Proving the existence of irrational numbers does not necessarily affect the simulation hypothesis, but some people have argued that it could be a possible evidence against it.
The simulation hypothesis is the idea that we are living in a computer-generated reality1. This simulation could contain conscious minds that may or may not know that they live inside a simulation. Some proponents of the simulation hypothesis suggest that glitches or errors in the simulation could be some evidence for it, but this does not explain why we would be simulated in the first place.
Irrational numbers are real numbers that cannot be represented as simple fractions2. An irrational number cannot be expressed as a ratio, such as p/q, where p and q are integers, q≠0. It is a contradiction of rational numbers. Irrational numbers are usually expressed as R\Q, where the backward slash symbol denotes ‘set minus’. Some examples of irrational numbers are √2, π, e, φ, etc.
One argument that irrational numbers could be evidence against the simulation hypothesis is based on the idea that irrational numbers would require infinite information to be encoded in a computer program3. Since a computer program is finite and discrete, it cannot store or process an infinite amount of data. Therefore, if we can find irrational numbers that are not formula-based (that is, they cannot be generated by a finite algorithm), then we would have proof that our reality is not a simulation.
However, this argument has some problems. First, it assumes that the simulation has to encode all irrational numbers explicitly, rather than approximating them or generating them on demand. Second, it assumes that the simulation has to use the same mathematical system and notation as we do, rather than using some other representation or encoding that could handle irrational numbers more efficiently. Third, it assumes that the simulation has to follow the same physical laws and constants as we observe, rather than using some other rules or parameters that could make irrational numbers irrelevant or nonexistent.
Therefore, proving the existence of irrational numbers does not necessarily affect the simulation hypothesis, unless we can also prove that the simulation has to use the same mathematics and physics as we do. However, this is very difficult to do, since we have no access to the underlying reality or the motives of the simulator. The simulation hypothesis remains a controversial and untestable idea that has many philosophical and scientific implications.
The history of irrational numbers and the simulation hypothesis are quite different, as they belong to different fields of mathematics and philosophy, respectively. However, they both have ancient origins and have been debated for centuries.
The history of irrational numbers dates back to the ancient Greeks, who were the first to discover and prove the existence of numbers that cannot be expressed as fractions of two integers1234. One of the earliest examples of an irrational number is √2, which is the length of the diagonal of a unit square. According to legend, a Pythagorean named Hippasus was the first to show that √2 is irrational, using a proof by contradiction. However, this discovery contradicted the Pythagorean belief that all numbers are rational, and Hippasus was allegedly killed or exiled for revealing this secret14. Other famous irrational numbers include π, e, φ, etc.
The history of the simulation hypothesis goes back to the ancient Chinese, Indian, and Greek philosophers, who proposed various forms of skeptical scenarios that questioned the nature of reality and our perception of it5. For example, Zhuangzi dreamed that he was a butterfly and wondered if he was actually a butterfly dreaming that he was a man5. The Indian concept of Maya suggested that the world is an illusion created by the divine5. Plato’s allegory of the cave depicted people who only see shadows of reality on a wall5. These ideas were later developed by modern philosophers such as Descartes, Berkeley, Hume, Kant, Nietzsche, etc. The simulation hypothesis in its current form was popularized by Nick Bostrom in 2003, who argued that we are likely living in a computer simulation created by a more advanced civilization5. This hypothesis has been influenced by science fiction, such as The Matrix, and has been discussed by scientists, technologists, and comedians.
最后编辑时间：2023年7月5日晚上11:14 所有者：xiuhao
::: ▶科学共识关于仿真假设的起源是什么？
仿真假设是指整个存在是一个模拟的现实，如计算机模拟1。这个模拟可能包含有意识的思维，可能知道或不知道他们生活在模拟中。该假设以其当前形式由Nick Bostrom普及，他认为以下至少一个命题是真的1：
1.人类级别文明达到后人类阶段（即能够运行高保真祖先模拟的阶段）的比例非常接近于零；或 2.后人类文明对运行祖先模拟感兴趣的比例非常接近于零；或 3.我们这种经验的所有人生活在模拟中的比例非常接近于1。
科学共识关于仿真假设的起源还不清楚，因为有许多不同的意见和赞成反对的论据。有些人声称有实证证据支持该假设，例如自然中的故障、异常或模式，表明计算起源2。其他人则认为该假说是非科学的、不可测试的或不实用的，并且混淆了科幻小说与科学3。有人指出，该假说具有悠久的哲学历史，可以追溯到古代怀疑主义、唯心主义或唯我论1。