Beautiful ecologies

SARBAJIT GHOSH

RECURSION is beautiful. I am wandering, but recursion is something that has planted its standard of complexity on my mind. Out of a singularity emerges an infinitely branched structure,1 something that looks like the image of a root system drawn by a primitive geometer. Out of a dream, emerges my consciousness into a world of complexity. A recursive tree perhaps?

I’ve been imagining the world around me warping – rotating, shearing, transforming.2 It almost seems like the universe glows with different forms and beckons my imagination to explore these forms. Form3 can be taught they said? I disagree. Form can be felt, form can be noticed and appreciated, but form cannot be imposed, form cannot be taught. Form is vivacious, form is alive, form is beautiful. The trees around me have form. Or do they? The boundaries of the tree exist in my realm of reality, but not for the army of ants who march prodigiously up and down the bark. Not even for the layers of mycelium under the ground, forming an infinite network. Nodes and edges,4 merge into a single, living, breathing life, one that resists a predictable form, but does not resist beauty.

The fog around me is thick. I can almost smell the fuzzy5 interconnectedness around me. Fog doesn’t need characterization; an ethereal peace permeates through it. I think about how this came to be. Predictability6 coming out of randomness? Projections of a static reality that is too simple for me to grasp? I do not understand. I want to.

My wander has taken on a different shade. Or rather, the shades are mapping into an infinite secrecy. Decomposition7 is all around me, as if they were kernels,8 hidden away from my vision. Its almost as if life is a string. All of us are perturbations on that string, coming from notes of harmonic motion, measurable, and yet intangible.

The cycles of life play around me. Do I think they are circles? They could be anything.9 Any convoluted structure where every point connects to its immediate neighbours will suffice to describe this cycle. Must they be studied? I am resistant to the idea. I sigh as I sit down on a rock. I am selfish. I want to speak in the language of cycles, all so that I can feel blissfully enlightened.

Cycles are self-similar, I imagine. A fractal whose boundary morphs infinitely. These morphisms are like seductresses. Beckoning, but stepping back, never wavering in appeal or their illusiveness.10 Illusions dance about, as I begin to tune into the music around me. One cricket chirps away, to the other’s playful cacophony, without the loss of generality.11

I am overwhelmed by a dangerous desire. I want all of this. This bliss is not enough. I must conquer, and I must subjugate. A fox crosses my path, and a mynah flits about. They break me out of that headspace. I remind myself that there are infinite imaginaries within what I consider real. I cannot have that which I cannot understand, appreciate, or love.

I am accustomed to useful abstractions. I live in a world of elegance, elegance that does not allow me to play.12 Can I abstract what I feel while I wonder? An imposing logic of yes and no? Logic isn’t imposing on ecological thought. Logic is just a path. Logic can be anything we want it to be.13 A placeholder that burdens none. I choose to live by some rules. So does nature. A set of irreversible axioms. An unchanging bedrock that can never be defaced by my appreciation for complexity.

I feel like I am sinking. Appreciation for the beauty of Experience overwhelms me. I am a small insignificant organic blob, that cannot hope to understand nature, just mutely observe its beauty. I remind myself: Truth needs personality. Truth needs intensity. Truth needs someone to be brave and seek it out. Galois14 knew that didn’t he?

I observe wild rabbits prancing around. No two rabbits are the same. They probably don’t taste the same either. And they exist in their own class, merely for the enforced grouping of an equivalence class15 on individuals existing in their natural state. Is nature really that rude? Or maybe my mind is? What I know, sires what I can ever know in the future. I am changing, or maybe I’m just slithering deeper into a snake’s lair, into a chasm of narrowness.

An elephant trumpets in the distance. A sonorous sound that reverberates. I know another sound that reverberates: a gunshot. Finality. Death. Emotionless abyss. And yet, I find emotion. Ululating, happy emotions, springing out of love. I see friendships everywhere. Friendship and love transcend boundaries. Is this world connected by linkages of love we just can’t see? I can only speculate. What I know for certain: affection that is commutative can be empowering. I think Niels Henrik Abel16 would tend to agree.

A honeycomb is here somewhere. I just can’t find it. I can hear it, close. A whole society exists in it, communicating, consuming, reproducing and repeating, in a rigid class system17 that has come to be over millions of years of Nature thinking hard. I’m trying to imagine the cells of the honeycomb in my head. A perfect pattern.18 I like to think that nature arranges itself into patterns. Patterns entail both rigidity and flow. A duality19 that everyone seems to talk about these days. I think patterns exist only where we choose to see them. Patterns exist for a formalism that can agree on how fast time moves.20

I can feel my arms and legs start to tire. I have been graphing my breath inside my head.21 It’s gotten heavier over time. I do not want to stop. I am not pushing forward, like my neighbourhood stoic. I am taking it all in. The more my body wanders, my self follows suit. I wonder what the end of my walk will look like. A deeper question creeps up on me. Can this walk go on forever? A walk that embodies asymptotic brilliance.22

I watch a fly, buzzing around a flower along my path. It probes and dodges, manifesting millions of energy transformations inside it into a bungled, jittery motion. A lizard watches on, lying in wait. Statuesque. It’s tongue lashes out, and my fly is gone. Some infinities are greater than others.23

I see an old fort emerging out of the fog24 in the distance. One might marvel at this serene, unmoving, and timeless trophy of cruelty, long past its prime. I hate its authority. But that’s because I’m not nature. I don’t think I can be. Nature doesn’t hate, it adapts. It is dynamic. Its state is inconsequential to itself. It changes, and change is consequential. Authority resists change. This fort will crumble. In time it will crumble, embracing its tendency to maximize entropy.

