Saturday, June 01, 2024

'the Mathematicks of the neatest Retiary Spider'





Recent media coverage on how the combination of climate warming and global air-traffic are encouraging new, exotic species of spider to inhabit Britain reminded me that observations on spiders are woven through the literary works of the philosopher-physician Sir Thomas Browne (1605-82). [1] 

A family portrait shows the infant Thomas on his mother's knee with a pet rabbit in his lap, and abundant evidence suggests that as an adult Browne possessed a rare empathy towards all living creatures, including his patients. His introduction of the word 'Veterinarian' into English language commemorates his love of animals.

Thomas Browne first declared an interest in spiders in his spiritual testament Religio Medici (1643)

'indeed, what reason may not go to School to the wisdom of Bees, Ants, and Spiders? what wise hand teacheth them to do what reason cannot teach us ?......in these narrow Engines there is more curious Mathematicks, and the civilitie of these little Citizens, more neatly set forth the wisdom of their Maker'. [2] 

Browne's curiosity about spiders typifies his interest in the small in nature. Assisted by the gift of sharp eyesight he jotted observations in his notebooks which were later worked into future publications, such as-
  
'Concerning Spiders much wonder is made how they fasten their webbe, to opposite parts'.

and - 'How some spiders lay a white egg bigger then their bodies, & though that kind bee but shorter legged, runneth about with it fastened unto their belly'. [3]

A recent publication notes-

'Spiders are dominant predators in virtually every terrestrial ecosystem. A marvel of evolution with species numbering in the tens of thousands, they have been walking the earth since before the dinosaurs. Spiders manipulate the silk strands of their webs to act as a sensory field, which vibrates across wide frequencies that they can read in detail. Young spiders spin silk lines that interact with the electrical fields in the atmosphere, enabling them to balloon across huge distances. Some spiders even gather in groups to impersonate ants in astonishing displays of collective mimicry'. [4]

In Browne's day the most comprehensive survey of insects along with their predatory hunter, the spider, was Thomas Muffett’s Theatre of Tiny Animals. Thomas Muffett (1553-1604) was an English naturalist and physician who supplemented the material he'd inherited from Edward Wooton and the Swiss naturalist Conrad Gesner for his book which was ready for publication by 1590. However, due to the expense of its wood-cut illustrations and a lack of interest in natural science in England at the time, it was not published until many years after Muffett's death, in 1634. 

Muffett was also an early supporter of the radical physician and alchemist Theophrastus Paracelsus (1493-1541) who encouraged physicians to investigate and experiment with nature’s properties in order to discover new remedies, the dawn of chemical medicine no less. Following Paracelsian teaching, Muffett included in his book a chapter which speculates on the medicinal potential of venom injected by the spider through its fangs into its prey, along with the need for a medical antidote to its poison. (Frontispiece of Muffett's book below) [5]

                                             

It was the Romantic poet and literary critic Coleridge (1772-1834) who once remarked that in Sir Thomas Browne there is, 'the humourist constantly mingling with, and flashing across, the philosopher'. A fine example of the poet's psychological observation  occurs in Browne's advice to a correspondent desperate for relief from the painful condition of gout to - 'Trie the magnified amulet of Muffetus of spiders leggs worn in a deeres skinne'. [6] 

Muffett's book is referenced a number of times in Browne's vast work of encyclopedic scope known as Pseudodoxia Epidemica (1646-72). Spiders are mentioned in a variety of ways in its compendious pages. 

Although often highly critical of artist's representations of mythic creatures such as the basilisk and griffin, Browne does not object to how spiders are portrayed in Heraldry-

'We will not dispute the pictures of Retiary Spiders, and their position in the web, which is commonly made laterall, and regarding the Horizon; although if observed, wee shall commonly find it downward, and their heads respecting the Center' [7] 

Giving credence to the eye-witness testimony of the  Belgian scientist and mystic Jean van  Helmont (1579-1644) a transitional figure in the history of science, who like Browne, subscribed to the doctrine of correspondences and signatures which interpreted the spider as a symbol of ill-omen, he states-

'And Helmont affirmeth he could never find the Spider and the Fly on the same tree; that is the signs of War and Pestilence, which often go together'. [8] 

Browne swiftly dismisses the received wisdom that there are no spiders in Ireland - 'Thus most men affirme, and few here will beleeve the contrary, that there are no spiders in Ireland; but we have beheld some in that country'. [9] 

And crucially, in a chapter titled 'Concerning other Animals, which examined prove either False or Dubious' he wields his scientific credentials in order to demolish the folk-lore myth of the supposed antipathy between a toad and spider, informing his reader-

'having in a glass included a toad with several spiders, we beheld the spiders without resistance to sit upon his head, and pass all over his body, which at last upon advantage he swallowed down, and that in few hours to the number of seven’.[10]

Browne’s vivarium experiment is exemplary of his scientific journalism, an eyewitness report written in early modern English on the results of a simple experiment; it also evokes a scenario in which the worthy physician is an intrepid hunter and capturer of spiders !

