoded into religious narrative, ritual and architecture.

It is said that when Pythagoras returned home, he began to attract followers, and this following was eventually organized into an order, whereby the initiates progressed through levels of rank. Pythagoras himself is described to have gone through similar (if not identical) processes of initiation in Egyptian and Babylonian Mysteries, and by most accounts it required a tremendous amount of time and dedication. Supposedly, one of the first stages of initiation into the Pythagorean order was a five year vow of silence.       

“These five years of silence accomplished two things. First, they trained the student's powers of self-reliance and intuition. Second, they gave him training in the secrecy obligatory for the higher degrees, wherein some of the secrets of the Mysteries were disclosed. Upon initiation every student was warned that "it is not lawful to extend to the casual person things which were obtained with such great labors and such diligent assiduity, nor to divulge the Mysteries of Eleusinia to the profane." (Theosophy, Vol. 27, No. 6, April, 1939 p. 245)

Cryptography (from Greek κρυπτός, - a mystery, and secret; γράφειν, - writing) can be traced back over 4,000 years ago, when the scribes of ancient Egypt and Babylon subtly transposed characters and their meanings. These types of ciphers are referred to as symmetric or secret key cryptograms which include any form where the same key is used both to encrypt and to decrypt (or decipher) the text involved.

Shakespeare’s contemporary, Francis Bacon described this sort of cryptographic methodology in his famous work Of The Advancement of Learning (incidentally this work was published around the same time as Shakespeare’s Hamlet was written)

"For Cyphars; they are commonly in Letters or Alphabets, but may bee in Wordes. The kindes of Cyphars, (befides the Simple Cyphars with Changes, and intermixtures of Nvlles, and Nonsignificats) are many, according to the Nature or Rule of the infoulding: Wheele-Cyphars, Kay-Cyphars, Dovbles, &c. But the virtues of them, whereby they are to be preferred, are three; that they be not laborious to write and reade; that they bee impofsible to difcypher; and in fome cafes, that they bee without fufpition. The higheft Degree whereof, is towrite Omnia Per Omnia; which is vndoubtedly pofsible, with a proportion Quintuple at most, of the writing infoulding, to the writing infoulded, and no other reftrainte whatfoeuer. This Arte of Cypheringe, hath for Relatiue, an Art of Difcypheringe; but fuppofition vnprofitable; but, as things are, of great vfe. For fuppofe that Cyphars were well managed, there bee Multitudes of them which exclude the Difcypher. But in regarde of the rawneffe they paffe, the greateft Matters, are many times carried in the weakeft Cyphars." (Francis Bacon, Of The Advancement of Learning 1605)

Since symmetric cryptograms are much more efficient in practice than asymmetric systems, they remain as the most popular cryptosystems in use today.

Throughout history it has been proposed that it was from the priests of ancient Egyptian and Babylonian religious mysteries that Pythagoras acquired both his philosophic concepts as well as his mathematical system. Because Pythagoras and his followers were intent on keeping their secret knowledge hidden from the world at large and divulging it only to the select few initiated into their brotherhood, it was Plato who finally revealed it to the world.

In Timaeus, Plato describes the origin and mechanism of the cosmos in terms of its fundamental structure made possible by five Pythagorean Solids. These five polyhedra are the tetrahedron, the cube, the octahedron, the icosahedron, and the dodecahedron each associated with a basic element of matter.

Socrates’ cosmologic description in Timaeus and his argument for the immortality of the soul in the Phaedo are two composite halves of the same doctrine (that of cosmos and psyche in other words macrocosm and microcosm).

Consider the following excerpt from Giorgio De Santillana and Hertha Von Dechend’s  Hamlet’s Mill:

