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As a follow-up to an earlier post, where I described how natural laws arise as a result of qualities, this post explores this idea further using an example. Since modern science grew out of the idea that matter is res extensa—i.e., that it has only one property of extension in space—this post also illustrates the lawfulness as a result of the addition of spatial extension. However, in this case, qualities exist as forms in space—e.g., triangle and circle—rather than merely area. Some implications of these ideas in regard to the nature of space—which emerge as a consequence of form interaction—are also discussed. Then we discuss how this thinking solves the problem of modern science and its relation to religion.

Adding Circles to Triangles

Most of us think of number addition as the summing up of quantities. But for the moment, let’s think about another kind of addition in which we add shapes rather than quantities. Let’s suppose that there are two shapes—a circle and a triangle—let’s call them C and T, and suppose that they have areas X and Y. The common understanding of adding two things thinks about adding X and Y, such that X + Y = Z, where Z is a bigger area, obtained by adding the sum of two areas. Let’s call this quantitative addition.

But we can also think of a qualitative addition in which the result is another shape that is neither a perfect circle nor a perfect triangle but something in between. The below picture shows this.

The addition of a circle to a triangle involves two considerations. First, what should be the combined area of a circle and a triangle? Second, what should be the shape of the combined area? If we only perform a quantitative addition of the respective areas, then, we will get a larger area, but we would have no idea of what its shape is. If instead, we can perform the addition of a circle to a triangle, then we not only get a quantitative idea about the total area, but also the shape of the resulting area.

Since the addition of shape is also the addition of areas, but the addition of areas is not the addition of shapes, therefore, the addition of shapes includes the addition of areas, but goes beyond it. Hence, if science was based on the addition of shapes rather than the addition of areas, then it would also go beyond the science that only adds areas. That is a precise example of “better mathematics” because it includes the results of the current mathematics, and yet provides something additional.

The Finitude of the Space of Qualities

A unique property of this space is that when you add a circle and a triangle, you get something in between a circle and a triangle. In contrast, if you add quantities, you get something bigger, which is beyond both the quantities. Thus, the sum of 5 and 10 is 15—which is beyond or “outside” both 5 and 10. However, the sum of a circle and triangle is something that is “in between” a circle and a triangle.

Essentially, if space comprised two locations—one a circle and the other a triangle—then upon adding these two things, the result would always be in between a pure circle and a pure triangle. If you add a triangle twice to a circle, then the result would be more triangular and less circular, than if you added the triangle and the circle only once. You could say that the pure circle and triangle are the extremities of your space, and the addition of these extremities always produces something in between them.

In technical terms, this space would be called bound because it has fixed extremities or boundary. In the simple example we are discussing, the pure triangle and circle are the extremities of our space, and the shapes that are in between a pure circle and triangle are also somewhere within the space bounds.

The space of quantities is thus infinite. If you add infinite numbers, then the result is infinity. But you can add triangles and circles infinite times and the result would always be in between a triangle and a circle. Therefore, the space of qualities is finite and bound because the addition of two things always produces something in between. The pure qualities—e.g., a pure triangle and a pure circle—are extremities, and everything obtained by the combination or addition of these qualities lies in between the extremes.

Finitude of Space in Vedic Cosmology

This idea of finitude of space is used to define many regions of space in Vedic cosmology. Examples of this finitude is a “planet” or more accurately Graha and the entire universe. For instance, if you are adding the things that have the quality of shape, then the space is bounded by pure shapes like triangle, circle, and square. As you go from the center of this space to the extremes, you can either get a pure circle, or a pure triangle, or a pure square. But you can never escape this space because there is nothing “beyond” a pure circle; that pure circle is the limit of the space, which you can never breach.

As we have discussed in an earlier post, the Grahas of Vedic cosmology are such finite “spaces” whose boundaries cannot be breached. We can travel for infinite time in this space, and that travel—which begins in the center—will be like converting an oblong shape slowly into a circle or triangle, such that the perfect circle or triangle would never be attained despite the infinite travel. The center of this space thus mixes all kinds of qualities, and the extremities are pure qualities. We cannot get “outside” this space of “shapes” by adding or combining any number of shapes. We will always be inside.

If we truly want to escape this “shape space”, then we have to go to another space—e.g., color space, taste space, smell space, touch space, etc. By adding shapes, we cannot produce color, taste, or smell. So, these qualities are outside the shape space. To escape the shape space, we have to change the quality—of the space itself. Quite simply, we have to add a new quality—e.g., taste—such that we are partially in the shape space and partially in the taste space. And then we can completely escape the shape space. Thus, space travel in Vedic cosmology requires changing the qualities of material existence. This is described as the change in the type of thinking, perceiving, judging, intending, etc.

