Foundation - Apophysics

Ideas from Matter

Apophysics is the unraveling of philosophy on the basis that we can measure physical objects in our reality. This series is an explanation of my philosophy.

Introduction

Apophysics is term I have coined to describe a way of doing philosophy on the basis of the measurability of matter. It is an intentional shift away from the term and field of metaphysics. Metaphysics was more-or-less coined by Aristotle or his editor in the phrase transliterated, ta meta ta phusika—the/that after the natural/physical. Aristotle sought to describe and understand things beyond the natural world in that book. He, like myself, put an emphasis on what could be seen and felt in the natural world, yet still felt it necessary to go beyond it. In doing do, he sought to understand first principles and the causes.

As you may recall from your undergraduate philosophy class, Aristotle describes four types of causes which objects have. There is a material cause—what the thing is materially made from. Then there is the efficient cause, which I think may be better understood as the agential or perhaps energetic cause—who or what put the energy into the object. We all know the formal cause, for Aristotle believed in matter and form, of course. This might otherwise be called the essence or even idea of the object. Finally, there is the final cause, the telic cause, or what the object’s significance is.

Immediately we see that there is more than meets the eye here than merely specifying the “causes” of objects. Like an eggshell in the omelet, at least the second and forth causes in this list imply distasteful things that I am not ready to admit of at the beginning of an investigation into first principles. We might assume, with Aristotle, that there is an efficacious cause to objects, and that they have significance, but… why? Surely these are not first principles, right? Am I the crazy one?

Then there’s the notion of form itself—what is he even talking about!? How is it that we are to understand these “causes” as prior to the object, when all we have for reference is the objects themselves. He is indeed logical, in the sense that a cause must precede its effect, but in what way does an objects form logically precede the object itself? In what way does an objects significance precede its existence? No! Surely, Aristotle has conflated terms by grouping together too many causes. Or, more likely, I don’t understand what he means by “cause”. Regardless, please excuse me while I flip the table.

Three-hundred and sixty degrees later, having the tabula rasa of a clear mind accompanying us, let is consider what might happen if we really do believe that matter is. Assume, with me, that matter is real, and from it, seek understanding of the causes and the first principles. Rather than examining that which is after or beyond the natural world, let us consider what we can glean from, apo, physics. If this foundation is laid, perhaps a great structure of philosophy may be erected upon it.

This introduction, called Foundation, provides the logical and mathematical framework in which apophysics works; its basis and foundation. The foundation is not the building. There is little useful about a foundation in and of itself, but it is indispensable in the construction of a good building. Similarly, those who seek only to use or even admire the building will probably not care to dwell on the significance of the foundation. It is merely instrumental. In this way, the following foundation is not meant to be understood by everyone. It is technical, in its own way, but does not make philosophically significant claims, except perhaps in its basic idea—that of the measurability of matter itself. As you will see in this series, I take the results of this to imply some significant things about our world.

Foundation

For any object o there exists data d which rigorously describes o.¹ We can imagine a machine that can convert o into d (perhaps with the accident of producing pure energy) and another machine that could instantiate o from d (perhaps given enough energy).² In the former case, there would exist f(o) = d, and in the latter, f’(d) = o.

If we take the set of all objects,³ O, we could take the set of all data, D, to be the set that rigorously describes all instantiated things.⁴ We can also take O at t to be the set of all instantiated objects within a particular snapshot in time, t, and similarly, D at t.⁵

It is possible to view relationships within D by introducing relational operators, r.⁶ r are rules which insert pointers over identical sets of data within d to a single, abstract instance of that data.⁷ For example, within any given D at t, there may exist some d which rigorously describe electrons;⁸ e1 and e2 are identical except for their spatial location, which is, ignoring quantum entanglement, probably the only metadata needed to rigorously describe them. Let a relational operator operate thusly: For each electron element in D, set its data to be a pointer to the data of the electron in conjunction with its spatial location. This notion of pointing to the data of the electron is like what we mean be the idea of an electron.⁹ Thus, we will call the data pointed to by relational operators, ideas. Let i be the symbol for an idea. We only admit i generated by r. A set of r may be called R.¹⁰ A set of i may be called I.

Any collection of r can be included in a given R, even if different operators overlap over the same data in a given d. We can represent d as a bitstring in its original form,¹¹ unchanged by r, and merely add pointers from data within d according to the various r in play.¹² In this way, there may be substrings or sets of substrings within d that point to various i, but the actual data in d does not change. In other words, r are nonexclusive with respect to data within d.

We have shown the relationships between d, o, r, and i. What is particularly compelling about this is that both d and i exist in the same abstract, uninstantiated way. When we consider D, we consider only the set of data which rigorously describes all instantiated objects. But what if we consider the set of all ideas, I, for a given R? If there are a finite number of objects, and therefore a finite amount of data, then there is also a finite number of ways to interrelate the data—a finite number of relational operators. Since relational operators generate ideas, there are a finite number of ideas.¹³ Intuitively, given a real O, and its corresponding D, and the maximal set R, the vast number of i in the corresponding I have no pointers to them, assuming a bounded universe from which O is formed.

