> Do you even know the definition of a Markov chain?
Dude, I've written several Markov chains, starting aged something like six while still learning to read. (Family had a Commodore 64, one of the books it came with had one as a coding example).
Markov chains are stochastic processes where the transitions between possible nodes have probabilities depending only on the current node, i.e. history is irrelevant.
So, right back'atcha, if you can't see how what I wrote is a proof of equivalence — you've got a way to map reality (of a human brain) onto a number between 0 and ~2^(10^17)*.
Or perhaps, despite your previous question being answered, your actual issue is that you were unaware that the laws of quantum mechanics give you a stochastic processes where the transitions between possible states have probabilities depending only on the current state?
* exponent times whatever the constant of proportionality is
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.
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.
> 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>
Dude, I've written several Markov chains, starting aged something like six while still learning to read. (Family had a Commodore 64, one of the books it came with had one as a coding example).
Markov chains are stochastic processes where the transitions between possible nodes have probabilities depending only on the current node, i.e. history is irrelevant.
So, right back'atcha, if you can't see how what I wrote is a proof of equivalence — you've got a way to map reality (of a human brain) onto a number between 0 and ~2^(10^17)*.
Or perhaps, despite your previous question being answered, your actual issue is that you were unaware that the laws of quantum mechanics give you a stochastic processes where the transitions between possible states have probabilities depending only on the current state?
* exponent times whatever the constant of proportionality is