“…if we did not have Plato’s Timaeus, it would be a hopeless task altogether to understand the reason which made it obligatory in those “archaic” times to watch the immense cosmic clock most carefully…Timaeus, that “topos” from which come and to which return all “rivers” of cosmological thought…When the Timean Demiurge had constructed the frame,” skambba, ruled by equator and ecliptic – called by Plato “the Same” and “the Different”…and when he had regulated the orbits of the planets according to harmonic proportions, he made “souls.” In manufacturing them, he used the same ingredients that he used when he had made the Soul of the Universe, the ingredients however, being “not so pure as before.” The Demiurge made “souls in equal number with the stars (psychas isarithmous tois astrois), and distributed them, each soul to its several star…the Timaeus and, in fact, most Platonic myths, act like a floodlight that throws bright beams upon the whole of “high mythology.” Plato did not invent his myths, he used them in the right context – now and then mockingly – without divulging their precise meaning: whoever was entitled to the knowledge of the proper terminology would understand them…Creating the language of the philosophy of the future, Plato still spoke the ancient tongue, representing, as it were, a living “Rosetta stone.” And accordingly – strange as it may sound to the specialists on Classical Antiquity – long experience has demonstrated this methodological rule of thumb: every scheme which occurs in myths…to which we have Platonic allusions, is “tottering with age,” and can be accepted for genuine currency. It comes from that “Protopythagorean” mint…that once, coined the technical language and delivered it to the Pythagoreans…Strange, admittedly, but it works. It has worked before the time when we decided to choose Plato as Supreme Judge of Appeals in doubtful cases of comparative mythology, for example, when H. Baumann recognized the myth of Plato’s Symposium (told, there, by Aristophanes) as the skeleton key to the doors of the thousand and one myths…Plato knew…that the language of myth is, in principle, as ruthlessly generalizing as up-to-date “tech talk.” The manner in which Plato uses it, the phenomena which he prefers to express in the mythical idiom, reveal his thorough understanding…” (Giorgio De Santillana and Hertha Von Dechend, Hamlet’s Mill, p. 306-311)

In the beginning of Timaeus a story is told of Solon the great Athenian statesman, poet and sage of antiquity who visited Egypt in search of knowledge long forgotten by his people. The Egyptian priest told him this:

“O Solon, Solon, you Hellenes are never anything but children, and there is not an old man among you…I mean to say…that in mind you are all young; there is no old opinion handed down among you by ancient tradition, nor any science which is hoary with age. And I will tell you why. There have been, and will be again, many destructions of mankind arising out of many causes; the greatest have been brought about by the agencies of fire and water, and other lesser ones by innumerable other causes. There is a story, which even you have preserved, that once upon a time Phaëthon, the son of Helios, having yoked the steeds in his father’s chariot, because he was not able to drive them in the path of his father, burnt up all that was upon the earth, and was himself destroyed by a thunderbolt. Now this has the form of a myth, but really signifies a declination of the bodies moving in the heavens around the earth, and a great conflagration of things upon the earth, which recurs after long intervals…” (Plato, Timaeus, p. 445)

The story told about Solon in the Timaeus has echoes of the stories told of Orpheus and Pythagoras who traveled to Egypt and Babylon in search of the secret wisdom from their priests. It was the Pythagoreans that Plato credits for the five solids of sacred geometry, these famous polyhedra known to us as the Platonic Solids were likely known to Pythagoras as the Egyptian or Babylonian Solids. One of these sacred geometric shapes is especially important to the current discussion - the dodecahedron - which is mentioned in both Timaeus and Phaedo (110B).

Plato associated the dodecahedron and its twelve faces with the twelve constellations of the zodiac which in turn divide the entire cosmos as described in Timaeus. It is very likely that ancient Babylonians, Egyptians along with Pythagoras shared the same association between the dodecahedron and the universe.

“If we accept the hypothesis that the ancient Egyptians knew the dodecahedron and its numerical parameters 12, 30 and 60, then the scientists of antiquity should not have been surprised, when they discovered that the cycles of the solar system are expressed by the same numbers (12-year cycle of Jupiter, 30-year cycle of Saturn, and 60-year cycle of the Solar system). Thus, there is a deep mathematical connection between the Solar system and this perfect spatial figure, the dodecahedron. Scientist of antiquity apparently came to this conclusion. This may explain why the Egyptians (and Plato) chose the dodecahedron as the “Main Geometric Figure,” that symbolizes the “Harmony of the Universe.” It appears that the Egyptians made all their main systems (calendar system, systems of time and angle measurements) correspond to the numerical parameters of the dodecahedron! According to ancient thought, the motion of the Sun on the ecliptic was strictly circular. By then choosing the 12 Zodiac constellations with the distance of 30º, the Egyptians were able to coordinate the yearly motion of the Sun on the ecliptic with the structure of their calendar year: one month corresponded to the apparent motion of the Sun along the ecliptic between two adjacent Zodiacal constellations! Moreover, the movement of the Sun one degree along the ecliptic corresponded to one day in the Egyptian calendar! Thus, the ecliptic was divided automatically into 360º. By dividing one day into two parts, the Egyptians thereby automatically divided each half of one day into 12 parts (12 faces of the dodecahedron) and introduced the Hour, a major unit of time. By dividing one hour into 60 minutes (60 planar angles on the surface of the dodecahedron), the Egyptians introduced the Minute, the  next important unit of a time. And of course this allowed them to introduce the Second (1 minute = 60 seconds), the smallest unit of time in that period…Thus, by choosing the dodecahedron as the Main Harmonic Figure of the Universe and by following strictly to its numerical characteristics (12, 30 and 60), the Egyptians designed a perfect calendar together with the systems of time and angle measurement that have stood the test over several millennia. These systems of course correspond to the golden mean “Theory of Harmony,” the underlying proportional basis of the dodecahedron…These surprising conclusions follow from a simple comparison of the dodecahedron with the Solar system. And if our hypothesis is correct (let somebody attempt to deny it), it follows that for several millennia mankind has lived under the standard of the golden section! And each time, when we look at the index dial of our watch based on the numerical parameters of the dodecahedron 12, 30 and 60, we touch the “Main Secret of the Universe,” the “Golden Section!” (Alexey Stakhov, Scott Olsen, Mathematics of Harmmony, p. 151)

