Recently, a science-technology-engineering-math-medicine (STEAMM) project that I’ve been working on was published! EquilibriUM is a print magazine being distributed across the University of Michigan campus, but can also be found online. While I helped edit and put the project together, I also wrote a piece about how two modern philosophers, Descartes and Spinoza, conceived of optics and epistemology. Because they take lenses as a symbol of how ideas are focused in the mind, their ideas on concept formation can be likewise understood as a symbol of their theories on light.

You can read the rest of the articles in the magazine and see this one in print-form here. I highly encourage that because the art and illustrations are so beautiful and engaging, and I’m really honored to have worked with the amazing group of graduate students to put this project together.

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Scientific ideas are always changing, updated by new observations and models. Tools and instruments are invented and perfected to push the boundaries of the observable world. Better telescopes allow us to see farther out into deep space and image black holes, while improved microscopes zoom into the atomic structures of proteins and inorganic compounds. These instruments augment and expand our five senses and let us ‘see’ what would otherwise be impossible. Using research equipment in this way not only changes science but also impacts how scientists wrap their heads around data and, in turn, form models and hypotheses that drive future research. Scientific findings impact not just thoughts and feelings but also actions and narratives about the world; for example, climate research permeates conversations about lifestyle, politics, and how individuals evaluate and face crises.

In the earlier days of science, the questions researched were much more basic: of what were objects made? How does light work? Without the instrumentation and knowledge that we have now, the models and philosophy of the time had a bigger impact on scholars’ understanding of the world, yet even today scientific practice and ideas play a large role in epistemology, or the nature of knowledge itself. Scientists and philosophers alike would probe, either via observation or thought, how humans understood the world. Rene Descartes certainly wasn’t the first person to posit answers to these questions, but as the so-called ‘father of modern philosophy’ his ideas still echo in philosophy classes and discourse alike. Descartes’s work with lenses offers a metaphor, paralleling how he imagined humans interpret visual perceptions to understand and rationalize the world around us. Even hundreds of years later, scientific theories and philosophical models continue to be entangled.

Illustration by Catherine Redmond. See below for artist’s statement.

Focus

During Descartes’s time, light was thought to travel as an outward push, bouncing off intervening air and objects. By analogy, Descartes described that sight is like a blind man tapping out a path between obstacles with a cane or a walking stick. Vision lets us ‘feel’ our way visually, as a bat uses air pressure for echolocation. Forces from other objects create air pressure, allowing light to accept and transmit this energy through and against other media. Since light radiation is like a projectile, he postulated, it can reflect and refract when it encounters substances other than air particles. We are able to see when this light enters our eye – through the lens and into the humor.

Through medical procedures and operations, it was known that neither the eye nor the lens are perfectly spherical and instead are more like ovals. This oval (or hyperbolic) lens can focus parallel rays into a single point (Fig. 1). Rays of light originating from a full-size object are focused on the back of the eye (where the optic nerve transmits the resulting image to the brain for identification). For Descartes, “[nature] wished to gather all the radiation of any visible object entering the opening of the [pupil] into a single point of the retina in order both that the point of the picture might be all the more evident, and the rest of the points of the picture might not be confused by extraneous rays whether stray or gathered together.” This means that the main object is brought down to a point, such that other parts in view aren’t distracting. From this observation, Descartes uses vision as an analogy for the formation of ideas.

Even though Descartes was first and foremost a rationalist, requiring that everything, however seemingly obvious from firsthand experience, be derived from first principles rather than observation, he concedes that “whatever I have up ‘til now accepted as most true, I have acquired from the senses or through the senses” [1]. Perhaps not everything needs to be proven through a series of mathematical proofs if there is a way to focus our attention and thoughts towards what’s true.

That’s exactly what lenses do with light: they bring a particular object into focus. “If one tries to look at many objects at one glance, one sees none of them distinctly. Likewise, if one is inclined to attend to many things at the same time in a single act of thought, one does so with a confused mind” [2]. Looking around a room, our eyes focus on particular objects, near or far, and everything else becomes a bit more blurry. Our eyes cannot see everything, yet our mind desires to know what is going on at all scales and places, even beyond our peripheral vision. Using lenses as an instrument, whether in a telescope like Kepler or a microscope like Hooke [3], we can see more of our world, but these distant objects are still brought down to a single point.

