The below essay was submitted to the Foundational Questions Institute essay contest for 2011. The subject was "Is Reality Digital or Analog?". This essay contains my ideas on the reasons why things exist, how infinite sets of elements would appear to different observers and the question of "why is there something rather than nothing?" and how the proposed solution to this question can be used to build a model of the universe. The essay can be downloaded in PDF format either at the end of this webpage or at http://fqxi.org/community/forum/topic/824
Reality is Digital, but Its Perception as Digital or Analog Depends on the Perspective of the Observer
Abstract
The subject of this essay contest is “Is Reality Digital or Analog?”. Here, I suggest that reality, or what I call existence, is, at its base, digital (ie, discrete), but whether or not it is perceived by an observer as digital or analog (ie, continuous) depends on the perspective of the observer. The rationale for this argument is as follows. First, I propose that a thing exists because what is contained within, or meant by, that thing is completely defined. A complete definition is equivalent to an edge or boundary delimiting what is contained within the thing. If existent things require the presence of a complete definition/edge/boundary to exist, this means that existence comes in the form of discrete, or digital, chunks delimited by this edge. Next, I describe how an infinite set of discrete elements appears to an observer as either discrete or continuous depending on the perspective of the observer relative to the set. I show how this situation may relate to the perception of a discrete reality as either discrete or continuous depending on the perspective of the observer relative to reality. Finally, using the above definition of an existent thing as having a complete definition, I propose a discrete, cellular automata-like model for existence.
Results
Before presenting my proposed solution to the question of “Is reality digital or analog?”, I first discuss some terminology. I consider, and will use interchangeably, “digital” and “discrete”, “analog” and “continuous”, “reality” and “the entirety of existence” and “real” things and “existent” things.
Why do things exist?
I suggest that for a thing to exist, the contents of, or what is meant by, that thing must be completely defined. For instance, books have edges and people have skin that completely define what is contained within. Even a concept or mathematical construct has a complete definition, or description, as to what is meant by that concept or construct. Would the mathematical construct “2+2=4” really exist if it didn’t contain within it the idea that two groups of two existent things are put together to form one group of four things? If one tries to visualize an existent thing where one doesn’t know what is contained within or meant by that thing, it is pretty hard to do. A complete definition is equivalent to an edge or boundary defining what is contained within. This complete definition, edge or boundary defines what is contained within and, thus, gives existence and “substance” to a thing. An example of this is that in mathematics, the curly braces, or edge, around a set signify that the elements contained within the set are completely defined. A set would not exist if the elements contained within it were not defined.
Some things may exist only in the brain (concepts, ideas, mental images, etc.), and others may exist only outside the brain (physical instantiation of a book, mountain, etc.). Some things that exist only in the brain such as the mental image of Jill Smith’s car may describe a corresponding, but different, existent thing outside the brain such as the physical instantiation of Jill Smith’s car. The mental image of the car and its physical instantiation are two different, existent things. Stated more generally, the mind’s conception of a thing is not the same as the thing itself. This point will be discussed more in the following sections.
One may argue against this materialist view and say that some things can exist neither in the brain nor in the physical world outside the brain but, instead, in some sort of abstract, Platonic realm. I respond: Please show me this realm. Point it out right now. Or, at least, provide some physical evidence for its existence other than one’s say so. Mathematicians and physicists often use this type of assumption-based reasoning when they say that mathematical and physical truths exist independent of anything physical1,2. Again I say: Show me this place where these truths exist. Until that can be done, this viewpoint cannot be argued rationally and certainly cannot be the basis of a hypothesis for explaining why anything exists.
Others have questioned the role of the edge, or periphery, in defining an existent state. For instance, Goldstick3 writes “There is no more basis for identifying a hole with its periphery than for doing the same with a bump. Rather, a hole and a bump are what are contained within those spatial bounds.” This statement incorrectly denies the importance of the spatial bounds in two ways:
Taken together, the above suggests that a thing exists because it has a complete definition, edge, or boundary that defines what is contained within and that gives existence to the thing. If existent, or real, things require the presence of a complete definition, edge, or boundary in order to exist, this means that existence, or reality, comes in the form of discrete, or digital, chunks, each delimited by their edges.
Both an infinite set of discrete elements and a discrete reality can appear as either discrete or continuous depending on the perspective of the observer
In this section, I discuss how an infinite set, N, would appear to different observers and show how this can also apply to our perception of reality. First, consider a set, N, defined as containing existent (ie, discrete), finite-sized elements such as balls whose numbers extend outward an infinite amount relative to any location and orientation of any one of the elements designated as internal observer O. That is, whereever O is in the set and in whichever direction O is “looking”, the elements of the set extend without bounds the same potentially infinite distance in all directions relative to O. O is one of the elements of N, and it can be any one of them. Given this, then:
Thus, relative to finite-sized internal observer O, set N would appear as a potentially infinite space composed of discrete elements.
