Why does the fact that our universe takes place in an incomputable continuous setting mean itās not implemented?
I do not think we have any empirical evidence that the universe is:
Continuous, because all measurements have a finite sensitivity.
Infinite, because all measurements have a finite scale.
Claiming the universe is continuous or infinite requires extrapolating infinitely far from observed data. For example, to conclude that the universe is infinite, people usually extrapolate from the universe being pretty flat locally to it being perfectly flat globally. This is a huge extrapolation:
Modelling our knowledge about the local curvature as a continuous symmetrical distribution, even if the best guess is that the universe is perfectly flat locally, there is actually 0 % chance it has zero local curvature, 50 % it has negative, and 50 % it has positive.
We do not know whether the curvature infinitely far away is the same as the local one.
In my mind, claiming the universe is perfectly flat and infinite based on it being pretty flat locally is similar to claiming that the Earth is flat and infinite based on it being pretty flat locally.
Sorry, I shouldnāt have used the phrase āthe fact thatā. Rephrased, the sentence should say āwhy would the universe taking place in an incomputable continuous setting mean itās not implementedā. I have no confident stance on if the universe is continuous or not, just that I find the argument presented unconvincing.
Interesting point.
I do not think we have any empirical evidence that the universe is:
Continuous, because all measurements have a finite sensitivity.
Infinite, because all measurements have a finite scale.
Claiming the universe is continuous or infinite requires extrapolating infinitely far from observed data. For example, to conclude that the universe is infinite, people usually extrapolate from the universe being pretty flat locally to it being perfectly flat globally. This is a huge extrapolation:
Modelling our knowledge about the local curvature as a continuous symmetrical distribution, even if the best guess is that the universe is perfectly flat locally, there is actually 0 % chance it has zero local curvature, 50 % it has negative, and 50 % it has positive.
We do not know whether the curvature infinitely far away is the same as the local one.
In my mind, claiming the universe is perfectly flat and infinite based on it being pretty flat locally is similar to claiming that the Earth is flat and infinite based on it being pretty flat locally.
Sorry, I shouldnāt have used the phrase āthe fact thatā. Rephrased, the sentence should say āwhy would the universe taking place in an incomputable continuous setting mean itās not implementedā. I have no confident stance on if the universe is continuous or not, just that I find the argument presented unconvincing.