The nature of paradox has exercised great minds throughout history. Pragmatically, E T Jaynes has argued that paradoxes are simply "mistakes gone viral"; if a paradox is the arrival at a seemingly absurd conclusion through seemingly sound reasoning from a seemingly sound premise, then the key word is, unsurprisingly, 'seemingly'. Paradoxes are simply traps for the unwary mind. Indeed, his dismissal of the St Petersburg lottery paradox is quite convincing.
Borges, on the other hand, emphasised absurdity; paradoxes offer a clue to the unreality of the observable universe. If the evidence is consistent with more than one possible world we have underdetermination; with precisely one world, certainty. But in the paradoxical the evidence is consistent with no possible world. This tells us that we are perceiving the unreal. It is with this in mind that I shall recount to you the nature of my preliminary experiments in time travel.
I had prepared a small closed timelike curve using, of course, a Deutsch array. My test object was a billiard ball (for the studious reader this may already call to mind the Polchinski paradox) which was to be sent some minutes into the past. My calculations had led to the bizarre conclusion that this was impossible, because the ball's exit from the apparatus after time travel would always prevent me from introducing it to the loop to begin with.
This was a highly odd prediction to say the least; if the ball's exit from the machine did indeed block the path to the CTC, then clearly I must have successfully introduced it in the first place. My prediction was that the experiment was impossible, but its impossibility is dependent upon its success. I concluded in the end that I must have made some mistake as there seemed to be no way in which the prediction could be correct. However, it appears I may have overlooked something as my attempt to conduct the experiment was far stranger than I had imagined, and with far more important implications.
I was exceptionally eager to find out what would actually happen so I worked into the early hours on the configuration script*. In the end my desire for sleep won, and I started work the next day. It took me barely fifteen minutes to solve the problem that had me beaten for hours the night before. I powered the unit on, ran the configuration script and set the camera running. At this point I changed my mind and decided to wait until later in the day. After a while, I was more enthusiastic than ever to get on with the work, and again made preparations. But, confusingly, as I made final tweaks I lost interest once again and put it off for a second time. This happened a further four times before I gave up, finally I believed. Again, after leaving the equipment for a short while I felt a strong urge to just get on with it and witness the results. I stopped myself, realising that I was caught in some sort of behavioural loop. Every time I gained enough enthusiasm to begin again, I lost interest while setting the equipment up and ended up exactly where I started. Not quite exactly. After a total of six fruitless attempts, seeing that my actions were futile ,I exerted an enormous amount of will and left things alone, despite my burning desire to continue the useless pattern of behaviour that had taken up the whole day.
The only conclusion that makes sense to me is that something is preventing me from completing these actions. I am not suggesting that any sort of cosmic will or consciousness is at play here. It just seems to me that we live in a universe where dropping billiard balls into time-like loop generators is not something that people do. Can I do it? I don't know. I just know that so far I have always chosen not to. I must resist the temptation to simply try again. All I can think of is that I could set up some sort of random delivery device which has a non-zero chance of introducing the ball into the loop. That will have to wait.
*All code will be published in the usual place.
Borges, on the other hand, emphasised absurdity; paradoxes offer a clue to the unreality of the observable universe. If the evidence is consistent with more than one possible world we have underdetermination; with precisely one world, certainty. But in the paradoxical the evidence is consistent with no possible world. This tells us that we are perceiving the unreal. It is with this in mind that I shall recount to you the nature of my preliminary experiments in time travel.
I had prepared a small closed timelike curve using, of course, a Deutsch array. My test object was a billiard ball (for the studious reader this may already call to mind the Polchinski paradox) which was to be sent some minutes into the past. My calculations had led to the bizarre conclusion that this was impossible, because the ball's exit from the apparatus after time travel would always prevent me from introducing it to the loop to begin with.
This was a highly odd prediction to say the least; if the ball's exit from the machine did indeed block the path to the CTC, then clearly I must have successfully introduced it in the first place. My prediction was that the experiment was impossible, but its impossibility is dependent upon its success. I concluded in the end that I must have made some mistake as there seemed to be no way in which the prediction could be correct. However, it appears I may have overlooked something as my attempt to conduct the experiment was far stranger than I had imagined, and with far more important implications.
I was exceptionally eager to find out what would actually happen so I worked into the early hours on the configuration script*. In the end my desire for sleep won, and I started work the next day. It took me barely fifteen minutes to solve the problem that had me beaten for hours the night before. I powered the unit on, ran the configuration script and set the camera running. At this point I changed my mind and decided to wait until later in the day. After a while, I was more enthusiastic than ever to get on with the work, and again made preparations. But, confusingly, as I made final tweaks I lost interest once again and put it off for a second time. This happened a further four times before I gave up, finally I believed. Again, after leaving the equipment for a short while I felt a strong urge to just get on with it and witness the results. I stopped myself, realising that I was caught in some sort of behavioural loop. Every time I gained enough enthusiasm to begin again, I lost interest while setting the equipment up and ended up exactly where I started. Not quite exactly. After a total of six fruitless attempts, seeing that my actions were futile ,I exerted an enormous amount of will and left things alone, despite my burning desire to continue the useless pattern of behaviour that had taken up the whole day.
The only conclusion that makes sense to me is that something is preventing me from completing these actions. I am not suggesting that any sort of cosmic will or consciousness is at play here. It just seems to me that we live in a universe where dropping billiard balls into time-like loop generators is not something that people do. Can I do it? I don't know. I just know that so far I have always chosen not to. I must resist the temptation to simply try again. All I can think of is that I could set up some sort of random delivery device which has a non-zero chance of introducing the ball into the loop. That will have to wait.
*All code will be published in the usual place.
