Uncommon Descent Serving The Intelligent Design Community

Infinitely wrong


Georg CantorI have blogged before on infinity, which holds a certain fascination for me. For one thing, I’m working on a thesis involving self-reference and the retreat into infinite recursion. And early in my Presbyterian life, I had to defend divine sovereignty and the infinities of power, knowledge and goodness from the inroads of Arminian rationalism and free will. So with a little practice, I’ve gotten quite comfortable with infinity, sort of like driving 80mph in the dark in a thunderstorm–the important thing is not to think about it too long. In this post, I want to think about it long enough to show that the Multiverse doesn’t save Darwin.

Georg Cantor, of course, couldn’t stop thinking about it and was driven mad. But before he went into the sanatorium, he produced a most remarkable result about sizes of infinity. Some infinities are bigger than others. For example, take the number line from 1 to ∞. It’s infinite of course. But now divide every number by the largest number on the line, and we have mapped the entire number line into the fractions between 0 and 1. So the rational numbers contain the entire integer number line between 0 and 1, and the rational numbers go up to infinity too. Then the rational numbers are at least ∞2 bigger. (Yup, I’m being sloppy, because Cantor also showed how to map x2–>x, so instead of calling it ∞2, he called it ℵ0 cardinality where integers and rational numbers have the same size infinity.)