A passage in Pseudodoxia reveals Browne unquestionably agreeing with his near exact contemporary and favourite author, the Jesuit priest, scientist and scholar of comparative religion, Athanasius Kircher (1602-80). In his Ars Magnesia (Art of Magnetism, 1631) Kircher included a chapter on musical cures for those bitten by spiders, such music, he believed, was evidence of the invisible, magnetic forces of attraction within music. Submitting to the authority of 'the learned Kircherus' but perhaps more significantly, not dismissing the possibility that music may possess curative properties, Browne states-  

'Some doubt many have of the Tarantula, or poisonous Spider of Calabria, and that magical cure of the bite thereof by Musick. But since we observe that many attest it from experience: Since the learned Kircherus hath positively averred it, and set down the songs and tunes solemnly used for it; Since some also affirm the Tarantula it self will dance upon certain stroaks, whereby they set their instruments against its poison; we shall not at all question it'. [11] 


Above - a page from Ars Magnesia [12]

The intricate geometry of the spider's web attracted the attention of natural philosophers throughout the 17th century including the Italian polymath Mario Bettini (1582-1657) whose Beehives of Universal Philosophical Mathematics (1656) like Browne's Pseudodoxia is a compendium of early scientific enquiries. Listed as once in Browne's library, each chapter of Bettini's book is a self-contained 'Beehive' in which a proposition or topic of early modern science is discussed, including Euclidean geometry, mathematics, acoustics, the camera obscura, optics, discussion on the flight of projectiles, the art of navigation, and the measurement of time. In chapter two of Bettini's book the geometry and mathematics of the spider's web are examined (below)[13].


Spiders and their webs are naturally to be found in Browne's Garden discourse, The Garden of  Cyrus (1658). Following the sequence of its full running title The Garden of Cyrus, or The Quincuncial Lozenge, or Network Plantations of the Ancients, artificially, naturally, mystically considered (1658) spiders are first considered artificially in terms of mathematics and geometry, they are next considered naturally, with an eyewitness description of their reproduction, and finally, at the discourse's mystical conclusion in  which highly original arachnid imagery occurs. 

Exemplary of the discourse's theme - 'how nature Geometrizeth, and observeth order in all things', Browne first describes the spider's web in mathematical detail and is appreciative of its beauty (the adjective 'elegant'  is encountered frequently throughout the discourse).

'And no mean Observations hereof there is in the Mathematicks of the neatest Retiary Spider, which concluding in fourty four Circles, from five Semidiameters beginneth that elegant texture'.

The proportional ratio of the spider's legs are also an 'artificial consideration', Browne informing his reader that  -'The legs of Spiders are made after a sesqui-tertian proportion'. (sesqui-tertian being the mathematical ratio of one plus one and a third).

Following these 'artificial considerations' spiders are next considered naturally with a superb example of Browne's observational skills-

'And he that shall hatch the little seeds, either found in small webs, or white round Egges, carried under the bellies of some Spiders, and behold how at their first production in boxes, they will presently fill the same with their webbs, may observe the early, and untaught finger of nature, and how they are natively provided with a stock, sufficient for such Texture'. [14] 


Illustration courtesy of  Silvanus Services 

Its not impossible that the word 'incubation' which Browne's credited with introducing into the English language may have derived from his empirical study of spiders' eggs 'at their first production in boxes' as from his ornithological studies. 

Not all of Browne's observations on spiders are woven into either Pseudodoxia or Cyrus. His notebook observation on  the material used by spiders for example - 

'Spiders are presently buisie in their texture upon the little stock of their moysture & soon exhaust themselves, without addition of nutriment, as we have tried in some hudled under the bellie of the damme, in a round folicle bagge wh. sticketh close unto it, by some lentous cement, mostly of the same matter with their webbe.' [15] 

Mention of retiary networks occur frequently in The Garden of Cyrus. While the spider's web is nature's network, Browne also names artificial networks, including, 'that famous network of Vulcan, which inclosed Mars and Venus'. His acquisition of Kircher's recently published work of comparative religion Oedipus Egypticus (Rome 1652-54) spurs him to mention the ancient Egyptian god Horus who's depicted in Kircher's reproduction of the Bembine Tablet of Isis, (a syncretic Roman artwork which is alluded to twice in The Garden of Cyrus) - 'Nor is it to be over-looked how Orus, the Hieroglyphick of the world is described in a Net-work covering, from the shoulder to the foot'. 

