The Structural Similarities between the Treatise and the Principia

Introduction

After the Principia, it became clear that a new kind of science had emerged in the world and which would later become known as physical science. Now, in this new era, after the Treatise, it has become clear that a new kind of science has emerged in the world which is known as metaphysical science.

The above is the current state of the progress of science, and as it now stands, science has two great books: the Treatise and the Principia.

The Principia which was written by Sir Isaac Newton gave us the physical laws of the universe while the Treatise written by me has given us the metaphysical laws of the universe.

Now, because the spiritual is greater than the physical, the Treatise is greater than the Principia; and as the physical precedes the spiritual, so has the Principia preceded the Treatise.

As it now stands, science has two great books: the Treatise and the Principia.Click To Tweet

The Principia and the Treatise mark the natural progress of mankind from the physical understanding of the universe to the spiritual or metaphysical understanding of the universe. 

And just as we find in the Principia the markedly identified physical laws of the universe, so we also find in the Treatise the markedly identified metaphysical laws of the universe. So, it is important that we compare the structural similarities between these two great books.

Furthermore, this article on the structural similarities between both books has come up because both books are coincidentally similar and it is in no way by any deliberate effort of mine.

When I began the Treatise, I never knew that it would end up having a similar structure to the Principia. It was after I had grasped to a large extent what the Treatise is all about that I saw that it inevitably looked like the Principia.

This similarity in structure between the Treatise and the Principia made me realize the great significance of the Treatise and how it is the first book that set explicitly the metaphysical laws of the universe just like the Principia was the first book that set explicitly the physical laws of the universe.

Now, how are the Treatise and the Principia structurally similar? The Treatise and the Principia are structurally similar in that they both consist of three books: book I, book II and book III. I first made mention of this in this page.

The Treatise and the Principia are structurally similar in that they both consist of three books: book I, book II and book III.Click To Tweet

This is how they are similar and not in the contents or focus of these three books respectively contained in them, which is why I said that they are only similar in structure and not exactly in content.

Let’s now proceed to discuss the contents of these three books in the Treatise and in the Principia.

Book I of the Treatise and the Principia

In the book I of the Principia, subtitled De Motu Corporum (On the Motion of Bodies), Newton presented his investigation of the motion of bodies in the absence of any resistance, and in this book, he also established the relationship between the curved motion of bodies and radially directed centripetal forces.

He showed us the connection between centripetal force and the law of areas and he discussed the relationship between velocity and the radius of a curved path to centripetal force. These centripetal forces were forces that varied with the square of radial distance.

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So, in the book I of the Principia, Newton showed us the origin and the importance of the inverse square law which he would further generalize in the Principia.

Newton analyzed the curved motion of bodies in all conic sections and for each of the cases examined the force was assumed or taken to originate from the center and to vary with the square of radial distance.

This is why in physics today, we talk formally about centripetal forces which are also what the gravitational force is, and it was Newton who set out in the Principia to give us the full understanding of centripetal forces and how they determine the curved motion of bodies.

Also, in the book I of the Principia, Newton delved into the analysis of what is now called the three-body problem and which involves the gravitational interactions between three bodies.

And in this book I of the Principia Newton gave us the proof that a spherically symmetrical body attracts other bodies as though all its mass were concentrated at its center.

We can, therefore, conclude, as have been said, that the book I of the Principia was focused on the non-resisted motion of bodies and on the centripetal motion of bodies and its application for the gravitational motion of bodies.

Now, in the Treatise, we also have a book I and the book I of the Treatise is majorly concerned about “the principles of motion for ponderable bodies” and which happens to be its subtitle. 

In the book I of the Treatise, we deal with the metaphysical laws or principles that describe the motion of ponderable bodies as the motion of electrical bodies was not the focus.

Also, the book I of the Treatise begins with a new presentation of the definitions and the principles of motion which are to guide our investigation throughout the Treatise.

In the Principia, we find that Newton presented two important preliminary sections: one was the Scholium and the other was the laws or axioms and definitions.

In the Scholium of the Principia, Newton gave us the definition of absolute space and time and also of relative space and time and he went at special length to discuss the differences between these two forms of space and time.

And in the section on laws and definitions, Newton defined some of the quantities of motion, such as mass, momentum, force etc., that he would later mathematically analyse and apply in the Principia. He also presented the three laws of motion which he would later continue to apply in the three books contained in the Principia.

But in the Treatise, the definitions of absolute space and time and the definitions of what would be adequately called the metaphysical quantities are all presented in the early path of book I and specifically in section I.

Only absolute space and time are explicitly defined in the Treatise because of its singular concern for the metaphysical laws of motion and not for the physical laws of motion which were the singular concern of the Principia.

These metaphysical quantities mentioned above are the familiar quantities such as velocity, acceleration, force, mass, momentum, etc. They are now called metaphysical quantities because in the Treatise they lose the physical descriptions they had from the Principia or classical physics and they now possess metaphysical descriptions.

