1+1=3?
Craftsmanship is more than just a labour of love, it is the beauty of mathematics brought to life in visible, manifested, and interactive form. But craftsmanship is also more than handiwork, it exists in thought invested, which though often visible might not be apparent to every eye. This thought, on the cusp of tangible and intangible, is where the sacred beauty of mathematics rests. Beauty is something so infinitely complex and impossible to quantify, and yet, in the same vein, it is something so simple that one can recognize it at a glance. In the paradox of simple and complex, beauty lies in a sense of completeness, not limited by subjective understandings of finished and unfinished.
Here at Lopez Contracting, it’s no secret that we have a love of beautiful mathematics. In particular, we have an affinity for recurring numbers which inform not only our craft but also our place in the cosmos. Namely, certain patterns our artistry anchors onto exist in the numbers 3, 7, 10 and 12, and the theatre that plays about between them. These numbers not only assist us in the construction of objective and universal beauty, but in fact have been revered across time and cultures as ‘perfect’ numbers, loaded with a spiritual and metaphysical significance to match their material form.
12: 12 represents both unity and diversity. Often described at the perfect number for a group, as it can be divided perfectly into subgroups of by 2, 3, 4 or 6. 12 is no stranger to significance, whether it be the 12 apostles, 12 Olympians, 12 tribes of Israel, 12 Imams or 12 petals of the heart chakra, this number is commonly seen in groupings of fluidity, which though sharing a centre, branch outwards to both diversity and inclusion.
Our philosophy of 12: Here at the shop, we keep this number at the front of our minds for product series which share a central core, and yet a fluidity of form. Take for example our ‘Optimized Space Structures’ (and do stay tuned for our related “Holy Shed!” blog). Here, 12 as a grouping concept plays an important role in how this project is able to branch out. For one, all our Optimized Space Structures share a central core, being that they are space, however, we are able to diversify them into a staggering variety of facilities. This is how these spaces becomes ‘optimized’.
10: 10 represents perfection and completion, as a conjugation of 4, representing the sacred purity of creation, and 6 which represents profanity of material or the agency of humankind. As such, 10 represents the final perfection and completion of a process, as well as the intersection of divine and profane in the totality of creation. Across cultures in the world, 10 represents a process towards perfect completion, be it the 10 biblical elements of creation, 10 Avatars, 10 Gurus, 10 commandments, or the ten nodes of the tree of life. The theme of ten is not only gradual perfection, but in the grand scheme of things, natural order from chaos. Afterall, when it comes to our handicrafts; we have ten fingers to work with!
In the words of the philosopher Aetius: “Ten is the very nature of number. All Greeks and all barbarians alike count up to ten, and having reached ten revert again to the unity. And again, Pythagoras maintains, the power of the number 10 lies in the number 4, the tetrad. This is the reason: If one starts at the unit (1) and adds the successive number up to 4, one will make up the number 10 (1 + 2 + 3 + 4 = 10). And if one exceeds the tetrad, one will exceed 10 too…. So that the number by the unit resides in the number 10, but potentially in the number 4.”
Our philosophy of 10: 10 is the process by which we perfect our product, with each iteration allowing us to not only foresee deficiencies in our process, but also improve upon them for the next in our iterations of 10. This process produces perfection, with a by-product of creative joy, experience and increasing efficiency.
Take for example our furnishings, developed for our own hands and hearts in iterations and sets of 10, such that the 11th, which is for the client, is the most aesthetically and effectively constructed, and we are left not only with a reminder of our process, but rather a blueprint of how to construct 11th iterations in equal perfection time and again. For us, the completion of 10 is akin to learning how to ride a bike for the first time- along the way it becomes eternal.
7: 7 represents transcendence from the profane and towards the divine. 7 can be divided into 3, 1 and 2 or it can be divided into 2, 2, 2 and 1. In either case, there will 1 which stands alone. Far from this being an asymmetrical imperfection, it in fact highlights the importance of the outlier and solo-standing 1. 1 essentially becomes the perfect centre for a symmetrical arrangement. this way, though the 1 has the least numeric value, it has the most emphasis. As such, 7 represents one amongst many which has transcended to a higher station. This is seen again across cultures across the world, most notably in our seven-day week which emphasizes the seventh day as a day of rest and reflection, thus completing a cycle to both perfection and sustainable continuance. It is for this reason that 7 is often used in biblical literature to describe the most high, who is alone in their power and like.
The number 7 displays its excellence in utility, structural strength and beauty best in expanded upon in sacred geometry. It makes complete sense that these perfect shapes were so venerated and used to represent a transcended divine through mystic mathematics and sacred geometry through recordable history, such as the seven circles within the centre of Metatron’s cube, or the seven lower nodes of ‘tree of life’ in Kabbalah, which transcend to the top three nodes of divinity (bringing one to the 10 of perfect completion. It’s no wonder the number 7 is used so often in the cultures of the world to denote transcendence and divinity, be it the 7 sages, 7 maidens or 7 stars or the 7th chakra of highest enlightenment which commonly appear across diverse beliefs. In the words of Maurice Maeterlinck, author of The Life of The Bee (1924):
“if intelligence from another world were to descend and ask of the earth the most perfect creation, I would offer the humble comb of honey.”