Alexey Stakhov and Scott Olsen also propose that the relationship between the dodecahedron and the apparent motions of the cosmos resulted in the development of the hexadecimal numerical system of the ancient Babylonians.

In the Phaedo, Socrates evokes the dodecahedron as a symbol of the world as part of a larger framework for his description of the doctrine on the immortality of the soul.

What makes the dodecahedron a suitable model for the cosmos, the world and the soul is the self-similar relationship between the whole and it’s constituent parts, a relationship between the three dimensional dodecahedron with the two dimensional pentagons which constitute it’s structure, a relationship which is made possible as the direct result of the Devine Proportion of it’s angles.  

Self-similar fracturing is possible with pentagons as a result of the φ ratio in the relationship of its angles.

According to Mario Livio the pentagon is “the most direct manifestations of the “divine proportion” (The Golden Ratio, p.155) the unique properties of pentagons are based on the fact that the diagonals of a pentagon cut each other in the ratio of φ. The derivation of φ in a pentagon produces a pentagram, a symbol which was the representation, simply enough, of a star in the night sky which in turn were considered to contain the celestial souls of men in the Babylonian, Egyptian and Pythagorean traditions, it is precisely this doctrine which is described in Plato’s Phaedo,  Socrates’ final argument in defense of an ancient and secret dogma on the immortality of the soul.

Consider Mario Livio’s description of the earliest known pentagrams found in Babylon, and the minimal extent (to which we can surmise) that this ancient civilization understood the geometry of the pentagon:

“Some of the earliest known pentagrams come from fourth millennium B.C. Mesopotamia. Pentagram shapes were found in excavations in Uruk (where the earliest writings were also uncovered), and in Jemdet Nasr…In Sumerian the pentagram, or its cuneiform derivative, meant “the regions of the universe…Studies of cuneiform tablets dating to the second millennium B.C., which were discovered in 1936 in Susa in Iran, leave very little doubt that the Babylonians of the first dynasty knew at least an approximate formula for the area of a pentagon…The Babylonians had a similar approximation for pi, the ratio of the circumference of a circle to its diameter. In fact, the approximations for both pi and the area of the pentagon relied on the same relation.”  (Mario Livio, The Golden Ratio, p. 43-44)

Uruk is the fortified city of king Gilgamesh from which he set out in search of immortality, and where he returned, engraving the secrets of his journey on clay tablets which he, according to the story, hid in a copper box guarded by a bronze lock, placed inside a temple in the center of the city, around which Gilgamesh built Uruk’s famous walls.

Weather intentionally or not, the φ ratio is found in the proportions of the Great Pyramid at Giza (within the mere difference of 0.1 percent) the most notable monument of an ancient civilization whose religion was deeply rooted in the doctrine on the immortality of the soul.

Pentagons, pentagrams and five pointed stars were common in ancient Egypt as well, Livio further writes:

“In spite of the fact that five-pointed stars appear quite frequently in ancient Egyptian artifacts, true geometrical pentagrams are not very common, although a pentagram dating to around 3100 B.C. was found on a jar in Naqadah, near Thebes. Generally, the hieroglyphic symbol of a star enclosed in a circle meant the “underworld,” or the mythical dwelling of stars at twilight time, while stars without circles served simply to signify the night stars.”   (Mario Livio, The Golden Ratio, p. 44)

To the ancient Egyptians the five-pointed star simultaneously symbolized the stars above (what Pythagoras called cosmos) and the soul within (which he called psyche); they believed the human soul to be made up of five distinct parts: Ren (name), Ba (identity), Ka (spiritual essence), Sheut (shadow), and Ib (heart).

