On the intelligibility of the universe and the notions of simplicity, complexity and irreducibility
By Gregory J. Chaitin. 2002
37 citations recorded by the source corpus.
We discuss views about whether the universe can be rationally comprehended, starting with Plato, then Leibniz, and then the views of some distinguished scientists of the previous century. Based on this, we defend the thesis that comprehension is compression, i.e., explaining many facts using few theoretical assumptions, and that a theory may be viewed as a computer program for calculating observations. This provides motivation for defining the complexity of something to be the size of the simplest theory for it, in other words, the size of the smallest program for calculating it. This is the central idea of algorithmic information theory (AIT), a field of theoretical computer science. Using the mathematical concept of program-size complexity, we exhibit irreducible mathematical facts, mathematical facts that cannot be demonstrated using any mathematical theory simpler than they are. It follows that the world of mathematical ideas has infinite complexity and is therefore not fully comprehensible, at least not in a static fashion. Whether the physical world has finite or infinite complexity remains to be seen. Current science believes that the world contains randomness, and is therefore also infinitely complex, but a deterministic universe that simulates randomness via pseudo-randomness is also a possibility, at least according to recent highly speculative work of S. Wolfram.
Subfields: Computational Theory and Mathematics, Natural Language Processing, Philosophy
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Computational Theory and Mathematics
In Natural Language Processing
- Graham Neubig
- Phil Blunsom
- Chris Dyer
- Dani Yogatama
- Kyunghyun Cho
- Mohit Bansal
- Wang Ling
- Noah A. Smith
In Philosophy
Citations in the corpus
- Learning and Evaluating General Linguistic Intelligence (2019, background): “ments, in addition to traditional performance metrics. The online code is rooted in information theory and is based on connections between generalization, compression, and comprehension (Wolff, 1982; Chaitin, 2007). In general, the separation between training and test sets is arbitrary, and there is”