Have you ever stopped to consider mathematical symbols as artefacts of creative design?
I hadn’t until I read about the history of the infinity symbol. The brightest minds had spent centuries trying to grapple with the concept of infinity. Long, convoluted monographs deliberated and mused over it. The abstract nature of the concept evaded the limited confines of language. And then, in his Treatise on the Comic Sections in 1655, the English mathematician John Wallis nailed it. He introduced a symbol which, with its endless shape, is so obviously and simplistically related to the concept that every word fell away, shed like useless layers of dead skin. This symbol, and mathematical signs in general are our only form of established universal language (emojis are nipping at the heals of maths however, and we might be on the verge of a new linguistic epoch with smiling poop faces and unicorns).
This is an impressive feat of design. If you create something that only a handful of people can understand or relate to, thats great, but the power of this expression is weak in comparison to that which anyone can readily comprehend. How you ‘interpret’ something is a distinct matter, not in the control of the designer, and an endless process of renewal. Design can, however, reach towards the lofty heights of perfection. In its most simple form, the infinity symbol presents something complete. Finished. A truth.
It would appear as though in design - and perhaps in mathematics too - the more simplistic and condensed the expression is, the more genius. Wallis’s genius, no doubt, involved a process of refinement, discarding and extraction. Draft after draft after draft, each one becoming more concise and concentrated. Eventually, the creation becomes so refined and clear in its meaning that it exudes something we may recognise as elegance.
There are many crafts and pursuits that we may consider as resonant with this pattern of refinement, reduction and simplification - poetry, dance, architecture and music, may be others. What about philosophy, or even law? Are many of our meaningful pursuits intended towards a pattern of iteration and condensation and simplification until we finally meet a point of essence, that can no longer be reduced. Is this the path towards all truth?
I recall a conversation I had with a fellow philosophy graduate student a few years back. I studied philosophy as a formal subject, and in conjunction with other related subjects throughout my time at Rhodes University. I kept at it not because I was good at it, but because I believed it was good for me. I struggle to express my ideas concisely. I can even be verbose, endlessly weaving more and more flowery and complex variations around a singular point. Philosophy calls upon you to say precisely what you mean. Every word is weighted, unpacked, considered as having the potential to mould and shift the meaning of the text. I found no other subject challenged and improved my writing and argumentation skills more.
This philosophy friend and I were chatting about the power tight, condensed articulation. His second major - and now career - was law. He explained that in legal quarters simplicity in your argumentation is highly valued. He admired a particular advocate that could slice through a complex case with razor sharp accuracy, chucking out everything but the most profound and expedient elements. Arguing against that must be exceptionally difficult. Its so simple, and therefore tight; its impenetrable.
But then he said suggested something I never forgot: although this is impressive and often successful, he doesn’t aspire to think in the same way because ‘its brutal’. He felt that the human ‘stuff’ gets shoved aside as superfluous, and that this advocate was a champion of logic, legal structure and argumentation, rather than to human justice. Messiness, elaboration, and contradiction is also where truth can be discovered. It can be just as important, if not more, to understanding the essence of a problem, concept or scenario. In short, it shouldn’t always be shaved off in the pursuit of simplistic elegance.
I should add here that the type of Philosophy we were offered was every bit Eurocentric and dominated by towering male figures of Western rationality. In fact, I remember some lectures on David Hume being reduced to a series of simple mathematic equations (I was most shoddy at Epistemology). This very fine lawyer and friend I speak of is, ironically, rather good at this form of thinking and he flourished. Nevertheless, he was able to acknowledge that allowing yourself to entertain and not lose sight of the convoluted and messy elements of a concept/scenario can be vital. This is the type of thinking that makes your head hurt. It frustrates you, bewilders you and drains you. Its often confounding, and the illogical, multidimensional nature of it is a central part of its very essence. It defies reduction and elegant design, because then it would become something else entirely.
Subaltern historian, Dipesh Chakrabarty speaks to this very issue in his salient work, Provincializing Europe. Chakrabarty argues that the very framework of Western rational thought (giving rise to the statutes of modern democracy and statehood) was a brutal imposition on the reality of South Asia. Imagine a street in downtown Delhi. At any moment there are multiple time frames, levels of economic development, legal practices, religious and spiritual dimensions, histories, linguistic frameworks, ontologies and ways of being colliding and fusing and separating and fluxing. It is quite literally a kaleidoscope of irrationality and this is its truth. It cannot be elegant, simple and reduced. Perhaps the same can be said for the streets of Kampala, Lagos and Cairo? These are ‘realities’ Wallis would have, no doubt, never stopped to contemplate from his Oxbridge office.
In what ways have the ideals of Western dominant culture shifted to include this kind of tenuous multidimensional reality? Is simplistic, impenetrable design - like the infinity sign - really the ultimate end of a creative process in the twenty-first century? Should this still be the ultimate goal? How can we define a new elegance in a new epoch of global power?
To me, when create, we are immersed in a seed of an idea that expands and contracts, pregnant with messy elaboration at one stage, and defined in its raw bones at others? Neither stage is an end, but rather a mutually fertile start. The truth is in the journeying.
Oh damn - that sounds like a convoluted description of infinity!