Jump to content

Ripheus23

Members
  • Posts

    1141
  • Joined

  • Last visited

  • Days Won

    2

Status Updates posted by Ripheus23

  1. Metafinity as the foundation of mathematics

    Let the finite and the infinite be relative or absolute. By absolute is meant a universal relation: x is absolutely y if in all relevant relations, x is y. For example, if x is to the left of all y, x would be absolutely leftwards (though this is not really possible, let us suppose). Accordingly, we have an order of four metafinite predicates: absolutely finite, relatively finite, relatively infinite, and absolutely infinite.

              Next, allow that there are two fundamental numerical questions: “Which one?” and, “How many?” A number is either an answer to some form of these questions, or eventually derives from such answers. Let us refer to numbers as answers to the first question by the term ordinals, the second cardinals. Numbers as answers, in some way, to both questions will be denoted surdinals (with reference, as will be explained far below, to the concept of surreal numbers). Numbers as answers to neither question, used purely to differentiate between some x and y, will be indexicals. Thence, to use the number 1 as a name for someone, and the number 3 as a name for someone else, is to use these numbers indexically; they are not subject to arithmetic as such, which is to be considered an ordering of numbers in themselves. So while we might add 1 and 3 when these are used as ordinal, cardinal, or surdinal numbers, we would never add them when using them indexically. —The four positive metafinite predicates are then generally correlated with four basic uses of numbers.

              Our axiom system is a set of axioms and their schemas used in mathematical proofs. The most commonly used such system is Zermelo-Fraenkel set theory with the axiom of choice, which has up to nine basic extralogical principles, some of which can perhaps be reduced to others or waived altogether. Now the attempt to provide a foundation for mathematics, using the concept of metafinity, involves the question (roughly enough put), “Assuming that there is some set of axioms and axiom schemas, why is the number of basic principles what it is?” So if ZFC set theory is true, the question is, “Why are there (as many as) nine such principles?” And according to the theory of metafinity, there would not be nine, but only four, generally correlated with the pairings of metafinite predicates and the numerical erotetic dyad. Indeed, this theory is telling us that we know how many axioms and axiom schemas to look for, without directly knowing as such what the system is.

              Let a logically irreducible number be a number occurring in the logical principles of the system. For example, if 0 and 1 are mapped to FALSE and TRUE,[1] then it is unnecessary to derive either number from the other using extralogical principles. Rather than by transconstructing 1 as the simplest successor of 0, for example, we have it immediately, here. Moreover, if this is true, then the classical set-theoretic definition of the ordinal 1 is false: being the simplest successor of 0 characterizes 1, but does not define it. 1 is not actually reducible to the set containing the empty set, or any such thing.

              If there are four axioms or schemas, here, what are they to be expressed as? Axiomatic structures are assertoric: the basic case is subjects and predicates, which in mathematics comes to numbers and operations thereon. At least one axiom will give us some numbers to work with, and at least one axiom will give us operators for them. Now in the metafinite context, we immediately know that we have numbers for all the metafinite predicates, so the classical axiom of infinity is encoded into the context. This gives us our basic case of a relatively infinite number, here  as an ordinal (and surdinal) and  as a cardinal. Arithmetical intuition, and set-theoretic transconstruction, vitiate the idea of a well-ordered sequence of operators, so that our second axiom will be one that gives us the hyperoperation sequence as such.[2] This sequence will be represented under the heading of the axiom of transcension.

              The existence of relevantly basic cases of the other metafinite numbers will generally be referred to under the heading of the axiom of transcardinality. This has it that there are relations among the metafinite predicates such that, starting from the transfinite cardinals, we can go on to situate the absolutely and relatively finite numbers fairly exactly. Until actual examples of what this situation means are provided, of course, this remark is not even quite programmatic but might appear rather mystical (at best).

