Physical Scales
Physical Scales
Assume the fundamental “timescale” is the Planck time
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UnitConvert[%]
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Potential number of steps:
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8.1×
60
10
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Assume a significant fraction of all relations get rewritten at every step....
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8.022×
184
10
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Lower bound on number of updates:
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6.5×
245
10
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Log[2.,%]
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816.566
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Any single replacement that does not die out must increase the number of relations by some factor (e.g. 2).
A significant fraction of the nodes in the universe must be getting rewritten at each “step”.
This would lead to node numbers like 2^10^245.
If no nodes are destroyed, the number of nodes is also the number of computations.
If the number of nodes is e.g. doubling at each step, the universe is getting exponentially closer and closer to the continuum......
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radius of universe / 2^(number of “steps”) ≈ 10^26 m / 2^(10^61)
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3.67×
-62
10
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Log[2.,%]
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-204.082
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I.e. by the time the number of steps is 204, one is potentially down to the Planck scale.