The metaphysical descriptions of these quantities became necessary as I further understood the metaphysical laws of motion. I saw that it is absolutely necessary for me to redefine these quantities to suit their new metaphysical applications.

This is the natural reason why we have the part on definitions and principles in the book I of the Treatise.

The parts on principles introduce four of the seven absolute principles of motion, one of which is the absolute principle of inertia and which is a redefinition of how this principle is understood in classical physics.

These absolute principles are now the new guiding principles for our understanding of metaphysical motion in the universe for both ponderable and electrical bodies.

Now, it is these new metaphysical definitions of these quantities that will make you understand the Treatise and how these metaphysical quantities represent the true form of reality.

All of the old physical definitions of these quantities that can be found in the Principia does not apply in the Treatise. This is because the Principia is physical, but the Treatise is metaphysical.

Having the understanding of this basic distinction between the Treatise and the Principia will make you understand their different importance in the so far progress of scientific knowledge.

It is also in this book I, in section I, that one finds the three metaphysical laws of ponderable motion. It is important to know that the Treatise divides our study of motion not just into uniform and accelerated motions but also into ponderable and electrical motions.

The former is the first consideration in the book I of the Treatise, and it is because of the distinction between ponderable and electrical motions that we have the book I and the book II of the Treatise in the first place. They are in no way an attempt to deliberately mimic the Principia.

So, just know that in the book I of the Treatise, we find the new definitions of the metaphysical quantities and it is focused on the investigation of “the [metaphysical] principles of motion for ponderable bodies”.

While the book I of the Principia is concerned about the motion of bodies in non-resisting media and the origin and nature of centripetal forces as they determine the motion of bodies on conic section forms.

Now, let’s discuss book II in the Treatise and in the Principia.

Book II of the Treatise and the Principia 

In the book II of the Principia which was divided into sections, Newton proceeded to inform us about the character of motion in a resisting medium. He also showed us how pendulums behave under air resistance.

In this book II of the Principia, Newton gave us his investigation of “hydrostatics and the properties of compressible fluids”. And he went further to show us how to derive the speed of sound in different resisting media.

He estimated the speed of sound in air to be about “1088 feet per second” and he assumed that the same analysis of the motion of sound in a medium should also apply to light.

A major part of the book II of the Principia was dedicated to refuting Descartes’s vortex theory which proposed that the heavenly bodies were propelled by “fluid vortexes that filled interplanetary space”.

Newton was of the opinion that the vortex theory did not really explain the motion of the heavenly bodies and as such were irrelevant. Newton would rather rely on his rigorously mathematical and practical methods of analysing these motions even if he cannot explain their causes.

Now, the book II of the Treatise focuses on “the principles of motion for electrical bodies”. Remember that in the book I of the Treatise, the focus was on “the principles of motion for ponderable bodies”.

The first section in the book II of the Treatise shows us the well stated metaphysical laws of electrical motion. And in this section, one finds the post-modern or metaphysical definitions of some of the quantities or concepts that will be applied in the later part of the book II of the Treatise.

So, the book II of the Principia was focused on the study of motion in a resisting medium and it informs us about hydrostatics and compressible fluids, while the book II of the Treatise shows us the post-modern investigation of the principles of motion for electrical bodies.

Having understood the afore, let’s now proceed to the book III of the Treatise and the Principia.

Book III of the Treatise and the Principia

The book III of the Principia is subtitled as De Mundi Systemate (On the System of the World). In this book III of the Principia, Newton gave us the further implications of his law of universal gravitation for astronomy and the broader universe.

He showed us how the inverse square law establishes the interaction between the heavenly bodies especially those in our solar system. He further gave us the study of tidal motions, the motion of comets, and the precession of the equinoxes etc.

The book III of the Principia was what further established the heliocentric view of the solar system and in this book III Newton gave us his study of the center of gravity of the solar system and how it deviates from the Sun primarily due to the mass of Jupiter.

Now, the book III of the Treatise subtitled “the structure of atoms and galaxies” gives us the implications of the so far discussed principles of motion in book I and book II for the structure of galaxies and atoms.

In the book III of the Treatise, the implications of the principle of universal equivalence for the structure of atoms and galaxies was largely presented and it is the main focus in this part of the Treatise.

In the book III of the Treatise, we shift our focus from just motion to the structure of the universe and of both the atomic and non-atomic worlds applying the principle of universal equivalence.

This is almost similar to the book III of the Principia which focuses on the structure of the solar system applying the law of universal gravitation.

I will now like us to proceed to the next section on crucial discussion where we can further compare these two great scientific books that have emerged to progress the course of science.

Crucial Discussion

A good look at the structure of the Treatise and the Principia shows that they both have the natural structures that fit their purpose.

The Principia sets out to unify celestial and terrestrial mechanics and this is why it has the structure that it has, and the Treatise sets out to unify the motion of ponderable and electrical bodies, and this is why it has the structure that it has.

