Wonder Hunter: The Flatland Story (6,000 characters)

Wonder Hunter: The Flatland Story

My name is Toshiro Tokoshie. I am a "Wonder Hunter." The world is overflowing with wonders, and I collect them. Why do I collect wonders? Because it seems to me that there is a solid reason behind the wonders of the world, and I am searching for that reason. But perhaps the most wondrous thing of all is that everyone else doesn't think these wonders are wondrous at all. That might be the biggest reason why I became a Wonder Hunter.

Today, we begin with the world of "Flatland," spun by Edwin A. Abbott in 1884.

1. The Two-Dimensional World: The Social Cage Hidden in Fable

"Flatland" is a completely flat, two-dimensional world that only has length and width. It is inhabited by shapes like triangles and squares, and the protagonist is a square named "A. Square." For them, the world has no up or down, and everything looks like nothing more than a "line."
One day, an incident occurs in Flatland. A three-dimensional "sphere," like us, passes through their world. For A. Square, it was an unbelievable sight. A "point" suddenly appeared in empty space, expanded into a "circle," then shrank back into a "point" and vanished. To A. Square, it could only be seen as a "miracle." However, even when he spoke of it, the other inhabitants could not understand. Given their common sense, it was impossible for them to comprehend a higher-dimensional world they knew nothing about.
But there is another reason why this fable is known to the world. In Flatland, the more corners you have, the higher your social status, and women are treated as mere "lines." It is depicted as a rigid society, like one trapped in a cage, that refuses to accept any new ideas. Yes, through this world, the author Abbott sharply satirized the Victorian society of his time. This is the first secret. What this fable confronts us with is the danger of believing that "the world we see is everything." Behind the world we perceive, there may be social rules and prejudices lurking like shadows that we are unaware of.
And then, I noticed another wonder. While A. Square's "surprise" at this time should indicate the limits of their perception, a strange contradiction lurks within it. The author Abbott provided "fog" and "touch" as ways for the inhabitants to identify each other's shapes. But if you think about it calmly, isn't the very act of a two-dimensional inhabitant touching corners to verify them implicitly premised on the three-dimensional freedom of "height" from looking down from above? If they could only perceive the world purely as "lines," even if a circle approached, all they would see is a change in the length of a line segment. If that were the case, it wouldn't be strange for the passing circle to appear as a lens-shaped image with pointed ends—like a Vesica Piscis. Nevertheless, Abbott insisted on depicting it as a "sphere." It is here that Abbott's own unconsciousness, which slipped into the depths of the fable, lies. The "perspective of height that captures the whole picture," which cannot be reached by two-dimensional logic, must have naturally entered the author's imagination. To me, this looks like the sprout of what I will explain later as "emergent perception." By combining limited one-dimensional information (changes in line length) over time, the brain arbitrarily constructs higher-dimensional images (surfaces or solids). I feel that this "unconscious emergence" is the true theme hidden in "Flatland."
From limited perception of low-dimensional information (lines), the brain recognizes high-dimensional images (surfaces) based on changes over time. It seemed to me that this "unconscious emergence" is the true theme hidden in Flatland.

