This gets reposted quite often.

The crux of the ongoing debate over the post has to do with the ambiguity of the stated requirements.

For there to be any rational discussion, you need to have proper unique definitions for what is being communicated. Without a definition (identity) no system of truth seeking will provide a definitive truth.

Most notably, "compression" has many different meanings currently in practical use. For example many people use the word compression and simply mean that the uncompressed size is more than the compressed size; lossy vs lossless doesn't matter when its good enough, all that matters is its been reduced, and an example of that might be H264 video.

Other more rigorous individuals will use it to mean entropy encoding, which has a strict definition, part of which is lossless, and in these cases they often view Shannon's theorems as gospel, and at that point they often stop thinking and may not try to sharpen their teeth on a seemingly impossible task.

These theorems are often very nuanced, with the bounds very theoretical or still undiscovered, though still seemingly correct. When someone is told something is impossible, they don't fully apply themselves to try to find a solution. Its a worn path that leads nowhere, or so they imagine.

This mindset of learned helplessness prevents a nuanced intuitive understanding of such problems and any advances stagnate. People take the impossibility at face value, and overgeneralize it (without that nuanced understanding), this is fallacy and it can be very difficult to recognize it when there is no simple way to refute it on its face.

Here is something to consider. Shannon's source coding theorem relies on the average uncertainty of probabilities as a measure of entropy (information). Some exploration is needed to understand what makes this true, or where it fails. It has been my experience that only a very few exceptional people ever attempt this process.

The main question that jumps out in my mind since compression has been a thing I've been interested in for years; is, can an average entropy in statistics tell us accurately whether this is true in systems with probabilities and distributions that are a mix of mathematical chaos but also contain regularity within their domains? Statistics can be unwieldy beasts, and act as regular sources of misunderstanding and falsehood without a very rigorous approach.

For a similar problem, people may find this article particularly relevant with regards to the chaotic 3-body problem in astrophysics.

https://www.aanda.org/articles/aa/full_html/2024/09/aa49862-...