Edwin Abbot, English schoolmaster and theologian is best known for his 1884 sci-fi novella, ‘Flatland’. Flatland tells the story of a two-dimensional world inhabited by two dimensional shapes which are sentient beings, like us three dimensional beings in our three-dimensional world. A square called A, who is the protagonist of the story happens to meet a sentient one-dimensional, point ‘Monarch’ and a three-dimensional sphere.
The one-dimensional point ‘monarch’ is the king of its world, as only a single point can exist in one dimension. Its inability to conceive of anything apart from itself, frustrates the square, as it tries to convince it of higher dimensions. The square is terrified by the sentient sphere, as it itself cannot imagine, or conceive of a third dimension. The story unfolds as a social satire, but what is pertinent to us is the question of how the sphere would have appeared to this square, or how the point monarch would have viewed this square.
A sentient square would perceive only front, back, right and left directions. It could never view a sphere because it could not conceive the third, up and down direction. It could not perceive the depth of the sphere, and just see lengths of its cross-sections, as it passed through the 2D plane which the author calls the ‘flatland’.
Is that difficult to imagine? Make a sphere move through a piece of paper in your mind. You will see innumerable lines of various lengths, first increasing, then decreasing, if you were a flatlander. If the sphere never passed through the flatland, never INTERACTED with it, the two-dimensional flatlander will never know of its existence.
These lines of various lengths appearing and disappearing would confuse the flatlander, would they not? It would think they were ‘many different things’ showing up on its land and disappearing. Now imagine you, a 3D being passed through this flatland, trying to talk to this sentient flatlander. It would hear your voice, and would only see innumerable lines, their lengths dependent on how you were crossing through the flatland. What a fright that would be for this befuddled two dimensional being! Say you wanted to express to it what the third dimension is, would you be able to? How could you explain the concept of depth to one whose cognition can only perceive left-right and forward-backward? Could you say look ‘up’ or ‘down’? No.
As you moved through this plane, it would believe many different things were interacting with it. It would create false ontological excesses.
Suppose now you visited this flatland every day, and spoke to more flatlanders to teach them about the third dimension. You might move in different ways in your crossing, and the flatlanders would see a confusing excess of lines, which could differ every day. Not only will the flatlanders create false ontological excesses, they would have produced tremendous relativity too, because everybody may happen to see different lengths.
Say you taught them about the third dimension and convinced them you are just a single entity. However, if they could not see you, they would try to construct, with their plethora of lines, many types of 3D entities. They will thus have created relativity, whereas your reality is absolute.
Remember the stunning, haunting portrayal of a tesseract, a four-dimensional cube in the movie ‘Interstellar’? The fourth dimension was ‘time’ if you remember, and three-dimensional cross sections of this tesseract were single frames or moments in time.
Imagine if the three-dimensional objects in our world were cross sections, mere shadows of higher dimensional objects? Why not? You could observe various shadows of the same object and assuming them to be different things, just like a flatlander. Not only could you be creating ontological excesses, but also producing relativism where there was none.
It is possible.
Plato sought to describe a similar, although a more philosophical idea, with his analogy of the ‘cave’. This cave metaphor expresses the ignorance of humans, when they make false assumptions about existence because of their limited viewpoints. In a thought experiment , Plato talks of a cave where people live chained, facing a wall illuminated by fire. The inhabitants can thus only see shadows of people who pass by, outside the cave. They make conclusions about the outside world only by its shadows. One of them happens to escape, and having seen outside reality for the first time, rushes in to tell the remaining of it wonders and free them. However, these men do not believe him, and declaring him mad refuse to leave the cave. So deeply entrenched are they in the familiarity of their ‘known world’, that they cannot and do not want to believe in a different reality.