Inside and Outside Space

Thinking of space in terms of qualities leads to yet another unique property, which is that something can be in two spaces simultaneously. Thus, because shape and smell are different spaces, therefore, if you experience both shape and smell (alternately) then you are moving from one space into another. At a given moment, you are only in one space, but in a time-averaged manner one could say that you are “here” and “there”. Why? Because some object has both smell and shape, so it is in two separate spaces simultaneously, and the locations are defined in different spaces, so they are also different.

This type of “here” and “there” simultaneously underlies the quantum non-locality problem in which a particle is said to be in two different places at the same time. Physicists find it paradoxical to think like this because they are thinking of a quantitative space. If we thought of space in qualitative terms, then it would not be paradoxical to say that something has both shape and taste, which are in different locations in different spaces, so the thing is simultaneously present in multiple places and spaces.

This problem is euphemistically called Schrodinger’s Cat Paradox in which the cat is simultaneously dead and alive, because the dead body is one location in space, and the alive body is another location. Of course, the cat cannot be simultaneously dead and alive, because consciousness moves from one body to another. But the same problem could be stated differently if we recognize that tasting and smelling are different states of consciousness, and consciousness moves from one location to another. If something has both taste and smell, then euphemistically it is present in two places at once.

The Problems of Res Extensa Science

The world around us comprises myriad qualities. In physics, these are called length, time, mass, charge, etc. Each of these qualities is a separate dimension even in physics. But in quality-based thinking, these are different spaces. Modern science treats all these spaces quantitatively. That is, you go on adding distances and you get an infinite distance. But modern science has found that this space curves upon itself. In short, instead of being infinite, it becomes “bound”, and that boundedness of space is called the “curvature” of space. This so-called “curvature” would not be a problem if we thought in terms of qualities because then we would recognize that there are many spaces—each of which is bound.

The problem however doesn’t end with the curvature of space, because in quantum theory we find that factually one thing is in two separate places, which contradicts our notion of space and locality (the idea that each thing is in one place). In present science, we also cannot reconcile quantum and relativity theories because relativity is based on the idea of locality (augmented by the finite speed of light) and quantum theory is non-local. Essentially, we are unable to reconcile the claim that space is curved and something is in two places at the same time. Why? Because holding both viewpoints simultaneously entails that something can be in two spaces at the same time, and in physics, we cannot think of how something can both be inside and outside of space (or inside two separate spaces). Solving the physics problem necessitates a logical contradiction—entailed by the idea of res extensa space.

The Notion of Hierarchical Space

All these problems are easily solved when we think in terms of qualities. Then, there is a space called “seeing” which contains subspaces called color, shape, and size. So, just by understanding sense perception we can grasp how these are separate spaces because size, color, and shape are independent properties—they are different spaces. And yet, something can have shape, size, and color, so it is simultaneously present in different spaces. The spaces are bounded so in res extensa thinking we can say that the space is “curved”. And something is both inside and outside the space—non-locality.

I have described all these properties of space as an inverted tree in which the root is the whole space, and the trunks are subspaces of that root. Then, the branches are subspaces of the trunks, etc. So, there are literally infinite spaces, and something can be inside and outside that space. This is not just a way of understanding Vedic cosmology, but the only way to solve the problems of modern physics.

And this way of thinking rests upon rejecting everything in modern science—i.e., res extensa thinking. Yes, there is extension or space in which everything exists. But that extension is defined based on qualities, rather than quantities. Adding two things in this space produces something “in between” the extremes, which leads to the notion that the space is bound. Likewise, something can be in two separate spaces, and all these infinite spaces are organized hierarchically just like an inverted tree.

The Problem of Infinities in Physics

Another related problem in physics is that of infinities. If you add something to itself infinite times, then you get an infinite result. But if you add circularity to itself, you only get a circle. So, you can add infinite circles and squares, and the result will be something in between a circle and a square. Thus, the addition of infinities is mathematically convergent in qualitative addition—it leads to a finite result. But the addition of infinities is mathematically divergent in quantitative addition—it leads to an infinite result.

These infinities appear in physics when we study the electromagnetic field. Since everything is inside the electromagnetic field (the space of the quality of charge), therefore, everything has an electromagnetic field. You add those individual fields and you get infinity. The “solution” to this problem is called Renormalization which is effectively like “zooming out” and instead of seeing infinite particles, you see fewer particles that are effectively “coagulated” which means that you don’t have to add a finite quantity infinitely. The question is: How much should you zoom out? The answer is: Whatever matches the observation! Thus, you tailor your theory to match the observation, proving your assumption.