Our philosophy of 7: 7 is a number replete in both world culture as well as nature, and manifests in both as sacred geometry. In our structures especially, 7 manifests most in the third factor of Vitruvius triad, namely in firmitas, or durability. As it were, seven is the number of spheres that would fit perfectly in a hexagon. Sphere packing, in particular, leads us to a honeycomb design which in both nature and the wider eye of society represents the most structural, most aesthetic and most space efficient cell-perforated structure. Given the repletion of both spheres and hexagons in the structural integrity of our products and projects, the number 7 is naturally the central concept.
7 as a central concept is more than just metaphoric, it is literally manifested best in emphasising the central circle within the sphere-packed hexagon. This central one circle represents the transcendent 1 which we explored earlier. We try to emphasize this central circle in our structures as much as possible. Take for example our hexagonal adjustable legs, with the adjustable pole conjoining perfectly with the central circle of our hexagonal post.
3: Fittingly enough, for us 3 represents a triad of concepts: sublime fecundity, unity and balance.
For one, 3 represents a sublime fecundity, which though often unmanifested is deserving of recognition. This conception is apparent in the sacred mathematics of Pythagoreanism, and one might be aware to Pythagoras’ personal connection to 3 given his most famous theorm. Pythagoreanism states that the geometric expression of the monad is the basis from wherein we may elaborate on geometric expressions. The monad represents the incomprehensibility of perfect and divine singularity, with the circle (essentially a polygon with infinite sides) emanating from it as an extension of infinity which is bound to singularity. As in mathematics, 0.999999 (repeating infinitely) is equal to 1.
This monad can be expanded when it is mirrored into a Dyad. Where Pythagoras recognized the monad as a point of transcended, unknowable, and singular, the dyad represented this same concept manifested into a material and profane realm. In a more spiritual outlook, the monad can be seen as a geometric representation of God, or the One, whereas the dyad represents dualism, comprehensibility, or the demiurge; a force that acts from and mirrors the divine the One. It is a contemplation of perfect singularity.
This dyad becomes the basis of all geometry to follow, and as such represents an irrational yet (for us) legitimate idea: 1+1=3.
1+1=3 is of course not meant to reflect the realities of the material world, rather it is an abstract conception which acknowledges the unmanifested element in any equation. For one, even within the two central points of the dyad, there is a third element, the interaction between the two, from within which the realm of geometry may be explored. This is of course represented as the line between the two points. It can also be represented in the vesica piscis, which highlights the shared space between the spheres of both monads in the dyad.
This shape represents much more than shared space, it is the creative power of the intersection within the dyad; it represents creative agency itself. This is why this symbol is repetitively used in cultures across the world to represent fertility or birth, from which all shapes may be drafted. It is no wonder that the Pythagoreans believed 3 to be the first and eldest amongst all numbers! It is interesting to note that if 7, the number of transcendence, is subtracted from 10, the number of perception, we are left with 3- thus making it the number of material creation!
Which brings us to our second major understanding of 3. As paradoxical as it may sound, 3 also represents or at least gestures at a whole and perfect unity. Afterall, without the dyad manifesting itself into the observable plane as 3, how would we come to know the One? 3 is, as such, a manifestation of the One.
This again is an idea found across the world, especially in divine trinities that emanate from an incomprehensible singularity. Take for example the Biblical Holy Trinity, within which there is the Father, the Son, and the Holy Spirit (creative agency) which are simultaneously distinct from a singular God and yet all singularly united with God. The Holy Trinity of Hinduism as well encompasses Brahma, Vishnu and Shiva, which distinct from one another, are contemplations on the perfect singularity. In Celtic shamanism, the number 3 had a similar meaning, the material element necessary for the union of the manifest and unmanifested. For the basis of every ritual, which aims to bridge the material and spiritual world, a shaman was required to bridge and hence conjoin both realms, being the third element necessary to conjoin into unity.
A three-dimensional object with three spokes were to hover and rotate within a 2D plane, it might for a resident of the 2D plane appear to be three different objects; however, this is because the resident cannot comprehend the 3-dimensional reality. Similarly, the nature of the three to the One is, as per the Pythagoreans, incomprehensible.
Finally, 3 represents balance. Both in a structural sense (think of a pyramid or tripod) but also philosophically, which serves as a perfect segway to…
Our philosophy of 3: 3 is present within a triad of triads, each represented by a symbol:
- ༜ Truth, Love, Beauty
- Φ Science, Religion, Art
- ☉ Mind, Heart, Soul
From reading this arrangement of triads horizontally instead of vertically, we come upon a related yet distinct triad of triads.
- △ Truth, Science, Mind
- △ Love, Religion, Heart
- △ Beauty, Art, Soul
These nine sets can be condescended into the Vitruvian triad, which is at the cornerstone of our work under the title the ‘Triple Crown’, namely, Firmitas, Utilitas, Venustas; or Durability, Utility and Beauty. These three we aim to balance perfectly in each of our products.
As for the transcendent idea of 1+1=3, the third in this equation is the unmanifested fecundity or that is invisible yet inseparable from the creative process. In essence, in our day to day work it translates to beauty in simplicity. For example, we’ve always maintained that there is a perfect synergy between a crew of two which leads to a burst of efficiency. This synergy does not exist in a crew of three, wherein clutter can actually decrease the efficiency of each member. Having a crew of two thus is often better than three, as whilst three do the work of two, two can do the work of three. Therefore, 1+1=3!
