Motion as the Effect

We have discovered the principal and most general errors of our sight with respect to extension and shapes.

We must now correct those into which this same sight leads us concerning the motion of matter.

This will be easy because there is so much relation between extension and motion that if we are mistaken in the size of bodies, then we are also mistaken in their motion.

The word “motion” ordinarily signifies 2 things:

1. A certain force that one imagines in the moving body which is the cause of its motion [cause]

This is used When we say that a ball has communicated its motion to another.

2. The continual transport of a body moving away from or approaching another body at rest [effect]

This is used if we simply say that a ball is in motion

“Motion” thus signifies both the cause and the effect together, which are however two entirely different things.

It seems to me that one is in very gross and even very dangerous errors concerning the force that gives motion and transports bodies.

These fine terms of “nature” and “impressed qualities” seem fit only to conceal the ignorance of false scholars and the impiety of libertines, as would be easy to prove. But this is not the place to speak of this force that moves bodies; it is nothing visible, and I speak here only of the errors of our eyes.

This chapter will talk about motion as the effect.

Our eyes do not teach us the magnitude or speed of motion considered in itself

Chapter 6 explained that our sight does not make us know the magnitude of bodies in themselves, but only the relation they have to one another, and principally to our own. From which I conclude that we cannot know the true or absolute magnitude of their motions either, that is to say of their speed and slowness, but only the relation that these motions have to one another, and principally to that which ordinarily occurs to our body; which I prove as follows:

We cannot judge the magnitude of the motion of a body except by the length of the space that this same body has traversed. Thus, since our eyes do not show us the true length of the space traversed, it follows that they cannot make us know the true magnitude of the motion.

This proof is only a consequence of what I have said about extension, and it has its force only because it is a necessary consequence of what I have demonstrated about it. Here is one that supposes nothing. I say then that even if we could clearly know the true magnitude of the space traversed, it would not follow that we could likewise know that of the motion.

The duration necessary for knowing motion is not known to us

The magnitude or speed of motion contains two things: the first is the transport of a body from one place to another, as from Paris to Saint-Germain; the second is the time it took to make this transport. Now, it is not enough to know exactly how much space there is between Paris and Saint-Germain in order to know whether a man went there with a fast motion or a slow motion; beyond that, one must know how much time he employed to make the journey. I grant therefore that one truly knows the length of this road; but I absolutely deny that one can know exactly by sight, or even by any other means whatsoever, the time one took to make it and the true magnitude of the duration.

This appears sufficiently from the fact that at certain times a single hour seems to us as long as four; and on the contrary, at other times four hours pass imperceptibly. When, for example, one is filled with joy, the hours last only a moment, because then time passes without one thinking of it. But when one is downcast with sadness or suffering some pain, the days last much longer. The reason for this is that then the mind is weary of its duration, because it is painful to it. As it applies itself to it more, it perceives it better; and thus it finds it longer than during joy or some agreeable occupation that makes it, as it were, go outside itself to attach it to the object of its joy or occupation. For just as a person finds a painting all the larger the more he stops to consider with greater attention the smallest things represented in it; or just as one finds the head of a fly very large when one distinguishes all its parts with a microscope, so the mind finds its duration all the greater as it considers it with more attention and perceives all its parts.

So that I do not doubt that God could so apply our mind to the parts of duration, by making us have a very great number of sensations in very little time, that a single hour might seem to us several centuries. For in short, there is no instant in duration, just as there are no atoms in bodies; and just as the smallest part of matter can be divided infinitely, one can also give parts of duration smaller and smaller to infinity, as is easy to demonstrate. If therefore the mind were attentive to these small parts of its duration through sensations that left some traces in the brain, of which it could remember, it would undoubtedly find it much longer than it appears to it.

But finally, the use of watches proves well enough that one does not know duration exactly, and that suffices for me. For since one cannot know the magnitude of motion in itself unless one first knows that of duration, as we have shown, it follows that if one cannot exactly know the absolute magnitude of duration, one cannot exactly know the absolute magnitude of motion either.

But because one can know some relations of durations or times to one another, one can also know some relations of motions to one another. For just as one can know that the solar year is longer than the lunar year, one can also know that a cannonball has more motion than a tortoise. So that if our eyes do not show us the absolute magnitude of motion, they nevertheless help us to know approximately its relative magnitude; that is to say, the relation that one motion has to another; and it is only that which is necessary to know for the conservation of our body.

Examples of the errors of our eyes concerning motion and rest.**

There are many encounters in which one clearly recognizes that our sight deceives us concerning the motion of bodies. It even happens quite often that things which appear to us to be moving are not moved, and that on the contrary those which appear to us as if at rest are nevertheless in motion. When, for example, one is seated on the edge of a ship that is going very fast and with a very uniform motion, one sees that the lands and towns are moving away; they appear to be in motion, and the ship appears to be at rest.

Likewise, if a man were placed on the planet Mars, he would judge by sight that the sun, the earth, and the other planets, together with all the fixed stars, made their revolution in about 24 or 25 hours, which is the time Mars takes to turn on its axis. However, the earth, the sun, and the stars do not turn around this planet; so that this man would see things in motion that are at rest, and would believe himself to be at rest although he was in motion.

I do not stop to explain whence it comes that he who would be on the edge of a ship would easily correct the error of his eyes, and that he who would be on the planet Mars would obstinately remain attached to his error. It is too easy to know the reason; and it will be found with even more ease if one reflects on what would happen to a man sleeping in a ship who woke up with a start and saw on waking only the top of the mast of some other ship that was approaching him. For supposing that he saw neither sails swollen with wind, nor sailors at work, and that he felt neither the agitation nor the jolts of his ship nor anything else similar: he would remain absolutely in doubt, without knowing which of the two ships was in motion; neither his eyes, nor even his own reason could discover anything to him about it.