At the begining of the 20th century three Russian religious heretics created what has become the most influential school of mathematics of our time. The Moscow School of Mathematics. They created something called Descriptive Set Theory and their students went on to create a body of mathematical theory called Topology among many other achievements, which, is now one of the cornerstones of the math used to develop modern physics. Their journey, set against a background of persecution, first by the Russian Orthodox Church and then by the Bolshevik and Communist revolutionaries, is fascinatingly described in this short book.
I am not a mathematician and do not pretend to understand the actual principles described in the book, but the basic ideas are fascinating and easily understood and the story of Egorov, Luzin and Florensky is one with universal appeal and provides food for thought for any person interested in how spiritual bravery, imagination and personal integrity can change our environment and ourselves.
I found this book at the UCLA Book Fair. Jean and I go every year. We sort of wander around and go into booths which pull us in for one reason or another. I buy random books that just sound interesting. This time I found a book called Little Brother by Corey Doctorow about how society is saved from an overly aggressive Homeland Security response to terrorism by a bunch of teeanage video gamers. The title is a play on George Orwell's Big Brother. A fun and interesting read. I recommend it. I didn't find anything else in my random booth visits.
Then just as we were leaving there was a lonely booth on our path toward the car which was the Harvard University Press. I wandered in and saw a bunch of really academic and business oriented books and was about to leave when I saw a book called "Naming Infinity". I loved the title, read the back cover and bought it.
There's some math in there which can be pretty hard to follow but it's not essential in order to enjoy the book. The main point of the book is that Set Theory, which had originated in Germany and developed further in France in the late 1800s and beginning of the 20th century, had become stuck. There were directions which Set Theory intimated at but which the French and German Cartesian Rationalists refused to explore because such directions seemed non rational and implied things about the universe which could not possibly fit into their worldview. It took a group of young mathematicians completely unencumbered by adherence to the rationlist viewpoint, who were in fact motivated by a heretical Christian mysticism, to break the stagnation which Set Theory had fallen into. And it was this mystical/revolutionary viewpoint which paved the way for modern math and physics.
Dmitri Egorov, Nikolai Luzin and Pavel Florensky were all mathematicians who, through Florensky's influence, became practitioners of something called Name Worshipping. This was a practice deemed heretical by the Russian Orthodox Church. These men held a view of the universe motivated by this practice which they believed allowed them to experience direct union with God through the repetition of the name of God. It was deemed heresy by the church because the church said that God could not be contained in something finite like a Name. Ultimately, hrough their practice of Name Worshipping they gained insights which allowed them to see that infinity can be contained within subsets of the mathematical Continuum and that special sets can be created by the process of naming. Hence the name of the particular aspect of set theory which they created: Descriptive Set Theory.
I found this fascinating for a number of reasons. As I said I don't understand all the math but it seemed to strongly imply that a finite bit of an infinite sytem could be mathematically shown to be capable of containing the infinite within it. And, based on the experience of these mathematicians, the idea that a name, such as Nam Myoho Renge Kyo, could indeed be a means to contain the infinity which it names within it and thereby provide a means to fuse with the infinite. And, of course it raises the question of whether it matters what name we use; God, Bog(the russian version of God),Jesus Christ, Nam Myoho Renge Kyo, Namu Myoho renge kyo, Om Mani Padme Hung. It seems that what matters is the human imagination and whether we are capable of finding a name or description through which we are able to deeply imagine that name as a descriptive set which contains ultimate reality within it. If so, then we may be able to use that name as a means to practice toward fusion with that ultimate reality.
Anyway, check it out if you get a chance. It's also a fascinating look into the lives of these people and how they each dealt with a society which became increasingly anti-religious during their lives while at the same time becoming more and more covetous of scientific and mathematical achievements of the school which they founded.
Bill
Posted by bill at August 18, 2009 12:14 AMBill,
Interesting opening on Set Theory. My wife some years ago, bought a book for me after college, it is about putting Set Theory into practice in solving structural engineering problems with various unknowns and using computer programming using array dimensional mathematics to resolve the various unknowns in order to design a concrete and steel bridge or thin slabs, or long beams, or various structural entities that can not be resolved with hand tools and simple mathematics using array mathematics.
Of course nowadays we have our PC's and I can buy and have bought various structural engineering programs that use Set Theory as their basis easily.
I guess you could say that this unique Set Theory was a necessity if science was to move forward, even if the Russian's did not see the inherent truth in the Set Theory, the original scholars did, and because of those scholars; with their never give up spirit; we have modern structural engineering tools at our disposal today.
