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Tag Archives: Hyperbola

Spinoza’s Optical Letters: Redux

As some know, primarily last summer I spent my time researching and theorizing on Spinoza’s lensgrinding and optical concepts, a largely underdeveloped field in Spinoza studies. The greater portions of my findings are listed here on this site under the sub-heading Spinoza’s Foci. A spearpoint of this research was uncovering the substantive arguments and conceptions that lay behind Spinoza’s rejection of Descartes’ optics, as found in his two letters 39 and 40, letters that have be nearly completely ignored by commentators on Spinoza, or if address, addressed in what seems a delinquent, or dismissive fashion. Spinoza is mostly thought to not know what he is talking about. On the other hand, Spinoza’s objections if carefully examined reveal both technically an alternate position on the problem of “spherical aberration,” but more deeply, a radically distinct conception of what vision is, in particular how it works as an insufficient analogy for consciousness. While Descartes wanted to emphasize the power of the central clarity powers of hyperbolic vision (both in the human eye, and in his proposed lenses), Spinoza understood vision and conciousness both as holistic events, ones best approached with the pragamatic appreciation of our limitations. I provide very little philosophical extrapolation here, though the implications are vast, perhaps running through down to the root of Idealism and Phenomenology. This epistolary commentary also does not touch on such other important factors such as the kind of lathe Spinoza likely used, nor much on his likely technique, and kinds of instruments he made and calculated for, which form a significant secondary branch of my research. Yet as these letters remain nearly the only first hand statement Spinoza made on optical matters, they are the anchorage point for anything else that is likely to be asserted.

For the convience of interested readers I here post a Word document version of my line-by-line explication of these rarely read and rather under-interpreted letters. I realized that the previous weblog versions were very difficult to read and browse through, hopefully something this version will correct. The two entries that can be found in this document are: Deciphering Spinoza’s Optical Letters and  Spinoza: Letter 40 and Letter 39. These are both the English translation of the two letters by Spinoza, and then my explication. This version is not footnoted (though there are citations), and it retains some of the idiocyncratic paragraphing and color coding. It is a 14,000 word document (48 pages), though Spinoza’s letters are only 900 words or so.

[click download]: Deciphering Spinoza’s Optical Letters Line by Line


Some Observations on Spinoza’s Sight

How The Two Philosophers “See”

I feel that there are some important things to say about my recent post, A Diversity of Sight: Descartes vs. Spinoza , but I am still undecided just how deep the influence of these thoughts run. So pervasive is the metaphor of vision and light within Western metaphysics, any identification of an ocular appropriation into the field of metaphysics, and the questioning of its radical truth or application, may have far reaching interpretive effects.

What may prove the advantage of this analysis is that it promotes a simplification. Like all simplifications it is misleading to take this as the whole story, but it does help us identify a core element of disagreement between the two Natural Philosophers. The difference between Descartes and Spinoza cannot be reduced to these two diagrams, of course. But there is an essential divergence in the thinking about vision as a metaphor for thought that is expressed in them. 

Descartes' Ur Image: The Hyperbola

Spinoza's Ideal Optical Eye

The first of these, for those uninterested in the optics under question in Spinoza’s letters 39 and 40, shows the capacity of a hyperbolic lens to focus any rays that are parallel to its central axis to a point along that axis. What the hyperbola provides is a schema for thinking about vision and clarity, the analogy of imagining that a focused image of the world that is “clear and distinct” is one where all the rays of a kind are brought to a mathematical ideal, poured into a point. We are not dealing here with all the details of lenses, and how they interact with the human eye and light in the fullness of their variety, but rather with a guiding diagram of what a lens should do – focus rays of light to a center point – and what that means for the experience of vision. For this reason, it is best to understand that this image for Descartes is likely intuitive of directions for investigation, steering both his theories and empirical observations.

The second of these is from Spinoza’s Letter 39, and works as a vivid contrast to Descartes’ Hyperbola. Instead of imagined parallel rays focusing down into an ideal point in the very center of the eye (which in some ways Descartes will conflate with the free Will), for Spinoza the Ideal Eye is one that in using the properties of a circle is able to focus rays parallel to a variety of axes (in fact, an infinity of axes). Rays coming from all directions are hoped to be focused across the back of the eye. And Spinoza sees the human eye (insofar as it does not have a spherical lens), as failing to achieve this kind of vision. Ideal mental vision, instead of being modeled upon a central point of focus, Spinoza conceives of as panoptical; that is, one “sees” as best as a human mind can the cross-section of rays as they converge from every direction upon the human being.

As admitted, this is truly a vast over-simplification, for much unites these two philosophers, and the kinds of radical divergences that Spinoza makes are must more diverse than this simple diagram comparison. But really there is something suggestively profound in this contrast. For one, in that Descartes’ hyperbola inheritance may be traced to Kepler’s Paralipomena its conceptual framework should be viewed as grafted from that Neo-Platonic Ideal, opening up the question of what aporias arise under such a graft (for instance, a point of focus in a Neo-Platonic realm, does not operate with the same powers or meanings as a point of focus does within a Will-driven conception of the soul). Additionally, Spinoza’s rejection of the naturalization of the hyperbola, and the analogy of center-focused human vision, has far-reaching consequences for the reading of the place of the Self in his philosophy of power and affect. If Ideal vision occurs across a field of foci, the periphery has no less a “truth” than any center. The margin does not merely, as Kepler says, “serve” the axis – so goes the critique in so many postmodern attacks on a philosophy of Presence – hence the margin is the very place where a search for truth is made, whether it be the margin of society or a comprehensive Totality of Being.

It is my hope that these two sketches of focus, one by Descartes and one by Spinoza, can help draw out the more refined differences of both philosophers, along an analogy of sight.