              Lastly, the axiom of transfinality collates all the relations of finality that appear in the mathematics of the numbers and their sets referred to here, and adds to them, in light of the metafinite context in total: therefore, in quintessential relation to the absolute infinite. Expressing the concept of an absolutely infinite number in a consistent way is the challenge to be met in this case, as the standard vectors of approach give rise to simple contradictions. By way of a very preliminary remark, the axiom of transfinality involves an extreme reimagining of the principle of foundation in set theory. In other words, though a naively infinite and descending sequence of sets is not to be presented, some infinite descending numerical sequence will be. As far as already-established mathematical systems go, a clear example of an analogy with what we will be looking for is the surreal sequence . But a transfinal sequence is meant to be advergent under absolute infinity, which is an absolutely strong relation to enter into, and so we will have cause to analyze phrases that appear in the literature such as “a set that might as well be as large as the universe V of sets” as well as the equation VV = V (and its cognates, e.g. “”).

              Think of the axioms, then, as introduction rules for types of glyphs. The axiom of infinity introduces the aleph glyphset in general; the axiom of transcension introduces the ascending arrow glyphset; the axiom of transcardinality introduces glyphs for juxtaposing the relatively infinite with the absolutely and relatively finite numbers; and the axiom of transfinality gives us notation for the idea of advergence under the absolute infinite. Logical conjunctions of two or more axioms or schema then yield further analogous or derivative glyphsets. The infinitary context also allows us to apply the axiomatic propositions in an infinitary way. There are therefore 23 such adjunctions of the axioms and their schemes to consider, which gives us much to work with, as will be seen.

     

    [1] For technical reasons, the logical system in use here will actually map FALSE to -1. Though in assertoric space, for a sentence to lack truth is for it to be contrary to the true, in simpler predicative space this is not so (that is, absence and opposition are different kinds of difference). Accordingly, though, -1 is also logically irreducible in the metafinite theory of mathematical foundations; it is not to be irrecursively defined, though it may be expressed, as the additive inverse of 1.

    [2] To try to consolidate and simplify matters as much as possible, I will be using a variant of Knuth arrow notation for this sequence throughout the text. As will be seen, if the aleph numbers can be assigned a minimum of two indices—a base and a compounding index—then it will be an elegant symmetry for the same assignment to hold of the transcension operator. That this symmetry obtains in fact will be illustrated by the overall system of notation as it is developed

  2. Regarding the concept of a metaindex and cardinalities defined therefrom.

    1.png

  3. https://math.eretrandre.org/tetrationforum/attachment.php?aid=222 Wild, it seems the omega hyperoperator might yield values of omega for all 2 ^{omega} nn equal to or greater than 3.

  4. I haven't said this anywhere, not even (directly) on Facebook. I got so distracted by my lack of readiness for the quasi-apocalypse we're going through that it didn't quite seem to make enough of a difference. I thought, "Well, I was told I wouldn't end up having to do anything," and since voila, the world came to a halt without my doing anything... But basically, mid-March, I was so frustrated, angry even, that I got myself worked up to go "make my stand" at the Trident base, I was ready for that, and then ZAM an incomprehensible pain started wracking me. A physical pain, my stomach or intestines or both or what were in knots, I still don't know why, I started throwing up for half a day, so there went my idea of overdosing on my meds in front of the Trident base's gates (my only thought, to sacrifice myself as part of some obscure proof), like if I just threw them up, well... And then the pain didn't go away until days and days later, after the lockdown started in earnest, and though the buses have still been running, although I still could've gone to Trigger Avenue or wherever, and walked the last distance... I didn't have the moral energy to do it. And again, besides, the world had sort of "ended" anyway, hadn't it?

    I'll admit to being afraid of dying, or of trying to die. I convinced myself that I would "wake up" in Heaven, to my cat no less, and I was imagining being in Heaven with my cat, like we were in this open field and he was trilling along and I followed him around, giving him the attention I failed to give him in the real world, content that I could be with this little creature who liked me so much... I also imagined following him out of the field, to a little house, I imagined my mom might be there (if she has died of her medical condition by now), and I would be reconciled with her, and maybe Heaven is after the actual end of the world, is "the World to Come" as they say, so then maybe I would go and meet up with other people who were lost along the way of my life, not lost to death like my cat and maybe my mom, but still... Yet in the wake of the plague and the lockdown, and the warnings we had about hospitals getting overwhelmed, I started to think, "No, I won't kill myself, I'll volunteer to work at the hospital, to help out during the crisis. That's how I'll stand up to Apollyon." I even went into my "Dean is so valiant" mode and thought that he would be volunteering, too, and that's how we'd reconnect.