In bringing this back to Buddhism and The Mystic Law, Nichiren says, "The law does not spread itself." Without people willing to work hard,with a no matter what attitude, the Mystic Law will spread, just as Shakyamuni Buddha and Nichiren predicted, "for ten thousand years and more."
Patrick
Posted by: Patrick at August 18, 2009 10:54 PM"What's in a name? A rose by any other name would smell as sweet."
Saddharmapundarikasutra
E=MC2
Are they valid by any other name?
Does their validity depend upon the fourth dimension, time/space?
There's a Yogi Berra-ism "What time is it? You mean now?" which closely encompasses the fourth dimension, time, with regards to the general theory of relativity: "What time is it? You mean here?"
Posted by: Joe Isuzu at August 18, 2009 11:06 PMHi Patrick,
Well you would probably actually understand the math in the book which I think would make it that much more enjoyable. I hope I didn't say anything too stupid about Set Theory.
Not sure how the comment about the law not spreading itself applies to what I wrote though. Can you explain?
Thanks,
Bill
Posted by: Bill at August 19, 2009 06:05 PMHi Joe,
Interesting comment. These guys (Florensky, Egorov and Luzin) seemed to beleive that certain words or sounds had particular power to encompass the infinite. So for instance they beleived that the "Bog" had particular power. They also seemed to beleive (I say seemed because these are things discussed only in passing in the book) that the universe had what the authors describe as "magical" properties. One of these properties was that the act of naming something is an act which creates a "thing" or set. While the authors, from a purely scientific viewpoint, see thatas a sort of magical thinking, I see it as a nother way of saying what buddhism says about names and things, ie, that naming things essentially creates things, or at least creates the delusion that things exist as seperate and self contained entities. The analysis of things as "baskets of skandas" is a sort of deconstruction of the process of set creation which we as human being do to our selves and our environment. "Name worshipping" whether the name is bog or Nam Myoho Renge Kyo is a way of creating a "basket" or "set" which contains everything and, in some way turns the poison of "naming" into medicine.
Personally, I like the sound of Nam Myoho Renge Kyo and the actual description of the set defined as ultimate reality which is contained in those sounds. Still, I am blown away by the insights gained by Florensky, Egorov and Luzin through their practice of fusing with God and therefore must respect the resonance of that "descriptive set" for them.
Not sure what relativity has to do with any of this but maybe you could explain your thinking? I like the Yogiism and agree that "what time is it? You mean here?" is a pretty good encapsulation of the special theory of relativity.
Bill
Bill
Posted by: Bill at August 19, 2009 06:35 PMI'm coming to appreciate mathematics more for having it told with all the stories attached. This was such a dull subject in school. I've got a book at home by Benoit Mandelbrot (with a co-author) that talks about "The Misbehavior of Markets." and tells the mathematics with stories about the trials and errors of economic theoreticians. In the process I learned all about Power Curves, "fat tales" versus the normal curve and the fact that economic events don't follow a normal curve, etc...
I have to read your book!
Posted by: Chris at August 19, 2009 07:02 PM"Not sure what relativity has to do with any of this but maybe you could explain your thinking?"
Oh, if only I could. Then I might understand what I'm trying to say.
Prophesy has always been an issue with me because deals with future-time. Mathematics, especially theoretical mathematics, can be excruciating exercises. But the result is that an individual in attempting to solve a problem can rewire their brain into non-linear thinking, coming to a conclusion which was a prediction based upon some kind of observable data. So in science one can "predict" something that may exist but does not yet at this "time" because it's existence has yet to be proven. That is all "timing" which Nichiren always said was the most difficult thing to comprehend and way more valid in it's impact than capacity or country. Country can be seen as "space". In science or Buddhism it's futile to think of time and space as separate items: it's Space/time. If you want to meet me not only do you tell me when, what time, but where, the place in space. Otherwise at 10AM I'll be on the Sky Deck of the Sears Tower in Chicago, and you'll be on the Observation Deck of the Empire State Building at 10AM, and not only will we be in the wrong space, but one of us will be an hour late and one an hour early. Hang in here.
So if something is being called by a name that resonates it's authenticity, (how's that for a leap) is it valid everywhere, someplace else in space and time, or does it depend on the space and time? If I go by what Nichiren says, it's validity depends on it's relative time to the space. Relativity.
Posted by: joe at August 19, 2009 08:04 PMNicely done! I like it! (And beleive it or not, it's sort of what I thought you were getting at.)
