The Binding of Isaac & Transparent Newcomb's Problem

post by suvjectibity · 2024-02-22T18:56:39.081Z · LW · GW · 0 comments

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When one person sees one thing and another sees something else in the same thing, then the one discovers what the other conceals. Insofar as the object viewed belongs to the external world, then how the observer is constituted is probably less important, or, more correctly then what is necessary for the observation is something irrelevant to his deeper nature. But the more the object of observation belongs to the world of the spirit, the more important is the way he himself is constituted in his innermost nature, because everything spiritual is appropriated only in freedom; but what is appropriated in freedom is also brought forth. The difference, then, is not the external but the internal, and everything that makes a person impure and his observation impure comes from within. 

— Søren Kierkegaard, Three Upbuilding Discourses, 1843, Hong p. 59-60

 

The structure of the Transparent Newcomb's problem & the Binding of Issac bears structural similarities to be explained shortly. But before doing this I would present a modification to the Newcomb's Problem that even better reflects the biblical story and brings the whole thing together in a manner that is more in line with what one may themselves face in their lives in its most challenging manifestations. 

Furthermore, I will take help of Kierkegaard's structuring and exposition of the challenge that the story of Abraham in the Binding of Issac presents. At the very minimum my hope is that this exposition help the reader bear a little any isomorphic challenge they themselves face in their lives and maintain grace and a semblance of sanity in the face of it.

We modify the transparent variant of the Newcomb's problem by introducing a "commitment" cost for the deciding to one-box (choosing box B), which will be reimbursed manifold in case the box B actually contains the favourable outcome (i.e. the Oracle has predicted one-boxing) but not otherwise. Let this commitment cost be denoted by the utility value -N . Hence, the fully conceptualised problem would be as follows: 

1. There are two boxes, box A & B. Box A is transparent & contains a reward given by utility value 1 . Box B is initially opaque & may either contain a reward with utility value 0 or M.
2. The agent is presented with choosing between two options: 
   1. Choosing either box B only ('one-boxing')
   2. Choosing both A & box B ('two-boxing')
3. The agent is allowed to choose twice between the above two options. After their first choice, the box B is opened and its contents are revealed. The agent then has the option to stick to their original choice or switch over to the other option. There is a perfect predictor, deemed the Oracle, which can predict the agent's final choice perfectly. Given this: 
   1. If the agent consistently chooses to one-box, the box B contains the reward [with utility value] M.
   2. In all other cases, the box B contains the reward [with utility value] 0.
4. The agent furthermore has to bear a commitment cost with the utility value  -N for choosing to one-box at any point (when making the first or the second decision).
   1. Let's that -N is equivalent to utter annihilation across the most important dimension in the agent's existence (in an intuitive sense) & that M is the polar opposite. M >>> N.

I will not pretend to have explored formulations of various decision theories enough to exhaustively apply them to this problem & show all consequences thereof. Perhaps I can explore that in a later post. Instead I will stick to the problem of the story of the Binding of Issac & showcase how it is isomorphic to it. 

1. If the agent chooses to two-box, & takes a look →
   1. If box B yields M, agent flips choice →utility ?? to bear:
      1. This world will never materialise. The Oracle will refuse to yield a reward on box B given the agent's original choice. 
   2. If box B yields 0, agent does not flip choice → utility 1 to bear:
      1. This is the normal state of safe affairs.
   3. If box B yields M, agent does not flip choice → utility ?? to bear:
      1. This world will never materialise. The Oracle will refuse to yield a reward on box B given the agent's original choice.  
   4. If box B yields 0, agent flips choice → utility 1 - N to bear:
      1. This is the state of unsafe affairs for the agent, hence it will never flip given the commitment cost. 
2. If the person chooses to one-box & takes a look →
   1. If box B yields 0, agent flips choice →utility -N to bear:
      1. This is the temptation on the face of which the agent has to remain unwavering, only willing to acknowledge the world states 2b or 2d and nothing else and no other possibility. This is the Kierkegaard’s Knight of Faith who is only able to do this. No one else even dares. One one else even tries. The rarest of them all.
   2. If box B yields 0, agent does not flip choice →utility -N to bear:
      1. This is the fear. The possibility of self-annihilation. But then again, given the person were really of a make-up so as not to change, this world-state is impossible, would never happen and hence remains an invalid one. This would upgrade to 2d. But the agent has to be willing to be of a makeup to not only accept the possibility of this but living only according to its design. 
   3. If box B yields M, agent flips choice →utility ?? to bear:
      1. This world will never materialise & degrade to 2a for two reasons: 
         1. The Oracle's foresight into the agent's flip & hence the impossibility of box B having M.
         2. The logical reason that M reward in box B is not allowed by condition 3a in the formulation of the problem above. 
   4. If box B yields M, agent does not flip choice →utility M-N to bear:
      1. This is the reward. A reward which while is the highest of rewards, is very difficult to see as something to be worth enduring the threats and torrents of uncertainty for. Humans can be expected to minimize uncertainty as soon and as much as possible instead of taking up a priceless reward by weathering it out. This world-state is winning in the face of self-annihilation.

