Today I finished Rudy Rucker's Infinity and the Mind.
I was first introduced to this book by Josh in summer 2001 while we were trapped in Lincoln, Nebraska for 3 days. At his father's place, he found this book to entertain me. His father gave him this book when he was in high school. Immediately I was drawn into the book, because it talks about many issues Josh and I had been discussing during the past few months. When I first met Josh, he tried to show me how to prove that there are more real numbers than natural numbers. We were both fascinated with numbers, especially prime numbers. Like Rucker, Josh was also a mathematician in set theory, and studied philosophy of mathematic logic. Perhaps reading this book early in life had influence Josh in his later choice of intellectual pursuit. When we got back to Pasadena, I bought a copy of the book, and was looking forward to more discussion with Josh. Unfortunately he was pre-occupied with other things and our discussion never passed the naming of ordinals and cardinals. I could never forget the amazing Hilbert Hotel. I was also excited to learn that infinity comes in different sizes, and the mere existence of infinity is to be questioned.
Soon I got lost in all the numbers and had to put the book down until the end of 2003 when I met Mike and asked him to read this book. He read it quickly, probably skipping many parts. We didn’t have many discussions about it, mostly because we had such startling opposite views of the universe that we could never find a place to start. We did agree that Rucker’s writing was more like personal notes he wrote for himself than a well-constructed thesis on the subject. I took up the book for a while and abandoned it again.
This book has been rated five stars by 15 readers on amazon.com, and is high on my reading list, so I’d decided to read it through once this summer.
Chapter one reviews the history of infinity, and introduces the concept of mindscape. Years ago I was excited about the idea of mindscape, but after I had the fortune to see the Reality as a whole, I found this idea rather intuitive and basic. I was happy to see the mention of the Absolute as part of the discussion of Infinity.
In terms of rational thoughts, the Absolute is unthinkable. There is no non-circular way to reach it from below. Any real knowledge of the Absolute must be mystical, if indeed such a thing as mystical knowledge is possible.Chapter two is about all the numbers. Again soon I became confused with the names of different infinities. Unless one can tightly grab onto the endless symbols Rucker introduced incessantly throughout the chapter (and the book) one would have a difficult time follow the text. Also his figures are ill-labeled. I don’t think I am missing much by skipping some of the paragraphs. I also skipped the two excursions because they are even more technical. The Reflection Principle is interesting.
The Reflection Principle is really a different way of saying "Omega is inconceivable." For "Omega is inconceivable" is the same as "there is no conceivable property P that uniquely characterizes Omega," and this is the same as "whenever P is conceivable property of Omega, then there must be other ordinals also enjoying property P."The description of the Pythagoreans reminds me of certain eastern philosophy on reincarnation.
The sect of Pythagoreans is best known for their belief in metempsychosis, or reincarnation. They believed that there is one cosmic mind or soul, that you are alive because a small piece of this soul is imprisoned in your body, and that the bit of soul that animates you will animate many other bodies before returning to full unity with the one big soul.... Presumably it was hoped that if in the course of your lifetime you could bring yourself into a close enough relationship with the One, then when your body died, the soul that vivified it might be able to return to the source instead of being force into another body.Another memorable quote about natural numbers:
Someone who is merged with the Absolute is in a position to "name" each and every natural number at once.Chapter three is titled "The Unnameable", and Rucker discussed the Berry Paradox and discussed the reality of Truth, among other subjects. It’s interesting to see how systematically and detailed he talks about the logic of "This sentence is false”, and even distinguishes it from “This sentence is not true". I skipped the more technical section of Richard’s Paradox, assuming it is along the similar line of the truth discussion. I was glad to find out that Rucker is also a Borges’s fan (I only wish I could write reviews of books and movies as clearly and originally as Borges). From Borges’s story about the Library of Babel—the library of all possible books, Rucker introduced a clever tool—to code each book into a natural number. Furthermore, the whole universe can be coded into a natural number, and thus we can think about the infinity nature of the universe the way we think about numbers.
Chapter four is about robots and souls, but the more interesting part is the three conversations Rucker had with Godel. I was happy to know that Godel is a mystic, partly because I am becoming more and more identified with the label mystic. Rucker wrote:
Godel shared with Einstein a certain mystical turn of thought…. A pure strand of classical mysticism runs from Plato to Plotinus and Eckhart to such great modern thinkers as Aldous Huxley and D.T. Suzuki. The central teaching of mysticism is this: Reality is One. The practice of mysticism consists in finding ways to experience this higher unity directly.Rucker also recorded their discussion on the passage of time.