Next, the view of set N relative to a hypothetical, external observer is discussed. Again, consider set N, which was defined above as having an infinite number of elements relative to any location and orientation of an element/observer, O, within the set. However, now assume that there is a second observer, P, outside this set and that P’s size relative to O is actually infinite. That is, P is of the same size “scale” as the entire set N, which is actually infinite relative to O. Therefore, P views the entire set N itself as of finite size, which means that P can see set N in its entirety. Given this, then:
Thus, relative to infinite-sized, external observer P, set N would appear as a finite-sized, discrete, existent thing with an interior continuous space. An important point is that these arguments don’t prove the necessity of an external observer, they just suggest how this observer, if it existed, would view the set.
Now, how does the appearance of infinite set N relate to our perception of reality? For one, the dichotomy between finite-sized, internal observer O’s view of set N as discrete and infinite- sized, external observer P’s view of set N as continuous is analogous to the dichotomy between the quantum physics-based view of reality as discrete and quantized and the general relativity- based view of reality as smooth and continuous. This analogy implies that both quantum physics and relativity can be thought of as different views from different perspectives of the same set. In this case, the observer is the mind of the scientist, and the set being observed is the infinite expanse of existence.
It is important for both quantum physics and relativity, as well as for any theory, to use an internally consistent perspective throughout the theory. For instance, if a theory describes space-time as discrete, indicating that the scientist/observer’s perspective is similar to that of internal observer O, then it should ideally use the same perspective in its calculations, such as in its calculations of probabilities. Assuming a continuous, real number-like distribution of probabilities while also assuming a discrete space-time would mean that the theory is switching back and forth in its perspective of reality. Conversely, if a theory assumes a smooth, continuous, infinitely divisible space-time, indicating that the scientist/observer’s perspective is similar to that of external observer P, then quantities that appear infinite in size relative to internal observers would be finite in size relative to P and the observer and thus would be attainable. In sum, perspective-switching within a theory may be warranted in some cases, but it can also cause internal inconsistencies, and the scientist should be aware of these and be cautious in their use.
The appearance of set N also has implications for mathematics, which is another way of perceiving and describing reality. The example of set N implies, at the very least, that the cardinality of an infinite set depends on the perspective, or reference frame, of the observer relative to the set. For example, within infinite set N, observer O would assign the set’s cardinality as equal to that of the set of integers, omega. However, outside set N, observer P would assign it a cardinality equal to that of the real numbers. Furthermore, the case of set N says that the perception of the integers as being a potentially infinite set of finite, discrete chunks (ie, 0-to-1, 1-to-2, etc.) and the real numbers within an integral range as being a continuum will vary depending on the perspective of the observer. That is, if the observer could decrease his size scale to that of the real numbers, they would appear as finite-sized and discrete elements instead of their usual external observer-based description as infinitesimally small. Additionally, a hypothetical external observer of infinite size would view the set of integers as a continuous, infinitely divisible space similar to how we observe the real numbers.
Together, the above reasoning suggests while reality is, at its base, discrete or digital, the appearance of reality as discrete or continuous will depend on the perspective of the observer (ie, the scientist’s mind) relativity to reality. Additionally, the perspective of the observer should be taken into account when using infinities in physics.
Why is there “something” rather than “nothing”?
In this section, I propose a solution to the question of “Why is there something rather than nothing?” and show how this solution leads to a cellular automata-like formation of a universe filled with discrete, or digital, chunks. The proposed solution is based on the definition of an existent thing given in the first section as having a complete definition.
In the first part of this section, “something”, “nothing” and “non-existence” will often appear in quotes because, as will be come evident, the distinction between them is not as clear as previously thought. Now, consider the question “Why is there something rather than nothing?”. Two choices for addressing this question are:
A. "Something” has always been here.
B. "Something” has not always been here.
Choice A is possible but does not explain anything (however, it will be discussed more below). Therefore, choice B is the only choice with any explanatory power. With choice B, if “something” has not always been here, then “nothing” must have been here before it. By “nothing”, I mean complete “non-existence” (no energy, matter, volume/space, thoughts/concepts, mathematical truths, time, minds, etc.). The mind of the reader trying to visualize this would be gone as well. But, in this complete “nothing”, there would be no mechanism present to change this “nothingness” into the “something” that is here now. Because we can see that “something” is here now, the only possible choice is that “nothing” and “something” are one and the same thing. This is logically required if we go with choice B.