In ancient Egypt, the symbol of a five-pointed star is closely associated with another equally ubiquitous symbol, the hieroglyph (and artistic symbol) known as Ankh, or the Egyptian cross. Both symbols share a myriad of meanings attributed to them as well as a very similar geometric shape, in fact both were closely associated with the human form. 

“In Egyptian art, the Ankh is pictured in the hands of the gods, and held to Pharaoh’s lips as if it were the breath of life itself. Its form (a not-so-subtle conjunction of the female and male generative organs) evokes the eternal powers of self-regeneration. With its oval head, outstretched arms, and slender stalk, it mirrors the human form. Indeed, ornate Ankh-shaped hand mirrors have been found in tombs of the ancient Egyptians. As if to affirm the great truth that the secret of life can only be discovered through self-reflection, the Egyptian word for mirror is ankh.” (Lon Milo, The Ankh: Key of Life  p. 3)

Ankh was also associated with the ancient Egyptian doctrine on the immortality of the soul.

“The ancient Egyptian “key of life” or “cross of life”…representing life, especially life after death…a key to esoteric knowledge and to the after-world of the spirit.”  (Jack Tresidder, The Complete Dictionary of Symbols, p. 35)

Much as was described about the symbolism of the five-pointed star, the Ankh hieroglyph also embodied the relationship between the macrocosm (the universe) and the microcosm (man).

“Judged from the macrocosmic point of view, that is of its analogy with the world, the Ankh-cross may represent the sun, the sky and the earth (by reference to the circle, the upright and the horizontal lines). As a microcosmic sign, that is by analogy with man, the circle would represent the human head or reason (or the ‘sun’ which gives him life), the horizontal arm his arms, and the upright his body. In sum, the most general significance of the cross is that of the conjunction of opposites: the positive (or the vertical) with the negative (or horizontal), the superior with the inferior, life with death.” (Juan Eduardo Cirlot, A Dictionary of Symbols, p. 70)

Today we know that the golden section manifests itself in the proportions of the helical structures of DNA molecules as well as spiral structures of galaxies.

The microcosm-macrocosm relationship between cosmos and psyche in the Mysteries of ancient Egypt, Babylon, Orphics and Pythagoreans is reflected in the Sacred Geometry of the pentagons, pentagrams, dodecahedrons and the Devine Proportions which give rise to fascinating geometric phenomena.

When the five points of the pentagram are connected by five lines, they form a pentagon along it’s outside border; another, smaller pentagon is also at the center of the pentagram, which itself gives rise to a pentagram containing a yet smaller pentagon in it’s center, and so on, ad infinitum. The perpetual imprisonment of a pentagon within a pentagram which is itself entombed within a pentagon is reflected in the most famous proclamation of both the Orphic and Pythagorean teaching - soma sema, - which states that the body is the tomb (or prison) of the soul.

Five pentagons of a same size, when connected around a center, also form a larger pentagon along their outside border as well as a smaller pentagon in the center, this smaller pentagon can thereby be further divided into five smaller pentagons forming a smaller one in their center, on and on again in increasing and diminishing directions of scale and dimension (in the case of a dodecahedron), ad infinitum.

This fractal self similarity is fraught with φ in the proportions of the angles and lengths of lines, in fact the Devine Proportion makes this unique geometric phenomenon possible, this mechanism of infinite geometric generation has been associated since the time of ancient Mysteries of Egypt, Babylon, Orpheus, Pythagoras, Plato and Euclid with the secret doctrine on the perpetual and infinite existence of the soul in the form of a unified theory which contains the fundamental mechanisms of the cosmos as well as the elemental principles which govern the human soul.

As Claudius states:

“She's so conjunctive to my life and soul, that, as the star moves not but in his sphere, I could not but by her.”  (Act 5, scene 7)

To the Pythagoreans, the pentagram represented the proportionality (analogia) of the entire universe reflected within the microcosm of an individual soul; they used the symbol of a pentagram which they called Hygieia (in honor of Asclepius’ daughter and granddaughter of Apollo) to identify each other as fellow initiates of a secret order. It was Pythagoras who is credited with being the first to refer to the universe as a kosmos which in Greek means “order” “total sum” “ornament” or “adornment.” Plato describes the Pythagorean concept of the kosmos in Timaeus as “one Whole of wholes" and as "a single Living Creature which encompasses all of the living creatures that are within it" (Timaeus 30d, 33a). This is precisely the self-similarity expressed in the organization of both Hamlet and Phaedo, all the more appropriate considering the common theme on the doctrine of the soul expressed in the two works.

