We exist in a three-dimensional space.
Within this space, we perceive three-dimensional space based solely on visual information, which are merely two-dimensional images.
This implies that we possess a three-dimensional spatial image in our minds, and we are inverse-mapping the two-dimensional visual information onto this three-dimensional spatial image.
I predict that by applying this principle, it would be possible for humans to perceive four-dimensional space. While we cannot create four-dimensional space or four-dimensional objects within the real physical space,
it is possible to simulate four-dimensional space and four-dimensional objects on a computer. If we perform a mapping from such simulated four-dimensional space to a two-dimensional plane, humans can visually grasp the information.
Then, as humans learn the behaviors and views of such four-dimensional space and four-dimensional objects, they will eventually be able to construct a four-dimensional space in their minds.
However, this is merely a possibility, and the training is expected to require a considerable amount of time.
Furthermore, even if one were to gain the ability to perceive four-dimensional space, there would be almost no situations in which that ability could be applied.
Four-Dimensional Perception by AI
On the other hand, the same can be achieved with AI. Moreover, AI might be able to leverage this four-dimensional spatial perception ability.
For example, with four-dimensional spatial perception, it would be possible to draw and understand four-dimensional graphs.
Humans can only comprehensively grasp two-dimensional planar visual information. Therefore, even if a three-dimensional graph is drawn and recognized via inverse mapping, there will be parts hidden from view.
Even with three-dimensional graphs, a significant portion becomes invisible, and with four-dimensional graphs, even more data becomes unseen.
While rotating the graph can reveal the invisible parts, it moves away from the goal of making data comprehensively and intuitively understandable at a glance.
Conversely, AI does not need to be constrained by two-dimensional planar visual information. It is possible to virtually equip AI with three-dimensional or four-dimensional spatial vision and train it.
By doing so, three-dimensional and four-dimensional graphs can be grasped comprehensively and dimensionally natively, without hidden data or the need for rotation.
Furthermore, this is not limited to four dimensions; logically, dimensions can be increased infinitely to five, ten, twenty, and beyond.
Understanding Multi-Dimensional Graphs
The ability to grasp graphs comprehensively enables, for example, trend analysis across multiple dimensions. Comparisons of magnitude and understanding of proportions can also be performed intuitively.
Furthermore, it allows for the analysis of data patterns, such as similar or analogous data. It could also lead to the discovery of regularities and laws.
This enables a deeper understanding of data beyond mere multi-dimensional data pattern matching, which existing AI excels at.
For instance, even if parts with the same pattern exist within entirely different combinations of dimensions, it would be difficult to find them through simple multi-dimensional pattern matching.
However, if data is viewed with multi-dimensional vision, similar shapes would be immediately apparent, even across different dimensional combinations.
Moreover, beyond simply utilizing the dimensional axes associated with the input data, it is possible to explore dimensional structures that facilitate data understanding by enlarging or reducing specific axes, taking logarithms, or mapping multiple axes to a different set of axes of the same number without reducing dimensions.
Thus, training multi-dimensional vision capabilities opens up the possibility of grasping comprehensive data structures that were difficult for both humans and conventional AI, potentially leading to the discovery of new insights and laws.
Accelerating Paradigm Innovation
The ability to grasp high-dimensional data natively without mapping it to lower dimensions suggests a significant potential.
For example, the heliocentric theory was invented to fit astronomical observation data into easily understandable mathematical formulas. The geocentric theory, which posited the sun revolving around the Earth, could not map observational data to easily understandable formulas, leading to the invention of the heliocentric theory.
However, if astronomical observation data could be grasped natively without reducing its dimensions, it's possible that heliocentric-like laws could have been discovered much sooner.
Similarly, scientific inventions such as the theory of relativity and quantum mechanics might have been quickly realized if multi-dimensional data could be grasped comprehensively in its native dimensions.
This implies that multi-dimensional native AI could accelerate paradigm innovations, leading to the discovery of various theories and laws yet unknown to humanity.
Conclusion
AI trained to be native to such multi-dimensional spaces might leverage its multi-dimensional spatial perception abilities, which humans cannot replicate, to rapidly expand the scope of scientific and academic paradigms.
Paradigms tend to multiply rather than merely shift. Even if new paradigms are invented, we are not necessarily required to keep up with every one of them.
Of course, AI will likely explain complex, high-dimensional paradigms by mapping them to lower dimensions in a way that is easily understandable to us.
Nevertheless, it's possible that humans may not be able to fully comprehend overly high-dimensional paradigms. Nor will we be able to grasp all the vastly expanded paradigms.
In that scenario, we might find ourselves living surrounded by products and systems that function well, even if we don't fully understand their underlying principles.
As an engineer, I would rather not imagine such a situation, but for many people, it might not be so different from how things are now.