    Then the hospital called and told me that they aren't doing the volunteer thing right now, and they weren't getting overwhelmed anyway. So I felt defeated again.

    On the other hand, I have never been so proud of my country. That's a strong thing for me to say. But so I saw that people were willing to do the social-distancing thing, regardless of the economic consequences, and even though the plague wasn't cataclysmic, especially not for younger people. But people were willing to try to prevent the elderly and other vulnerable groups from getting mass-infected, so willing, they threw away the naive utilitarianism that it seemed like they might defer to so often, or maybe they'd never really deferred to it that much anyway? So yeah, I was and am proud, of course not only of America, but pretty much the entire world at this point.

    It feels like a possible turning point, in other words: again, some kind of end to the world, not the end I spent my life readying myself for, but still. And I still think the Trident ships are demonic, still think I'm in the shadow of Apollyon's throne, and all that, and I still wish I could make a stand, still wish that my own darkened world (my terrible life) would come to a meaningful end, but I don't know what to do. I've gone back over my set-theory analysis again, have had to reevaluate it to some extent as I've learned more, and I have so much more to learn, and though my "proof" of the Continuum Hypothesis still seems solid and all, I haven't been able to do anything with it. I can't even post new questions on the Mathematics Stack Exchange anymore because the ones I already posted didn't have a consistent enough upvote, in fact were often downvoted enough that my contributions to the community are not considered worthy enough of the site for now; so no more feedback on that hand. All the professors I've emailed: no reply.

    So on another level, my paranoia is resurging. This might in part be due to medication backsliding, although to be sure my medication wasn't doing anything except making me feel vaguely sicker, ultimately, anyway: more confused, more breathing/blood pressure problems, yadayadayada... But so on this level, I've also started wondering if there's more to the danger of the plague than the governments of the world have admitted, as if either the real danger is still to come, or things are worse than are being reported, or even if there isn't that much of a real danger and governments are taking advantage of the situation to move ahead with some questionable plan that they already had and just needed a pretext to put into effect. I'm so confused, in other words, and still in the position of having to ask myself, "What am I supposed to do about it? Am I supposed to do anything?" And my feelings of defeat continue and intensify.

    So on the worst level, I feel guilty, or at least almost guilty, like there is something I should do, that I failed to do, and worse, did the opposite of. I can say, "Well, I really was going to go make my stand, I can't blame myself for an unexpected and overwhelming gut pain knocking me down, in fact I ought to be proud enough (or whatever) that I really would've made my stand had it not been for that pain, right?" But I don't know if that's worth saying, if anything I've intended to do or have done is worth that much. I don't know that anything I've ever done has been worth that much. My sense of social connections is evaporating virtually in total, I meet people and have no expectation of long-term relations with anyone, everything as such is just a wild blur in my mind, like, "Today I know this person, tomorrow I'll know someone else, and so on," which is just killing my sense of reality in general, you know? Like there is no real reality anymore, in a weird way.

  5. Confusion on my part, haha!

    1.png

  6. https://www.wolframalpha.com/ can be used to check some of my statements about transfinite arithmetic. For example, inputting "aleph 0 ^ aleph 0 ^ aleph 0" yields the same answers as "(aleph 0 ^ aleph 0) ^ (aleph 0 ^ aleph 0)" (but note that if you don't use the parentheses like that, you get a different answer) and also "beth 1 ^ beth 1" yields the same answers as the three-step staircase (thus indirectly verifying that c ^^ 2 = aleph-0 ^^ 3). Now there's no way I know of to use up-arrow notation in Wolfram Alpha, so conversions would have to be manual (conversions for checking, that is), but I think the basic information proofs are still helpful.

  7. Something I didn't emphasize clearly enough: 

    1.png

    1. Ripheus23

      Ripheus23

      The second line might seem false but is actually true owing to the rule indicated on the first line for evaluating a power-tower (under aleph-omega), namely in descending order (if there are no parentheses).

