I don’t quite understand how actual infinity differs from potential infinity in this context. Time in ToR is considered one of the dimensions of space. How can space be considered “potential infinity”? It subjectively looks like that to a forward-traveling observer. But usually we use the paradigm of objective reality, where everything is assumed to exist equally. Together with the past and the future, if we recall ToR again. Are we supposed to have a special case here, where we need to switch to the paradigm of subjective reality?
I am familiar with the idea that “the information that enables us to act best is true”, but it seems to me to be just a beautiful phrase, because in most cases, in order to develop a model that enables us to act best, we still have to be guided by “truth” in the old, ordinary sense. That is, we obtain some initial “atoms of truth” through experience, but later we have to take care of their logical consistency. And we are not quite right to call some high-level construction “truth”, even if it works well, if it does not logically agree with the “atoms” we used to create it.
This case is free from this problem, since practical verification in this area is impossible. But still, the feeling of some hypocrisy in front of oneself does not disappear. To admit at least in the edge of consciousness the possibility that “the Universe is not X” and at the same time use only “the Universe is X” in calculations—there is some kind of contradiction in this. This is either an act of doublethink (for an agnostic) or an act of politeness (for an ultrafinitist).
The difference between repeating patterns could manifest itself if there were interactions between them. But here reality rather speaks in favor of ultrafinitism. If the hierarchy of complication of structures with interactions could continue to infinity (even at the cost of slowing down the interactions), then theoretically we could find ourselves at any level of the hierarchy. Then we most likely would not see the “bottom of the hierarchy” (Planck’s limit). However, we see it. Therefore, either the hierarchy is finite, or something prevents interactions between levels, or some factor prevents the emergence of too high-level observers.
However, only the first option directly speaks in favor of ultrafinitism. The second and third options—like your reasoning—are valid only in the paradigm of subjective reality.
“Heat death” is also the end of time only in the paradigm of subjective reality. Moreover, only for an anthropocentrically minded observer, from whose point of view one state of “white noise” is no different from another.
Before Einstein, in the era of Newtonian ideas about time, it was believed that the magnitude of the past that had already taken place could be infinitely large. St. Augustine disagreed with this, but he had rather religious reasons.
I don’t quite understand how actual infinity differs from potential infinity in this context. Time in ToR is considered one of the dimensions of space. How can space be considered “potential infinity”? It subjectively looks like that to a forward-traveling observer. But usually we use the paradigm of objective reality, where everything is assumed to exist equally. Together with the past and the future, if we recall ToR again. Are we supposed to have a special case here, where we need to switch to the paradigm of subjective reality?
I am familiar with the idea that “the information that enables us to act best is true”, but it seems to me to be just a beautiful phrase, because in most cases, in order to develop a model that enables us to act best, we still have to be guided by “truth” in the old, ordinary sense. That is, we obtain some initial “atoms of truth” through experience, but later we have to take care of their logical consistency. And we are not quite right to call some high-level construction “truth”, even if it works well, if it does not logically agree with the “atoms” we used to create it.
This case is free from this problem, since practical verification in this area is impossible. But still, the feeling of some hypocrisy in front of oneself does not disappear. To admit at least in the edge of consciousness the possibility that “the Universe is not X” and at the same time use only “the Universe is X” in calculations—there is some kind of contradiction in this. This is either an act of doublethink (for an agnostic) or an act of politeness (for an ultrafinitist).
The difference between repeating patterns could manifest itself if there were interactions between them. But here reality rather speaks in favor of ultrafinitism. If the hierarchy of complication of structures with interactions could continue to infinity (even at the cost of slowing down the interactions), then theoretically we could find ourselves at any level of the hierarchy. Then we most likely would not see the “bottom of the hierarchy” (Planck’s limit). However, we see it. Therefore, either the hierarchy is finite, or something prevents interactions between levels, or some factor prevents the emergence of too high-level observers.
However, only the first option directly speaks in favor of ultrafinitism. The second and third options—like your reasoning—are valid only in the paradigm of subjective reality.
“Heat death” is also the end of time only in the paradigm of subjective reality. Moreover, only for an anthropocentrically minded observer, from whose point of view one state of “white noise” is no different from another.
Before Einstein, in the era of Newtonian ideas about time, it was believed that the magnitude of the past that had already taken place could be infinitely large. St. Augustine disagreed with this, but he had rather religious reasons.