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So, I have been doing some reading trying to quantify a statement made about the Cthulhu Mythos, and I've grown a bit...confused. I am looking for some help.
So, the statement is from "The Whisperer in Darkness:"
"The blasphemies which appeared on earth, it was hinted, came from the dark planet Yuggoth, at the rim of the solar system; but this was itself merely the populous outpost of a frightful interstellar race whose ultimate source must lie far outside even the Einsteinian space-time continuum or greatest known cosmos."
So, next in my research I went to learn what Einsteinian physics is, and simply put it's the modern interpretation of physics and includes grand notions such as 1+1=1, 1+1=0, and all of quantum physics. So, I started researching quantum physics and came across this paper when I was trying to learn about the interaction/use of cardinal numbers in quantum physics. In said article is this paragraph, which is the main source of my current...difficulties:
"Notice that in Q the standard notion of identity is not defined for some entities (definition 7.1v). Now, the identity concept is essential to define many of the usual set theoretic concepts of standard mathematics, such as well order, the ordinal attributed to a well ordered set, and the cardinal of a collection. Since identity is to be senseless for some items in Q, how can we employ these notions? One alternative would be to look for different formulations employing methods that do not rely on identity. Another possibility would be to introduce these concepts as primitive and give adequate postulates for them. Concerning the notion of cardinal, there are interesting issues we should acknowledge. First of all, in Q, there cannot be well-orders on quasi-sets of indistinguishable m-atoms. Really, a well-order would imply, for example, that there is a least element relative to this well order, a notion which could only be formulated if identity was defined for m-atoms, for this element would be different from any other element in the quasi-set. Second, the usual claim that aggregates of quantum entities can have a cardinal but not an ordinal demands a distinction between the notions of ordinal and of cardinal of a quasi-set; this distinction is made in Q by the introduction of cardinals as a primitive notion, called quasi-cardinals." -Page 25
So...does this mean quantum physics includes and "exceeds" all cardinal numbers/sets as "primitive" or is it just saying they fail to explain the things quantum physics deals with? More to the point, does this mean the Mythos' tiering should be based on (parts of it) exceeding Einsteinian physics to such a high degree (being how lowly Mi-Go are in the grand schemes of his work)? I would like some help sorting through this, as I will admit my understanding of many of these concepts is a bit...limited. Thank you in advance.
So, the statement is from "The Whisperer in Darkness:"
"The blasphemies which appeared on earth, it was hinted, came from the dark planet Yuggoth, at the rim of the solar system; but this was itself merely the populous outpost of a frightful interstellar race whose ultimate source must lie far outside even the Einsteinian space-time continuum or greatest known cosmos."
So, next in my research I went to learn what Einsteinian physics is, and simply put it's the modern interpretation of physics and includes grand notions such as 1+1=1, 1+1=0, and all of quantum physics. So, I started researching quantum physics and came across this paper when I was trying to learn about the interaction/use of cardinal numbers in quantum physics. In said article is this paragraph, which is the main source of my current...difficulties:
"Notice that in Q the standard notion of identity is not defined for some entities (definition 7.1v). Now, the identity concept is essential to define many of the usual set theoretic concepts of standard mathematics, such as well order, the ordinal attributed to a well ordered set, and the cardinal of a collection. Since identity is to be senseless for some items in Q, how can we employ these notions? One alternative would be to look for different formulations employing methods that do not rely on identity. Another possibility would be to introduce these concepts as primitive and give adequate postulates for them. Concerning the notion of cardinal, there are interesting issues we should acknowledge. First of all, in Q, there cannot be well-orders on quasi-sets of indistinguishable m-atoms. Really, a well-order would imply, for example, that there is a least element relative to this well order, a notion which could only be formulated if identity was defined for m-atoms, for this element would be different from any other element in the quasi-set. Second, the usual claim that aggregates of quantum entities can have a cardinal but not an ordinal demands a distinction between the notions of ordinal and of cardinal of a quasi-set; this distinction is made in Q by the introduction of cardinals as a primitive notion, called quasi-cardinals." -Page 25
So...does this mean quantum physics includes and "exceeds" all cardinal numbers/sets as "primitive" or is it just saying they fail to explain the things quantum physics deals with? More to the point, does this mean the Mythos' tiering should be based on (parts of it) exceeding Einsteinian physics to such a high degree (being how lowly Mi-Go are in the grand schemes of his work)? I would like some help sorting through this, as I will admit my understanding of many of these concepts is a bit...limited. Thank you in advance.
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