    2. Ripheus23
  8. A Novel Eschatology

    Let us suppose (we are going to make a good number of extreme suppositions) that, long ago, humankind had developed a civilization that, while not as powerful as ours is, nevertheless was much more powerful than even Rome or elder China, say. While it is unlikely that they manufactured nuclear weapons in the modern sense, there is a small amount of evidence that radioactive materials might have been used in an “elevated” form (e.g. in Mohenjo Daro) at various remote points in antiquity and before. At some point, wars relating to these and other materials consumed this ancient civilization to naught, leaving us the remarkable structures of Macchu Picchu, the Giza pyramids, Stonehenge, and so on, as a testament to the might of what was then lost.

                Among the survivors of those days were the precursors to the Israelites. There is some evidence that YHWH, among those (hypothetical) survivors, began His “life” as a god of metal. But inasmuch as the Hebrew scriptures “translate” the tetragrammaton as a code for the divine self-assertion, “I am that I am,” we might suppose that “YHWH” is ultimately no more a simple proper name than it is just a descriptive term. Suffice it to say that the proto-Israelite metallurgical YHWH was not really the One God YHWH of the Hebrew scriptures.

                Now the Book of Daniel (and the Second Letter to the Thessalonians, implicitly citing the Danielite text) says that the human enemy of the Messiah (now known variously as the Antichrist or the Beast from the sea), in the “last days,” will set himself up as a god in himself, as the embodiment of a heretofore unknown, unrecognized “god of fortresses” placated by offerings of precious metals and other such treasures. The Gospel of Matthew notes that representatives of the false eschatological religion will perform signs and wonders so as to deceive “even the elect, were this possible.” This religion, therefore, must appear very similar in form and content to Judaism and Christianity. The easiest sum of this and the rest of the above is: the antichurch will present itself as worshiping YHWH, but this will be the forsaken god of metal from the end of an older human world, not the Father of the Son, Jesus Christ.

                Why would an evil lord of metals be the image of ultimate darkness as such? Uranium is not emerald ooze or ore, but a typical metal in regular appearance. By means of its power, humankind has formed a “god of fortresses” (to contain and uphold the dire weaponry) that has subverted the political integrity of every people, nation, tribe, and tongue: all are beholden, directly or not, to the forbearance of the “great powers,” such that the threat of nuclear holocaust holds all humanity hostage to itself—trapped in the “fortresses” of the great lands. The discoverers and inventors of the threat sometimes saw themselves as having achieved divine stature, as unleashing a deity of death and destruction (“I have become Death, destroyer of worlds,” as Oppenheimer said).

                America on some (fundamental) level has always imagined itself to be the truest example of the New Rome, not only the inheritor but the transcendental successor to the apex predator of human antiquity. We can see how far America has carried out its antichristian foundations in this, that when the US state made of itself an ideological soldiery (in the holocaust of Vietnam), the prerequisite explanatory appeal was to a clearly Beastly system:

    The conquered people are not [always] forced at gunpoint to change their ways, but “all participation in public life, whether political, cultural or economic, is conditioned on acceptance of the new faith.” (Michael McClintock, Instruments of Statecraft, chapter 12)

                Rarely do we find such an explicit (if unintended?) evocation of the “prerogative” of the Antichrist, his False Prophet, and the image of the Beast thereof: “It forced all the people, small and great, rich and poor, free and slave, to be given a stamped image on their right hands [their deeds] or their foreheads [their beliefs], so that no one could buy or sell except one who had the stamped image of the Beast’s name or the number that stood for its name” (Revelation 13:16-17).

    Fire from heaven

    Although YHWH in the “Old Testament” is depicted as having entire cities destroyed by fire from heaven, Christ mysteriously enough claims that it will go better for Sodom and Gomorrah, at the final judgment, than it will for several other cities (Matthew 10:15). According to some copies of the Gospel of Luke, Christ actually goes so far as to ask His disciples once, “Do you know what kind of Spirit it is that we serve? For the Son of Man came not to destroy life but to save it” (Luke 9:56), and this in reply to a request by the disciples for celestial incandescence to be visited upon some unfaithful village in Samaria. Now there is apparently little to no archaeological evidence for the story of the ancient Israelites under Moses and Joshua going about physically slaughtering entire peoples in the land of Canaan, and it fits with the typological method of scriptural interpretation to suppose that those genocidal legends are allegorical for the ideological efficiency of monotheism versus polytheism: as Jewish philosophers (prophets, as per the definition of Maimonides) testified to the intellectual and emotional superiority of faith in One God instead of many, pagan regions variously converted en masse to monotheism of various forms (exclusivistic Ra-worship in Egypt for a time, say, or Zoroastrianism in Persia, being seeds or samples of such foreign processes).

