We exist in a three-dimensional space.
Within this space, we perceive three-dimensional space based on visual information, which is merely a two-dimensional image.
This means that our minds hold an image of three-dimensional space, and we inverse-map two-dimensional visual information onto this three-dimensional image.
I predict that, by applying this principle, humans could potentially perceive four-dimensional space. While we cannot create four-dimensional space or four-dimensional objects in real physical space,
it is possible to simulate four-dimensional space and objects using computers. By mapping this simulated four-dimensional space onto a two-dimensional plane, humans can visually grasp the information.
Then, if humans learn the behaviors and views of such four-dimensional space and objects, they will eventually be able to create a four-dimensional space in their minds.
However, this is merely a possibility, and such training would likely 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 this ability could be applied.
AI's Perception of Four Dimensions
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, AI could draw and understand four-dimensional graphs.
Humans can only grasp visual information on a two-dimensional plane at a glance. Therefore, even if a three-dimensional graph is drawn and recognized via inverse mapping, there will still be hidden parts obscured from view.
While a significant portion of a three-dimensional graph becomes invisible, a four-dimensional graph would conceal even more data.
Although rotating the graph can reveal hidden parts, this moves away from the goal of intuitively grasping data at a glance.
Conversely, AI does not need to be constrained by two-dimensional planar visual information. It is possible to virtually imbue AI with three-dimensional or four-dimensional spatial vision and train it.
This would allow AI to grasp three-dimensional and four-dimensional graphs in a dimension-native, panoramic way, without data being hidden or requiring rotation.
Furthermore, this is not limited to four dimensions; logically, dimensions can be increased infinitely to five, ten, twenty, and beyond.
Understanding Multidimensional Graphs
The ability to grasp graphs panoramically enables, for example, trend analysis across multiple dimensions. Comparisons of size and understanding of ratios can also be done intuitively.
It also allows for the analysis of data patterns, such as similar or analogous data. Furthermore, it can help discover regularities and laws.
This goes beyond mere multidimensional data pattern matching, which existing AI excels at, enabling a deeper understanding of data.
For instance, even if identical patterns exist within combinations of entirely different dimensions, simple multidimensional pattern matching would likely struggle to find them.
However, with multidimensional vision, if the shapes are similar, they should be immediately recognizable, even across different dimensional combinations.
Moreover, beyond simply using the dimensional axes accompanying the input data, it is also possible to explore dimensional structures that are easier to understand the data by expanding or contracting specific axes, logarithmically transforming them, or mapping multiple axes to the same number of different axes without reducing their dimensionality.
Thus, by training the capability for multidimensional vision, it becomes possible to grasp data structures panoramically—a task difficult for both humans and conventional AI—opening up the potential for discovering new insights and laws from them.
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 understanding, which posited the sun revolving around the Earth, could not map observational data to comprehensible formulas, leading to the invention of heliocentrism.
However, if astronomical observation data could be grasped natively without dimension reduction, heliocentric-like laws might have been discovered much sooner.
Similarly, scientific inventions such as the theory of relativity and quantum mechanics might have been realized much earlier if multidimensional data could have been grasped panoramically in its native dimensions.
This implies that paradigm innovation, leading to the discovery of various theories and laws yet unknown to humanity, could be accelerated by dimension-native AI.
Conclusion
AI trained to be native to multi-dimensional space, leveraging its multi-dimensional spatial cognitive abilities—which are beyond human emulation—may rapidly expand the scope of paradigms in science and academia.
Paradigms tend to multiply rather than merely shift. Even if new paradigms are invented, we are not necessarily required to keep pace with them.
Of course, AI will likely explain paradigms discovered in complex dimensions by mapping them to lower dimensions in a way that is easy for us to understand.
Nevertheless, paradigms of excessively high dimensions might remain beyond human comprehension. Furthermore, it will likely be impossible to understand all of the vastly expanded paradigms.
In such a scenario, we might find ourselves living surrounded by products and systems that function effectively, 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 much different from how things are today.