Posted by: Bill at August 19, 2009 08:22 PMAncient Prophesy depended on either a hypernormal or transcendent perception of reality; modern prophesy depends simply the ability to see trends and how human factors interract.
Mandelbrot's book shows the dangers of trying to predict the future, but at the same time shows that certain predictions simply flow from the nature of human reality. For example, the just passed financial meltdown, and the next one, are all very predictable. What one can't predict is when. One can figure ways to mitigate the problem.
I can predict it will rain in the famous Desert in Chile. What I can't predict is how many hundreds of years into the future it will do so. I can give a confidence of say 80% that yellowstone park will eventually erupt in a cataclism. But my prediction would be a guess, and in any given year the odds are probably a lot less, like .1% or yeas. Yellowstone's hotspot could simply shift someplace else. It's granitic lavas could simply cool into granite and form the basis for some future manhatten.
To be able to spot trends is how some people speculate and make money. When they do so on a faulty basis they aggravate problems into disasters as our financial mavens did last year. Chaos theory shows that when there are a lot of variables, sometimes some of those variables cancel each other and "roll up" so that things seem predictable -- until something (often something small) changes. This is called the "butterfly effect" after a weather experiment that had huge differences in outcomes based on initial variants smaller than the strength of the wind caused by a butterfly beating its wings.
Human morality plays a huge role here. Wall Street tried to set up the equations for their financial instruments so that heads they win, tails we lose. They succeeded in creating creative "insurance" instruments with no backing, and even more creative bundles of financial instruments and bets on financial instruments. All this fell apart predictably, but they planned to make money off of it. The butterfly is greed and that one ought to be called "Mothra."
The ones left holding the losing bets were AIG and people buying homes on the expectation that the home's value would inflate. The ones who bought those bets were some of the richest people in the world. AIG went bankrupt. The Fed and Treasury bailed them out -- so who is going to pay those bets? We will. We assumed them so that AIG could keep paying bonuses to the perps.
I can't blame Bush for this anymore because now Democrats are doing the same thing. Instead of rolling up the bad bets, the Fed has doubled down. I can predict more trouble to come. I can't predict when its going to happen, and I can hope that it won't happen and folks will take preventive measures to keep that baby from being born.
That is prophesy in the modern world. Not much different from prophesy in the ancient world except its less gut and more observation. Maybe names do have such power. Those Russian mystics weren't saying anything much different from what Jewish Mystics were saying 2000 years ago, and why the actual pronunciation of the Four letters that form the Hebrew name of God are lost. It wasn't "Bog" but it was yeh Ho Way Ha or something like that. To mystics Nam Myoho Renge Kyo is just another name for the ineffable mystic God of the mystics.
Posted by: Chris Holte at August 19, 2009 09:51 PMBill,
In relating the Set Theory to the Mystic Law; both spread by human resolve and not merely by their existence alone.
Set Theory became mainstream, because the authors and scholars fought to spread this understanding even against religious and authoritarian rule, not mush different than the Wonderful Law as expressed in the Lotus Sutra and Nam Myoho Renge Kyo becomes mainstream.
I would not have a book on computer applications of Set Theory as it relates to array mathematics, if not for the diligent fighting spirit of those scholars afore-mentioned, nor the True Happiness associated with the Mystic Law for the same reason.
Just as you wrote, "is one with universal appeal and provides food for thought." This "spiritual bravery, imagination, and personal integrity," as you noted are the human endeavors to spread the "basic Ideas," are the spirit that I speak of when I noted "The Law does not spread by itself" The rest of the quote goes on to encourage people to spread the law responsibly.
I hope this clarifies my understanding.
Patrick
Posted by: Patrick at August 19, 2009 10:26 PMI would like to add something to Patrick's point. Obviously without the effort of people to make these ideas known, there could be no application of the ideas. But, these people were fearless in their pursuit of mathematical proof, regardless of the established views of their contemporaries. Their bravery was not so much in the promotion of their ideas as it was in the pursuit of ideas which seemed to fly in the face of orthodoxy. Their's was the passion of a mystic to see reality directly regardless of where that led them. It was only much later that the practical application of these purely theoretical ideas became clear.
Bill
Posted by: Bill at August 19, 2009 10:51 PMChris,
Very Orwellian. "Organization" has an inherent quality built into it, enabled by the nature of any organization, to attract to it individuals who will foster the survival of the organization over the individuals who comprise it, regardless. Greed, avarice, dominance are by products of any organizations evolutionary spiral.