The following is a very loose discussion on various aspects of the world-state cases in the modified transparent Newcomb's problem (as presented above) and how the story of the Binding of Isaac & of what Abraham is going through, helps understand it a renewed light: 

1. The question of identity is the central point in transparent Newcomb’s problem & the story of Abraham. The possibility of temptation & its ability to reveal your identity makes transparent Newcomb's problem at its core more interesting than it's regular equivalent. An aspect of one's identity which matters here literally the most is a certain self-consistency in the face of absolute annihilation.
2. Choosing to believe in the existence of a manifold reward, through the existence of an Oracle, even in the face of total annihilation differentiates the winning agent. What Kierkegaard understood was it was the former that was exactly the challenge. Belief in the Oracle was the only way in which the entity could elevate to a state which while is mythical and the highest one could aspire to, most people would never opt for in face of simple but absolutely certain reward and sustenance.
3. So what kind of world would it be in which such an Oracle were possible? It seems like the kind of world Kierkegaard describes. The kind of internal structure needed to make this occur can be expected to be rare, both from frequentist as well as Bayesian points of view:
   1. The person chooses to one-box as an inherent risk on their part that they may live in a world where things such as Oracles do not exist.
   2. They must be willing to make a fool out of themselves in the face of safer options where thriving is certain. The option to two-box is certain payoff for the agent. One-boxing is certain to bear outcome and the agent can see this bearing results for others around him and see them thrive. His choice will be public even though all his actions are private. People talk about him, laugh, mock him, consider him a fool behind his back. But the very act of foolishness that this requires and the act of surviving it without wavering even as the entire interior of one’s being is oriented against oneself is what builds the kind of the entity to win against this very challenge.
   3. Willing to have the faith needed, and if not faith, a propensity of self-annihilation which is always a real possibility. Is the propensity for self-annihilation enough or is faith required here as well?
   4. Self-annihilation is a real-possibility in the face of the uncertainty of the existence of an Oracle. The existence of the Oracle is something that can never be verified but one models the world on its existence. If the model bears fruits, the Oracle is determined to exist. But the evidence is at best superficial (in that it's just presenting correlations) and not actual causal proof which can establish its existence itself.
4. This challenge also asks for what can be called pre-commitment for the lack of a better term. The use of the pre-commit terminology are sometimes insufficient to the purposes of what happens within Abraham internally in the story of the Binding of Isaac. The first person movements involved in pre-commitment are these:
   1. How does one pre-commit in this case & then stick to it over time? Over time is the challenging part in the face of the world. One week in which Abraham has to come to terms with himself and his choice. One week in which he has to reconcile in himself the possibility of self-annihilation, even accept it and still be convinced and have faith that he will win even in the face of the absurdity of absolute worldly loss. One week in which he must remain a being whose faith and convictions cannot be shaken even in the face all evidence otherwise and the absolute, irreconcilable absurdity of this.
   2. The unwavering involved in this choice and the continuation of this over time is the challenge. This unwavering necessarily by the very logic of the world and how it works must be rare to come about. Both in terms of the frequency of beings and in terms of the effort required to achieve this in the first-person sense in one's own life. The process involved must necessarily involve a factor of both pre-effort factors which must be rare to come about for a being and effort factors which require massive discipline and effort to obtain (often determined by previous skills possessed).
   3. The journey goes on for seven days, upto Mount Moriah at which point Abraham must bind his son against his cries, take out his butchering knife, and puncture his neck. Who is there to witness him? Is he mad or is he great?
5. Difference between the regular Newcomb’s and its transparent variant, on why the latter is more interesting, given that it reveals the structure of the agent's very being in question:
   1. The transparent variant reveals the structure of a being given that it is only a being of a certain kind, and who must necessarily be very rare due to the very difficulty involved in the movement towards the higher choice, that is able to one-box and win. Or rather to one-box and than choose again to one-box i.e. be consistent across time, stick to his choice to one-box. Self-annihilation under the last case is an impossibility simply because the Oracle would know this being to be someone who would never flip and to never punish it with the negative payoff in the first place. But then again, to be a being who sticks to the pre-commitment is the rarest quality especially when faced with absolute self-annihilation. One must empty oneself. Kenosis. 