Pythagorean use of the pentagram as a way to identify each other underscores the secrecy associated with this sect and serves as a basic representation of a cryptographic methodology associated with their doctrine.

It would appear fitting, that Hamlet being a play on the subject of the soul begins with two guards both of whom demand that the other identify himself (as friend or foe), and Plato’s Phaedo with the primary inquiry of who was present in the prison with Socrates the day he died, whether there were “friends” or “strangers” there to hear his final words – which were incidentally – regarding a dept he owed to the god Asclepius (the father of Hygieia, and Apollo’s son)

Although the scope of this presentation does not allow for a more detailed examination of the relationship between the texts of Hamlet and Phaedo, yet I hope that the comparison illustrated here sufficiently presents the hypothesis of a close structural and thematic correlation between the two works in a historical context.  

It remains to mention that the influence of Plato’s philosophy on Shakespeare’s work has only recently been proposed notably by Leon Craig, Of ​​Philosopher Kings: Political Philosophy in Shakespeare's Macbeth and King Lear (2003); Barbara Parker, Plato's Republic and Shakespeare's Rome: A Political Study of the Roman Works (2004) and most recently by Ronald Gray, Shakespeare on Love: The Sonnets and Plays in Relation to Plato's Symposium, Alchemy, Christianity and Renaissance Neo-Platonism.(2011) which is an expansion on an article Dr. Gray published in 2006 titled Will in the Universe (with the same subtitle). However, the crown jewel of Shakespeare’s canon - The Tragedy of Hamlet has remained on the sideline, until now.

Upon a close analysis of the complex relationship which arises out of the juxtaposition between Hamlet and Phaedo within the larger context of Plato’s other works, particularly the Republic, Shakespeare’s likely motive for this remarkable methodology soon becomes evident.

In the Republic, Socrates refers to an “ancient quarrel” between philosophers and poets, a rivalry particularly relevant to Socrates' own life and one of the major factors leading to his execution. 

The rivalry between philosophy and poetry indeed precedes Socrates’ quarrel with the tragedians of his day. This conflicting relationship is exemplified in Greek mythology by the identical twin gods of Apollo (the patron god of philosophers) and Artemis (patron goddess of poets) who represented the sun and moon respectively. And the moon’s reflective role in this mirrored relationship does not escape Socrates’ reasoning, for he denounces the imitative arts (and tragic poetry in particular) precisely for their reflective natures.

In the Republic, Socrates defends the “rejection of imitative poetry” and states that “the tragic poet is an imitator, and therefore, like all other imitators, he is thrice removed from the king and from the truth” he likens their methods of imitation to “turning a mirror round and round” whereby the products of their craft are mere reflections of ideas which are themselves imperfect representation of higher essential forms.

Compare this to Hamlet’s criticism of dramaturgy “to hold, as 'twere, the mirror up to nature…I have thought some of nature's journeymen had made men and not made them well, they imitated humanity so abominably.” (Act 3, scene 2)

Precisely for this reason the tragic poets are exiled by Socrates from his Kalipolis - the ideal state described in the Republic. However he subtly states an exceptional provision to this banishment, as follows:

“Notwithstanding this, let us assure our sweet friend and the sister arts of imitation that if she will only prove her title to exist in a well-ordered state we shall be delighted to receive her…” (Plato, Republic)

This is the call, which Shakespeare, as a master of tragedy and a philosopher of equal merit, was challenged to answer. This is the likely motive for what was explored here - a unique and highly elaborate way in which the text of Hamlet (most famous of all tragedies) reflects the text of Phaedo (the cornerstone of western philosophy) in structure and substance.

We see that Shakespeare heard and accepted the challenge posed by Socrates two millennia earlier, and Hamlet was his reply, earning its right to exist in a well-ordered state of perfection in perpetuity.

Bibliography

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Bacon, Helen. “Poetry of Phaedo” Cabinet of the muses 1999

Bromiley, Geoffrey W. The International Standard Bible Encyclopedia 1995

Cirlot, Juan Eduardo A Dictionary of Symbols 2002

Craig, Leon Harold. Of Philosopher's and Kings: Political Philosophy in Shakespeare's Macbeth and King Lear. 2003

DeSantillana, Giorgio. Hamlet’s Mill. 1969

Dupuis, Charles François. Origin of all Religious Worship. 1798

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