Posted on 11/30/2004 6:21:11 PM PST by betty boop
"The Mystical Theology of the Eastern Church" is one of the best books ever written.
The downward tendency should not be resisted directly. To attempt it is to experience the despair of Romans 7.
The spiritual life is lived by cooperating with grace -- and voila! -- in some secret way the carnal man melts away. Sort of like walking on water. Sort of like leaven in a lump. Sort of like the wind blows.
Yes. To resist consciously is like trying to not think of an elephant. And yes, Grace coupled with desire for the higher goal, completion in God, is like floating away.
Interesting, however there is no number for infinity in the real number system. The symbol for infinity (which corresponds to the idea of eternity) represents a process that goes on forever, e.g. adding real numbers together forever. But it isn't a number. It is a direction.
However Liebnitz developed the calculus by assuming the existence of infinitesimals--infinitely small numbers larger than zero but smaller than the smallest non-zero real number. In the first semester of calculus, when you learn the Liebniz notation for differentiation, dy/dx, the instructor will tell you that is not a ratio--it's just a symbol for taking the derivative of y with respect to x. But that isn't the way Liebniz thought of it. To him it was indeed a ratio, i.e. the slope, of two infinitely small numbers.
Integration is of course the inverse of differentiation. And here again Liebniz thought of it as the summation of an infinite number of infinitely small areas. This rather amazing feat results in a finite, real number. This is the way that mathematicians thought of the calculus for 200 hundred years until Weierstrauss came along with his rigorous concept of limits. So for the past 100 years calculus has been defined only within the real number system. Infinitesimals and infinitely large numbers have been banished from the classroom.
Well, almost. Abraham Robinson discovered the hyperreal number system in the 1960s which includes the real numbers along with infinitesimals and infinitely large numbers. With this development, he defined an infinitesimal calculus in a rigorous way. But, unfortunately, it has never caught on with the teaching profession. Others have done this with the superreal and surreal numbers, but they haven't caught on either.
Looking forward to pondering this - thanks for sharing.
The existence of a real person by the name of Plato, living at the time alleged for him, is amply attested to by an enormous body of work produced over a very long and very productive lifetime, in which certain themes ever recur, seeking ever better theoretical solutions, which the writer had the modesty to propose as "myths."
Myth gets a bad rap these days. Yet I think Eric Voegelin was entirely correct to say that "the myth remains the legitimate expression of the fundamental movements of the soul" (Order and History, Vol III, 1956.)
I think this is what Plato actually had in mind, in his work; which is why he did not leave us with a "systematic philosophy"; but only with the openness of mythical language.
Plus the other thing one notices about this magnificent corpus is that it is the creation of a world-class literary artist.
All in all, I think it is indisputable that this lifetime's work was effectuated by a single unified personality, who went by the name of Plato. And he had enough friends around in his day to attest to the actuality of his personal existence.
But then, you alreay know all that, don't you, RW? I think you're just "funning me!"
His academy far outlived him, and that early Christian said something like I am the Truth, the Way, and the Life, which is similar to saying I am Plato. Plato means Road, or the Way. There is a lot of Plato in Christianity.
Doc, tell me truly: Do you think this is a reasonable assumption?
Excellent post, stripes. I hope to reply tomorrow; for it's late now, and I need to get some sleep. (Another workday tomorrow, ya know.)
Till then, pleasant dreams and sleep tight.
It is in projective geometry. It's not in affine geometry. Get with the (Erlanger) program, Betty.
IEEE arithmetic on reals treats infinity and -infinity (and indefinite) as ordinary numbers (with some special rules.) The proposed Language Independent Arithmetic standard has three zeros too (in some versions), plus zero, ordinary zero, and minus zero. This makes many computations run much more smoothly.
The Apology is my favorite followed by Phaedo.
My lifetime dream is to someday play the part of Socrates in a theater. It's an obssession of mine. I can't help it.
Now a few quotes from "the man who knew nothing" taken from The Apology of Socrates.
"And to you and to God I commit my cause, to be determined by you as is best for you and me."
"I cannot in a moment refute great slanders; and, as I am convinced that I never wronged another, I will assuredly not wrong myself."
"The life which is unexamined is not worth living."
"I would rather die having spoken after my manner, than speak in your manner and live."
"The difficulty, my friends, is not in avoding death, but in avoiding unrighteousness; for that runs faster than death."
"The hour of departure has arrived, and we go our ways -- I to die, and you to live. Which is better, God only knows."
"Be of good hope in the face of death. Believe in this one truth for certain, that no evil can befall a good man either in life or death, and that his fate is not a matter of indifference to the gods."
"The ancient oracle said I was the wisest of all the Greeks. It is because I alone, of all the Greeks, know that I know nothing."
Good night and Merry Christmas to all. And, sorry for being off topic.
The idea of a limit has been around awhile, but it wasn't sufficiently rigorous until Weierstass. Newton sometimes thought of the calculus he invented as a limit (intuitive and nonrigorous), sometimes as infinitesimals, and sometimes as velocity (he invented it to answer questions in physics). Cauchy made a big improvement in the idea of a limit, but he still used infinitesimals to define it. It was Weierstauss who introduced the epsilon and delta condition as the definition of a limit, and using only real numbers. Weierstauss's approach is the one taught in calculus today.
And yes, Weierstauss is the father of modern analysis.
Richard Hamming was always complaining about this method of looking at things. I couldn't ever get him to give a better one though.
I may not have anything useful to bring to the table, but I'm much appreciating the meditations.
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Thanks
The philosophers teach the masses suffering, the priests fill their minds with false hope and demand obedience, the scientists simply stare them down.
Hi stripes! Been thinking about your statement that the Church Fathers reject the idea that Christianity, "at its deepest level" perceives the cosmos as a self-revelation of God. You wrote, "this Platonic perspective many be true for some theologians, but it is not an indisputable fact for Christianity as a whole and certainly not at its deepest level."
The article cites both St Gregory and St. Dionysius the Areopagite, substantially to the contrary. I think we may be on the brink of a doctrinal dispute, which is just exactly where I don't want to go with this.
Notwithstanding this reservation, to give evidence of the sectarian influence which can be brought to bear on this question, I might cite the example of Dionysius the Areopagite. Apparently, the Roman Church does not recognize him as a saint, though it seems the Eastern Rite does. (The only St. Dionysius Rome seems to recognize is St. Dionysius, Bishop of Corinth, c. 170 A.D.) The Catholic Encyclopedia refers to him as the "Pseudo-Areopagite." I gather there is some doubt at the Vatican as to whether this Gregory was indeed the Greek converted by St. Paul in Acts. Notwithstanding, the Roman Church seems to hold Dionysius in very high regard for his collossal intellect and deep spirituality....
In any case, when I read the lines from this Dionysius quoted in the article, they are unmistakeably evocative of the Platonic world concept. I also find such resonances in both St. Paul and St. John. I just can't help myself: I know it when I see it. And it seems to me that just because I find these resonances in the Holy Scriptures does not in the least detract from the maxim, sola scriptura. The Holy Scriptures "tell us truly but not exhaustively," as Francis Schaffer says. That leaves a whole lot of scope, it seems to me, for reflection and interpretation, by the grace and in the light of the Holy Spirit.
FWIW.
Thank you so much, freeagle, for your kind words. I'm so glad you enjoyed the article!
Thank you so much, A-G, for your very kind words. And especially, thank you for all the help you have given me over the past many months -- ideas, references, suggestions, advice -- all so very deeply appreciated! Hugs, girl!
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