                Accordingly, the False Prophet, however, will as his preeminent “sign” of power unleash “fire from heaven” on behalf of the Beast and the Beast’s image. Now there is one nation, above all others, who has indeed unleashed “fire from heaven” at many times and in many places: America, first and foremost in Japan, also to some degree in France and Germany (and a few other countries, during the Second World War, I believe), then massively in Korea, Vietnam, Cambodia, and Laos. (Granted, other nations have inflicted the same or similar flames on this or that land, but no other to the degree or extent that the US military has.) It is in America that the falsest forms of Christianity have taken pride of place in much government decision-making, public or covert (by this I mean that even notions like “Christian Identity,” a racist formulation that is brother to Nazism, are on the minds of at least some of our leaders, here or there, now or then). It is America that has the unique potential to betray the reconstituted Israel—the means, the motive, and the opportunity, even.

                Who is like the Beast, therefore? I think it is easy enough to see who is so in our day, at least.

    1. Ripheus23

      Ripheus23

      Civilian death tolls per nation (resulting from major air wars) (these numbers are my own opinions after 10+ years of statistical research and analysis)

      Non-American (all during WW2)

      Germany vs. USSR: 500,000

      UK vs. Germany: 400,000

      Japan vs. China: 350,000

       

      American

      Japan: 500,000 (but possibly 900,000, as per the USSBS)

      North Korea: 750,000 (but possibly 1,500,000, per one of Curtis LeMay's claims about overall North Korean deaths)

      South Korea: 250,000 (but possibly 500,000)

      North Vietnam: 100,000 (but possibly 200,000 or more, per the official postwar Vietnamese government and my own analysis)

      Laos: 300,000

      Cambodia: 300,000 (but possibly 600,000 or more, as per various other estimates)

      N. Vietnam, Cambodia, and Laos considered as a unit: approximately 1,000,000

      South Vietnam: at least 1,000,000, possibly 1,500,000 or more [note: South Vietnam was not only subject to the largest tonnage of bombing ordnance simpliciter, out of any nation in known history, but also to an inconceivable near-400,000 tons of napalm, to be contrasted with c. 10,000 as used on Japan during WW2, say]

      Total: approximately 3,500,000 to 4,500,000 [likeliest range; can be reinforced by considering sums for smaller campaigns]

    2. Ripheus23
  9. The Final Apocalypse

    86380696_10158022249912910_6231611304382038016_o.jpg

  10. Ԙ: The Final Power, Part 2

    The Shield defends Ripheus with a surety as of wild gold, and as true, for he alone holds it in valor. But this valor is only enough to preserve this one man as he ascends the last staircases of destruction's transfinity. Everyone else not here in the City falls and rises in the self-desecrating magma of the apocalypse, gasping for words of horror at each rise and fall of the crystal Forms of Evil and Nothingness.

    Armirex stands alone at the base of the four towers, watching skyward in despair and hope.

    Some of the others reach out, try to cross over to...

    Like calliopes of massacre, the shifting stairwells up which Ripheus goes trespass upon themselves darkly. Again and again the Shield saves him from being smashed apart by their cataclysm of murder. Sinstone breaks in torrents, rocking the ascent to the parapet that runs parallel to Apollyon's ray of fire and light.

    ... as they live and die they live up...

    Ripheus makes it to the parapet. He looks through an aperture onto the artificial plateau, bearing first witness to the ramparts of destruction's flame. Within which he intends to stand...

    ... to interpose himself between goodness and the Form of Evil...

    ... they live up, up, upward into the City...

    ... he braces the Shield for his entrance onto the parapet, slanting it as he passes the boundary of the Destroyer's radiant wake. Blocking the passage of that radiance, the Shield yet blocks only a small halo therefrom: enough for Ripheus to survive and endure through this end.

