Studying His Word and His Works

This is the ninth of eleven Letters of Euler I will rewrite and post on the subject of infinitesimals (the infinitely small), an idea that is fundamental to a good understanding of calculus. Yes, this is the ninth letter on infinitesimals, but letter XV=15 in Volume 2 of Euler’s book.  Click here to read the previous letter.

Reflections on the System of Monads.

It would be a great pity, however, that this ingenious system of monads should crumble into ruins. It has made too much noise, it has cost its partisans too many sublime and profound speculations, to be permitted to sink into total oblivion. It will ever remain a striking monument of the extravagance into which the spirit of philosophizing may run. It is well worth while, then, to present you with a more particular account of it.

It is necessary, first of all, to banish from the mind every thing corporeal, all extension, all motion, all time and place, for all these are mere illusion. Nothing exists in the world but monads, the number of which undoubtedly is prodigious. No one monad is to be found in connection with others; and it is demonstrated by the principle of the sufficient reason, that monads can in no manner whatever act upon each other. They are indeed invested with powers, but these exerted only within themselves, without having the least influence externally.

These powers, with which each monad is endowed, have a tendency only to be continually changing their own fate, and consist in the representation of all other monads. My soul, for example, is a monad, and contains in itself ideas of the state of all other monads. These ideas are for the most part very obscure; but the powers of my soul are continually employed in their farther elucidation, and in carrying them to a higher degree of clearness. Other monads have, in this respect, a sufficient resemblance to my soul; each is replete with a prodigious quantity of obscure ideas of all other monads, and of their state; and they are continually exerting themselves with more or less success in unfolding these ideas, and in carrying them to a higher degree of clearness.

Such monads as have succeeded better than I have done are spirits more perfect; but the greater part still remain in a state of stagnation, in the greatest obscurity of their ideas; and when they are the object of the ideas of my foul, they produce in it the illusory and chimerical idea of extension, and of body. As often as my soul thinks of bodies and of motion, this proves that a great quantity of other monads are still buried in their obscurity; it is likewise when I think of them, that my soul forms within itself the idea of some extension, which is consequently nothing but mere illusion.

The more monads there are plunged in the abyss of the obscurity of their ideas, the more is my soul dazzled with the idea of extension; but when they come to clear up their obscure ideas, extension seems to me to diminish, and this produces in my soul the illusory idea of motion.

You will ask, no doubt, How my soul perceives that other monads succeed in developing their obscure ideas, seeing there is no connection between them and me? The partisans of the system of monads are ready with this reply, that it takes place conformably to the perfect harmony which the Creator (who is himself only a monad,) has established between monads, by which each perceives in itself, as in a mirror, every development produced in others, without any manner of connection between them.

It is to be hoped, then, that all monads may at length become fo happy as to clear up their obscure ideas, and then we should lose all ideas of body and of motion; and the illusion, arising merely from the obscurity of ideas, would entirely cease.

But there is little appearance of the arrival of this blessed state; most monads, after having acquired the capacity of clearing up their obscure ideas, suddenly relapse. When shut up in my chamber, I perceive myself but of small extension, because several monads have then unfolded their ideas: but as soon as I walk abroad, and contemplate the vast expanse of heaven, they must all have relapsed into their state of dullness.

There is no change of place or of motion; all that is illusion merely: my soul remains almost always in the same place, just as all other monads. But, when it begins to unfold some ideas, which before were but very obscure, it appears to me then that I am approaching the object which they represent to me, or rather that which the monads of such idea excite in me: and this is the real explanation of the phenomenon, when it appears to us that we are approaching to certain objects.

It happens but too frequently that the elucidations we had acquired are again lost; then it appears to us that we are removing from the same object. And here we must look for the true solution of our journeyings. My idea, for example, of the city of Magdeburg is produced by certain monads, of which at present I have but very obscure ideas; and this is the reason why I confider myself as at a distance from Magdeburg. Laft year, these same ideas suddenly became clear, and then I imagined I was traveling to Magdeburg, and that I remained there several days. This journey, however, was an illusion merely, for my soul never stirs from its place. It is like an illusion when you imagine yourself absent from Berlin, because the confused representation of certain monads excites an obscure idea of Berlin, which you have only to clear up, and that instant you are at Berlin. Nothing more is necessary. What we call journeys, and on which we expend so much money, is mere illusion. Such is the real plan of the system of monads.

You will ask, Is it possible there ever should have been persons of good sense, who seriously maintained these extravagances? I reply, there have been but too many, that I know several of them, that there are some at Berlin, nay perhaps at Magdeburg.

23d May, 1761.