This has been for a very long time an unsatisfactory aspect of particle physics, but as with all unsatisfactory things in modern science, people find ways to make them more respectable. Those very things that make the science respectable are actually hurdles in the progress of science.

The Need for Novel Mathematics

All these problems and their solutions require us to step beyond current thinking about quantities. We cannot continue to add areas of triangle and circle to get a bigger area. We must rather learn to add circles and triangles themselves. In this new type of addition, the result is in between the qualities added, not greater or beyond the two quantities added. This is the conclusion we are led to by studying Vedic cosmology, and it is the only conclusion that can resolve the problems of modern physics.

Now, you might say: But we can observe the quantities! And the answer to that problem is that whatever we call quantity is also a quality. Take for instance the quality of “size”. We think it is a quantity, but it is factually a quality. The top of the universe is the biggest size, and the bottom is the smallest size. But the biggest size is not infinity. And if you add anything inside this space, the result would always be finite. It can sometimes seem to approach the top—i.e., become bigger. But it will never be infinite. Why? Because “size” is a quality—there is a “biggest” and “smallest” size quality. So, even when we are talking about quantities, the quantitative addition is not always correct.

This fact produces bizarre results in arithmetic such as Ramanujan’s proof that 1 + 2 + 3 + … = -1/12. We think that adding numbers linearly will produce an infinite result, but it doesn’t. Why? Because we are adding qualities such that the result is always finite. This may sound interesting to many people that many infinities in physics are made finite by using such results—that are completely counterintuitive. The above result of linear addition is for instance used in String Theory. Without such results—which rely on qualities rather than quantities—physics will have far more problems than it does presently.

Thus, the problems of modern physics entail new ideas of space, but that idea also requires us to change our ideas about addition and subtraction. When we get deeper into this issue, then we find that to add things across two different spaces, we must also violate basic principles of logic because the same thing is inside and outside. A good example of this problem in modern physics is that we cannot add mass to charge, and mass and charge are treated as separate independent physical properties. However, if we apply the qualitative addition, then the combination of mass and charge produces something “in between” mass and charge, just like the addition of a circle and a triangle. This “in between” thing is neither mass nor charge, but it is approximately described by using two separate types of properties.

The logical problem is that the combination of mass and charge is neither mass nor charge, and yet it is both mass and charge. This is just like saying that the oblong shape is neither a circle nor a triangle, and yet it is both circle and triangle. How can something be neither two things and yet both those things? In fact, how can something be neither of two logical extremes—e.g., neither true nor false, and both true and false? The inability to think of such things then points to the problems of the failure of logic itself.

Thus, thinking about qualities—or what I call semanticism—requires a revision to everything we have upheld in modern science. This includes the ideas of matter, space, numbers, and even logic. The alternative way of thinking is intuitively accessible, but it requires unfamiliar concepts. The change has to begin with logic, then progress into the nature of numbers, then into theories of space, and finally into the description of matter. That theory will explain everything that science cannot explain today. But everything that science explains today would also be explained in a completely different way.

The Relationship to Religion

The understanding of Vedic religion involves unintuitive ideas such as God is inside everything and outside everything. When He appears in this world, then He is not material; He is still transcendental. The deity of God is factually metal or stone, but this deity is also outside the material space. Owing to numerous such contradictions, the conclusion is that all this must be inconceivable. And that inconceivability makes religion fundamentally opposed to the rationality of modern science.

The breakthrough in thinking about this problem is that (a) science is also inconceivable just like religion—that inconceivability is locality and non-locality, inside and outside, two separate things and yet neither of those things, and yet both of those things, and (b) religion and science are inconceivable in the same way, because the problems of inside and outside, here and there, local and non-local, everything at once and yet none of these things, appear as much in religion as in science.

The same problem appears in the study of consciousness. The soul’s consciousness is everywhere in the body, and yet it is transcendent to the body. So, the soul is “inside” the body and yet “outside”. An advanced soul can be in this material world and yet also be at once in the spiritual world. Similarly, the soul is many qualities at once, and yet, it is none of these (individually separated) qualities.

The problems of matter, consciousness, and God involve the same level of and the same type of inconceivability. It is only because the inconceivability of matter is suppressed from the popular vision, and scientific propaganda hides the problems innate in science, that an illusion of conceivability of science and the inconceivability of soul and God is produced in the popular imagination.

If, however, we study all these problems, then we can make the breakthrough in thinking where the problems of matter, soul, and God are equally perplexing, and perplexing in the same way. That will then point us to the necessity to think semantically—about the soul, matter, and God. That thinking can begin with science for those who are so interested, but it would not be contrary to religion. Indeed, when the perplexity of science is solved, then religion would no longer seem perplexing.