Existence of hyper-dimensions
String theorists have come at a roadblock with the eerie problem of the eight extra dimensions in nature. String theory proposes that at their deepest levels, forces and particles are tiny vibrating strings of energy. These strings vibrate at different frequencies to produce variegated notes, as in a guitar. These distinct, varying frequencies give particles and forces their unique properties. This theory is now the best contender for that elusive ‘Grand Unifying Theory’, as it creates the bridge between the non-reconcilable properties of the micro and the macro world. It is an elegant mathematical model which could explain, at least on paper, the quantum smallness of the singularity of a super-massive blackhole. For the beautiful equations of string-theory to hold, they must consider eleven dimensions of nature, eight more than the three we humans know of. Scientists cannot detect these extra dimensions, as they are curled up tiny, a phenomenon they call ‘compacture’. It will not serve us to examine ‘compacture’ more that to just understand science’s inability to ‘see’ these dimensions, even with cutting edge technology.
String theorist Brian Greene says this inability is not because the sophistication of experimentation has not reached that level, but because they are beyond ordinary human cognition. They are hyper-cognitive.
This discovery of the hyper-dimensionality of existence that pops out of the state-of-the-art, pioneering physics of string theory has become official. In fact, scientists are now telling us that gravity in three dimensions may be electromagnetism in four. Meaning, considering just four dimensions for the sake of this argument, only the force of electromagnetism exists, but seen from our three-dimensional perspective, we observe gravity plus electromagnetism. In effect then, we have created two forces out of one, because we see shadows from different angles, in crude words, of the same single force. We have created false ontological excesses, more forces in place of the one true force. To make matters spookier, as leading scientists conjecture, all the four forces observed in nature, electromagnetism, the electro-weak, the electro-strong force and gravity could be mere shadows, cross sections of a singular hyper-dimensional force. Because of our limited cognitions, we have created many forces out of one, produced contra distinct fields of study and research, and given rise to subsequent relativity.
Brian Greene, who is also an ardent science populizer, tells us that the same elementary particle, by existing in extra, hyper dimensions seems to appear to us as an electron in one snapshot, or a proton in another. We might not realize, but the same particle was appearing to us, just like the same sphere might appear as lines of differing lengths to a flatlander. In fact, there could be a single particle, or at least lesser than what scientists have dreamed up, entire families including cousins of elementary particles! It’s like you were taking a snapshot of the same person from different angles, and declaring them to be different people.
What is the point of this ‘head-hurting’ feature of string theory, you may ask. So what?
Well , this discussion is important to shine light on two important things. First, that our cognitive apparatus defines and limits our perception of reality i.e. we can see as much as our cognitive structures will allow us. Second, relativity might arise from these perceptual limits and errors. We believe things exist, or don’t, and we support the belief by proof our cognition provide us, and proof is ample or not. It might be a deceptive red herring to conclude many things exist from the multiple shadows we see. Relativism then, my truth vs yours, might be a distraction from the actual truth.
Coming back to the mundane world from our cross-dimension trip, consider an example: A bat ‘sees’ upside down, in black and white, it uses echolocation for detection i.e. it produces sound waves which echo off objects, giving it precise estimates of distance, size and shape of prey. It can ‘detect’ objects as fine as flies or even human hair, through its echolocation skills. It has a different cognitive apparatus from us. If we could develop the cognition for echolocation, wouldn’t that be cool?
We could be super-humans of a kind. Concede just for a moment, that there is another species which possesses the cognitive structure to detect the extra dimensions, which we cannot. Why not?
A bat ‘sees different’ from me, so why cannot another specie ‘see’ the extra dimension which I cannot? Reality for this specie would differ from us then. Say ‘dark matter’ could interact with them, and they could know its properties, attributes, it would be a part of their ‘glossary’ of reality. Possible, why not? Their knowledge paradigm would be different or even more comprehensive than ours.
Does this not set you thinking? If the apparatus of our perceptions, our cognitive structures, shape what we can ‘see’ and what we cannot, how could we pass judgements on what is real or what is true? The eight extra dimensions are there, irrespective of whether we are aware of them or not. Reality confined to the limits of our perceptual abilities is not complete reality then. Could we then proclaim science will reveal all there is to know, sooner than later? We cannot declare cognitive supremacy over a bat or a hypothetical specie, with any certainty. How could we could then declare knowledge supremacy over higher realities, over higher truths?
What is true reality then? What is true knowledge?
Are there more modes of knowing, apart from the current scientific framework?
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