:PROPERTIES:
:ID:       1b1a8cff-1d20-4689-8466-ea88411007d7
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#+title: duality
#+author: Preston Pan
#+html_head: <link rel="stylesheet" type="text/css" href="../style.css" />
#+date: <2023-06-10 Sat>
* is it One or is it Two?
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
world. For example, this one, that wants to explain everything.

*** The problem of explaining 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.