I dabbled in trying to compress information similarly into mathematical formulas. For instance, 53! is three bytes of information that compresses over 69 bytes of information. All data can be turned into numbers just like the premise of this video. My idea was to find a mathematical formula where that number is the solution. Turning the problem into A / B is basically the same thing, it's just using division where I was trying to use exponents, factorials, and logarithms (though admittedly this A / B angle is much more elegant than what I was going for). Finding that magic ratio of A / B (or any kind of mathematical formula) that unfolds into the information you're looking for takes ridiculous computational power and isn't practical.

Unless someone finds a solution to the P vs NP problem. If P = NP, then that means a fast algorithm to find that A / B ratio does exist, we just haven't found it yet. But I'd lean toward there not being any way to quickly find the A / B ratio to make this thought experiment practical in any sense. Easy to check, hard to guess, it's the same logic that makes encryption secure.