It's also in The Garden of Cyrus that Browne alludes to the goddess of wisdom Minerva and the myth of how spiders originated- 

'But this is no law unto the woof of the neat Retiarie Spider, which seems to weave without transversion, and by the union of right lines to make out a continued surface, which is beyond the common art of Textury, and may still nettle Minerva the Goddesse of that mystery'. [16]

The ancient Greek myth of how the goddess Minerva engaged in a weaving contest with the mortal Arachne and its consequences is narrated by the Roman poet Ovid in his epic poem the Metamorphoses. In Ovid's Metamorphoses the myths of ancient Greece are linked by a common theme of transformation. A chaotic universe is subdued into harmonious order, animals turn into stone, men and women are rewarded and punished by gods and goddesses for their deeds to become trees, birds and stars. One of the most influential works in Western culture, Ovid’s Metamorphoses was a valuable source of information and inspiration to poet, painter and scholar throughout the Renaissance. A Latin edition of Ovid’s verse. along with translations in French and Italian, as well as a popular 1626 English translation by George Sandys, are all listed as once in Browne’s library. [17]

Ovid tells how the talented shepherd’s daughter Arachne challenged Athena to a weaving contest. When Athena, the goddess of wisdom couldn't find fault with Arachne’s tapestry she became angry and hit her with a shuttle. Ashamed of her offense, Arachne attempted suicide by hanging herself but instead Athena  transformed her into a spider condemning her to create webs for eternity. A cautionary tale of hubris, lack of humility and a warning to those who would challenge the gods,  Ovid depicts Athena’s transforming of Arachne thus –

‘You may go on living, you wicked girl, but you must be suspended in the air forever. …Then as she departed, she sprinkled Arachne with the juice of Hecate’s herbs. Immediately, at the touch of this baneful poison, the girl’s hair fell out, her nostrils and her ears went too. And her head shrank to nothing. Her whole body became tiny. Her slender fingers were fastened to her sides, to serve as legs, and all the rest of her was belly; from that belly, she yet spins her thread, and as a spider is busy with her web as of old’. [18] 

16th century woodcut

Imagery of the spider spinning its web features in the drowsy, mystical conclusion of The Garden of Cyrus. At the approach of night, sleep and dreams the learned doctor, reluctant to pursue his quincuncial quest any longer, aware of how the day's thoughts and actions are distorted in dreams, poetically declares-

'We are unwilling to spin out our awaking thoughts into the phantasms of sleep which often continueth precogitations making Cables of cobwebs and wildernesses of handsome groves'.

Browne's arachnid imagery shares an uncanny affinity to arachnid imagery by the German literary figure Johann Goethe (1749-1830. In the Second Part of the tragic drama Faust its protagonist, doctor Faust, reflects at the approach of night, sleep and dreams -

'How logical and clear/the daylight seems,
Till the night weaves us/ in its web of dreams !' [19]

Both Browne and Goethe allude to the illusionary nature of life through imagery involving the spider's web, a deceptive, near invisible trap of entanglement, not unlike the veil of Maya, or world of appearances in Buddhism.  And in fact the two literary figures share a remarkable affinity not only in arachnid imagery but also scientific outlook. A  strong case can also be made for Urn-Burial and The Garden of Cyrus and Goethe's Faust Part I and II both utilizing the commonplace Renaissance schemata of Microcosm and Macrocosm as thematic templates in their sequential progression.

In essence, with its fixation on the inter-related symbols of the number five, quincunx pattern and retiary network, The Garden of Cyrus is a literary work which is highly influenced by the humanist scholar Pico della Mirandola (1464-94) who introduced and developed Pythagorean 'philosophizing with number' into mainstream Renaissance thought. 

In Pythagorean numerology number acquires a metaphysical symbolism capable of enabling speculation upon theology, cosmology, geometry, mathematics and music. Pythagorean concepts involving number, astronomy and geometry inspired devout early scientists and hermetic philosophers alike throughout the Renaissance. The German astronomer Kepler (1571-1630) as well as Van Helmont, Bettini, Kircher and Thomas Browne all subscribed to the Pythagorean idea that mathematical truths could be discovered through analysis of number, geometry and pattern in Nature. Spiders along with bees were thought to be a Heaven-instructed mathematicians capable of 'geometrical forethought' and in possession of knowledge transcendent to humanity. The eight-legged spider and its ability to construct a complex geometric pattern attracted their attention for possible clues towards discovering hidden mathematical truths.

In Browne's hermetic vision of universal connectivity, The Garden of Cyrus, 'the mathematicks of the neatest retiary spider' and 'the mystical mathematicks of the City of Heaven' are intrinsically related to each other in microcosm-macrocosm harmony.

Finally, in the age of the world-wide web, itself a complex invention of wonder, not unrelated to illusion, its interesting to note that Browne is credited as introducing the word ‘network’ in its context of an artificial construction into English language. Its amusing to think that the word 'network' used today to describe broadcasting, communication and transport connectivity, originates in no small measure from Thomas Browne's contemplation of one of nature's marvels, the retiary spider and its web.