The One has variously been called the Good, God, the Cosmos, the Mind, the Void, or (perhaps most neutrally) the Absolute. No door in the labyrinthine castle of science opens directly onto the Absolute. But if one understands the maze well enough, it is possible to jump out of the system and experience the Absolute for oneself.
I asked Godel my last question: "What causes the illusion of the passage of time?"Godel has found. Rucker is still seeking.
Godel spoke not directly to this question, but to the question of what my question meant--that is, why anyone would even believe that there is a perceived passage of time at all.
He went on to relate the getting rid of belief in the passage of time to the struggle to experience the One Mind of mysticism. Finally he said this: "The illusion of the passage of time arises from the confusing of the given with the real. Passage of time arises because we think of occupying different realities. In fact, we occupy only different givens. There is only one reality."
Chapter five is on the One and the Many, the most philosophical chapter of the book. Rucker probably does not have the One figured out, but it’s interesting to see how he compares the One and the Many in a rational way. First I quote what he quotes of Plato's Philebus:
We say that the one and many become identified by thoughts, and that now, as in time past, they run about together, in and out of every word which is uttered, and that this union of them will never cease, and is not now beginning, but is, as I believe, an everlasting quality of thought itself, which never grows old. Any young man, when he first tastes these subtleties, is delighted, and fancies that he has found a treasure of wisdom; in the first enthusiasm of his joy he leaves no stone, or rather no thought, unturned, now rolling up the may into the one, and kneading them together, now unfolding and dividing them; he puzzles himself first and above all, and then he proceeds to puzzle his neighbours, whether they are older or younger, or of his own age that makes no difference; neither father nor mother does he spare; no human being who has ears is safe from him, hardly even his dog, and a barbarian would have no chance of escaping him, if an interpreter could only be found.This young man Plato describes is me. Haha! Indeed I am still fancy that I have found a treasure of wisdom.
St. Gregory and the Reflection Principle (again):
No matter how far our mind may have progressed in the contemplation of God, it does not attain to what He is, but to what is beneath Him.
Given any proposed description DESC of V, there will be a partial universe V_alpha that satisfies DESC as well. Any specifically described universe of set theory turns out to be only one of the V_alpha sets, and not the whole universe.More on mysticism:
There are, indeed, things that cannot be put into words. They make themselves manifest. They are what is mystical. (Wittgenstein)
Mysticism is the simple awareness of the direct identity of the individual soul and the Absolute.Rudolf Otto in Mysticism East and West describes two different types of meditations that people practice in order to feel united with the Absolute: the Inward Way (Not that, not that), and the Way of Unity (And that also). “Nothing is the same as Everything.”
Rucker also contemplates, “the Void and Everything can perhaps, in a momentary way, be experienced as the same”. In my own experience, the Void comes right after Everything, and when I had arrived at the Void, I went around and around saying Everything is Nothing, Nothing is Everything, and I am Everything…I AM.
The very last section is on Satori. Rucker quotes D.T. Suzuki:
Vijnana can never reach infinity. When we write the numbers 1, 2, 3, etc., we never come to an end, for the series goes on in infinity. But adding together all those individual numbers we try to reach the total of the numbers, but as numbers are endless this totality can never be reached. Prajna on the other hand, intuits the whole totality instead of moving through 1, 2, 3, to infinity; it grasps things as a whole. It does not appeal to discrimination, it grasps reality from inside, as it were.Here clearly Suzuki declares that true reality can only be grasps from inside, from the whole, because it simply is. However, Rucker still argues the whole is only one of the two aspects of the true reality. I am not sure if he understand what he quotes of Suzuki of what Satori is:
The oneness dividing itself into subject-object and yet retaining its oneness at the very moment that there is the awakening of a consciousness—this is satori.Rudy Rucker wrote this book in 1982 when he was about my age. Perhaps he has reached another stage in his search. Despite of many inadequacies I found in this book, it nonetheless has showed me fascinating new ways of thinking about the universe. For this I am grateful. I would rate this book 4 out of 5 stars.
p.s. I feel I am much slower than 5 years ago. I don't seem to be able to comprehend complex systems as effortlessly as I used to. Is this a sign that my brain power is declining? I do need to do more active reading and thinking to keep up.