King_Anarchist
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A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
How can I troll my own thread? :confused: It's interesting that you mention theology because that's exactly what a ToE is about (at least for me). I'm a pantheist so one could say that I equate God to reality which is the totality of all that exists (whatever that might be). A study of reality is then a study of God. A TOE must be a complete description of reality, otherwise it's not everything it's a theory of. Reality contains much more than quanta, don't you think? Consider the abstract and Platonic Forms. The discipline that deals with this kind of ToE is math, philosophy, and the philosophy of science and math. I don't think it's falsifiable so it's not a science problem, at least not as a whole. Science may one day come up with a ToEP, a theory of everything that is physical but that neglects everything that is not physical. Let me try to be clear although much of this is covered in the link in the top. If reality exists then it is structurally equivalent to a mathematical structure. I'll call the antecedent the reality hypothesis (RH) and the consequence the mathematical universe hypothesis (MUH). I seek to argue that RH implies MUH. (This is based on the works of Max Tegmark [1], for example with some modifications.) A complete description of reality is called a ToE (theory of everything). <ul type="square">[*]The RH implies that for a description to be complete, it must be welldefined also according to nonhuman sentient entities (say aliens or future supercomputers) that lack the common understanding of concepts that we humans have evolved, e.g., "particle", "observation" or indeed any other English words. Put differently, such a description must be expressible in a form that is devoid of human "baggage". [*]The RH implies that a ToE has no baggage. [*]There are many equivalent ways of describing the same structure, and a particular mathematical structure can be defined as an equivalence class of descriptions. Thus although any one description involves some degree of arbitrariness (in notation, etc.), there is nothing arbitrary about the mathematical structure itself. [*]Something that has a baggagefree description is precisely a mathematical structure. [*]Therefore, the physical reality described by the TOE is a mathematical structure. What is meant by the expression "mathematical structure?" [1] provides an intuitive explanation of what a mathematical structure is by saying, "all mathematical structures are just special cases of one and the same thing: socalled formal systems. A formal system consists of abstract symbols and rules for manipulating them, specifying how new strings of symbols referred to as theorems can be derived from given ones referred to as axioms." The precise definition is available upon request. Intuitively, the "phrase reality is structurally equivalent to a mathematical structure" means two things: <ul type="square">[*]There is a onetoone correspondence between reality and the set of symbols of a mathematical structure and [*]This onetoone correspondence 'preserves truth' when statements are translated from the language of reality to the language of a mathematical structure. Preservation of truth means a statement in a language of reality is true if and only if it is true in a mathematical structure. [1] M. Tegmark, The Multiverse Hierarchy, arXiv:0905.1283v1 (2009) [0905.1283] The Multiverse Hierarchy I am familiar with the argument clinic skit. Superficially I see the resemblance between this and that. :D 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
You sure everything is made of quanta? :devil: 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
QM has jurisdiction only over quanta. :cry: 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
Exactly. The process of iterating the "define all words in this sentence" operation can go on indefinitely but with finitely many words in the language, eventually there are "cycles". I call the words for which that operation is very short atomic. In other words, if you define a word and then define the words in that definition, and when you do that you get the original word. 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
What isn't a verbal circle? :confused: 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
Indeed: what about that? Which statement? If supporting conditions are necessary for anything to be possible, then 'anything' is conditional rather than absolute. A conditional nature of 'anything' actually places a limit on 'anything' so 'anything' really isn't 'anything'. 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
Maybe it would be helpful to attempt to clarify what I mean, albeit with a possibly lack of descriptive power. Reality is this. 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
"Reality exists" is a condition without a supporting condition that proves my argument. In the document, I wrote about how the "external reality hypothesis" leads to the mathematical universe hypothesis (MUH)... The argument still works if we drop the word "external". 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
Reality exists. 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
This is a mathematical theory not a scientific one based on the premise that the universe is a mathematical structure (which follows from other premiseswhich may or may not be true :yum: ). So it's not predictive. 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
Not exactly sure which absolute quantities you're referring to. What I try to do is detail what is, essentially, a structure containing* all other structures. Assuming the mathematical universe hypothesis (which was argued to follow from the external reality hypothesis by Tegmark), such a structure basically represents the universe. *Containing isn't quite right but it might suffice for this discussion. If you mean that it depends on other theories then yes absolutely. Finite/infinite are jargon words in math which may or may not correspond to what one might intuitively call finite/infinite. Within the context of math there are ways to define these terms. If we've developed the machinery to define the set of natural numbers and onetoone correspondences, then a set is finite if there is a 11 correspondence between it and any set of the form {0,1,...,n}. A set is called infinite if it is not finite. Another approach is to start by defining an infinite set first. A set is infinite if there is a 11 correspondence between it and a proper subset of it. (Proper subset of a set means a subset in which at least one element of it is absent.) Then a set is finite if it is not infinite. 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
I just realized that I can greatly simplify this. I don't think I need to resort to exotic set theories which will make it a bit less objectionable. woot 
On the computational capabilities of physical systems part I: the impossibility of infallible computation http://arxiv.org/abs/physics/0005058 In this first of two papers, strong limits on the accuracy of physical computation are established. First it is proven that there cannot be a physical computer C to which one can pose any and all computational tasks concerning the physical universe. Next it is proven that no physical computer C can correctly carry out any computational task in the subset of such tasks that can be posed to C. As a particular example, this means that there cannot be a physical computer that can, for any physical system external to that computer, take the specification of that external system's state as input and then correctly predict its future state before that future state actually occurs. The results also mean that there cannot exist an infallible, generalpurpose observation apparatus, and that there cannot be an infallible, generalpurpose control apparatus. These results do not rely on systems that are infinite, and/or nonclassical, and/or obey chaotic dynamics. They also hold even if one uses an infinitely fast, infinitely dense computer, with computational powers greater than that of a Turing Machine.

A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
That image is a collection of pixels which approximate squares, which are polygons. If I said "then it is possible to draw something that is both a circle and a 100gon" one might say "maybe you can" due to the closeness of the two... So saying a triangle would be the most "dramatic" demonstration of an "impossible feat". ;) 
A mathematical definition of the universe
King_Anarchist replied to King_Anarchist's topic in TTI Archives
For better or for worse, everything is an inescapable conclusion from the premise that anything is possible. Some pathological example might be "if anything is possible, then it is possible to draw a square circle." I agree.