See also




Notes

[1] Exotic spiders flourishing in Britain
[2] Religio Medici Part 1 : 15 
[3] Miscellaneous writings Keynes 1946.
[4]  The Lives of Spiders: A Natural History of the World's Spiders 
pub. Princeton University Press, June 2024
[5] Muffett’s Insectorum sive Minimorum Animalium Theatrum listed in the 1711 Sales Catalogue of Browne's library page 18 no. 51
[6] Miscellaneous writings Keynes 1946
[7]  Pseudodoxia  edited Robbins OUP 1981 
      Book 5 chapter 19 24-27
[8] Book 2 chapter 7 
[9] Book 7 chapter 15 line 23
[10] Book  3 chapter 28
[11] Book 3 chapter 27
[12] Ars Magnesia. 1631 Herb.  Sales Catalogue page 30 no. 53
[13] Fucaria & Auctaria ad Apiaria Philosophiae Mathematica 1656
Sales Catalogue page 28 no. 16
[14] Cyrus Chapter 2
[15] Miscellaneous writings Keynes 1946 
[16] Cyrus Chapter 3
[17] Over a dozen books by Ovid are listed in the 1711 Sales Catalogue 
[18] Ovid Metamorphoses Book 6 lines 1-150 
[19] Faust Part 2 lines 11411-2

Acknowledgements

* Many thanks to Julie Curl for her illustration. With her professional skills of the inter-related fields of archaeology, botany, zoology and illustration Ms. Curl shares several of Browne's interests which have cast new, interpretative light on the philosopher-physician. 

See Sylvanus Services for more information.

* See also 

* Although  Thomas Muffett (1553-1604) had a daughter, no earlier reference to the nursery rhyme Little miss Muffett can be found before 1805.

Little miss Muffet
Sat on a tuffet
Eating her curds and whey.
Along came a spider 
Who sat down beside her
And frightened miss Muffett away.
 
* Arthur Rackham's illustration of the well-known nursery rhyme has a spider of terrifying proportions who ambiguously raises his hat to Miss Muffett.

                                     

* The Spanish artist Velasquez (1599-1660) in his late masterwork Las Hilanderas or 'The Spinners' (1657) alludes to the ancient Greek myth of Arachne. It was however not positively identified as depicting Arachne and Minerva's spinning contest until 1948, almost 300 years after first painted. (below)

                   

* The rock band 'The Who's 1966 song 'Boris the Spider', written and sung by bassist  John Entwhistle, seems to prophetically name a short-lived, future British Prime Minister.

* 'The Kiss of the Spiderwoman' (1985) links the spider to the archetype of the femme fatale.

Tuesday, March 05, 2024

A Browne bookshelf

 

I've found these books on Thomas Browne to be useful over the decades. From left to right - 

* Collected Works of Thomas Browne Religio Medici edited by Reid Barbour and Brooke Conti. pub. Oxford University Press 2023

* Approaches to Sir Thomas Browne, The Ann Arbor Tercentenary Lectures and Essays. edited by C.A.Patrides pub. Uni. of Missouri Press 1982

* The Opium of Time: Gavin Francis pub. Oxford Uni.Press 2023 

* Sir Thomas Browne- Joan Bennett
pub. Cambridge Uni. Press 1962

* The Strategy of Truth – Leonard Nathanson  pub. Uni. Of Chicago 1967

* Sir Thomas Browne: A Doctor’s Life of Science and Faith - J.S. Finch pub. Henry Schuman N.Y. 1950

* 4th edition of Pseudodoxia Epidemica (1658) with Urn-Burial and The Garden of Cyrus appended.

Thomas Browne Selected Writings ed. Kevin Killeen pub. Oxford Uni. Press 2014 

* Thomas Browne: A Biographical and Critical Study - Frank Huntley pub.  Uni. of Michigan 1962

*The Miscellaneous writings of Sir Thomas Browne edited by Geoffrey Keynes pub. Faber and Faber 1946

*  2 of the 3 volumes of The Works of Sir Thomas Browne edited by Simon Wilkins  pub. Henry Bohn 1832

Not included in photo -

*  A Catalogue of the Libraries of Sir Thomas Browne and Dr Edward Browne, his son. A Facsimile Reproduction  with an Introduction, Notes and Index by J.S. Finch. pub.  E. J. Brill 1986 (Essential for understanding the extraordinary range of Browne's interests and studies).

*  The Major Works of Sir Thomas Browne edited and with an Introduction by C. A. Patrides Penguin  1977 (First favourite).

*  Peter Green Writers and their Work no. 108 pub. Longmans and co. 1959 ( brief but insightful essay 36 pp )

* King James Bible (1611). Fundamental to Browne's spirituality, frequently referenced throughout his writings and a major influence upon his literary style.