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It's like gravity, collisions, and interstellar objects. Some starting points escape and go on ... forever. Some kind of structure there that Collatz probing i
by keepamovin 1y ago
It's like gravity, collisions, and interstellar objects. Some starting points escape and go on ... forever.
Some kind of structure there that Collatz probing is sketching
- apetresc 1y agoExcept the Collatz Conjecture is almost certainly true, and there are no starting points that go on forever. Or did I miss the point of the analogy?
- keepamovin 1y agoNo you didn't misunderstand, I think. I thought there were some values that went on forever! edit: however we could consider the weaker definition of "forever", and consider there are some outliers that go on "for a long time" per post title, probing structure with these loops and spokes. :D
- sfblah 1y agoThe conjecture is that there are no values that go on forever, but it's as yet unproven.
- keepamovin 1y agoThere probably are some very large values that go on forever. It's interesting how the structure of numbers must change at some point. Seemingly just based on magnitude, but in huge scales, some kind of density of structures related to factors builds up and eventually hits a critical point. And "island of forever". Collatz island, above what we've tested. It will be cool to discover that. I wonder how big it is? Probably hundreds of millions of decimal digits. But it's likely dense enough that if you randomly search and land on the island, you probably have a good chance.