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I did not know that I had a favourite ant species until I learnt about Cataglyphis fortis[1]. Here is an excerpt from a research paper that talks about it navigation abilities[2]:

Foraging desert ants, Cataglyphis fortis, continually keep track of their own posotions relative to home— i.e., integrate their tortuous outbound routes and return home along straight (inbound) routes.

This is the sort of navigation strategy a human child might invent: Keep a track of how far you walked and how much you turned. Then to get back home you can either reverse all your steps OR calculate the home-vector and possibly find a shorter path home.

How would you (a human) track steps and direction? I'd probably just count the number of steps I took and use relative markers in my environment to keep track of directions (ex. "Took 100 steps after exiting the Student center then took a left-turn from the Portman sculpture to reach my favourite food-truck").

What about Cataglyphis fortis? Turns out they can do something similar and have a better mechanism for direction:

1. Legs act like an odometer to measure distance
2. The Sun as a compass to measure the direction after every turn.

What’s truly impressive is that these ants have enough intelligence to perform path integration and calculate an approximate home-vector. The ants can see a lot more of the world that one might think.

This sent me down a rabbit hole and I started researching animal perception and how they see the world. Here are my top three picks:

1. Sound: Bats construct a 3D image of the world using echo-location [3]
2. Sight: Mantis shrimp have special photoreceptor classes that produce a color/polarization not necessarily high in spatial detail but far more rich compared to that of humans
3. Touch: Star-nosed mole uses the “star” shaped nose to sample the soil 10–15 touches/sec; prey can be identified and eaten in ~120 ms

Together, these creatures remind us that the world is never given ‘as it is,’ but only through the sensory logics each species can deploy. Organisms perceive the world in terms of action possibilities (climbable, graspable, edible), not neutral measurements. For me this raises several questions: what is the internal world model of the ant? How do the ants experience the world? Could humans be the ants for some other species? Turns out there is an entire field dedicated to answering these questions: Biosemiotics [4]. Biosemiotics is the study of how living beings interpret signs from their environment, effectively treating perception as a form of meaning-making.

The world’s superstructure is embarrassingly larger than any one creature can grasp. Each organism samples it through a narrow species-tuned aperture carved by sensors, effectors, and needs. What I call "reality" is this negotiated slice. As our aperture widens or sharpens, our internal model of the superstructure improves. In Biosemiotics literature, we find the word "Umwelt", coined by Jakob von Uexküll for a species-shaped slice of reality, that I will use throughout this essay to refer to this aperture [5]. From the wiki for the lazy:

He argued that organisms experience life in terms of species-specific, spatio-temporal, "self-in-world" subjective reference frames that he called Umwelt

I will use the word "Umwelt" in this essay although across traditions, the insight repeats: what we see is a shadow, an appearance, a species-shaped slice.

1. Māyā (माया)
2. Plato’s Cave
3. Kant’s Phenomena vs Noumena
4. What's It Like to Be a Bat? by Thomas Nagel (perhaps my fav)

The core thesis of this essay is that meaning is actively constructed through the limited aperture of a creature i.e. Umwelt. Evolution rewards creatures that do not merely accept their partial slice of the superstructure, but continuously estimate, refine, and widen it. Every model we build is a provisional bridge between the incomprehensible whole and the tiny piece we can grasp. The act of building these bridges is where meaning itself arises.

A transform is nothing mysterious: it is simply a systematic way of reshaping a problem so that structure becomes visible.

At its simplest, a linear transform is just a rule that maps vectors to other vectors:

where A is a matrix. You can get real creative with what goes on in A and it becomes super-duper fun. For example if I define A as follows, I can perform a rotation in plane by an angle of $\theta$:

To turn a square into a diamond, i.e. rotate by 45${}^{\circ }$ ($\theta =\pi /4$):

Scaling, and shearing are other such familiar examples.

Imagine a Mr. Rick Tangle, a primitive bootstrapped intelligence that only knew about squares. For several years, Rick thought that squares are the only shapes that exist. But one day the shape-gods reveal a diamond to him. Rick spends a few more years thinking that the world now has two shapes (square and a diamond) then the shape gods decide to give him a little more cognitive affordances and he discovers the linear transform. Now, Rick gets creative and start trying out different values for $A$ and suddenly, he discovers the trapezoid! Rick starts getting a bit cocky and now thinks he discovered the trapezoid before the shape gods. Rick then get sent to the shape-hell.

This might seem very silly to you. You'd be tempted to think that "any intelligence that sees a square and a diamond would OBVIOUSLY know that square and the diamond are the same FUCKING THING!!! ITS A ROTATION! EVERYONE KNOWS ROTATION!". But trust me, the human brain has, for a long time, lacked the ability to clearly perceive connections between seemingly unrelated manifolds of the superstructure.