   2. This disciplined structure of being-over-time is not captured by the regular Newcomb’s problem because the choice is singular in time and there is no temptation towards. But the time upto that choice can too be seen as an unfolding in which the agent decides on the option to take up. Combined with the cost to one-box the regular variant closely becomes similar to the transparent variant.
   3. The essence of the difference is the transparency of Box B before the final choice is made. Hence while in the regular variant, the choice occurs without viewing the results, and hence the agent is not factoring in the actual contents of Box B, but only the statement that the Oracle is accurate, their choice is hinged on the faith in that statement alone. Whereas in the transparent variant the agent’s choice is also based on the actual contents that will be visible in Box B. In case the constitution of the agent is to choose box A & B to save himself of the possible annihilation in choosing box B, the agent will have lost the world anyway.
   4. The temptation to change choices is the unique thing here. Change choices on the basis of what is revealed to be in box B if one choses it. This ability to choose to then partake in box A or not, provides an escape to the agent on the possibility of annihilation. Why is this escape not possible in the regular variant?
      1. Abraham is not exactly given this choice at escape really. He is provided with the choice to disobey which is the same as two-boxing. He is provided with a week in which he must carefully decide on what to do and the being that he is constituted of must do certain movements which makes it certain that the choice he takes will be that of genuinely being able to sacrifice his son, he cannot escape the death that will come from it. He must bear the possibility head-on. The price of choice must be looked at right in the face. This makes it somewhat different from the transparent variant where the choice to back out comes at a point where the agent has “peeked” behind the curtain. But the very strategy of tip-toeing would change the result in this case.
      2. But this ability to “peek” also makes it similar to the Abraham’s case where the the very wavering of faith in the Oracle while simultaneously being fully ready to realistically pay the price of his son’s sacrifice equate each other. This ability to “peek” here is the temptation.
   5. Subjective experience and the internal movements involved in this must necessarily have to be factored in for this to make sense. The subjective experience and the movements therein are what reveal the nature of the being in the problem of the Binding of Isaac and the transparent variation of Newcomb’s paradox.
   6. Abraham is alone for the most difficult phase of his whole life. The time from when he hears the Oracle’s instructions to the time until when he must raise his butchering knife to kill his son with absolute certainty, he must go over all of this alone and the world around him, the entire world that bears its rationality and good sense must dissolve into nothingness. His greatness is lone. His movements have nothing in front of the judgement that must come from his tribe at large or his own family and his own life at large were they to get to know of the thing that he is about to do when the hours pass. His silence has multiple purposes. On the surface it is means for others not to interfere with the Oracle’s instructions that Abraham absolutely embodies and wishes to pass. On the other hand the purpose of this silence is also that he knows even if he tells them, even if he tells his own wife Sarah, they would never understand him. He would be physically interfered with, that is for sure. But he would also be mentally interfered with. But even more, this challenge of faith, he knows the Oracle has set it only in store for himself and no one else. There is nothing, no social judgements, no common sense, no higher principle, no seniority, no elder, no motherhood, no fatherhood, no moral principle of which basis the world functions that he can summon in order to justify his actions. His test is a lone one and he must act alone and choose alone and stick to that choice along with all the suffering or rewards it would bear on him or not bear on him. There is a very basic and strong possibility this man is just a psychotic murderer who fully believes in his actions to be right. The angel who stops him, will it arrive? This last question as asked by us, itself makes it sure that it will never arrive for us and that our own hands must stop our actions. Non-falsifiable principles that go against all worldly principles and carry about with them the actual possibility of self-annihilation.
   7. The days are seven from his house to Mount Moriah and then he must prepare for the sacrifice which takes a whole morning. The final act must be done slowly, deliberately and in full sense of the consequences of his actions. Detachment would not work here. 
   8. He revealed to Isaac his fate beforehand during the journey, why? His son was begging him, trying to reason about him for seven days straight upto the point where they reach the top of Mount Moriah where the act was to be performed. Was he free to run away? Was Isaac free to disobey? Would Abraham have allowed that to happen? His words could have in no world convinced or put any reasons to Abraham’s actions for Isaac. The full repercussions and implications of his actions would never be understood by him until perhaps ages later when Isaac would be faced with similar challenges in his own life. Would he then have become reconciled to the idea that it would have been alright if he had died that day by the hands of his Father those many years ago atop Mount Moriah. 

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