Borromean Rings for Beginners

[Terry_Sampson]

• Who has ever heard of Borromean Rings?
• This is what they look like:
  
• Neat, huh? Well check out what The Guardian has to say about them:
  • The image above is the Borromean rings, three interlinked rings that have the curious property that when any one of the rings is removed, the other two are no longer linked.
  • The rings are studied by mathematicians and have long been used as a metaphor for the interdependence of three parts, since either all three are linked, or none are. (The name comes from the Borromeo family of Renaissance Italy, which had the pattern on their coat of arms.)
  • You cannot make a physical version of the Borromean rings with three perfect circles as illustrated above, but you can if you bend the circles slightly out of shape, or if you use non-circular loops. The global scientific body for maths, the International Mathematical Union, has a 3-D version of the Borromean rings as its logo, below.
    
• Wikipedia offers a few more details: Borromean rings are named after the House of Borromeo, whcih included them in its coat-of-arrms:
  
  
  • See if you can find them.
• " The link itself is much older and has appeared in the form of the valknut, three linked equilateral triangles with parallel sides, on Norse image stones dating back to the 7th century. For kicks, watch this Youtube The Valknut as Borromean rings to see how to draw the Valknut.
  
• A stone pillar in the 6th-century Marundeeswarar Temple in India shows three equilateral triangles rotated from each other to form a regular enneagram;
  
  
• The Borromean rings have been used in different contexts to indicate strength in unity. In particular, some have used the design to symbolize the Trinity. A13th-century French manuscript depicting the Borromean rings labeled as unity in trinity was lost in a fire in the 1940s, but reproduced in an 1843 book by Adolphe Napoléon Didron.
  
  
  • Didron, A. N., Millington, E. J., Stokes, M. (1851). Christian Iconography. United Kingdom: H.G. Bohn.
  • Didron and others have speculated that the description of the Trinity as three equal circles in canto 33 of Dante’s Paradiso was inspired by similar images, although Dante does not detail the geometric arrangement of these circles. The psychoanalyst Jacques Lacan found inspiration in the Borromean rings as a model for his topology of human subjectivity, with each ring representing a fundamental Lacanian component of reality (the “real”, the “imaginary”, and the “symbolic”).
• The rings were used as the logo of Ballantine beer, and are still used by the Ballantine brand beer, now distributed by the current brand owner, the Pabst Brewing Company. For this reason they have sometimes been called the “Ballantine rings”
• Adding some serious "Right brain imagination, McGilchrist found reason to quote Marie Sinclair, the 19th century Countess of Caithness, from her book "Old Truths in a New Light: An Earnest Endeavour to Reconcile Material Science with Spiritual Science and with Scripture) [Chapman & Hall, 1876] where she says:"It is generally, although erroneously, supposed that the doctrine of the Trinity is of Christian origin. Nearly every nation of antiquity possessed a similar doctrine. St Jerome testifies unequivocally, “All the ancient nations believed in the Trinity”’. An image of the Trinity that helps me is that of a book. What is the book? Is it what was present in the mind of its writer? Or the tangible volume on the table in front of me? Or what goes on in the mind of the receptive reader? Clearly it is each and all.”
• For those of you unfamiliar with the Countess: see: Marie Sinclair, Countess of Caithness. For those of you eager to read her book. Old Truths in a New Light, Or, an Earnest Endeavour to Reconcile Material Science With Spiritual Science, and With Scripture. When you get back to Earth, feel free to share. I’m sure McGilchrist “Right-Brain” folk will be eager to read your adventures.

[St.Roymond]

As a grad student in math my younger brother made a set of Borromean rings with Mobius strips. He dropped it into his D&D RPG world as a mysterious device of unknown but substantial power.

[marta]

@Terry_Sampson

You cannot make a physical version of the Borromean rings with three perfect circles

This is crazy my first reaction was: this is just Russian wedding ring.
But it isn’t!
Here’s what it is:

Clearly, you can see that you could remove one without the other two falling apart.
Mind blown

[Mervin_Bitikofer]

Yeah - no! My mind did a double-take too. You can take three wires and turn them into loops by twisting the ends together. But then make the third wire weave in and out of the other two (like in the picture) before twisting its ends together, and voila! They won’t come apart (short of breaking the loop) - but any two of them alone are not interlocking!

My mind blown along with yours!

-Merv

[MarkD (A Whateverist, not a Christian)]

Very cool even if it doesn’t refer in any way to what might have happened to Middle Earth if Boromir had managed to fleece the ring from Frodo.

[St.Roymond]

@MarkD

Very cool even if it doesn’t refer in any way to what might have happened to Middle Earth if Boromir had managed to fleece the ring from Frodo.

Now you’ve got me picturing the three rings for the elven kings as Borromean Rings.

[MarkD (A Whateverist, not a Christian)]

Changed my mind. I’ve moved on from TMWT for the most part.

[Mervin_Bitikofer]

I’m too old to decipher initials anymore I guess! What is TMWT?

[Terry_Sampson]

• McGilchrist’s book “The Matter With Things”.
• Mark’s cuttin’ anchor and sailing away just when the Trinity is getting interesting. The Countess of Caithness’ introduction of the Borromean Rings really jazzed up the subject.

[Mervin_Bitikofer]

Thanks for the quick rescue … you’d think I’d be all over that from recent context - but I’m a champion at dropping stuff.

[Terry_Sampson]

• Gee, too bad; We haven’t even gotten to the Reincarnation part of the Countess’ book “Old truths in a new light, or, An earnest endeavour to reconcile material science with spiritual science and with Scripture”.

[MarkD (A Whateverist, not a Christian)]

If there is more you’d like share I’ll look it over but I had been going to say a search on my Kindle (which I only use with TMWT) for that author turned only a mention in the bibliography but nothing quoted in the text that I could find. So I was going ask for your source but the truth is I’m very unlikely to pursue anything now. I’m enjoying mor good lit and very content with that.