One of the most profound instances of this is the Fourier series, introduced by Joseph Fourier in the early 19th century to study the flow of heat. Fourier claimed that any periodic function could be decomposed into a sum of sines and cosines.

Mathematically, for a periodic function f(t) with a period of 2π:

with coefficients

This was a radical shift. What looked like an opaque function $f(t)$ in the “time domain” could be transformed into a transparent spectrum of frequencies $\{c_n\}$ in the “frequency domain.” In other words, Fourier showed that complex signals could be understood by breaking them down into their underlying frequency components. The move from $f(t)$ to $\{c_n\}$ is one such analogy for how humans expand their aperture.

Another, older example is the invention of logarithms by John Napier in 1614. We did not have calculators back then and all calculations were done by hand and of course were prone to errors. Especially multiplication and division. Now look at this beauty:

With this transform, astronomers could handle massive planetary tables that would otherwise have been intractable. Here, again, the superstructure (planetary motion) did not change; but the human aperture widened. The human Umwelt of arithmetic was restructured by a transform into one more capable of grappling with the cosmos.

What Fourier and Napier achieved mathematically mirrors what biology achieves evolutionarily: the active construction of better estimators. We begin with a coarse function $F$, apply a transform, and emerge with $F^{\prime }$, a model closer to the truth.

The ant applies path integration to refine its sketch of the desert. The human applies Fourier analysis to refine its sketch of sound. Both are engaged in the same act of updating an Umwelt.

This gives us a generalizable pattern. Our perception is an estimate. Our intelligence is a transform engine. And the history of science is a cumulative widening of the aperture through transforms that map messy phenomena into spaces where coherence appears. Also we don't end up in shape-hell like Rick.

In the pervious section, we established that mathematical transforms are effectively a mechanism to widen our Umwelt. We engage our evolved reasoning abilities to invent new tools and discover new math. The brain transforms fragments of sensory input into coherent expectations. What we experience as “reality” is not raw data but the brain’s provisional world model. However, humans invented (or discovered?) math and the complex information tooling AFTER evolving the intelligence that we have now. Wait... But how did we even get here?

I believe that over the course of a few million years, the human brain evolved complex emotions as a reward mechanism for genes that produce higher pattern matching and complex reasoning in humans. The traces of these reward signals are still around: joy and humor as internal reward signals, guiding the genetic search through the vast fitness landscape of possible world models.

Let's try to deduce the reward functions for an African Wildebeest. To continue survival, it's reward function needs to promote genes that produce more offsprings and more importantly, faster reflexes (i.e. short-term thinking). However, expanding the Umwelt is not a simple reflex task. It requires pattern matching across time, abstraction, and the ability to sustain inquiry into domains that do not yield immediate rewards. Evolution, in effect, faced a credit-assignment problem: how to incentivize organisms to invest energy into difficult, long-horizon reasoning when survival often depends on short-term gains. Complex emotions were the solution.

There are some similar hypothesis out there, for example the "Somatic marker hypothesis" [6]. To quote the wiki:

"Somatic markers" are feelings in the body that are associated with emotions, such as the association of rapid heartbeat with anxiety or of nausea with disgust. According to the hypothesis, somatic markers strongly influence subsequent decision-making.

Many species survive with simple reinforcement signals: hunger, fear, mating drive. But for whatever reasons humans faced selection pressures for long-term cooperation, symbolic thought, tool use, and cultural transmission. Perhaps I will research and write another essay on selection pressures on early humans. For now, let's continue with what I find funny.

I'd say that humor is what it feels like when the brain applies a transform, discovers an unexpected alignment, and for a split second glimpses more of the superstructure.

I find puns quite funny since a pun relies on two very different semantic manifolds being mapped through a phonetic transform. In math terms, this is like applying a projection: the two words are very different in the semantic domain but map closely in the phonetic domain.

Back to Mr. Rick Tangle:

But:

The brain holds both mappings at once and feels the incongruity collapse into coherence (or when my brain goes "this shit's mad funny lol").

More examples from the internet:

1. “Time flies like an arrow. Fruit flies like a banana.” (semantic vs syntactic parse)
2. “High On Potenuse" by Key & Peele

There are more mathematical transforms that you could perhaps map to humor strategies:

1. Inverse Transforms:
   1. Why don't scientists trust atoms? Because they make up everything
   2. "Georgina and Esther and Satan" by Key and Peele
2. Iterative Transforms:
   1. Any call-back humor: For example Rick Tangle going to hell referenced in section II. Im sure there are better examples out there.
   2. Again "Georgina and Esther and Satan" by Key and Peele every time they say "with my prayers" in the skit.