In the Principia, Newton examined under one conceptual framework which is called Newtonian mechanics the motion of celestial and terrestrial bodies. And he was able to place the description of the motion of celestial and terrestrial bodies under the same three set of laws which would be called Newton’s laws of motion.

However, in the Treatise, I examined under one conceptual framework which I call absolute relativity the motion of ponderable and electrical bodies. And I was not able to place the motion of ponderable and electrical bodies under the same three set of laws like Newton did for the motion of celestial and terrestrial bodies.

Why is this so? This is because it is impossible to place the motion of ponderable and electrical bodies under the same set of laws. The distinction between their motions is very real and fundamental to our understanding of the universe.

Also, this distinction between the motion of ponderable and electrical bodies was why was very difficult to unify quantum mechanics and relativity. It is why the quantum world of particles and the macro world of bodies have always seemed to be unconnected.

But what we needed was not a set of laws that unify both the motion of ponderable and electrical bodies, rather what we needed was a single conceptual framework that describes the motion of ponderable and electrical bodies.

This is so that we would no longer have two separate theories, relativity and quantum mechanics, that describe the motion of ponderable and electrical bodies respectively. This conceptual problem is what has been resolved by the Treatise.

Thus, in the Treatise, you will find that the motion of ponderable and electrical bodies are treated in two separate books, book I and book II respectively.

It is natural to expect that the conceptual approach to the unification of celestial and terrestrial mechanics which Newton applied in the Principia cannot be what should necessarily apply to the unification of ponderable and electrical mechanics.

Understanding the different unification problems and how they are differently resolved by the Treatise and the Principia will further show you why their respective structures are natural and fitting.

Furthermore, the unification problem the Treatise resolved is of far-reaching implications than that of the Principia and this is because the Treatise is concerned about the exact laws upon which the universe was laid.

This calls for a different conceptual approach in order for us to resolve the problem.

Also, talking about conceptual approach, it is noteworthy to mention that in the Principia, Newton applied geometrical procedures in order to unify celestial and terrestrial mechanics, but in the Treatise, I applied algebraic procedures in order to unify ponderable and electrical mechanics.

So, the Principia is geometrical while the Treatise is algebraic. This should be among the fundamental distinctions between the Treatise and the Principia.

The Principia is geometrical while the Treatise is algebraic.Click To Tweet

In addition, I must further make it clear that the Principia is physical and this is because of the magnitude of the unification problem in physics it confronted.

The Principia, with the benefit of hindsight, was not about the true laws of the universe. It was just about the physical universe and how it can be unified.

This position is further supported by the discoveries of the late 19th and early 20th century which challenged Newton’s laws of motion and which showed that Newton only scratched the surface of reality.

The revolutions of modern relativity and modern quantum mechanics revealed to us that they were underlying operations of the universe that are beyond what Newton’s laws could have captured or assumed.

It was in the face of these undeniable objections against Newton’s laws of motion that we found an urgent need for the true theory of the universe that will capture these indicated underlying operations of the universe and this urgent need is what has been served by the Treatise.

And in the accomplishment of this service, the Treatise introduced us to the metaphysical nature of the universe and not to the physical nature of the universe like the Principia did.

We are now learning from the Treatise that the operations of the universe have been hidden and underlying only because we have not come to know about the metaphysical laws of the universe.

This is similar to the Principia which made us know that the unity of the celestial and terrestrial mechanics have only been hidden because we did not know about the physical laws of the universe which Newton exposed.

So, by the exposition of the metaphysical laws of the universe as found in the Treatise, we now see almost effortlessly the unity of the micro and macro worlds which has been sought for more than eight decades now.

The conclusion, therefore, is that the Principia being about the physical laws of the universe cannot be about the unity of all things and about the true picture of reality which are what the Treatise is about since it is about the metaphysical laws of the universe.

It is important to now see how the Principia which is concerned about the physical laws of the universe is structurally similar and conceptually different from the Treatise which is concerned about the metaphysical laws of the universe.

This is what this article has set out to inform you about the progress of science so far. Science now has two great books: one is the Principia for the physical universe and the other is the Treatise for the metaphysical universe.

Conclusion

In this article, I have just gladly informed you about the similarities between the Treatise written by me and the Principia written by Newton.

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I would say that these two books are important in their respective spheres being the physical universe and the metaphysical universe.

But more than the recognition of their respective significance is the recognition of the fact that only one can represent the true nature of reality, and in this comparison, the Treatise stands out as the true representation of reality.

These two books, the Principia and the Treatise, are respectively the zeniths of the two revolutions of science, which are the scientific revolution of classical physics and the great scientific revolution of post-modern physics.

Both books are a testament of the natural progress of man and of science from the physical understanding of the universe beginning with the Principia to the metaphysical understanding of the universe that has already begun with the Treatise.

Until next time,

I will be here.

– M. V. Echa

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M. V. Echa

M. V. Echa

My message is the universe, my truth is the universe, and this blog contains all you need to know about the universe, from the true nature of reality to the long-sought unity of the cosmos — which is the big picture!