From e9a6b2006f08c3a48ab4e64d6c84a4ff4e62d411 Mon Sep 17 00:00:00 2001 From: Preston Pan Date: Fri, 23 Jun 2023 11:45:28 +0800 Subject: Add a lot of new content; uses exwm now --- mindmap/duality.org | 79 +++++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 79 insertions(+) (limited to 'mindmap/duality.org') diff --git a/mindmap/duality.org b/mindmap/duality.org index a87536c..48e433b 100644 --- a/mindmap/duality.org +++ b/mindmap/duality.org @@ -10,6 +10,9 @@ Is it me, or is it you? Is it false, or is it true? Many things can be explained by a bimodal or binary system. Everything, from boolean logic to art, any system whose goal is to make a prediction. +My hypothesis is that whenever someone believes something, the opposite +belief is equally valid. In order to demonstrate, let me introduce: + ** The Great Filter No, not the one about aliens dying or something. I'm talking about the everyday systems that you use in order to make predictions about the @@ -19,3 +22,79 @@ world. For example, this one, that wants to explain everything. Because this is indeed a system that explains everything, I must also demonstrate why it might be impossible to explain everything. I'll give the argument in a short set of syllogisms. + +1. If something must explain everything, it must also explain itself. +2. If it explains itself, it means it is circular by definition, and therefore not objective. +3. If it does not explain itself, then it does not explain everything, and it is therefore incomplete. + +So either the system we're describing is circular, in which case it is arbitrary and subjective, +or it is incomplete. So there's no way to construct any system with both qualities. Right? + +*** The problem with the problem with explaining everything +Notice that our above set of syllogisms is extrapolative. This means that it makes predictions +about what is possible about a system. Due to this, the system results in some duality: +either a valid system is incomplete or subjective. And there's another problem too: the system applies to itself. + +If either systems are subjective or incomplete, then the system we are using to describe subjective and incomplete +systems is also subjective. Which presents a problem: we have no reason to believe that this framework is worth +believing in at all! +*** The problem with the problem with the problem with explaining everything +But the fact that the system applied to itself breaks it is just a confirmation that our predictions are accurate! +We predicted that things that explain themselves must be circular, and we were correct! +*** etc... +The claim is that we can do this forever, although even this statement can go on forever. What's interesting +is that it seems like there's an inherent link between duality and [[id:654280d8-82e8-4a0e-a914-bd32181c101b][infinite]] [[id:8f265f93-e5fd-4150-a845-a60ab7063164][recursion]]; infinite self reference. But the real question is: is this +statement about frameworks true, or is it false? Well, according to the principle of duality, both of them can +be true. + +** The Filter is based on what you choose to believe +So what you think is true or false is just what you choose to be true or false. Of course, even this statement is an infinite contradiction +and confirmation, but what I am trying to communicate is that what you believe filters what's true and what's false, and as a result, +leads to different prescriptions, or different actions for the same situation. In this way, frameworks act like filters. They shield us +from the infinite opposite side of what we currently believe. Does this "filter" I am describing exist or not? + +** Of course it Doesn't! +The mindmap explains everything, without a filter. + +* The problem and solution with duality +The theory of duality is self deconstructing and self constructing in the same way via self reference. If the opposite stance is valid, +that means that not believing in duality is valid, but that also is a data point that confirms our hypothesis. + +We're also describing duality using a dual framework here, which is another pretty interesting thought. + +* Logic Explains Duality +Logic is a self affirming structure, and that might give you the clue that it is also self destructing. Nevertheless, one of the axioms +of logic is: +\begin{align*} +p \neq \neg p. +\end{align*} +This statement filters for binary, or as I would call it, dual mode frameworks, and gets around the principle of explosion. We have an intuitive +understanding of truth and falsehood, and we can use those general terms whenever there is a mutually exclusive divide. In short, you can view +the logical framework as an abstraction of all other dual frameworks. I propose that you can do analysis on all dual frameworks in much the same +way group theory does analysis on groups. + +* Programming Explains Duality +Of course, there is logic in programming, but that is kind of boring. What I am going to explain here is a recursive, binary structure known +as the binary tree. It seems like you can model a lot of things in this way as well; John Conway's surreal numbers are a manifestation of this +phenomenon. +#+begin_src python :exports both :results output +class BinaryTreeNode: + def __init__(self, value): + self.left = None + self.right = None + self.value = value + def insert(self, value): + if value < self.value: + if self.left is None: + self.left = BinaryTreeNode(value) + else: + self.left.insert(value) + else: + if self.right is None: + self.right = BinaryTreeNode(value) + else: + self.right.insert(value) +#+end_src +Currently, all that this binary tree has is an insert method, but that is all that is needed in order to see the [[id:8f265f93-e5fd-4150-a845-a60ab7063164][recursion]] in the structure. +Each node "height" is self similar, and it works of a dual-mode sorting algorithm. That is, smaller values go on the left side, and bigger +values go on the right side. -- cgit