You no longer have to wait for the shape-gods to reveal a new shape. You can create meaning. You can create humor by applying transforms and see if you find them funny. For example, my pun-sensitive brain came up with this comic when I heard the phrase "I bid you adieu!":

Humor is just one glimpse of how complex emotions scaffold the active construction of meaning. Laughter rewards us for noticing hidden bridges between concepts, but the same architecture underlies other affective states as well. Awe, joy, sorrow, pride, even grief.

But not all expansion is real expansion. Sometimes what feels like growth is distortion. Heartbreak is the clearest example. When we fall in love, we are not only relating to another person; we are extending our Umwelt around them, weaving them into every projection of our future. The brain rewards this expansion with intense emotions such as infatuation, anticipation, joy because it believes the aperture has widened. But when the relationship shatters, so too does the world-model we built. All the dreams that seemed like expansions are revealed as distortions, and the penalty is sorrow. A crush functions in miniature the same way: we accumulate scattered traits into the fantasy of a “perfect partner,” and when someone fits enough of those traits, they suddenly snap into our internal model. The aperture feels wider, and we call it attraction. Yet as reality asserts itself, mismatches appear, and the model collapses in an instant. Sometimes the apertures are constructed quite irrationally. For example, in my early twenties, I had a crush on any woman who watched One Piece but then I got the "ick" when they ranked Naruto above One Piece. The “ick” is nothing more than our Umwelt correcting itself.

This cycle of false expansion and painful correction has been recognized across traditions. In Hindu and Buddhist texts, the practice of Vairāgya (detachment) teaches monks to visualize beauty as temporary. They are taught to imagine the young as aged, the glamorous as decaying. This is an Umwelt correction mechanism. You mihgt notice that modern support groups do for grief, what Vairāgya does for attachment. They provide a structured correction to the internal world-model, gradually aligning it back with the superstructure. In both cases, meaning is not abandoned but recalibrated. The biology that punishes heartbreak is the same biology that rewards reconstruction.

Flow is the lived proof that the Umwelt can temporarily synchronize with the superstructure. It is the state where perception, action, and meaning form a single closed loop, so tight that no energy is wasted in self-conscious correction. Psychologist Mihaly Csikszentmihalyi called this flow. I wonder if the peak flow is what Hindu mystics called it Samādhi; Sufi poets called it Fanāh. Across traditions, the insight emerges that the aperture of human awareness, usually narrow and noisy, suddenly dilates and aligns with the larger structure in which it is embedded. I want to maximise this experience.

Art is one of the privileged doors into this state. Lately I've been studying the artwork of Yuming Li. In the painting above, the figure is both there and not-there. The face is partially occluded, the outlines dissolve into fields of color, and the background oscillates between form and abstraction. What begins as realism gives way to impressionism, then into expressionism. I've noticed as an artist, I find more satisfaction in movement from accurate representation to the creative re-structuring of perception itself. Perhaps that is because each stroke tests and corrects the Umwelt, each color chosen widens the aperture. I wield the powers of the shape-gods.

Flow is peak reward, but it is not a hack. It is expensive. It requires skill, attention, and years of slow Umwelt-expansion before the aperture is large enough to sustain it. Going from drawing realistically, then breaking realism to invent new styles feels like transcendence. The flow state is the active construction of meaning at full stride and perhaps our best shot at seeing the superstructure.

And if there must be a conclusion, let it be this: we have to resist becoming mere consumers of meaning. The biology of joy and sorrow was given to us to create meaning over millions of years. We honor that inheritance by painting, composing, racing, building, writing by leaning into the aperture and stretching it wide. The desert ants also have some share of this inheritance. Perhaps, in its own way, Cataglyphis fortis was truly happy the moment it stitched its crooked path into a perfect home-vector. And maybe that is all any of us are doing.

Critique

The essay is open for critique. Drop me an email at shivbhosale97@gmail.com with subject: "essay critique" and I will add your points in this section. Also please point out any inaccuracies / mistakes in the essay.

Footnotes:

1. https://en.wikipedia.org/wiki/Cataglyphis_fortis
2. https://www.pnas.org/doi/10.1073/pnas.85.14.5287
3. https://pmc.ncbi.nlm.nih.gov/articles/PMC2927269
4. https://en.wikipedia.org/wiki/Biosemiotics
5. https://en.wikipedia.org/wiki/Jakob_Johann_von_Uexk%C3%BCll
6. https://en.wikipedia.org/wiki/Somatic_marker_hypothesis