The Distance to the Sun

In the Ethics, Spinoza says more than once that the sun appears to us to be about 200 feet away and that it continues to appear that way even when we have become aware of its true distance. For reference, 200 feet is about a third of a standard city block (at least in Chicago), and that seems to me to be much too close.

How might Spinoza have arrived at the figure of 200 feet? Can we come up with a better estimate?

12 thoughts on “The Distance to the Sun

  1. While it doesn’t change the number all that much, weights and measures had largely not been standardized in the seventeenth century. Hence, the same unit of measurement (a foot; an acre; a mile) might refer to a different length. Taking regional variation into account, it’s quite possible that Spinoza’s figure should be interpreted as plus or minus fifty of our feet.

  2. In Spinoza’s terms there is a distinction between “modes of extension” and “modes of thought.” In the case of the sun, it is 200 feet away in the mode of thought; that is a reality in the sense that a person uses the sun at this distance in his thinking; say the way a child will put the sun in a picture right above the house, not far away at all. You may feel 200 feet is too close, but you show you also have a thought-mode distance for the sun which is different from its distance in a mode of “extension” (ie, astronomical or mathematical). Perhaps you would prefer the to be, say, a football field away. It is a matter where you put in a personal cosmology. Science increasingly embarrasses people into thinking this kind of distinction is irrelevent. But it remains operative psychologically, and certainly in poetry and art–which have no less truth value. And in Spinoza’s time, apparently, equally real to the philosopher.

  3. I understand and completely agree with Spinoza’s underlying point, but I’m mystified as to why he thinks 200 feet will be a generally accepted figure.

  4. I assume he is proposing this 200 feet as a decided (even spectacular) contrast, to the astronomical distance established by science. It is mostly to establish the category of thought-distance, and different people are bound to describe the sun’s distance differently. But it will always be a feature of the personal landscape, so to speak–and therefore not very far away at all. The point is that despite differences, it never is subjective. I would call this “the literal poetic” (after Owen Barfield). In a corrolary matter, the moon is approximately as far away as the nearby streetlamp–in my poetics.

  5. Heraclitus thought that the sun was about the size of a foot. The sun and the moon have about the same apparent diameter (about a half a degree). If I did the math right, a foot wide object with that apparent magnitude is 229 feet away. So Spinoza thought that the moon looked about as far away as Heraclitus thought the sun looked.

  6. I misread the original post. Never mind about the moon. Heraclitus and Spinoza thought that the sun looked about the same size and distance.

  7. In de anima, Aristotle describes the same “sun is a foot” measurement. Apparently the argument went like this: lying on your book, stick your foot in the air, and the sun is about the same size as your foot. The Thomist who explained this said the explanation came from one of the Greek commentaries.

  8. I make mistake after mistake. (It’s been a long time since I’ve tried to use trigonometry.) A non-trig version of the calculation: if half-a-degree of a circle is a foot long, then the whole circle is 720 in circumference. Dividing by 2pi to get the radius, and you end up with 115 feet.

    So, a foot looks the size of the sun at about 115 feet away. If the sun were 200 feet away and looked the size that it does, it would be 1.75 feet across [2pi(200)/720]. Maybe that’s within the margin of error for comparing Ancient Greek and Early Modern Dutch feet, and maybe it isn’t.

    In the spirit of experimental history of philosophy, I lay on my back and stuck my foot up. If some scholiast said that the ancients thought that the apparent length of your foot in that position was the same as the apparent diameter of the sun, he was crazy. You get a much more reasonable result by just looking down at your feet and considering their apparent width, but really, I think, your feet still too wide for that.

  9. Spinoza took the number from Descartes’ use of the same in his Dioptrique (1637), 6th discourse:

    “From this is follows that even our common sense does not seem capable of accepting by itself the idea of a distance greater than one or two hundred feet, as can be verified from the fact that the moon and the sun, which number among the most distant bodies we can see, and whose diameters are approximently 1 percent of their distances, normally appear to us as one to two feet in diameter at the most, notwithstanding that we know well, through reason, that they are extremely large and extremely far away. This is not because we are unable to conceive them as any greater than we do, since we can easily conceive of towers and mountains which are far larger; rather it is due to the fact that, not being able to imagine them further away than one or two hundred feet, it follows from this that their diameters cannot appear to us as more than one or two feet.”

    At its time Descartes’ text was the definitive text on optics, and very widely read. It is quite likely that Spinoza’s use of the example is a reference to Descartes’ passage, a passage he would have expected his readers to have been familiar with.

    Spinoza’s passage:

    “when we look at the sun, we imagine it as about 200 feet away from us, an error that does not consist simply in this imagining, but in fact that while we imagine it in this way, we are ignorant of its true distance and the cause of this imagining. For even if we come to know that it is more than 600 diameters of the earth away from us, we nevertheless imagine it is near. For we imagine the sun so near not because we do not know its true distance, but because an affection of the body involves the essence of the sun insofar as our body is affected by the sun” (E2p35s).

    “…because of a certain affection of the body…” may very well have Descartes concluding explanation for our confusion over the size of luminious bodies, due to its brightness which contracts our pupils. As Descartes writes,

    “We are also deceived because white or luminious bodies…always appear to be a little closer…Thus their reason for appearing closer is that the movement with which the pupil contracts in order to avoid the force of their light is so joined with the power that disposes the entire eye to see close objects distinctly (by which we judge their distance) that the one can hardly occur but that the other does not also occur to some extent, just as we cannot completely close the first two fingers of a hand, without the third finger bending a certain amount as if to close with them.

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