2. The Three-Dimensional World: The Cage of Assumptions Hidden in Perception

The way the inhabitants of Flatland live might be a mirror reflecting our own world.
From here on, I will talk about my own hypothesis, which combines several established theories.
We can perceive length, width, and height. Therefore, we must think of ourselves as three-dimensional beings who can freely move through three-dimensional space. But is that really the case? What we call "height" is at most about 100 kilometers, the Earth's atmosphere. Compared to the observable universe's diameter of about 93 billion light-years, the ratio is approximately 10 to the power of minus 22. Our freedom in the height direction is negligible on a cosmic scale.
In other words, we are too limited to be called three-dimensional beings. I have decided to call this state "2.1-dimensional beings." Though, I think it would be more appropriate to call us "2.000...1-dimensional beings."
Certainly, we have the function of stereoscopic vision through both eyes. However, that "true 3D sense" works accurately only at close range, and it weakens rapidly as the distance increases. When it comes to distant scenery, the brain is merely estimating depth from various clues, as if deciphering a painting. For example, it reconstructs a sense of depth from planar information using painting rules such as "things further away are smaller and look hazier." Distant mountains and stars actually only appear on our retinas as two-dimensional images. The fact that distant views feel three-dimensional is nothing more than the brain supplementing three-dimensional images based on past experience and learning. This state could be grasped as an analogy for the Indian philosophical concept of "Maya," or illusion. This Maya is a philosophical concept where the "illusion" that had its prototype in ancient Upanishadic philosophy was completed by Shankara as a rigorous system that regards the world as a projection of ignorance.
There are two interesting pieces of circumstantial evidence for my hypothesis that "we live in a substantially flat world."
One is the "Flat Earth theory."
I have no intention of questioning the truth or falsehood of the claim that the Earth is a flat disk. What is noteworthy is that there is a strange similarity between the "physically flat world" they claim and the "substantially flat world" I propose.
The second is a product of human intelligence, "non-Euclidean geometry."
Non-Euclidean geometry deals with curved space itself (spherical, hyperbolic). Its essence is not flattening, but for convenience, it is sometimes mapped and expressed in a planar model. In other words, it means there are times when it resembles the workings of our brains.

3. The Third Inference Method: The Cage of Thought

Here, let's look at the evolution of the logic of knowledge, which is also our "tool of thought," in three stages.
The first stageis the "deductive method" created by Aristotle of ancient Greece, which sometimes becomes a cage that binds thought. Let's explain that case with this beautiful syllogism that humanity has long held as truth.

• Major premise: All people die if their heart function stops permanently.

• Minor premise: This person's heart stopped permanently due to an extraction surgery.

• Conclusion: Therefore, this person has died.