To obtain knowledge about the world our minds must similarly focus concepts and ideas to a ‘single point,’ or an integrated framework. If we don’t have a clear mental model, then as we collect more data the concept we are investigating is harder to put into focus because there is no grounding center. By finding perspective to make our vision clear and distinct, we remove the confusion, increasing the signal amongst the noise.

Perspective

Descartes’s single-axis theory of concept formation certainly does not describe epistemology in its entirety and has been criticized throughout philosophical discourse, even by his contemporaries. As an experienced lens grinder [4], Baruch Spinoza had a different perspective on the theory of light, and a different theory of the soul and epistemology. Following in the rationalist tradition around 30 years after Descartes, Spinoza posited that there are two types of knowledge: random experience and reason. The former comes from raw observations of nature and our surroundings, but does not give us any ideas, because our five senses are not enough to obtain understanding. Reason, on the other hand, synthesizes the impressions derived from the senses and connects them to other objects. For Spinoza, the resulting ideas are attributable to God and the laws of nature. Information obtained through our five senses would never be enough to know or understand nature, but Spinoza still postulated that the mind can have an “adequate knowledge of God’s eternal and infinite essence” [5].

Spinoza’s paradigm-shifting notions did not stop at religion and theology but extended into how he considered the interplay between vision and the mind. Instead of parallel rays focusing to one ideal point (like Descartes), for Spinoza, the eye was able to focus light to a variety of axes. Where Descartes’ single-axis lens represented his belief in clarity for clarity’s sake, Spinoza thought that vision represented many perspectives being focused within the eye (Fig. 2). In rejecting the single-axis model and its analogy of center-focused human vision, instead Spinoza suggests that with vision occurring across a field of foci, the periphery has no less truth than the center. “It is certain that, in order to see an entire object, we need not only rays coming from a single point, but also all the other rays that come from all other points. And therefore it is also necessary that on passing through the glass, they should come together in as many other foci” [6].

Descartes’ theory is closer to how actual light is bent and focused in a lens (perhaps ironic given Spinoza’s practical familiarity with delicate glass lenses). But here Spinoza’s describing an ideal eye: that window into the soul, where focused light is an analogy for synthesized concepts. Spinoza thought that a single-axis lens would limit how much information is gathered and focused. Rather than being the combination of many clear and distinct ideas, truth for Spinoza is the combination of everything in one’s field of view. Because he knew that his panoptical or multi-axis lens was not realistic physically, Spinoza considered the human eye and its perceptions inexact, bolstering his rationalistic philosophy. In order to maximize understanding, the mind must utilize tools and work to bring concepts and observations together:

The most perfect method [for understanding] will be one which shows how the mind should be directed… As [the mind] understands more things, at the same time [it] acquires other tools which facilitates its further understanding… The more the mind understands Nature, the better it understands itself… and will become then most perfect when the mind attends to or reflects upon the knowledge of the most perfect Being [God or Nature].

According to Spinoza, the only way to have a clear model of the world around us is to continue to see with multiple perspectives and to continue to update and expand what we see and how we see it. This conception of how to contextualize the world is what we might nowadays call ‘intersectional’ for its similarity to viewing topics through the lens of different interest groups or cultures.

Illuminated

While Descartes’ theory of light through a lens was more correct than Spinoza’s, their models of the lens parallel their respective philosophies. Both of these models for epistemology have some validity: we gather information about the world through our senses and, depending on whether we are trying to deeply understand it and focus down to a point or put that point within a bigger context, we use Descartes’ or Spinoza’s “lenses,” respectively.