If “something” and “nothing” being one and the same thing is logically required for choice B, then instead of saying “That cannot be. Something and no thing are not the same.”, it would be better to accept what is required and try to figure out how it could be rather than continuing to deny it. So, how can “something” and “nothing” be one and the same? First, consider “nothing”, or “non-existence”. This was defined above as the lack of energy, matter, volume/space, thoughts/concepts, mathematical truths, time, minds, etc. In other words, the lack-of-all. This lack-of-all means that the mind of the reader trying to visualize this would also be gone. The lack-of-all, in and of itself, completely defines the entirety of what is present, that is, nothing at all. In fact, the lack-of-all is the complete definition of what is present. It tells you exactly what is there. It is completely self-defining. Nothing else is needed to say or define exactly what is present. As described above, a complete definition or description is equivalent to an edge or boundary defining what is present and giving existence to a thing. Therefore, the lack-of-all, or what has previously been referred to as “non-existence”, is actually an existent state.
If non-existence is an existent state, why is so hard to visualize it as such? One reason is that we visualize non-existence within our minds, which exist. Next to our existent minds, nothing just looks like nothing. But, in doing this, as described in the first section, we are confusing our mind’s conception of non-existence with non-existence itself. This cognitive artifact makes it appear as if non-existence is just nothing and not the complete definition of what is present and, thus, an existent state. If we could somehow see non-existence itself (which we, of course, cannot) and not just our mind’s conception of it, we would see that only once all, including the mind, is gone, does non-existence completely define the entirety of what is present and, therefore, become an existent state.
Another way of saying the above is that because our minds exist, our mind’s conception, or visualization, of non-existence is dependent on existence; that is, we must define non-existence as the lack of existence. But, non-existence itself does not have this requirement; it is independent of our mind and of existence. Only non-existence itself, in which the mind is gone, completely describes, or defines the entirety of what is present and is thus an existent state. This idea of distinguishing our mind’s conception of a thing and the thing itself of course applies to all issues and not just to non-existence.
Overall, what we have always called “nothing”, or “non-existence”, is actually an existent state, or “something”. The reason we have considered them to be different is the artifactual confusing of our mind’s conception of non-existence and non-existence itself. Furthermore, because the existent state formerly called non-existence contains no parts, it is the most fundamental of existent states and is, indeed, the fundamental building block of existence. Referring back to the original question of “Why is there something rather than nothing?”, this also suggests that both choices A and B were correct: “Something” has always been here, but it is one and the same as “nothing”.
Now, how can the equality of “something” and “nothing” be used to build a model of existence? If what used to be called non-existence is actually an existent state and is indeed the fundamental building block of our existence, then it is also the most fundamental of “physical” particles that compose our existence. As such, it must have physical properties that allow it to function as this most fundamental of physical particles. Thus, by discussing the question of “Why is there something rather than nothing?”, we are actually discussing
fundamental physics. Somewhat similar ideas have been proposed by Tegmark and others1,2 . So, what can we say about the physical properties of a complete definition or existent state?
I refer to the above type of thinking, that merges philosophy with physics, as philosophical engineering. I believe this type of bottom-up, logic-based reasoning offers the best path forward for both metaphysics and physics for understanding the nature of existence. Like all physical theories, philosophical engineering must be internally consistent, be able to explain physical phenomena and provide testable predictions. This work is currently being pursued by the author.
If at this point, you are having some doubts, remember that no one knows what is inside what are currently considered to be the most fundamental of physical particles: electrons, photons, and quarks. All we really know is that these particles are existent states. As such, they are no different than the existent state that has been previously referred to as non- existence. Furthermore, no one has yet explained where energy comes from in the universe. There must be some physical mechanism. Finally, whatever the mechanism of our universe’s formation and expansion, there must be, at its base, something that exists, some mechanism that this existent thing can produce more existent things and some way that these things can interact to cause energy and motion. The mechanism proposed here is not only logical but meets all these criteria.
Conclusion
In conclusion, I am proposing that existence is, at its base, discrete or digital, but its perception as digital or analog/continuous depends on the perspective of the observer. Also, the most fundamental discrete building block of existence is the existent state previously called non-existence. Finally, a cellular automata-like model of the universe was proposed based on the properties of the existent state previously called non-existence.
References
1. Max Tegmark, “The Mathematical Universe”, Foundations of Physics, 38 (2008): 101-150, especially p. 16.
2. Dean Rickles, “On Explaining Existence”, “Foundational Questions Institute Essay Contest”, 2010, http://www.fqxi.org/data/essay-contest-files/Rickles_Rickles_fqxi_2.pdf
3. Daniel Goldstick, “Why is There Something Rather than Nothing?”, Philosophy and Phenomenological Research, 40, 2 (Dec. 1979):265-271, especially p. 270.
4. In J.H. Conway and N.J.A. Sloane, “Sphere Packings, Lattices and Groups”, 3rd ed., (Springer- Verlag: New York, 1999), especially p. 21.
Copyright 2011