True Nature: Notes on Spirit and Science

Mathematics is (from one point of view anyway) the study of a particularly rigorous and precise kind of knowledge. Although it is quite specialized, it nonetheless can open us up to insights into the nature of knowledge in general. One example of this comes from the mathematician Kurt Godel, who proved two remarkable theorems that shook the foundations of mathematics. If we reflect on these theorems, they have the potential to shake the foundations of our own knowledge as well.

Before Godel proved his two theorems in 1931, a number of eminent mathematicians were engaged in a program whose goal was to objectify all of mathematics, i.e., make it into a complete and consistent system of symbols and rules for manipulating them. One motivation for this program was to eliminate inconsistencies and paradoxes in mathematics that might be hidden in vague intuitions and informal arguments. The idea was that if you could make all your assumptions and rules of reasoning completely explicit in a system of symbols and rules for manipulating those symbols, then there would be no room for inconsistencies to creep in. The challenge was then to find and make explicit a set of axioms and rules of logical inference that would provide a foundation for all of mathematics. If such a goal were realized, using the rules of logical inference we would be able to deduce every truth of mathematics from the axioms by manipulating symbols in a completely explicit and mechanical way, without appeal to any intuitions or informal arguments. Mathematical knowledge would be completely objective.

Godel pulled the rug out from under this program and showed that it is impossible to objectify all of mathematical knowledge in this way. Assuming that a set of axioms is consistent and sufficiently complex to define basic arithmetic, Godel proved that there are mathematical truths that can not be proved within the system itself. The system, in other words, is incomplete. It can not encompass all truths. Even if one were to expand the system by adding another axiom or two, Godel’s theorem says that there would still be another truth that is beyond the power of this expanded system to prove. Thus, it is impossible for mathematical knowledge to be completely objectified. Or, to put it another way, there will always be a dimension of mathematical knowledge that transcends any objective system of mathematics. There will never be any final mathematical system, any complete and explicit description of mathematical truth. Like an eternal spring, mathematics flows from an inexhaustible, hidden source.

Like the program to objectify all of mathematics in one system, we sometimes think that we can understand all of reality with our logical systems of thought. Whether it be a grand unified theory of physics or a master philosophical system, there is a tendancy to think that reality can be defined and captured by systems of thought. Or we slip into the opposite extreme and think that reality can not be known at all. What Godel’s theorem suggests, however, is another possibility. Rather than viewing our quest for deeper knowledge as an ultimately futile project whose goal is to completely capture reality in an objective system of thought, we can see it as an invitation to participate in deeper and more subtle communion that infinite source from which all objective knowledge arises. Although objective systems of thought can comprehend only a limited part of reality, our knowledge is not limited to objective systems of thought.

Since Fritjof Capra’s Tao of Physics popularized the parallels between quantum physics and Eastern mystical philosophies, some people have concluded that quantum physics implies a mystical worldview. But does it really?

First, we should recognize that quantum physics admits multiple philosophical interpretations, and they are all consistent with the empirical predictions of the theory. There is the Copenhagen interpretation, the many worlds interpretation, the Bohm interpretation, and dozens more, depending on how fine you draw your distinctions. Included among this variety of interpretations are several mystical interpretations.

Second, there is no agreement on which interpretation of quantum physics is correct. Why not? Because nature does not tell us which interpretation of quantum theory is correct. Physicists may favor some interpretations over others, but that is a matter of cultural consensus, and not based on scientific evidence. In short, there is no scientific proof for any one interpretation. We just don’t know exactly what reality quantum physics points to.

However, while quantum theory may not tell us exactly what our world is, it does tell us what our world is not. There are some very definite constraints it places on how we view reality. In particular, quantum theory is incompatible with naive realism, the view of reality that takes for granted that things exist objectively “out there” independent of each other and separated in time and space. That is one thing it does share with mysticism. And there are other parallels as well. So, although quantum physics does not prove, validate, or imply a mystical worldview (or any other worldview), it can be interpreted in a way that is compatible with mysticism.

Because scientific facts cannot determine for us one unique interpretation, we must choose among those interpretations that are compatible with the theory and the facts. When we make that choice, we must bring in other extra-scientific criteria if we are to make more than a random choice. One criterion is to seek a coherent worldview that is comprehensive of the broadest range of human experience. An interpretation of quantum physics that is compatible with mysticism has the virtue of bringing our overall understanding of reality into greater harmony and coherence.

Most of us are naive realists: we are convinced there are “facts” that are simply given to us, and there are “things” that really exist “out there.” We can’t walk through walls, move mountains, or make the sun rise just by wishing it. Reality has its own laws that are completely independent of what we want or think. Or so we believe. But is it really true?

Upon closer examination, those “objectively given” features of our experience are mere conventions, habitual ways of interpreting experience that are so deeply conditioned that we have become unconscious of them. We can see how this might be the case by considering a few examples, starting with an obvious one.

The border between the US and Canada is a convention. It does not exist in reality, but is a geopolitical division that people created and agree upon. It is arbitrary in the sense that the border could have been drawn somewhere else. Yet, for practical purposes, it is a fixed feature that we all live with as if it had an objective existence. Even though it is ultimately imaginary, it is a very useful thing to know about and helps us understand many things about the relationships between people who live in different parts of North America.

It is not difficult to see that the US-Canadian border is a convention, and has no objective reality. Other distinctions, though, seem very objective at first, and it takes a closer examination to see that they are really just conventions. For example, consider the boundary between land and ocean along the Pacific shoreline of North America. It seems that the shoreline objectively exists, and is not a mere convention. It seems that nature has determined where to draw the shoreline, and we can’t just move it like we could move the US-Canadian border. It seems objectively real.

