I'm too ignorant to say anything useful about description vs. theory. All I was talking about is whether one can build a machine that discovers patterns without a theory. And my answer is No. But my answer depends on the "minimal" qualifier. A theory, in this sense, is simply a collection of theorems, provable sentences in a given language. (It seems like a natural extension to include *candidate theorems* -- hypotheticals -- that may or may not be provable, which may match a more vernacular conception of the word "theory".)
And to go back to Jochen's 2nd post <http://friam.471366.n2.nabble.com/New-ways-of-understanding-the-world-tp7599664p7599668.html>, it seems to me like a machine capable of discovering a theory of everything would *need* a prior language+axioms capable of expressing everything that physics (and biology, etc.) can express. And that implies a higher order language, a language of languages [⛧]. The "try random stuff and see what works" *fits* that meta-structure. A machine capable of shotgunning a huge number of subsequent languages *from* a prior language of languages, could stumble upon (or search for) a language that works. Such meta languages are *schematic*, however. So when people like Tegmark assert that the universe *is* math, there's ambiguity in the word "math" that some people in the audience might miss, much like the ambiguity in the word "logic" that Nick often glosses over. Which math? Which of the many types of math best matches physics? Is it the same type of math that best matches biology? Psychology? Etc. Of course, if we go back to Soare's definition of "computation" and require it to be _definit_, then it's not clear to me such a schematic AI, pre-programmed with a language of languages, *could* be constructed. But if we relax that requirement, then it seems reasonable. [⛧] But a language of languages is still a language. Similarly, a theory of theories is still a theory, which is why even such a schematic AI would *still* require a prior theory. On 12/1/20 6:17 AM, Marcus Daniels wrote: > It seems to me the taxa of life are a description not a theory. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com archives: http://friam.471366.n2.nabble.com/ FRIAM-COMIC http://friam-comic.blogspot.com/