    Already, however, he is driven back by the weight of the light pouring forth unto him. This is the fire of the Final Power enmeshed with the ferocity of Apollyon. Those words, "Nothing can be done to stop the one who comes to end that which does not exist," Ripheus thinks back to.

    Hammered by the might of desolation, the Shield forms a wake of its own in the ray. As incandescence surges around him, Ripheus feels the stone on which he stands melting. Step by step, Apollyon raptures him towards the parapet's edge, and he sees the melting of the stone as a slow river carrying him along with the rapture.

    ... assembling at the base of the fourfold tower...

    --And a flicker of Apollyon's power sails off, rams into the Shield directly. Gripping the Shield's handle, Ripheus flies off the parapet, down towards portals opening from the physical plane that reveal friends and enemies and others come to fight or not. Ripheus warps the Shield like a kite and after harrowed sailing amidst the sapphire period of the light he manages to hit ground at a safe velocity and angle.

    The rest of the ensemble having arrived, one of them--[add name later]--runs up to the man of Troy. Talking to him while looking at the gem of Evil, she asks, "What is happening?"

    Hanging his head, Ripheus explains the situation: and the gem explodes again: and again the nova of the seraph hydra floods the streets of the City.

    1. Ripheus23

      Ripheus23

      *Wherefore Ripheus makes it to the parapet.

    2. Ripheus23

      Ripheus23

      *carrying him along with the rapture.

      Wherefore does he resist? What is there not to resist? Defiance can be defeated, though.

    3. Ripheus23

      Ripheus23

      *intoxicated magma of the apocalypse,

  11. Ԙ

    ... the Insignia of Ripheus...

    1. Ripheus23

      Ripheus23

      ... or the Icon of...

      ... or the sigil of...

      ... or the mark of...

      ... or the Glyph of...

      ... Ripheus.

  12. light-in-the-sci-fi-city-54213-1920x1200

    Nice picture I found, long ago, but posting it here instead of FB (where I originally shared it).

  13. I still don't know what to do about the problem of Apollyon in the real world. I would guess, maybe, that the "let's reprogram the Form of Evil" narrative has to have a wildly different IRL counterpart, since there's no Keyscape, there's already a Savior, etc. The "let's corrupt the world with romantic injustice" notion fits the profile, so to speak, but that makes displacing the Form of Evil into no goal at all for Apollyon, who instead is just using that Form's power to try to destroy the world, as it goes. But how (on Earth!) am I supposed to fight that?

    Not saying it's impossible, just that I don't get it, right now. I suppose I will down the road but I don't know how much farther down the road I've got to go.

  14. Two illustrations...

    1.jpg

    2.jpg

    1. Ripheus23

      Ripheus23

      The first is an image of the beginning of the final battle between Apollyon and Ripheus, when the Destroyer destroys the Form of Evil and then the Form of Nothingness (into which Evil has been transformed), recreating all possible evil at once.

  15. Cool Lovecraftian image I found:

    310px-Azathoth.jpg

  16. A correction! I think.

    1.jpg

  17. Well if I'm not supposed to give Dean the solution to the Continuum Hypothesis, then who should I give it to? Everyone else I've tried has been just as unresponsive as Dean himself haha.

    1. Ripheus23

      Ripheus23

      "When you don't know whether or how you're supposed to sacrifice yourself..."

  18. The Hounds of Carnap

    2ѭ = Ѩ

    This equation captured my mind: it was decidable--algorithmic, and suggestive. I had come up with it as a result of my studies in higher set theory, the doctrine of Richard Carnap's regarding the "telestial cardinals."

    Or from my perusal of more occult, if no less deviant, texts, sources as old as the Pnakotic manuscripts or as accursed as the Xenschernalia.

    Or from all such sources, I confess.

    I had stumbled upon the theory of cardinal "telestialism," as it was also known, secondhand. The weirder, sillier name for it was coined by quasi-adherents of different stripes than Carnap himself: the Hounds of Carnap, they were called, after the fiends of the dimension of Tindalos in Lovecraftian mythology. I had no idea why they thought of themselves as hounds, after all.

    Certainly no clue why they would adopt the moniker of a type of monster.

  19. If I could get a job at the hospital, that'd be so sick [haha]. I wonder what my prospects are.

×
×
  • Create New...