Why? How does this improvement translates to more financial gains?

because with that knowledge, you will be able to decompress 0 dollar to infinite dollars which the storage mafia will pay you for not publishing your breakthrough in making them obsolete.

Let's say you really find a new, much much better compression algorithm for texts. I do believe that soon new applications will appear that will make use of the whole storage space that existing data storage devices can offer.

Are you possibly hinting at the endless stream of "new generation iWasteware camera, now with 2 gigapixel sensor" in combination with camera apps that put a (high) limit on the lowest resolution one can choose?

I did not have exactly this application in mind, but I was aware that this kind of waste does exist for many commercial applications when I was writing my reply.

sorry, who exactly is the storage mafia?

The idea is that sufficiently powerful compression is indistinguishable from artificial intelligence, which can be used to make even more money.

Being that smart translates to more financial gains.

because, then you will have beat pied piper in the market.

Well, if you achieve this, you'll basically have proven that something (a bunch of information) equals nothing (no information). So 1=0.

Once you have that, becoming rich is trivial. Multiplying both sides of the equation by one trillion, 1 trillion = 0. So open a bank account with $0, now you have one trillion. Easy.

A funnier (although grimmer) way: let p be the world's population. Multiplying both sides of the equation by (p-1) you get p-1=0. Thus, p=1. If you assume that you exist (which is a reasonable assumption, following Descartes's reasoning) you now own all the wealth in the world.

I think personally I can compress $1b into 0 within a week, but $1tr would be a real challenge. Another thing I should point out that I don't support compressing people (for now).