We can extend this idea by considering what happens when we remove information from d: d’ = d - x, where x is a subset of the information in d.¹⁴ Here, d’ is no longer the exact data-like representation of o, but is only d - x over d representative of o.¹⁵ Furthermore, there are many d’ that are equally representative of o.¹⁶ Accordingly, we could generate new i by introducing a fuzzy sort of r which checks for similarity among d and inserts pointers over similar parts in different d to the respective i. This would, of course, be lossy.¹⁷ For a given R, D, and I, if R includes lossy r, we could calculate confidence intervals or probabilities with respect to a given d and the corresponding i. This facilitates probabilistic reasoning, adding significant flexibility to the model.¹⁸

Let A = {D, I, R}, where A can be called the apophysical non-space.

1. This is just a claim that mathematics can describe matter precisely, as in physics. As far as I know, this is relatively uncontroversial, although hubristically so, as we’re nowhere close to achieving this. While he isn’t particularly “mainstream”, I have hope that Stephen Wolfram and his work on computational physics, or more generally, computational science, will at least support my claim. For the foundations of his project, see Stephen Wolfram, A New Kind of Science (Wolfram Media, 2002), https://www.wolframscience.com. Of particular interest to philosophers is his principle of computational equivalence, which shows that there is a limit to complexity that lies below the limit of what is possibly computable. This includes the mind. His work is also online at https://writings.stephenwolfram.com.

I am not particularly concerned with mereology at this stage. Any object o could be any finite thing, from the universe down to a subatomic particle or perhaps something even smaller.

Little needs to be said about the nature of d. It could be any sort of abstract representation of o, so long as it rigorously “defines” o. This could include having embedded in d a wide range of information and metadata about o. Likewise, there could be many equivalent (or computationally equivalent) forms of d for any given o. The point, for now, is that d could theoretically exist.

2. Instantiate here means, to cause an instance of; to represent in a material instance. I.E. just to make physical, as opposed to only “existing” in a data-like form.

3. In this version of the paper, much of the mathematical notation has been removed for formatting reasons. Substack does not current support things like subscript and does not have a formula editor.

4. As an aside: I believe that a computer that exists within a universe with D in its memory is paradoxical due to irreducibility. However, if it were to exist, universe itself could be accurately viewed as that computer.

5. These snapshots are not necessary to the theory, but much like computer vision views things in terms of frames and pixels, I find that it is helpful to view things in snapshots. Technically, t is just another relational operator (explained below).

6. Relational operator may not be the best term for this, as it refers both to relationships and the mathematical concept of a relation or operation. The term ‘rule’ is better, but it is perhaps too generic. “Idea-generating idea” is much more descriptive, but I think people would mistakenly prejudge these to be circular.

7. Pointers, as a concept in computer programming, contain an address to some other object. The core concept is exactly as I use it here.

8. Here, I take electrons as an example of an object in O, and hope that my readers don’t find this too inconceivable. In other words, I acknowledge that electrons may be composite.

9. To clarify, the data that perfectly describes an electron are what our notion/idea of an electron imperfectly portrays—it is imperfect only to the extent that our minds do not symbolically represent the electron that is equivalent to the actual data of the electron. This hints at my epistemology.

10. R can contain rules which generate any idea (abstract object) you want. I know this is a big claim, left unproven in this paper. But if there are a finite number of ideas… (see two paragraphs down)

11. A bitstring is a string of bits—a bunch of 0s and 1s in sequence. This is the fundamental structure of data in traditional computers. This paper does not require the formating of data as bitstrings, but is it a typical and easy way to talk about the format of data.

12. This is what I meant by the phrase, “insert pointers over identical sets of data within d” when I defined r.

13. Finding the exact number is a combinatorics problem that is beyond the scope of this paper.

It is worth noting that I am not permitting relational operators to operate on ideas. However, since there is an idea for every possible relational operator, every possible idea already exists, even without letting r work on i. If I were to allow r to take i, there would be an infinite number of ideas, requiring a more robust set theory to handle.

14. I use the term information rather than data here because I am going to use the term information in my future discussion of epistemology. I find this wording to be the clearest, given that data already is used to refer to the whole of d for a given o.

15. This is to say that d’ fractionally represents o. It is still an imperfect image or representation of o.

16. Let d be represented by a bitstring of length n, and x be a bitstring of the same length with k bits which are 1. d’, then, has n choose k (binomial coefficient) possible ways to be wrong, and thereby n choose k equally wrong possibilities.

17. The term, ‘lossy’, refers to a property of some compression algorithms which cause data to be lost during the compression process. If d were compressed by a lossy algorithm, d’ would result from uncompressing d.

18. This paragraph is not necessary to the model itself. But I find it so central to how I actually think about the model that I can’t help but to include it. It also serves as an initial example of how the fundamental model can be extended upon in order to make it more “practical”.