4 ms·

Great, we're making progress. Give me the dimension of the Hilbert space, the wave function, and the unitary operator that corresponds to your daily activities

Great, we're making progress. Give me the dimension of the Hilbert space, the wave function, and the unitary operator that corresponds to your daily activities in terms of a Markov chain. Take all the time you want to figure it out.

ben_w 2y ago
If you accept such things exist, my point is already made. ∃, ∎
- benchmarkist 2y ago
  It's just formal game but you still haven't managed to write down the state space nor specify the transition probabilities for a single atom let alone a person.
  - ben_w 2y ago
    > It's just formal game but you still haven't managed to write down the state space nor specify the transition probabilities for a single atom let alone a person. False. I've given you the state space. It's the one defined by 2^(k*10^17) bits. That's your state space. I don't know why you have a hard time with this concept, it doesn't seem particularly challenging to me. I've also said, in what I thought was quite clear language, that writing down the transition probabilities for even a system significantly simpler than a human brain would require so much information that by the Bekenstein bound it would require a universe substantially larger than this one to avoid becoming a black hole. If you're not going to accept that the very specific things you asked for — things which you seem to accept exist — are already sufficient to be proof that quantum mechanics and by extension all of reality including humans are in the set of things defined by Markov chains unless I literally destroy the universe by writing the function down in that fashion, then we're done. Or are you shifting the goal posts when you wrote this?: > and the unitary operator that corresponds to your daily activities in terms of a Markov chain Given that what actually fits into a comment box is either a super-high-level representation where it's transitions at a macro level like "sleep" -> "get up" -> "go to work" etc. or a super-low-level representation like iħ ∂ψ/∂t |ψ> = (H^)|ψ>
    - benchmarkist 2y ago
      So do you realize the absurdity of your original statement or do you want to keep going?

ben_w 2y ago

If you accept such things exist, my point is already made. ∃, ∎

benchmarkist 2y ago
It's just formal game but you still haven't managed to write down the state space nor specify the transition probabilities for a single atom let alone a person.
- ben_w 2y ago
  > It's just formal game but you still haven't managed to write down the state space nor specify the transition probabilities for a single atom let alone a person. False. I've given you the state space. It's the one defined by 2^(k*10^17) bits. That's your state space. I don't know why you have a hard time with this concept, it doesn't seem particularly challenging to me. I've also said, in what I thought was quite clear language, that writing down the transition probabilities for even a system significantly simpler than a human brain would require so much information that by the Bekenstein bound it would require a universe substantially larger than this one to avoid becoming a black hole. If you're not going to accept that the very specific things you asked for — things which you seem to accept exist — are already sufficient to be proof that quantum mechanics and by extension all of reality including humans are in the set of things defined by Markov chains unless I literally destroy the universe by writing the function down in that fashion, then we're done. Or are you shifting the goal posts when you wrote this?: > and the unitary operator that corresponds to your daily activities in terms of a Markov chain Given that what actually fits into a comment box is either a super-high-level representation where it's transitions at a macro level like "sleep" -> "get up" -> "go to work" etc. or a super-low-level representation like iħ ∂ψ/∂t |ψ> = (H^)|ψ>
  - benchmarkist 2y ago
    So do you realize the absurdity of your original statement or do you want to keep going?