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You're missing the point. Knowledge is a physical arrangement of neurons. If there are a finite amount of atoms, there's a finite arrangement of atoms. Neurons

You're missing the point. Knowledge is a physical arrangement of neurons. If there are a finite amount of atoms, there's a finite arrangement of atoms. Neurons are made from atoms. The fact that such a limit obviously exists contradicts the notion of infinite growth, regardless of how large that limit appears. The power of exponentiation ensures that this limit is practically within reach. If the premise of infinite growth is wrong, then we should be thinking of alternatives sooner rather than later. That was my takeaway from the article.

zuhayeer 3y ago
Knowledge is compression, and thus it can be infinite
whatshisface 3y ago
The number of ways to arrange things grows exponentially with the number of them. Sounds fine to me...
- gnramires 3y ago
  Sure, but the number of ways to arrange things is practically not of direct (that is, linearly proportional!) relevance or value to humans. For example, that you can arrange things in 2^1000000000000 different ways in a hard drive is not that interesting, and certainly the hard drive's "practical utility" is nowhere near proportional to such number: if it was, hard drives would be an utterly unimaginable miracle. Instead, their utility is (arguably) proportional to log(number of states), i.e. the number of bits it can store, which is 1Tbits. Because things we care about need energy to function, and atoms to operate, any seemingly reasonable/practical definition of value or utility cannot grow exponentially for too long, or it will quickly exhaust those resources. That said, we can indeed refine say our software to some extent. But it's important to keep in mind software has significant limitations as well, and complexity theory gives lower bounds on problems of practical relevance. We might get a few percent faster (in terms of number of operations) sorting algorithms (and merge sort), for instance, but no more, at least for random inputs. I think less clear are say quality of life or new experiences afforded by new media, new novels, new games, new ways of seeing things. I think there is indeed significant improvement to be had, but also we probably shouldn't get carried away this is some kind of infinity: all things are limited when it comes to a life. I do think simply lifting everyone to a good condition (mostly emotional and basic needs) has a very surprising and large coefficient of gain.
  - whatshisface 3y ago
    If you want an example consider if everyone was healthy and immortal and spent their time telling and hearing infinite permutations of words and stories.

zuhayeer 3y ago

Knowledge is compression, and thus it can be infinite

whatshisface 3y ago

The number of ways to arrange things grows exponentially with the number of them. Sounds fine to me...

gnramires 3y ago
Sure, but the number of ways to arrange things is practically not of direct (that is, linearly proportional!) relevance or value to humans. For example, that you can arrange things in 2^1000000000000 different ways in a hard drive is not that interesting, and certainly the hard drive's "practical utility" is nowhere near proportional to such number: if it was, hard drives would be an utterly unimaginable miracle. Instead, their utility is (arguably) proportional to log(number of states), i.e. the number of bits it can store, which is 1Tbits. Because things we care about need energy to function, and atoms to operate, any seemingly reasonable/practical definition of value or utility cannot grow exponentially for too long, or it will quickly exhaust those resources. That said, we can indeed refine say our software to some extent. But it's important to keep in mind software has significant limitations as well, and complexity theory gives lower bounds on problems of practical relevance. We might get a few percent faster (in terms of number of operations) sorting algorithms (and merge sort), for instance, but no more, at least for random inputs. I think less clear are say quality of life or new experiences afforded by new media, new novels, new games, new ways of seeing things. I think there is indeed significant improvement to be had, but also we probably shouldn't get carried away this is some kind of infinity: all things are limited when it comes to a life. I do think simply lifting everyone to a good condition (mostly emotional and basic needs) has a very surprising and large coefficient of gain.
- whatshisface 3y ago
  If you want an example consider if everyone was healthy and immortal and spent their time telling and hearing infinite permutations of words and stories.