Hello Lawrence,
As a layperson I am not going to pretend to understand these new approaches and the maths being utilised but in your conclusions you state interestingly,
"Chaitan has advanced ideas that mathematics is not something that exists in any sort of coherent whole-
ness. It is more a sort of archipelago of logically consistent systems that sit in an ocean of chaos [21].
This chaos is a set of statements that are purely self-referential and have truth or falsehood by no logical
reason.
Possibly the quantum vacuum is similar. It may be a tangle of self-referential quantum bits, where
some sets of these exist in logical coherent forms. These zones of logical coherence might form a type of
universe. These logical coherent forms are then accidents similar to Chaitan0 s philosophy of mathematics.
It is very dicult to understand how this could be scientically demonstratedャ yet maybe regularities inシッpセシpセphysics described by mathematics exist for no reason at allョ「シッpセシpセツasicallyャ the mystery of the quantum vacuum is really expressed as the ァhierarchy problemァョ ノ think if you stare at the so called hierarchal gap then that is where the state of physics is at todayョ ノ like the idea of entanglement defining geometry somehow and this may be inherent in the blank space ィvoidゥ where the particle desert existsョヤhe ツig ヌap ィor whatever you may call itゥ maybe the potential pool from which the multiverses are generaed or at least some indication that the multiverse do indeed existsョ ヘaybe ヌユヤ convergences are different for different ユniversesョ チlsoャ maybe it is a matter of physics becoming more aligned with mathematics toward the quantum gravity realmョ ノn that we live in a エト world our physics ィニrom ヌreek physikaゥ is generally found to work ィempiricallyゥ from the platform of the sensory ィsensationゥ because of the physical nature of things at our low energyョ モensory as apart from intelligenceョ チt some point the physics may blur into the mathematics and the senseュdata ィempiricalゥ will be left behindョ ヤhis implies that intelligence will discover things by ァexplanatory powerァ and that the empirical apparatus ィmachinesゥ no longer yield anything useful in upward and onward explorationsョ ヘaybe エト is unique in that it implies a physical world in which physics is a workable contextョ ノf so then there might be an 「 end of the machineィsゥァ such as the フネテ where it just cannot yield the pure mathematical result as a physical ィsensationュobservationゥョ ヤhen we are at the 「end of physics「 in a different sense and a brave new world of mathematics ィexplaining thinsゥ is awaitingョ ィヘaybe the meaning of life is not エイ but エト サュゥ ゥ ノf you look at the hierarchal gap as a ァzen koanァ then there is more there than meets the eyeョシッpセシpセmark