The Dao has different presuppositions than geometry. In order to develop a better understanding of how these differences can be considered to be not much more than a reorganization of our understanding of nature, let us challenge the absoluteness of these 3 presuppositions.
The purpose of challenging these presuppositions is not to attempt to demonstrate that the models of nature that seem so natural to speakers of English are somehow wrong. Nor is it the intention to claim that the Chinese model of the Dao, frequently used herein in comparison, is somehow superior. The purpose is to demonstrate that each culture holds a distinct and isolated perspective on nature, and to encourage the idea that a more encompassing, unified context that reflects the various cultures of our species has the potential to enable a much more powerful and useful model of nature.
Geometry reflects the presupposition that space is infinite. This is the third presupposition in the list. Is this an accurate assumption? Space may well indeed be infinite. However, space might not be infinite. There is no compelling scientific evidence that space must be infinite. Some scientists consider there to be some modern evidence, but it is not conclusive, and anyway such evidence would not have been available to the original Greek developers of geometry 2,300 years ago. The most important evidence that space is infinite is simply the fact that Euclidean geometry assumes that space is infinite. From the perspective of Euclidean geometry, it is reasonable to assume that space is infinite. The reason is that geometry ignores the notion of time. As there is no time, then there can be no motion in space, and without motion there can be no mass in space. Since the model of geometry does not support the notion of mass, points in space must indeed be considered to be infinitely small, and anything composed of geometric points must be infinite.
Since newer models of nature support the notion of time, and therefore motion and mass, the notion of infinity is not mandatory, as it is in geometry. We could simply choose to assume instead that space is finite. The primary Chinese model of nature, the Dao, certainly makes such an assumption. If we were to work from the assumption that space is finite, instead of infinite, and see where that leads us, the implications prove to be very useful and insightful.
What are some of these implications? If space were considered to be finite, the status of the point would evolve. Although the 3 concepts of the line, the plane, and 3 dimensional space correlate to the 3 dimensions of space, there is another concept that does not currently correlate to a dimension, the concept of the point. Why is it that the point is not considered to constitute a distinct dimension, but is instead considered to represent no dimensions? The reason is that it is presupposed in geometry that space is infinite, and that all components of space are either infinitely large or infinitely small in each dimension. The point is considered to be infinitely small in all dimensions, such that the point by itself is not recognized to have any existence in space. The point exists, but it exists without occupying any space at all. In other words, although points form the basis for all that exists in space, points themselves exist without existence in space.
This would not be the case if space were considered to be finite. In finite space, the length, width, and height of the point would each be finitely small, such that the point would exist in space, and therefore the point would be considered to constitute a dimension that is as significant as, yet distinct from, the other 3 dimensions as the numeral 0 represents a concept that is as significant as, yet distinct from, the Arabic numerals 1 through 9. In other words, just as we recognize 10 significant distinctions in Arabic numerals, and not only 9, even though one of the 10 is 0, in like manner we would recognize 4 dimensions in space, and not only 3, even though one of the 4 represents 0.
Assuming that space is finite, the point can reasonably be considered to constitute a dimension, such that there would be recognized to exist 4 dimensions of space. Since we are now assuming space to be finite instead of infinite, we should adopt terms that better reflect the finite nature of space. Instead of the dimensions of the point (which is infinite), the line, the plane, and 3 dimensional space, we should refer to these as the dimensions of the point (which is finite), the line segment, the area, and the volume.