New ideas continue to challenge the validity of older models, more starkly in scientific contexts where old models can become outdated by new discoveries [7], but in philosophical inquiry, scholars are more often finding and re-contextualizing past ideas. In terms of Cartesian concept formation, it’s mostly accepted that we form concepts through observation followed by focusing down to essential characteristics of the particular object or idea [8]. Similarly, the “single-axis” lens model of epistemology finds a new home in reductionism, where an idea or phenomenon is dissected and broken down into its distinct components. The “poly-axial” theory, perhaps, has more of a contemporary footing with perspectivism, which states that people’s perspectives will keep them from obtaining objective facts [9], or relativism, which takes each individual’s perspective as its own truth within the cultural context in which it was formed. Until recently, epistemology has focused on how individuals form beliefs and knowledge structures – both Descartes and Spinoza described the process of a single person. In contrast, social epistemology takes into consideration that our ideas and values can be acquired from or inspired by others. At the very least, sharing ideas, results, and models with others allows for the ideas to take hold within a community. Sometimes it takes a lot of effort for ideas to be adopted within a scientific or cultural framework. For example, astronomers like Nicolaus Copernicus and Galileo Galilei, despite their observations and careful measurements, had to argue with their communities in order to switch the accepted model of an Earth-centered solar system to a sun-centered one. These shifts within particular fields of research only impact future research if their idea is adopted into the larger social contexts [10]. Perhaps without the Copernican Revolution, Kepler would not have had the right knowledge and mindset to calculate the laws of planetary motion with his telescopes. Perhaps without Kepler’s careful mathematics of telescope lenses, Descartes might have had a very different theory of lenses, and a very different model for epistemology.

In an increasingly interdisciplinary world, our goals, projects, and research can combine knowledge that individuals, groups, and cultures have obtained through experience and link them together in a common and accessible explanation. This idea of consilience is to synthesize reductionist ideas and combine them into something more, integrating aesthetics with science and culture with technology. This is analogous to physicists’ goal of a unified field theory [11], but on a much larger scale, including nonscientific fields. Scientific models, especially theories of light and lenses, have drastically changed since the times of Descartes and Spinoza, largely due to inventions and technology that let us answer questions on new scales and dimensions [12]. We don’t have to look much farther than The Internet to see how a technological tool profoundly influences our culture and societal values. As new tools are invented and implemented, we must be mindful of how they change our perspectives, and in turn how they influence our research and knowledge-gathering.

Footnotes

1. Descartes, Meditations on First Philosophy, Med 7.
2. Descartes, Regulae, Rule 9
3. Both contemporaries to Descartes
4. Descartes noted “specialists like hunters and sailors train themselves to look at very distant objects and engravers or other artisans who do very subtle work to look at very close ones,” suggesting that experience and training, we can alter our own lenses to identify particular details that are critical in constructing our world views. Discourse on Method, Discourse seven.
5. Spinoza, Ethics, 2p29. No other philosopher in history has been willing to make this claim, but no other philosopher has really identified God with Nature in the way Spinoza did. We may well appreciate this delineation today in an era of separation between Church and State, but during Spinoza’s time this was blasphemous and got him excommunicated from his very traditional Amsterdam Portuguese-Jewish congregation for “his wicked ways,” “abominable heresies” and “monstrous deeds” despite not having published his ideas. Since he never referred to this period of his life in letters or journals, it’s difficult for us to fully understand why he received this harsh punishment from his community.
6. Spinoza, Letter 40 to Jelles, Trans. Samuel Shirley.
7. Kuhn, The Structure of Scientific Revolutions & Lakatos, Falsification and the Methodology of Scientific Research Programmes (1970)
8. For example, we learn “tree” by seeing many types and species of trees and then coming to the definition of ‘woody perennial plant, typically having a single stem or trunk bearing lateral branches at some distance from the ground’ such that height or leaf shape has nothing to do with tree-ness. Aristotle’s Categories
9. Nietzsche, Will to Power
10. Kuhn, The Structure of Scientific Revolutions (1962)
11. A so-called “Theory of Everything” to unite quantum mechanics and relativity.
12. Now physicists know about electrons, photons, and the Heisenberg uncertainty principle. See Feynman, QED (1985) for an accessible explanation of quantum mechanics and light.