To see that the shoreline is a convention, we have to look a bit deeper. It seems the border between land and ocean must be drawn in a particular place because we have overlooked quite a few implicit assumptions and ambiguities. For example, the shoreline might seem quite clear in most places, but where do we draw the shoreline at the mouth of the Columbia river? The Pacific shoreline there is no longer a border between land and ocean. We could draw a straight line across the mouth of the river between points of land on opposite sides, but nature doesn’t tell us which points to use. Or we could define the shoreline at the mouth to be a border between salty ocean water and fresh river water, but where exactly is the distinction between these types of water? The one dissolves continuously into the other. At what specific concentration of salt does the fresh water become salt water? There is no clear boundary between the two, and where we decide to draw the line is our choice, a mere convention.

Even at the boundary between land and water, if we look closely we’ll also see that the distinction there is not so clear. Consider a beach where the ocean is far out at low tide and very near at high tide. Where do you draw the shoreline? Moreover, the ocean waves are constantly rolling in and out. Where, exactly, is the border between ocean and land as the water moves up the sand and gradually sinks into it? Even if you considered it at one instant in time, there is no objective way to draw the line. If a 1/16 inch thick film of water covers the sand, is that “land” or “ocean”? What if it is 1/32 inches thick? 1/64 inches? Nature does not come with answers to these questions. It does not tell us exactly where to draw the shoreline. The “shoreline” is a convention that depends on an agreed way to answer these questions.

Try this kind of analysis yourself with anything you think is objectively “out there.” Upon close analysis, all we can find are our own decisions to agree to draw boundaries using one convention or another. Although these conventional ways of drawing boundaries help us communicate our shared experience, they are not imposed upon us by nature. They do not have objective existence in reality itself, but are part of the way we all interpret (often unconsciously) our experience.

Does this mean that it is possible to move mountains? In the framework of conventional reality, no. In a certain sense, though, it is possible to move mountains, albeit not in the usual senses of “move” or “mountain.” It is possible to experience the world in radically different ways that, although perhaps quite unconventional, are not any more or less real than other more conventional ways.

What (if anything) does quantum physics have to do with consciousness? Does quantum physics provide a connection between mind and matter, or a mechanism for the mind to affect the physical world?

These are very controversial questions, and there is no consensus about the role of quantum physics in the relationship between mind and matter. Many physicists simply “shut up and calculate” (as Richard Feynman put it) and ignore the philosophical problems. But quantum physics does challenge our way of understanding reality.

The central problem is this: According to quantum physics, an unobserved physical system has various entangled properties, but when the system is observed only one of these properties is seen. This fundamental difference between observed systems and unobserved systems is at the heart of the measurement problem in quantum physics. What is the nature of this transformation (called the “collapse of the wavefunction”) from an unobserved combination of multiple possible properties to a single observed property? What causes it? How does it happen? When does it happen? Does it really happen at all?

There are two approaches to answering these questions about measurement. The first approach assumes that collapse is a real physical event, and then provides some explanation for what causes it, when it happens, and how it happens. For example, some people have argued that consciousness is somehow involved in collapse. Others have taken this argument a step further and proposed that individual conscious volition can select how the collapse takes place. Such control, however, would constitute a violation of the laws of quantum physics as they are now understood. Thus, our present understanding of quantum physics does not provide a mechanism for the mind to influence matter, or for us to “create our own reality” as some have put it.

The second approach to the measurement problem assumes that collapse is not a real physical event, and then provides some explanation for why it nevertheless still appears to happen. The proponents of this approach point out that there appears to be no particular time or place where collapse can be experimentally established to have taken place. For example, quantum eraser and delayed choice experiments suggest that collapse is not a physical event tied to a particular time or place. Moreover, it was proved (by John von Neumann) that the place where we consider collapse to have taken place can be shifted arbitrarily without changing the results of the measurement. In other words, it is unobservable. But perhaps the most convincing argument against collapse is the fact that it is in blatant violation of the laws of quantum physics. It is quite unscientific to assume the existence of some physical process that is both unobservable and violates the laws of physics.

So, if collapse is not a physical event, what is it? And why does it appear to happen? Here is one way to understand it. Just as the earth appears to be flat on small areas where its curvature is negligible, so quantum systems appear to have collapsed on macroscopic scales where entanglement is negligible. The process of collapse is analogous to approximating a small area of the earth’s surface using plane geometry. Although it is convenient and quite accurate to view a small area of the round earth as if it were flat, approximating that small area with a flat earth model is not a physical event or process. So, thinking that collapse is a real event is like thinking that the earth somehow really becomes flat when we look at small areas of it and can’t see the curvature. Just because we ignore something doesn’t mean it no longer exists. The laws of physics tell us that the quantum entanglements continue to exist, even when they become so subtle that we can’t observe them.

In a sense, collapse is something that consciousness does. But it is not doing something to the physical world. It is a shift in our view of the physical world. More precisely, collapse corresponds to ignoring certain subtle aspects of the world (i.e., entanglements between quantum possibilities) and approximating the world with a classical model. Collapse is not a physical event, but a collapse in our vision from a more complete and expansive reality to a limited approximation. This approximation becomes an illusion if we forget that we have ignored something and mistake our limited view for all of reality.

If we could develop sufficiently subtle instruments of observation so that we could become conscious of the quantum entanglements that are not normally observable on the macroscale, we would become aware of a more complete reality rather than being limited to the thin slice that remains after we ignore all the subtleties. We would not “create our own reality” but simply free ourselves from a limited view of reality that we had created for ourselves. Thus, we don’t create our own reality, we create our own illusion. Through ignorance we create illusion, and we free ourselves from illusion not by creating reality, but by ceasing to ignore it.

(To read more on this subject, see my articles Questioning the Scientific Worldview and The Illusion of Materialism.)