Redundant information can be described by „information that is present in my different parts of a system“. John Wentworth gave a more formal example, if redundant information being described by a resampling process.
According to him, redundant information can be found via a resampling process. E.g. imagine comparing the genomes of different people. You want to find out the information that is shared between them, i.e. redundant. To do that, you first track which genomes are frequent. Then you throw away one genome and try to rebuild it by resampling it, conditional on all the other sampled genomes. E.g. there might be a certain mutation that is present in most genomes, so it is likely that it will be present in the discarded genome as well.
John Wentworth provides more examples in his post.
Source: Wentworth, J. (2022) ‘Abstractions as Redundant Information’. Available at: https://www.alignmentforum.org/posts/vvEebH5jEvxnJEvBC/abstractions-as-redundant-information (Accessed: 20 March 2023).
Chan, L., Lang, L. and Jenner, E. (no date) ‘Natural Abstractions: Key claims, Theorems, and Critiques’. Available at: https://www.alignmentforum.org/posts/gvzW46Z3BsaZsLc25/natural-abstractions-key-claims-theorems-and-critiques-1 (Accessed: 19 March 2023).