I walk toward the streams next to the old fort. Some of them feed the moat around it. The fort is built out of recognizable shapes: a structure that has been bred by an imagination stuck inside a panopticon of regularity. Am I being too harsh? Shapes are useful. Extremely useful. They are describable. Then again, the best kinds of beauties are indescribable, incomprehensible, and vast.

I watch the water in the streams around me, tumble over rocks. I am feeling something. The only word I can associate with it is ‘indeterminism’. I know where the water flows, but I really don’t. I know how it flows, but I really don’t. I think I know how it feels between my fingers, and even that feels different at every instant. I have always marvelled at randomness. Saying that we have understood it, is a fallacious statement, that can be born only out of misplaced bravado.

I sit down beneath a tree, right next to a stream. I start to count the leaves, except now, I think of myself performing some ancient ritual of the forest. The powers that I use to count the leaves allow me to describe things. Progressions reduce counting to triviality. This is a slippery slope. I am starting to tame scale in my head. Soon, progressions25 will progress into ‘progress’26. Illusions of progress. Power is subjective. To wield it, I don’t need to speak its language, just know the abbreviations that act as its perverse levers.

The water flowing around me knows more than I ever will. Knowledge around me is ebbing and flowing; quite literally. I can feel the infinite memory of the water. Ghosts of the past. A sprite of things that have been, staring into my eyes, unblinking and real. My mind feels soft and amiable to ideas I used to scoff at. The supernatural is real. Supernaturality is interesting because it is the stochasticity27 in reality.

I can listen to myself. I can feel the life I am breathing. Creation, destruction, uncountable, unmeasurable. And yet we count. We measure. We quantify. We abstract. We do not feel. We do not breathe.28 Our shining attempts at taming the wild and unknowable, seem to be leading back to disorder. The same kind of disorder that fills a colouring book of a child who hasn’t been ‘taught’. The same of kind of disorder that I hear in the sounds of streams around me.

The streams all flow, with microscopic violence, but with emergent tranquillity. They meet and play around. Intermingle. Cut and weave through the amorphous landscape. My wander is nearing its end. The complement of the set of my ordinary senses29 tell me that something magical is nearby. Magic is revealing Herself. The playful streams are joining back into a singular gush of water. Singularity, of a different kind. A crow is sitting on a branch nearby.30 It caws at me. It understands, doesn’t it? Beauty is in recursion.

Footnotes:

1. Infinite recursive stacks. Here’s how they look: https://www.cs.cornell.edu/courses/cs3110/2012sp/lectures/lec20-master/lec20.html

2. Transformations in vector space. To learn more: https://www.math.hkust.edu.hk/~mabfchen/Math111/Week7-pdf

3. Abstract sense of form in mathematical objects.

4. Nodes and Edges are the building blocks of graph theory. More on that: https://www.maths.ed.ac.uk/~v1ranick/papers/wilsongraph.pdf

5. Fuzzy set theory. Characteristic functions of the elements of these sets show levels of membership as opposed to 0 or 1.

6. Predictability here draws from ideas in Probability Theory.

7. Decomposition of matrices in linear algebra. A visualization can be found here: https://en.wikipedia.org/wiki/Singular_value_
decomposition#/media/File:Singular-Value-Decomposition.svg

8. Nullspace of a linear transformation, used here as a metaphor for information that is not immediately apparent

9. Different geometries exist, other than the usual Euclidean geometry we are used to. Here’s a quick summary: https://sites.math.
washington.edu/~king/coursedir/m445w05/notes/non-euclidean.pdf

10. Visually, fractals look the same if we keep zooming in. Some images of the Mandelbrot set: https://stackoverflow.com/questions/53658296/mandelbrot-set-color-spectrum-suggestions

11. Without the loss of generality, is a statement used in a lot of proofs in formal mathematics, depicting a loose form of symmetry that doesn’t affect the final result.

12. Mathematicians seems to fixate on the aesthetics of their work, sometimes more than the significance of their findings. A ‘proof by beauty’, if you will.

13. There are several systems of formal logic out there, not just binary. More on this here: https://plato.stanford.edu/entries/logic-manyvalued

14. Evariste Galois, known for proving the insolvability of the quintic, abstract algebra and group theory. More on him: https://mathshistory.st-andrews.ac.uk/Biographies/Galois/

15. Equivalence classes in modular arithmetic, or more generally in abstract algebra.

16. Commutative groups are called Abelian groups, named after Niels Henrik Abel. More on commutative groups: https://brilliant.org/wiki/abelian-group/

17. Evolutionary adaptation, not imposed social organisation.

18. Regular Polygons are easy to work with. Completely unrelated structures unravel if translated to a polygon

19. Duality also seen in Boolean logic.

20. Formalism in mathematics is starting to be debated, especially among eastern philoso-phers of mathematics.

21. Mathematicians often can intuit how a function looks on a graph as second nature.

22. Formal mathematics is built on infinities. Stephen Strogatz, Infinite Powers: How Calculus Reveals the Secrets of Universe. Houghton Mifflin Harcourt, Boston, New York, 2019.

23. Infinities can cancel each other too, as seen in some applications of mathematics in theoretical physics. Read more here: https://www.cantorsparadise.com/do-mathemati
cians-get-concerned-about-how-infinities-are-dealt-in-physics-70c901e501dc

24. This emergence is akin to how a solution to an untenable problem ‘emerges’ from a fog in the head of our mathematician protagonist.

25. Arithmetic, Geometric, Harmonic and others.

26. A flawed idea of progress in modernity.

27. The proverbial error term in what we consider objective reality. More on the error term in statistics: https://www.stat.
berkeley.edu/~census/epsilon.pdf

28. Laments on the commodification of mathematics.

29. My mind’s eye.

30. Like humans, crows can imagine recursion too.