Chaitin argues that the human spirit is capable of doing both practical things and impractical things which may have practical consequences later:
At least for me, it was purely philosophical. I was interested in incompleteness. I was interested in more practical stuff, but it looked very difficult. And now what is it? Algorithmic information theory goes back to the 60s. What are we now?
It’s 60 years later. Hector McNeil and his collaborators are using practical approximations to this ideal theory and for practical applications.
Oh, this is the biggest joke of all: The halting probability Omega is totally unknowable. It’s uncomputable, but you can calculate it in the limit from below. You look at more and more programs, you see which ones hold and that way, the halting probability keeps going up, your estimate keeps going up. But it’s very, very slow this process. But in the limit of infinite time, you can calculate it in the limit from below.
Well, the joke is that Hector McNeil has proposed using this as a new cryptocurrency that he calls Automacoin. This is a serious proposal because Bitcoin, the most popular cryptocurrency, uses an immense amount of computing power. Really scary amount of computing power that didn’t even exist before. But it’s all going for this. It’s not terribly useful computation except for financial transactions. But what Hector’s Neil has basically proposed is to calculate the bits of Omega in the limit from below.
This gives you a cryptocurrency where what you calculate is very, very useful. It’s useful in the way that Marvin Minsky pointed out, that it tells you the best theories for things. The most concise programs with things. That can be used for making predictions.
News, “Why “impractical” things like philosophy are actually quite useful” at Mind Matters News
Takehome: Gregory Chaitin reflects on the fact that if he had to do practical work 60 years ago, there wouldn’t be practical research today based on the Omega number.
But that raises a question: If materialism were true, why does theoretical stuff matter so much?
See also: Omega number: Getting to know the unknowable number, more or less