Du Châtelet’s Views on Our Perception of Space
Émilie du Châtelet discusses how space appears to us in a manner similar to Newton’s conception of it. She argues that while the mathematical principles governing the motion of heavenly bodies are constant, our perception of space changes depending on our relative position and velocity. For example, when we are stationary on Earth, we see objects as having a specific shape and size. But if they were in a spaceship traveling at high speed, they would see those same objects as smaller and more elongated.
Du Châtelet’s theory provides a scientific explanation for the phenomenon known as “perspective” or “distortion.” Similarly, she argues that our understanding of space is based on our experience of objects in the physical world and that space is not an entity in and of itself (Du Châtelet, n.d.). Instead, space is the collection of relationships between objects in the world. Du Châtelet also provides a detailed analysis of how light affects our perception of space. She explains that when we see an object illuminated by light, we see it as being at a certain point in space.
When Émilie du Châtelet stated that space must appear to us to be void and penetrable, she illustrated that space is an abstract concept. It cannot be seen or touched and must be imagined to be understood. She said space is penetrable because we can imagine objects passing through it. This property of space is essential for understanding the world around us, as it allows us to conceive of objects traveling through it. This ability enables us to envision concepts such as distance and movement, which are crucial for navigating our physical world.
Du Châtelet mentioned that the mathematics we use to describe the physical world (physics) is continuous (Du Châtelet, n.d.). In other words, the equations that govern how objects move and interact are based on smooth curves and lines rather than on steps or jumps. This enables us to predict the behavior of objects accurately over time and space. Mathematical discontinuous models would not be able to account for the physical world similarly.
Personal Opinion Regarding Du Châtelet’s Arguments
Leibniz’s Calculus as a Superior and Enduring Framework
I disagree with Du Châtelet’s claim that we think of space as Newtonian rather than Leibnizian. Firstly, Leibniz’s calculus is more elegant and concise than Newton’s and is still used today. Newton’s calculus is less concise because it employs more notation and specific steps, making it difficult to follow.
Leibniz’s calculus is more concise because it avoids these extra steps and relies on a few key ideas that are easier to understand (Huang & Oliveira, 2020). Leibniz’s calculus also employs the concept of an infinitesimal, a minimal quantity that can be approximated by any finite number, thereby making calculations simpler and more elegant. Lastly, Leibniz’s calculus allows for reversing a sequence of operations, making it easier to verify results and identify errors.
Many of the calculus techniques that Leibniz developed are still in use today. For instance, the method of taking derivatives is still used to find rates of change, and integration is still used to find areas under curves. Leibniz’s notation for derivatives and integrals remains in use today (Ely, 2019).
In fact, many people who study calculus never learn any other notation because it is universally accepted. Ultimately, Leibniz’s conviction that mathematics can be applied to describe the physical world remains a significant goal of mathematics today. Scientists and mathematicians continue to explore the relationships between mathematical concepts and physical phenomena.
The Complexity and Accuracy of Newtonian Mathematics
Secondly, I disagree with Du Châtelet that the principles of Leibnizian mathematics are more complex to understand than Newtonian mathematics. Newtonian mathematics is complex because they are a more accurate representation of the physical world. In classical mechanics, for example, Newton’s laws of motion accurately describe the movement of objects in terms of their mass, velocity, and direction (Kubricht et al., 2017).
This level of accuracy is necessary to enable scientists and engineers to build everything from spacecraft to bridges. The downside to using such an accurate mathematical approach to solve problems using Newtonian methods can be challenging in mathematics. However, this level of complexity is more than counterbalanced by the increased accuracy it provides.
The Limitations of Newtonian Mechanics at Extreme Scales
Thirdly, I disagree with Du Châtelet’s view since Newtonian mechanics may be adequate for describing our everyday experience of reality. Newton does not consider gravity’s effects at very large or very small scales. Newtonian mechanics breaks down at very large or very small scales.
At massive scales, the universe is governed by general relativity, which considers the effects of gravity. At extremely small scales, quantum mechanics is necessary to accurately describe the behavior of matter and energy (Banik & Zhao, 2022). Therefore, while Newtonian mechanics provides a good approximation for most everyday situations, it is not entirely accurate when describing the behavior of objects under extreme conditions.
For example, general relativity is needed to accurately describe the behavior of astronomical objects such as black holes and neutron stars. In Newtonian mechanics, gravity is a force that acts between masses, decreasing as the distance between them increases (Banik & Zhao, 2022). However, gravity’s effects are negligible and can be ignored over vast distances (the size of the solar system). At the other extreme, at minimal distances (the size of an atom), gravitational forces become incredibly strong and can no longer be ignored. In fact, they often play a significant role in chemical reactions and atomic-level processes.
Questioning Conception of Space as a Substance
Du Châtelet’s discussion of how space appears similar to Newton’s conception of it is also centered around the idea that space is an infinite, three-dimensional container in which all objects exist. This container is uniform and without shape or form (Du Châtelet, n.d.). Objects in space can only be described in terms of their distance from other objects. Newton’s conception of space was based on his belief that space was a “container” in which all objects exist and move. He believed that space was absolute and had no shape or form.
Moreover, Du Châtelet’s view that space is a substance is also not convincing. If space were a substance, it would be impossible for objects to move through it. Additionally, Du Châtelet’s view does not explain why there are different densities of space in different parts of the universe.
On the other hand, there are a few reasons why Newton’s view that space is an abstraction is convincing. First, explains the meaning of space: space is the three-dimensional coordinate system in which all physical objects exist. It is the framework in which all matter exists and moves (Du Châtelet, n.d.).
But how do we know this? We know it because we can measure it. We can measure the distances between objects and their positions in relation to one another. However, distance and position are abstract concepts; they do not exist in reality; they only exist in our minds. For example, when someone looks at a table, they see an object with a particular shape, size, and color.
References
Banik, I., & Zhao, H. (2022). From galactic bars to the hubble tension: Weighing up the astrophysical evidence for milgromian gravity. Symmetry, 14(7), 1331. Web.
Du Châtelet E. (n.d.). Foundations of Physics, 1740. Chapter 5.
Ely, R. (2019). Teaching calculus with (informal) infinitesimals. Calculus in Upper Secondary and Beginning University Mathematics, 42-66. Web.
Huang, X., & Oliveira, B. C. D. S. (2020). A type-directed operational semantics for a calculus with a merge operator. In 34th European Conference on Object-Oriented Programming (ECOOP 2020). Web.
Kubricht, J. R., Holyoak, K. J., & Lu, H. (2017). Intuitive physics: Current research and controversies. Trends in Cognitive Sciences, 21(10), 749-759. Web.