"Mothra" Love it! Right on! "Yahweh"
Posted by: joe at August 20, 2009 12:18 AMBill,
I was force fed math as a kid; but rebelled. I do think in terms of the general & specific; which comes up in Tiantai / Nichiren Buddhism. There are actually two concepts in Tiantai. One of these, 通別 {tsubetsu} -- shared & distinct; might match up to set theory. It is similar to the concepts of generalization and discrimination. For example, all dogs have some general or shared characteristics; they are the Canine Set. However, each breed has its specific or distinct attributes; various subsets.
The other is 総別 {sobetsu}; which is used in the context of the Lotus Sutra. It is usually translated as the general and specific; or universal and particular. Neither translation conveys the meaning as used in the Lotus Sutra. I do not have a good translation. Perhaps broad and narrow? Inclusive and Exclusive?
The curious thing is that source teaching {honmon} is conveyed as the specific; while the trace {shakumon} is conveyed as the general. So is the trace teaching the Universal? It seems like it ought to be the other way round? I guess it is the way it is because the Source Gate is unique to the Lotus Sutra[ while the Trace Gate is found in all of the Sutras.
I might have this backwards; I but think the Holy Name would attempt to be a formula that would put everything back into one set? The common thread in the fabric of space-time? So one might say Bog in the general, and things are specifics. But the Lotus Sutra seems to tell us that Bog {the Source Gate Dharma} is specific; and created spatial - temporal things things are generalizations.
Posted by: robin at August 20, 2009 03:03 PMHi Robin,
That is interesting and it does seem counterintuitive that the source is specific and the trace is general, but I don't really know what those terms mean. The more I read about buddhism the more I realize that words often have very specific technical meanings and it's easy to get things confused by interpreting those words based on my superficial understanding. I've been reading a book recently called "On Knowing Reality". It's a translation of one chapter of treatise by Asanga written way back when at the beginning of the Mahayana teachings. What's interestring is the commentary and how Asanga and some of his followers were classified as beleivers in the "Mind Only" school of buddhist thought. The idea that everything is simply a product of mind.
The translator and commentator makes a convincing (to me) argument that the whole mind only interpretation is a misunderstanding of certain key phrases. Where followers interpreted remarks by Asanga and others as meaning that there is only mind, when in fact what Asanga was saying was actually meditative instructions to realize that our view of phenomena and even the most glorious mystical visions should be seen as "merely mind" and not be taken as a direct experience of reality. Exactly the opposite of how it came to be interpreted.
So, I guess that's a long way of saying I just don't know how to interpret what you're saying about the source and the trace. Regarding your comments about Bog being an attempt to put everything back into one set sounds about right. Just like it sounds about right for the set defined by Nam Myoho Renge Kyo.
But, as always, I could be and most likely am wrong.
Bill
Posted by: Bill at August 21, 2009 06:40 AMThank you for the thought provoking blog.
>>> "So, I guess that's a long way of saying I just don't know how to interpret what you're saying about the source and the trace. Regarding your comments about Bog being an attempt to put everything back into one set sounds about right. Just like it sounds about right for the set defined by Nam Myoho Renge Kyo."
I do not know either; and there is some comfort in that. Not saying that ignorance is bliss. I find a comfort in addressing things I do not understand. Still, I intend to understand it; someday. Right now, when I try to sort this point out, my mind goes into a loop.
All of the Sutras teach certain things. Those teachings are "tsu" or shared. Each also has its central theme; that teaching makes it "betsu" or distinct. Nichiren asserted that certain teachings make the Lotus Sutra distinct. [I think most of those are found in the Nikayas; albeit hidden in plain sight.] iirc, the ten thusnesses, the 三世間 {san seken}, the prediction of Buddhahood for women, miscreants, shravakas, and pratyekas; the Buddha's awakening in the remote past, the Bodhisattvas who emerge from Underground, ...
The Lotus Sutra has two transmissions. One is the "so" or general transfer. That one is for all the beings who attended; including the provisional Bodhisattvas. This relates to the trace or imprint gate teaching. Traces 迹 {shaku} are also called provisional 権 {gon} because they are transient 無常 {mujo}. The Buddha who awoke in the world for the first time is called the Trace Buddha. This also relates to the gradual 漸 {zen} and acquired 始 {shi} awakening.
The other is the betsu or specific transmission.
This is only for the Bodhisattvas that emerge from underground. This relates to the source or origin gate teaching. The Source 本 {hon} is also called True 実 {jitsu} because it is constant 常住 {joju}. The Buddha who awoke for the first time is the Source Buddha. This also relates to the immediate 頓 {ton} and innate 本 {hon} awakening.
