Lee Smolin discusses a class of facts that are evoked:
"I would like to propose that there is a class of facts about the world, which concerns
structures and objects which come to exist at specific moments, which, nevertheless, have
rigid properties once they exist.
Let us call this possibility evoked."
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He provides a table of how a fact and it's existence can be described:
Has rigid properties and existed prior? The fact was discovered
Has rigid properties and did not exist prior? The fact was evoked
Has no rigid properties but did exist prior? The fact was fantasized (Smolin does not elaborate on this in the paper)
Has no rigid properties and did not exist prior? The fact was invented
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Roberto Mangabeira Unger and Smolin hypothesize two principles to describe Smolin's view, temporal naturalism:
The singlular universe, all that exists is part of one singular universe
The reality of time, as in reality is not timeless
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With all this in mind, yes circles always did have a ratio of circumference to radius of pi. This is a property of the singular universe, and is a fact that was thus discovered.
The universe of mathematical possibilities that does not describe the universe was not discovered, it was evoked.
P.S. Please forgive the formatting of this response!
1.In the real universe it is always some present moment, which is one of a succession of moments. Properties of mathematical objects, once evoked, are true independent of time.
2. The universe exists apart from being evoked by the human imagination, while mathematical objects do not exist before and apart from being evoked by human imagination.
> In the real universe it is always some present moment
That is rather naive. The entire succession of moments can be described as one object, in which time is a dimension. The unfolding through time is just the subjective experience of the human consciousness.
Some H.264 video also appears to unfold, presenting a depiction of events frame by frame. Yet, at the same time, it's also just a 1.2 gigabyte file: a giant integer.
http://arxiv.org/abs/1506.03733
Lee Smolin discusses a class of facts that are evoked:
"I would like to propose that there is a class of facts about the world, which concerns structures and objects which come to exist at specific moments, which, nevertheless, have rigid properties once they exist. Let us call this possibility evoked."
====
He provides a table of how a fact and it's existence can be described:
Has rigid properties and existed prior? The fact was discovered
Has rigid properties and did not exist prior? The fact was evoked
Has no rigid properties but did exist prior? The fact was fantasized (Smolin does not elaborate on this in the paper)
Has no rigid properties and did not exist prior? The fact was invented
====
Roberto Mangabeira Unger and Smolin hypothesize two principles to describe Smolin's view, temporal naturalism:
The singlular universe, all that exists is part of one singular universe
The reality of time, as in reality is not timeless
====
With all this in mind, yes circles always did have a ratio of circumference to radius of pi. This is a property of the singular universe, and is a fact that was thus discovered.
The universe of mathematical possibilities that does not describe the universe was not discovered, it was evoked.
P.S. Please forgive the formatting of this response!