An Unsimulated Simulation

The Simulation Hypothesis Bob is an alien in an alien universe with a googol times as many resources as the entire earth combined. Bob decides, as anyone would do in his situation, to simulate a universe. Bob builds an enormous supercomputer Bob writes a program that simulates a universe Bob lets it run Bob just so happened to pick some rules that cause an emergent universe to form, with a big bang, and galaxies and stars and planets. On one of those planets intelligent life evolves, a civilization develops, and an organism named Alice is born. Alice, a conscious being like yourself, lives her life unaware that she resides within a simulated universe.[1] The simulation hypothesis can explain why our universe exists, but it moves the question to explaining why Bob’s universe exists. Many people can accept it as possible in theory. Let's see where the assumption that it is possible can lead. ... Alice's Computable Function Does Bob need to be aware of Alice's existence in order for her to exist? In many simulation hypothesis scenarios, it is not required for the builder to be aware of life for it to "exist". It is hard to imagine Bob intricately watching every organism of the universe he created, even if he monitors a few. From Alice's perspective, she is unaware of Bob or the fact that she is in a simulation. If Bob is not required to be made aware of Alice's existence, then clearly Alice does not exist as a representation within Bob's mind, and instead exists as some internal representation within Bob's computer, some binary information encoding the states of all the atoms that make up her mind. This is perhaps not surprising, and is what many people think of when they think of the simulation hypothesis. However, since Bob need not be aware, there is no frame of reference for what satisfies an internal representation. Why not? Can't we make restrictions on how Bob's computer stores this internal representation? Let's push it and see if we can draw a line somewhere. Note that "Alice's universe" also includes its laws (the code that runs it), and that a "representation" contains the stored information along with whatever unpacks it. A high precision encoding of Alice's universe The same encoding, but every byte is inverted The same encoding, but stored as a lossless compressed .zip file Any arbitrary lossless compression algorithm The next step would be a lossy compression algorithm that cannot perfectly recover Alice. Here though, we can draw a line; some of Alice is gone, and in the extreme case, all of her. We started with the assumption that #1 can be Alice, so as long as the input combined with the decompressor can recreate Alice, we should accept it[2]. Let's assume Bob's program is a state machine, and that Alice sprang into existence at state mjx-container[jax="CHTML"] { line-height: 0; } mjx-container [space="1"] { margin-left: .111em; } mjx-container [space="2"] { margin-left: .167em; } mjx-container [space="3"] { margin-left: .222em; } mjx-container [space="4"] { margin-left: .278em; } mjx-container [space="5"] { margin-left: .333em; } mjx-container [rspace="1"] { margin-right: .111em; } mjx-container [rspace="2"] { margin-right: .167em; } mjx-container [rspace="3"] { margin-right: .222em; } mjx-container [rspace="4"] { margin-right: .278em; } mjx-container [rspace="5"] { margin-right: .333em; } mjx-container [size="s"] { font-size: 70.7%; } mjx-container [size="ss"] { font-size: 50%; } mjx-container [size="Tn"] { font-size: 60%; } mjx-container [size="sm"] { font-size: 85%; } mjx-container [size="lg"] { font-size: 120%; } mjx-container [size="Lg"] { font-size: 144%; } mjx-container [size="LG"] { font-size: 173%; } mjx-container [size="hg"] { font-size: 207%; } mjx-container [size="HG"] { font-size: 249%; } mjx-container [width="full"] { width: 100%; } mjx-box { display: inline-block; } mjx-block { display: block; } mjx-itable { display: inline-table; } mjx-row { display: table-row; } mjx-row > * { display: table-cell; } mjx-mtext { display: inline-block; } mjx-mstyle { display: inline-block; } mjx-merror { display: inline-block; color: red; background-color: yellow; } mjx-mphantom { visibility: hidden; } _::-webkit-full-page-media, _:future, :root mjx-container { will-change: opacity; } mjx-math { display: inline-block; text-align: left; line-height: 0; text-indent: 0; font-style: normal; font-weight: normal; font-size: 100%; font-size-adjust: none; letter-spacing: normal; border-collapse: collapse; word-wrap: normal; word-spacing: normal; white-space: nowrap; direction: ltr; padding: 1px 0; } mjx-container[jax="CHTML"][display="true"] { display: block; text-align: center; margin: 1em 0; } mjx-container[jax="CHTML"][display="true"][width="full"] { display: flex; } mjx-container[jax="CHTML"][display="true"] mjx-math { padding: 0; } mjx-container[jax