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I'm a bit late responding to your questions, I beg your indulgence. Neil: Cantor got the same answer from his constructivist critics, whom I label the "left wing" critics--many of whom are positivists and agnostics, if not atheists. Mung: Yes, Yes, Yes, Yes, Yes, Yes, and absolutely Yes. Longer answers below. bornagain77: while Hugh Ross' numbers are big, they presuppose some sort of combinatorics. The point of Sir Roger's number is that it involves permutations, not just combinations. My point is that QM coherence adds yet another layer of a continuum of permutations, another layer of infinity to Sir Roger. The continuum is a difficult infinity to address, and it is somewhat surprising it arrives in "quantum" mechanics, but it is there in "entangled states". ciphertext: since you appreciate what infinity did to Cantor, you really must read the book I linked to earlier, "The Infinite Life" http://www.amazon.com/Naming-Infinity-Religious-Mathematical-Creativity/dp/0674032934 The point of the book is that Russian Orthodox mathematicians were able to go where Cantor couldn't because they had spiritual fortitude to handle the infinities. A really cool thesis, that religion not only equips you to do science, but enables you to go where no mathematician has gone before... Back to you Mung: Infinity is physical. Just as dividing by zero is a physical operation. In human experience we have things like "non-linear effects" or "saturation" that prevent infinity from hurting us, sort of like Sir Roger's thesis that naked singularities are always found in nature clothed. This does not make the singularity go away, it just enables it to coexist peacefully with nature. Mathematics loves infinities. A palimpset of Archimedes indicated that even that ancient Greek could use infinities in his proofs. Lots of math theorems use infinity in their proofs. If infinity didn't exist, then neither would these obviously necessary theorems. There is a curious intersection between math and physics, between numbers and reality. It was Nobel prize winner Eugene Wigner who gave a speech on "The unreasonable effectiveness of mathematics". I like to think of it as divinely ordered, so that the Trinity requires the numbers 3 and 1, and from that, all math is derived. Just as infinity is necessary for the physical and mathematical, it is necessary for the spiritual. I can't tell you how many heresies are based on monotheism and ditheism. Transcendance and immanence. Parmenides vs Heraclitus. Arminianism was the camel's nose, as far as Jonathan Edwards was concerned. It was the introduction of Enlightenment rationality into Puritan Calvinism. It replaced all the Puritan churches of Boston with Unitarian churches. Think of it, they went from 3 to 1 over the issue of Arminian/rationalism. So of course there is a mathematical side to Arminianism. Free will is a mangling of infinity, because it tries to apply the rules of heaven to earth, and the rules of earth to heaven. But heaven is infinite, and earth finite, so Arminianism is a category mistake, a seriously flawed transfinite algebra. Do you seriously think that blog commentators are capable of understanding transfinite algebra? Of course God is infinite. That is like asking if God is God. Unless of course, you are a panentheist. But I will assume you were asking an orthodox question. In what way could God NOT be infinite: wisdom, knowledge, goodness, existence? What are you thinking? Robert Sheldon
I remember reading a book, a short biography of Cantor and his work with transfinite numbers. It was entitled The Mystery of the Aleph, Mathematics, the Kabbalah, and the Search for Infinity by Amir D. Aczel. (ISBN: 0-7434-2299-6) I thought the book very interesting. At least in terms of how it described the relationship between the degradation of Cantor's mental "state" with respect to his increased focus upon understanding infinities. Reminded me of how a computer's processing "state" could be considered degraded when an application monopolizes the processor's time in its attempts to ponder "imponderables" (i.e. division by zero, infinite loops, very large numerical sequences [pi], etc...) ciphertext
Actually Joseph 10^500 multiverses does not even come close to what is needed to explain this one: This following article illustrates just how far string theory would miss the mark of explaining the fine-tuning we see even if it were found to be true: Baron Münchhausen and the Self-Creating Universe: Roger Penrose has calculated that the entropy of the big bang itself, in order to give rise to the life-permitting universe we observe, must be fine-tuned to one part in e10exp(123)?10^10exp(123). Such complex specified conditions do not arise by chance, even in a string-theoretic multiverse with 10^500 different configurations of laws and constants, so an intelligent cause may be inferred. What is more, since it is the big bang itself that is fine-tuned to this degree, the intelligence that explains it as an effect must be logically prior to it and independent of it – in short, an immaterial intelligence that transcends matter, energy and space-time. (of note: 10^10^123 minus 10^500 is still, for all practical purposes, 10^10^123) http://www.evolutionnews.org/2007/06/baron_munchausen_and_the_selfc.html bornagain77
10^500 multiverses needed to explain this one... Joseph
Even supposing Multiverse is true, it does not necessarily negate the ID hypothesis. See: Shift Happens, Many Worlds, One God scordova
correction, the question marks before the exponents should be the approximately equal sign, they did not format correctly. bornagain77
OT, updated reference from Hugh Ross: Probability for occurrence of all 816 parameters ? 10^-1333 dependency factors estimate ? 10^324 longevity requirements estimate ? 10^45 Probability for occurrence of all 816 parameters ? 10^-1054 Maximum possible number of life support bodies in observable universe ? 10^22 Thus, less than 1 chance in 10^1032 exists that even one such life-support body would occur anywhere in the universe without invoking divine miracles. http://www.reasons.org/files/compendium/compendium_part3.pdf Hugh Ross - Evidence For Intelligent Design Is Everywhere - video http://www.metacafe.com/watch/4347236/ bornagain77
Unlike some, I'm not all ga-ga over your appearance here even though I am certain that I can find a dedicated Presbyterian in my lineage. But nevertheless I extend a hearty welcome. I have a few questions: What is the relationship between infinity and the physical? What is the relationship between infinity and the mathematical? What is the difference between the physical and the mathematical? What is the relationship between infinity and the spiritual? How does any of this relate to Arminianism? Do you really think that people here at UD are capable of intellectually grasping the essentials of this debate? Final question: Is GOD infinite? Mung
I'm not sure why people see anything important here. As a mathematician, I rather like Cantor's ideas on infinity. However, I understand them to be constructs of the human mind, and not metaphysical entities. As for the multiverse - I am currently taking that as a speculative hypothesis, rather than settled science. I'm doubtful that it could ever be considered more than a useful mathematical model (as contrasted to a metaphysical account). Neil Rickert
The multiverse was concocted as a way to have impossibly unlikely events possible. Fair enough. I can imagine a universe where the laws of physics allow a tornado tearing through a junkyard to leave a 747 in its wake. It just doesn't happen to be this one. A royal flush is a common poker hand, but not here. With the multiverse, we may imagine a place where random events produce specified complexity and information. It just doesn't happen here. So the multiverse isn't any help explaining what we observe in this universe. jpg564
Dr. Sheldon, It is an honor to see you posting here at UD. Another analogy is that of a lock and key system. There are an infinite number of ways to make locks and keys. The fact that lock and key systems can be implemented in an infinite number of ways does not make them some how probable. Protein systems are lock and key systems. Even if there are infinite universes, it still does not imply they will be probable! Great POST from a fellow presbyterian. :-) scordova
Here is a related video on Cantor Georg Cantor - The Mathematics Of Infinity http://www.metacafe.com/watch/4572335/ Cantor's work actually plays into the story of three other men's lives,,,, Ludwig Boltzmann, Kurt Gödel and Alan Turing the entire video is here: Dangerous Knowledge 1 of 2 http://video.google.com/videoplay?docid=-8492625684649921614# bornagain77

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