This is a sort of half-baked theory I was playing around with in my head. Maybe someone else will know where to take it from here?

Fractal Polarism

Information and physical reality are inexorably linked together, like two poles on a magnet. To say that information is predicated on physical reality would be to lose sight of how much the two depend on each other.

This puts reality into a seemingly precarious form of dualism. Yet I would term this a type of property dualism: information and the physical are both two manifestations of the same single phenomenon. Information tells material how to be and material tells information what to be. Neither can exist without the other. Like I said above, they’re like two poles on a single magnet: inseparable.

This is where the polarism aspect of what I’m calling fractal polarism comes from. But why fractal? Fractals have a non-integer topological dimension, with, for instance, the Koch snowflake being something like 1.262 dimensions. Because of the self-similarity and interdependence of the physical and non-physical – matter and information – the true nature of reality falls somewhere between monism and dualism.

The informational detail of physical reality is greater than the physical reality itself. An electron is a one-dimensional object – its Aristotelian substance is that which has only subject and not predicate, analogous to having surface and no volume. Yet, informationally speaking, an electron takes up space and has properties in the form of its quantum state. This gives the electron a dimensional ratio within itself, given that the electron is composed of both the physical and informational. That means this ratio is within a self-similar object, giving it a fractal dimension – it is the property dualism within this polar ontology.

This idea of fractal polarism is a descriptive metaphysics. That the material and information are both aspects of the same single phenomenon, yet information occupies dimensions beyond the material. That means a fundamental particle is one thing occupying more dimensions than itself, therefore being a sort of infinite self-similarity, giving it fractal dimensions.

There are two takeaways here. The first is that information, contra John Searle, is something that actually exists in reality, though as a property dualism of matter. The second is that one thing can exist in this sort of dualism wherein it both exists as the physical, one-dimensional object while simultaneously existing as multiple dimensions of abstract information space, which is occupied by the particle’s quantum states, which are its information states.

This fractal dimension, consisting of an abstract information space with the real spatial dimensions of the object particle, can be thought of as similar to the information space in Claude Shannon’s information theory. The difference is that this abstract space, just like a quantum field when it is at a zero value, actually exists as a fundamental part of our reality. The effects of it can be observed in quantum mechanical experiments.

In quantum mechanics, when measuring the polarization of a photon, for example, contained within the quantum fluctuation is the abstract probability space. It exists in a state of uncertainty until measured, at which point the intensity of the polarized light decreases with a probability based on its polarized state. It isn’t some trick of mathematics or hidden variable – the probabilistic nature of the photon exists as an information space.

Causality

All dualist theories have issues with causality: how is it that this non-physical substance interacts with the physical world? If a soul or some other sort of spiritual substance could interact with matter, it would be able to break the first and second laws of thermodynamics. So, how exactly does this abstract information space interact with matter?

To say that it interacts with matter is thinking about it the wrong way. It’s in the fractal dimensional aspect of object particles that interaction happens at all. We have to remember that maintaining local gauge symmetry in electrons requires the information within the local phase of the electron interacting with the electromagnetic field. Asking how information and matter interact isn’t even the right question; the real question is how matter could ever interact without the information aspect.

There is also an element of recursive causality between a particle and its own information. The collapse of the wavefunction isn’t necessarily an observer effect, but an informational effect. Remember that information is the resolution of uncertainty, according to Shannon. The collapse of the wavefunction is when all the quantum states become known – they’re viewed as physical while simultaneously the information becomes known. But the particle was always physical; it’s the information aspect that is unknown. That means it is the physical that signals to the informational, causing the unknown to become the known.

The takeaway from this recursive idea is that physical objects can actually have a causal relationship with their own informational aspect. As I said, information tells material how to be and material tells information what to be – the information causes the quantum field fluctuations while the physical material causes the information to take on a state.

The Medium of Information

Some modern scientists take on a Pythagorean way of thinking about math, with numbers themselves being fundamental and our material world being contingent upon the mathematics. This puts math in a prescriptive relationship to reality rather than descriptive. The metaphysics discussed above is a similar metaphysics in that it takes information processing to be fundamental.

However, I’m proposing that mathematics is only one medium in which processing can occur. The processing that occurs in the informational space of matter is of a different kind that mathematical processes, though it can be described mathematically. This medium of information processing is the missing piece in causality that David Hume claimed as the reason why we could never know whether some event B was caused by a preceding event A.

Mathematics describes reality in the materialist sense while this other medium of processing describes reality in the informational sense. While the math of information theory is descriptive, this other medium is prescriptive: the informational aspect of reality occurs in the language of this other medium. Being able to understand this medium of information processing would require a whole new set of operations outside of mathematics, although math may have some use in describing it, just as in information theory.

This may seem to run afoul of the causal exclusion principle. Why invoke this other medium when mathematics is sufficient for understanding the informational aspect of quantum bodies? I propose that mathematics, though possibly necessary, is not sufficient. The evolution of a spin-half particle’s wavefunction through time can be described by the Dirac equation. However, this only describes the material reality by predicting what one will find in an experiment. An evolving particle, though, also has an evolving informational space. There are simple preserved symmetries, though, such as the quantum states themselves and the Pauli exclusion principle, which means the fractal dimension of the information-matter property duality is also symmetric with respect to the evolving informational space. The point is, though, if we wanted to know, for instance, what causes the wavefunction collapse itself, we would need to come up with a new medium for doing such calculations. It’s in the causal relationship between observation and wavefunction collapse where the information space comes into play.

Informational causality also implies that, just like with material bodies, there can be informational multi-systems.

The Mereology of Information

When atoms bond together, they become molecules. The study of the rules for bonding behavior falls under chemistry. But what does it mean for the information aspect of matter when this sort of bonding occurs?

Physical components coming together to form a structure generate something that is greater than the sum of its parts. A single carbon atom – even one bound to four hydrogens – cannot hydrolyze nucleotide bonds in proteins, but if that same carbon atom becomes part of a protease enzyme, then it can participate in such an undertaking. Indeed, to describe anything on a macroscopic scale as “just a collection of atoms” is missing, quite literally, the big picture.

This same mereological fact is also true of the informational space aspect of reality. This can be thought of in simple terms as each electron in a metal having different quantum states due to the Pauli exclusion principle. That same metal can be used in a transistor when processing information on a computer. Now that metal, on a larger scale (relative to single electrons) is involved in information processing.

The information processing done by a computer, though, is doing mathematical calculations. However, given the informational aspect of matter, it should also be possible to do calculations within the second medium of information processing.