The decision of whether to use dice or not CANNOT be made with dice. Easily proven because if you could then you could roll on never rolling, and keep going until a contradiction.
This is actually a great example of what we could call the Prior. Which is a version of SRH. You can't go back into time to before where you started, which is actually NOW. This is exploited in the 2002 version of the Time Machine where Dr. Alexander Hartdegen builds a time machine to go back in time to save his fiancée only to discover that once saved the cause of making the machine is gone and to maintain consistency, and avoid contradiction, she is killed in some other way. Of course there is the even bigger problem that to be back in time before the invention of the machine already opens up this inconsistency. And, as extremely well noted, once back in time you can kill your mother and create an inconsistency as bad as any SRH. From this we conclude that time travel is impossible, unless some condition exists which limits freedom to maintain consistency, or we should allow incompleteness where we allow existences that do not belong to "this universe." So if Time Travel is possible, then the Mother Paradox means our universe is not total and there are existences that do not depend upon it (isomorphic with provable where we take prove to mean depend upon the current axioms and combination rules - which maps to existence and laws of physics). Let see where Quantum Physics takes this, cos I've never realised explicitly that SRH says that Time Travel is impossible before (in an ordinary consistent and complete (knowable) Universe anyway). Okay lets say is this proof of God? Well SRH does say we can't know everything already so its the same conclsuion that there will always be unknowns complete outside the known universe. One unsettling thing tho is Godel, a committed Christian, did fashion a logical proof of God and I don't think it was this... why not? Have I got something wrong that the great Godel dismissed?? Scary indeed!
I'm only scribbling down a note here, and know I have handled this again and again in the blog, but forget what it was previously called.
In a "Hermeneutic Loop" you have to start somewhere. And that somewhere sets the loop you are in ALREADY. You always start IN a state of affairs. You cannot start from a black canvas and construct a situation or meaning. You start IN a situation and simply move somewhere else.
Logicians will complain. But you can decide on your logic framework and axioms from scratch and then explore the consistency and completeness of those axioms. But the 2007 version of SRH was saying even in this situation there is the prior of the logician them self. Faced with a page of schema and axioms for a logic will be meaningless unless you have some basic training in logic itself. Things have use and mention. The "use" requires training that lies outside the schema. There is always Prior. I know Hofstadler discusses at length inner and outer messages and what can be recovered by aliens exploring symbols. I will need to reread but I would venture that there is nothing fixed here; there is no message that we can write on a Voyager space craft whose "meaning" we can assure. I know some scientific constants were encoded so that aliens might know these and work backwards to decode. But this is making some assumptions based upon our own "prior." Is there an "objective" reality that is entirely separate from the sender and receiver? I would say no.
So returning to the simple case of using dice. Unless we use the dice for everything then we must make choices about when to use dice. Can these choices we defined in a rule. NO!
The proof is that we can use self-reference as done before to break this. Using coins: Heads and we ignore the outcome. Something is wrong. That something was in how we decided the question. "Using Dice" is a choice made Prior, like an axiom that we chose. And depending on the result we can reject that choice.
It also means that the outcome is heavily influence by this choice.
In reality we don't use dice for simple choices only those choice we are "unsure" about. Or perhaps those things we don't really want to do we put to the dice.
"dice" i'm using for any random choice. In reality I use coins with Yes/No answer.
So suppose we use the dice as a final "get out" clause. Shall I go for a jog? There is a 50/50 chance. So effectively all the coin flips are doing is reducing the number of things I don't want to do by 1/2.
This is not very scientific, as I don't flip coins on all the things I do want to do.
"Coin flips" quickly become dominated by the Prior, that is the conditions under which we use dice/coins at all.
And isn't this necessarily true. We cannot escape the "loop." Whatever we decide to do is already heavily influence by where we are. Buddhism and Present Moment is great here. You must start where you are, so let you brain catch up with NOW. Stop thinking about past and future and get established in the NOW. This is the launch pad from which to inspect the Past and the Future anyway, so get feet firmly on this launch pad before coins or anything.
=== 100 Prisoners
Had a great example of this is reality. An ICT room with a 100 PCs named in order PC1..PC100. Over time PCs have been removed, fixed and returned randomly or have been borrowed and returned and put back out of order. What algorithms do we have for returning them to the right order?
Well the definitive solution is to go through all the PCs get its name and move it to the right position. But suppose there is only room on the table for one. We must move it to a gap.
Well one solution which is not a complete solution but always improves the situation is : when you find a computer that is in the wrong place, swap it with the one in its correct place. If we also keep going until we have the right computer in the starting place then we will have completed a "Rainbow Loop" like in the 100 Prisoners. Now not all Rainbow Loops are very long, so its a good short term algorithm. I did this the other day and the 1st swap fixed it.
This illustrates an example of things being in a "loop." When you sit as a computer that is in the wrong booth you are automatically in a loop and you can trace a path through all the out-of-place PCs until you get to the one which should be in your booth.
This is the basis of the Enigma crack, finding Hash table collisions and the 100 Prisoners problem.
But being in loops is actually the central observation of all existence, and creates the Prior situation which underpins Self-Reference problems.
Self-Reference as observed creates loops, and creates algorithms that do not halt. TODO is the "Goto" really a self-reference!!!
While calling a function on itself recursively looks like recursion in the machine code doesn't this just Goto the code again?
So actually assuming code and logic are isomorphic, isn't the real problem in the Goto? What is the logical version of Goto? We can do away with "this" then and replace with "Goto x." And if this is where we are going then the "strong SRH" we defined which needs an Entity referring to Itself is no longer needed.
In fact note: Constructivism is at the heart of this.
The Strong-SRH and the weak-SRH actually differ in construction. Strong-SRH needs an actual entity to do the referring, while weak only needs a name.
"This is false" looks like Strong-SRH in that we can deduce an actual sentence is needed.
While "Ex | x is false" only becomes a problem under binding. And under Godel Numbering is even more abstract as it depends upon isomorphism between numbers and formulae.
Just check whether Godel Numbering is something that PM can do. In other words do the theorems exist within PM or are they meta theorems??? Really should have sorted that by now!!
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