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A thought-experiment from medieval physics?


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Kerry Magruder


If this engraving depicts anything about medieval science, it would have to be not the shape of the earth, but the common medieval thought experiment, derived from Aristotle via Stoic commentators, regarding concepts of place and finitude:

"If you thrust your hand beyond the outermost sphere, would your hand be in a place?"

Consider a related question:

"What is outside of the universe?"

Is this a scientific question? Is it asked by scientists today?

Here is Aristotle's answer, at the conclusion of a long and careful exploration of time, place, space, motion, and the finitude of the universe:

"It is therefore evident that there is no place or void or time outside the heaven [i.e., the outermost sphere of fixed stars]. For in every place, body can be present; and void is said to be that in which the presence of body, though not actual, is possible; and time is the number of movement. But in the absence of natural body there is no movement, and outside the heaven, as we have shown, body neither exists nor can come to exist. It is clear then that there is neither place, nor void, nor time, outside the heaven. Hence whatever is there, is of such a nature as not to occupy any place, nor does time age it; nor is there any change in any of the things which lie beyond the outermost motion...." On the Heavens, Bk. I, ch. 9.

For Aristotle, then, the universe is finite, and is not surrounded by matter or even by void space. Whatever is beyond the universe does not occupy space and is not subject to time.

Medieval scholastics subjected Aristotle's basic concepts like place and time to searching analysis and modification. As part of this process, thought experiments like the following were often employed: If a man could travel to the outermost sphere of the heavens, what would happen if that man tried to extend his arm or push a lance beyond the outermost sphere? This popular question was first raised by the Stoics, and became widely known through the 6th century commentator on Aristotle, Simplikios of Athens.

Some medievals, such as Albert of Saxony, argued in the spirit of Aristotle that no one could extend anything beyond the outermost sphere, because there would be no place or space there to receive it. Others disagreed, citing divine omnipresence and omnipotence. This rejoinder comes from Jean Buridan, an arts master at the University of Paris in the early 14th century:

"It would not be valid to say that he could not place or raise his arm there simply because no space exists into which he could extend his hand. For I say that place is nothing but a dimension of body and your place the dimension of your body. And before you raise your arm outside this last sphere nothing would be there; but after your arm has been raised, a place would be there, namely the dimension of your arm."

"What lies beyond the outermost sphere of the universe?" If the universe has a limit, an outermost sphere (as they believed), then what lies beyond? Is it nothing, not even empty space? Or is it an extra-cosmic void, in which God is omnipresent? Could one stick one's hand into it? If so, would one's hand exist in any place? Or is place confined to the cosmos?

Perhaps those 14th-century questions sound like the ultrafine hair-splitting the middle ages is renowned for. To the contrary, they were questions explored with logical rigor which led to drastic revisions in the fundamental definitions and postulates of Aristotelian physics. They're just thought experiments, of course, but they played a significant role in the transformation of the concept of "place" into the quite different infinite-in-all-directions "space" of Euclidean geometry and Newtonian physics. Indeed, they remain of interest to many cosmologists of our own century who speak of the universe being "finite yet without boundary."

For a magisterial study of medieval concepts of "place," see Edward Grant, Much Ado About Nothing (Cambridge University Press, 1981).

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  • Kerry Magruder, page last revised: 7/28/2003
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