Dynamics and Vis Viva: An Introduction
July 7, 2010 • 8:51PM

The incredible blunders made by the professional fool René Descartes on the laws of motion were an amusing inspiration for Leibniz's discovery of the true principle underlying physics: dynamics. Specifically, Leibniz demonstrated that understanding the power of motion is impossible if you are guided by your senses: only the mind can understand power.


JASON ROSS: The concept of Dynamics is key to understanding LaRouche's economic outlook. This video will introduce a necessary component of Dynamics, Leibniz's discovery of vis viva in opposition to the absurdities of Descartes on the laws of motion.

Now, most people have heard that Descartes is a great genius: a thinker, a philosopher, a geometer. After all, he invented graph paper, plenty of reasons for staying in bed till lunchtime, and ways to sound intelligent in a coffee shop, making vacuous remarks like, “I think, therefore I am”. In reality, Descartes was a total moron, whose theories of almost everything were completely wrong. His enormous ego made him a perfect tool for the pro-empire propaganda faction in science. Future programs will cover his optics and his philosophy. Here we'll demolish his laws of motion.

So, to start with, let's take a glimpse into a world obeying Descartes's laws. [video with music]

While the phenomena you just observed looked completely absurd, they are all in accord with the laws of motion, as Descartes laid them down. His incredible errors helped spark the way for Leibniz's discovery. [video and music]

Considerations of nature, and the desire to build machines, prompted thoughts about the laws of motion. And while theories of this sort go back to the Greeks, those of Descartes stand out for their mathematical nature, and their physical incoherence. To measure the power of motion, Descartes introduced a quantity he called the quantity of motion. This was suggested by his senses, and he measured it as the mass of an object times its speed. For example, he would say that a bowling ball moving at two miles per hour, has the same quantity of motion as a bullet shot from a rifle. [video with sound]

According to Descartes, the motion of complex systems could be understood as a certain quantity of motion being maintained and transferred among the components.

Let's calculate out an example. Here the croquet ball on the left, with a mass of one and a speed of six, hits a billiard ball, with a mass of one-half. The croquet ball has a quantity of motion of its mass times its speed, or one times six, which gives six. Descartes writes that when a larger object strikes a smaller one at rest, the two move together, maintaining the quantity of motion. Combined, the mass is one and a half, so the speed must now be four, to have a product of six, as the quantity of motion.

In another example, Decartes says that when a moving object strikes a stationary one, equal in size to itself, the moving object bounces back, with three-fourths of its original speed, while the other object gets one-fourth of that speed. Has that ever happened to you? Descartes did maintain the same quantity of motion, but here are seven examples of collisions, maintaining the same quantity of motion [video with music]

Among these possibilities, Descartes chose arbitrarily [video with music]

As Leibniz would later write, of Decartes's three-fourth's rule,

“I'm not sure of how anything more foreign to reason could have been thought up on this matter. It is beyond understanding how such a thing could have occurred to the mind of this distinguished man.” [video with music]

Confronted with these ramblings of Descartes, the young scientist and statesman, Gottfried Leibniz, realized Descartes's immense errors, and was the first to discover the true principle behind motion: Dynamics. Leibniz used his mind, rather than his senses. He always thought about the future—politically, economically, and scientifically. So rather than looking at present appearances, Leibniz considered the unseen causes that bring about visible effects, and thought about the potential for future power, that lay in the present, including in motion.

As a way of measuring mechanical work, mechanical power, Leibniz considered the lifting of a weight. Each foot that a mass is raised takes the same effort, and raising an object that weighs twice as much takes twice the effort. Leibniz reasoned that the mass of an object, times the height it was lifted, measures the mechanical work involved. As a pulley system makes clear, lifting four pounds one foot, is the same as lifting 1 pound four feet. This is a good start, but moving bodies don't usually lift others. How can we measure the power of motion itself?

Leibniz used the pendulum, as a way of connecting motion with the lifting of a weight. As the pendulum swings back and forth, it has a speed at the bottom of its swing, capable of raising it back up to the top. Here we have our desired connection between motion and lifting of a weight. It had been discovered that a falling body attains a speed in proportion to the square root of the verticle distance that it had fallen. Or, inverting the statement, the height to which a body can ascend, is measured as the square of its speed.

So now, return to Descartes. He says that an object of mass two and speed one, has the same quantity of motion as as mass one and speed two. But look at the work they perform. [video with music]

The weight of two ascends one unit of height, giving a work power of two, while the weight one ascends four units, giving a total of four. Thus, equal quantities of Descartes's quantity of motion brought about different results. This means that Descartes wasn't really measuring the power residing in moving objects, but only glancing at the effects of this power. The power to act is what is real.

This means that rather than looking at the mass times the speed, looking at the appearance of a moving object, we have to consider the future work that motion can perform. That's measured as the mass times the height it can ascend, or in terms of motion, mass times speed squared.

What is the speed squared?

It certainly does not suggest itself to the senses intuitively, but it is understandable by the mind. This quantity, mass times speed squared, was called, living force, by Leibniz, or, vis viva, in Latin. The power that lies behind motion, is measured as vis viva. It is this quantity that is maintained, rather than the quantity of motion.

As a visual demonstration, here are a series of example collisions between different bodies. [video with music]

Descartes's theory is on the top, and Leibniz's below. [video with music]

As Leibniz pointed out, there's only one condition that Descartes got right. Let's see those again. [video with music]

Since the power of a moving object varies as its speed squared, this means that the motion of even very small bodies, provided their speed be great, can represent a great power. Take steam for example. Each molecule of water vapor is tiny, but it can contain a great power. The introduction of steam engines marked a new stage in human economic development. And Leibniz himself was personally influential in the spreading of the steam power. His work directly increased the economic power of mankind.

So Leibniz was right, while Descartes was proven totally wrong, centuries ago. So why is Descartes still considered an authority by the credulous today? What political objective is served by enforcing stupidity? We'll have more on that later. That's all for now. This has been an introduction to Leibniz's vis viva. [video with music]