tghts.txt

What is math concretely?

From the outside, it resembles a group of people talking to each other. The theme of the discussion loosely depends on what was said before and no one really knows how it all started.

You can join in if you want but you will need to speak some dialect first. An implicit algorithm is used such that the people can agree on the validity of what is being said.

Some people have started to translate the discussion from the original set of evolving dialects into programming languages. In this new setting, the implicit algorithm can be made explicit and the translation checked mechanically. If no mistake is found in the algorithm or in the translation, we can be confident that what was said is indeed valid.

Given such an explicit algorithm and a complete enough record of the discussion, we could store a full verified translation. But this translation would be fairly redundant and we could try to compress it. Doing so, we would see that the bytes with the highest compression ratio would map to "fundamental" sayings in the discussion and the low compression ratio bytes that could not be compressed further would map to "surprising" sayings.

Given such explicit algorithm, we could in theory build an other algorithm enumerating and storing all the valid sayable things. Assuming the machine translation process was invertible and had a complete record of the people talking, we could halt this algorithm once it had enumerated all the saying ever pronounced. We could then filter out the ones that weren't (pronounced).





It would produce an ever growing database but its content would be extremely redundant. You would need to compress this stream of data to make it less regular and more interesting. 

The bytes with the highest compression ratio would map to the most frequently referred sayings in the discussion. These would be the "important" sayings. A saying would be considered "surprising" if it mapped to hard-to-compress bytes in the stream.

By sharing this compressed partial stream of verifiable discourse with peers they would replicate the validation and storage, ensuring that the streaming and compressing process could continue.

Note for computer scientists: You can increase the Kolmogorov complexity of a recursively enumerable tree by pruning it. The enummerating algorithm provides a lower bound on the complexity of the infinite stream but partial views of this same stream can have higher complexity (i.e. the frontier is (almost) everything).