There seems to be no logic more certain than this, and I think it was difficult to escape from this cage of logic for a long time.
The second stageis the "inductive method" presented by Francis Bacon. He pointed out that there is a blind spot of "time" and "change" in Aristotle's static logic. In the deductive method, if the premise is correct, the conclusion is also correct. However, there is no guarantee that the premise will hold true forever. Bacon noticed this blind spot and advocated "observe and experiment" as a countermeasure. His method was called the "inductive method" as a dynamic attempt to derive general rules from past experience and test them in the future.
Once, the premise that "if the heart stops, a person dies" was considered an almost unshakable truth. However, in the latter half of the 20th century, with the progress of medicine, heart transplantation (1967) and artificial heart-lung technology were established, and furthermore, with the development of circulatory assist devices and artificial hearts, this premise changed to a conditional one. In other words, it became possible to say, "Even if your heart stops, a person does not necessarily die immediately." Of course, this is a metaphor and does not deny Aristotle's classical logic itself. However, through such cases, I think we can confirm that observation and experimentation by the inductive method can relativize the major premise of the deductive method and break its cage.
But even such deductive and inductive methods still have a formidable cage of "being obsessed with established facts." In other words, they are not good at dealing with the future that has not yet appeared. Therefore, in front of unconventional geniuses who changed the world, such as Copernicus and Einstein, it stood as a large cage of fixed ideas and preconceptions. And there is a history that minority geniuses have rewritten the world only when they could refute the common sense and established facts of their time.
Here is where thethird stageof inference method, abduction, becomes necessary.
Abduction is an inference method that provides a tentative explanation for unknown phenomena or contradictions by setting up a "leaping hypothesis" such as "If this were the case, couldn't everything be explained?"
While deduction derives a conclusion from a premise and induction derives a law from observation, abduction goes back and forth between the two. In other words, according to the words of its proponent, Charles Sanders Peirce himself, he calls this method both "abduction" and "retroduction," explaining it as a cycle of observation -> hypothesis (i.e., abduction) -> derivation of results (i.e., deduction) -> verification (i.e., induction).
And the important point is the "leaping hypothesis." This can be the key to breaking through the cage of "being obsessed with established facts" that deduction and induction alone cannot, and in fact, it seems that the geniuses in history have broken through that cage in that way.
P.D. Ouspensky states in "Tertium Organum" that "irrational intuition leads to higher truth as a 'psychological method'." His position is that it is necessary to step into a realm that cannot be captured by analysis through reason alone with an intuitive leap. I think this hits the essence of abduction.
Presented as an example of this is the proposition "A is A, and also non-A." This is an attempt to grasp a relationship that is considered a contradiction in normal logic as something that can be established simultaneously from a higher perspective.
For example, let's think about the word "love." In modern Japanese, "love" is often spoken of as a noble emotion of caring for others. On the other hand, in Buddhist thought, for example, the "love" in the Twelve Links of Dependent Origination means "attachment" and is said to be the cause of life's suffering.
This is just a trivial example of the difference in words between thoughts with different histories and backgrounds, but I introduced it as proof that the proposition "A is A, and also non-A" can actually exist.
But even if you take just one such example, isn't there room to accept the fact that the world is full of this kind of fluctuation of words? In other words, isn't it enough to cool down a bit and overturn the cage of assumptions, like reflexively imposing fixed ideas that "A=not A is illogical"? And surely, I don't think the essence of true "irrational intuition" is at this level.
And finally, let me introduce a theory of modern physics called the "holographic principle." This is a hypothesis of "encoding onto a boundary surface" motivated by research on black holes. While the generalization to our universe and "gravity = origin of quantum entanglement" are still at the hypothesis stage under active research, the revolutionary idea in theoretical physics that, limited to specific spacetime, "the world of gravity in the universe" and "the world of particles at the edge of the universe" havethe same information like a mirroris famous. The radical point of this theory is that even gravity is an emergent phenomenon that "comes into being as a result" from lower-dimensional laws.
And don't you think the holographic principle, which says "gravity is not a representative force of the universe as everyone thought until now, but an emergent phenomenon," is exactly abduction?
I realized that the wonder of the 2.1-dimensional being I explained earlier has the same structure as this theory. That's why I borrowed the name "emergence" from the holographic principle and coined the term "emergent perception." Just as physics explores the possibility that a three-dimensional universe is born from two-dimensional information, my hypothesis considers that our three-dimensional spatial recognition is born from one-dimensional or two-dimensional sensory data. But this doesn't mean we are lamenting that we cannot become three-dimensional beings. For example, what if we obtained something like a soul or a spirit body, were released from the surface of the Earth, and could move freely through the solar system and the galaxy? Don't you think that is when we can confidently assert, "We are three-dimensional beings"?
And this is the abduction I will explore from now on.
The three cages this story taught us—social prejudice, the Maya of perception, and the spell of thought—still surround us even now. That is why I continue the adventure of stepping beyond those cages.

The ancient map of knowledge referenced in this adventure

I will record the great adventurers of knowledge who served as my guideposts in this hunt, and the maps (literature) they left behind. This list itself might become an entrance to a new wonder.

• Fable of Dimensions: Abbott, E.A. (1884). Flatland: A Romance of Many Dimensions.

• First Tool: Aristotle. (c. 4th century BCE). Organon.

• Second Tool: Bacon, F. (1620). Novum Organum.

• Suggestion for a Third Organon: Ouspensky, P.D. (1912). Tertium Organum.

• Proponent of Abduction: Peirce, C.S. (1903). Pragmatism and Abduction.

• Explorer of Paradigm Shifts: Kuhn, T.S. (1962). The Structure of Scientific Revolutions.

• Pioneer of the Holographic Principle: 't Hooft, G. (1993); Susskind, L. (1995).

• Concept of Illusion (Maya): Rigveda; Upanishad; Śaṅkara.

• Paradox of Love: Plato. (c. 360 BCE). Symposium; Saṃyutta Nikāya.

• AdS/CFT Correspondence: Maldacena, J. (1998).

[Note]
This story was created as an homage, out of respect, and inspired by the following books:

1) In Search of the Miraculous: Fragments of an Unknown Teaching
2) Tertium Organum: The Third Canon of Thought, A Key to the Enigmas of the World
3) A New Model of the Universe
P.D. Ouspensky

Flatland: A Romance of Many Dimensions (Blue Backs 315)
Edwin A. Abbott

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