However, if we look at from the point of view of sets; the Source Buddha would seem to the shared, universal, and general pattern of all Buddhas; while the Trace Buddha would be a distinct, particular, and specific example, within the general set.
>>>when in fact what Asanga was saying was actually meditative instructions to realize that our view of phenomena and even the most glorious mystical visions should be seen as "merely mind" and not be taken as a direct experience of reality. Exactly the opposite of how it came to be interpreted.
That is becoming the current view, that the early founders of mind-only were talking about what we would call epistemology -- how we know things or psychology -- how the brain works; not ontology -- the nature of existence or physics -- reality.
gassho
robin
"The attributes of Nirvana are eightfold. What are these eight? Cessation [nirodha], beauty [subha], Truth [satya], Reality [tattva], constancy [nitya], bliss [sukha], the Self [atman], and transcendental purity [parisuddhi]: that is Nirvana." -- Mahaparinirvana Sutra
Posted by: robin at August 21, 2009 09:57 AMEpistemology and Ontology. Thanks. I knew those were words I wanted to use but wasn't sure which was which so I just used my own words. Ultimately though it is fascinating how passages intended to describe and warn people not to become attached psychological states associated with meditation got twisted into the exact opposite of what was intended.
Makes me wonder if these buddhist dudes should be more careful to state what they are trying to say more carefully. Of course Asanga would probably say that the people he was talking to knew exactly what he meant and how could he possibly account for the way words got changed over the years and through the process of translation into Chinese and Japanese? And, to boot, his whole deal is how thinking we know what something is just because we have a name for it is the root of delusion. The curse of discursive thought and the proliferation of delusion through associative thinking based on an assumed and unquestioned view of reality based not on direct knowledge of reality but based on the perception of reality through the filter of language.
So you've got me thinking about the specific and general and maybe this makes sense. From a technical buddhist viewpoint the source gate is specific to the lotus sutra while the trace gate is found generally in all sutras. From a commonsense intuitive perspective though the source teaching would be the general set which incorporates all of reality within it while the trace gates are narrow and specific to particular methods of teaching. Or something like that.
Which would get us right back to how easy it is to misunderstand buddhist teachings if we don't realize that words have specific technical meanings which maybe were generally understood at the time they were written and might not mean what we think they mean now. I guess Asanga would say that this general idea that we know what something is or means because we unquestioningly accept the meaning it has for us is certainly reflected in the buddhist community specifically becasue in fact it is the underlying delusion of human beings generally.
Bill
Posted by: Bill at August 21, 2009 06:47 PM>>>>"From a technical buddhist viewpoint the source gate is specific to the lotus sutra while the trace gate is found generally in all sutras. From a commonsense intuitive perspective though the source teaching would be the general set which incorporates all of reality within it while the trace gates are narrow and specific to particular methods of teaching."
I think you have got it now. Sets and subsets; generalization and discrimination; shared and distinct; the general and specific; the universal and the particular; are effective ways of sorting things out. These are tools of analysis; they do assign not a fixed attribute; which is which is relative to one's perspective.
>>>> "Which would get us right back to how easy it is to misunderstand buddhist teachings if we don't realize that words have specific technical meanings which maybe were generally understood at the time they were written and might not mean what we think they mean now."
That is where upaya or approach 方便 {hoben} and the ultimate 究竟 {kukyo}; as well as the provisional or tentative 権 {gon} and the true or real 実 {jitsu} become useful tools. I try not to get too attached or too unattached to 'perspectival' or opinionated views.
One thing; I think Nichiren Buddhism does point us to an ultimate intangible super-set; which is an affirmative awakening to truth.
Posted by: robin at August 22, 2009 04:39 AMI love this discussion of how the 'rational' (mathematical) world is being seen as growing/developing to fit our construct of spirituality - of course it does - it will continue to be proved in accordance to whatever view each of us holds - because we (euphemistic we - I am doing nothing) are doing the proving and we can prove anything we want. And make it happen. I love that Nichiren buddhism led me to this world view and I love how I feel having it and I love you guys that spend all this time putting pieces together so I have a smorgasbord from which to choose what I want to believe. Thanks for making it easier for me in such an interesting way. (Yes, I am a nacissist LOL)
P.S. Outside the buddhist world this is happening too.
P.S.S. Would you believe I actually saw Mothra in theatrical release? (At a drive-in of course ;-)
Posted by: Laurie at October 17, 2009 06:46 PM