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Mathematics & the Solstice (Read 7391 times)
augoeideian
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Mathematics & the Solstice
Jun 21st, 2007 at 10:29am
 
Hi all, hope you all well  Smiley I came across this and thought dave_a_mbs might appreciate it;

It is well known that the inscription over the door of Plato's school was intended to exclude anybody who was unacquainted with the science of Mathematics, from participating in the teachings of the Master. Whatever we may think of the historical truth of this tradition, it is based upon the correct understanding of the place that Plato assigned to mathematics within the domain of human knowledge. Plato intended to awaken the perceptions of his disciples by training them to move in the realm of purely spiritual being according to his “Doctrine of Ideas.” His point of view was that Man can know nothing of the “True World” so long as his thought is permeated by what his senses transmit. He demanded that thought should be emancipated from sensation. Man moves in the World of Ideas when he thinks, only after he has purged his thought of all that sensuous perception can present. The paramount question for Plato was, “How does Man emancipate himself from all sense-perception?” He considered this to be an all-important question for the education of the spiritual life.

Even when mathematical thought ventures beyond the limits of sense-perception, it yet retains the strictness and sureness of true thought-control.

“Learn to emancipate thyself from the senses by mathematics, then mayest thou hope to rise to the comprehension of ideas independently of the senses”: this was what Plato strove to impress upon his disciples.

- Great I haven't even grasped my timetables!!

Happy Summer or Winter Solstice everyone  Smiley

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dave_a_mbs
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Re: Mathematics & the Solstice
Reply #1 - Jun 21st, 2007 at 2:27pm
 
Hi Caryn-
Wow, that picture is beautiful!  - It's interesting that I'm using Ubuntu (a Debian Linux system) - "peace and god will to all".

(For those who haven't thought about Linux as yet, it has open source code so that you have thousands of people available to help with any little problems, it almost never crashes, is almost impossible to hack, and the Ubuntu family is dedicated to free upgrades forever. They have a web presence that tells all about it.)

You're right, I began life as a Platonist. As the astronomer Eddington used to tell people, a description is nice, but when you can put something in numbers and use them to predict and describe, then you really have understanding.

The interesting part of all that is that in the end the math and logic vanish and all there is left is awareness of the Transcendental One.  Not even thought. Just awareness.

Maybe  can put that into an equation next week? Smiley

PUL
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Boris
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Re: Mathematics & the Solstice
Reply #2 - Jun 21st, 2007 at 4:39pm
 
This is odd, because all thought requires images originally derived from
the senses. Higher thought is derived in turn from these images.

Mathematics is in a sense abstract, because when you count something,
assigning a number to something, that is the beginning of mathematics,
and abstract thinking. Some cats seem to know how many kittens they
have. That could be described as a beginning of abstract thought.
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vajra
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Re: Mathematics & the Solstice
Reply #3 - Jun 21st, 2007 at 5:54pm
 
Not too sure that intellectual thought like maths amounts to real understanding. It's surely a mind made system of concepts that's presumed to predict or to be a facsimilie of reality, but which does not/is not.

Buddhism would argue that only holistic non relative (realised) awareness and intuition can connect with reality - that otherwise our conditioning causes us to see only what fits our pre-conceptions. Which in turn are driven by our egotistical orientation - we seek to perceive only that which we mistakenly think will make us happy. (and thus bring about the gold fish bowl of striving/grasping under the control of apparent but actually almost non existent free will)

Intellectual/conceptual thought as Plato held is nevertheless an important step in moving us beyond blind instinctive emotionalism - to bring head as well as heart into our decision making.

20th century history though has rather amply demonstrated the pitfalls and limits of heartless intellectual thought - our cult of the intellect has created a  world without heart. Fortunately there's been a considerable rising of compassion more recently - the Age of Aquarius and all that implies.

Gurdjieff, Buddhism and other traditions talk of the Jacobs ladder. That man (both over an individual lifetime, and collectively over subsequent generations) progresses from brute self interested instinct (felt as emotion) to intellectual understanding of the limits of this to the dawning of compassion/heart/care for others (felt also as emotion, but the opposite of self interest) to integration and balancing of the head (intellect) and the heart (the full range of emotions).

Man 1, man 2 and man 3 so to speak...
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spooky2
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Re: Mathematics & the Solstice
Reply #4 - Jun 21st, 2007 at 8:02pm
 
Yes you're all right! Augo, you pointed at the most influencing (still) western philosophic concept; for a long time it wasn't, but it rose again with the beginning of the modern age, say in the 15th century. It has brought great benefit and great damage as well.

As a by-product of this philosophic view natural science and engineering arose, but unfortunately, this philosophy itself has brought more bad than good I'm afraid, because it falsely took the objectivable (countable, exactly measurable, inter/over-subjective) as the basis of all, which then left people suddenly alone in a meaningless only-objective world where, odd enough, for the "me", "I" was no place, it just doesn't fit in in this concept. Not everyone of course is realising this in a philosophic way, but many feel the results of it; an erosion of the own personality and meaning, of spirituality and sense of beauty, of perception of the surrounding and the place of "me" within it.

This philosophy is by no means founded in logic, it is more a belief, with, admittedly, philosophic reasonning. But it is not more logic than to state that finally everything is consisting of green cheese.

So, I'd rather want to promote the phaenomenologic approach in philosophy, which is to describe and systematize the undistorted first-hand human experience. And this is best done not so much by mathematics, but rather by a very sensitive handling of language in it's richest form; this kind of language is getting out of use in an almost dramatic speed; even our elite is more and more babbling in a convolute of administrative and technical terms without much understanding of what really counts, what is important, what should be done, and what the heck they are saying doing here and now at all?!

Spooky

P.S. Boris, that with the kittens, some clever birds can do similar things I've heard, but I think it is not so much the beginning of abstract thinking, but the ability to see something "in one view", I mean the mothercat sees her kittens, and realises the group isn't complete, but without counting them, or thinking "who" is missing. I also would say, not counting is the start of abstract thinking, because in a primitive way it is like giving names, similar like when I shout "uooaa" when I see a big predator cat running over to me, and "woow" when I see my meal before me. The cnackpoint is the understanding of the number as a set, like in set theory. This is what children learn about the age when they come to school (they don't have to be good in set theory to get it).
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augoeideian
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Re: Mathematics & the Solstice
Reply #5 - Jun 22nd, 2007 at 5:20am
 
Indeed, indeed Ubuntu – the language of our forefathers - Nkosi (Father) Sikelel’ (Bless) iAfrika (Africa) Sounds like a good equation to implement.

Thanks for your replies this is a great discussion – all we need now, together with Plato, is Aristotle, Philo and Heraclitus to pop up and it’ll be as if we are in Athens mussing upon life!

Dave, I think you described the art of mathematics with great reason; "The interesting part of all that is that in the end the math and logic vanish and all there is left is awareness of the Transcendental One.  Not even thought. Just awareness".  

With this in my understanding; the thought control of logic reason transcends into higher awareness.

Boris yes I agree in a sense mathematics is abstract however in its abstractness there is a goal of logic within the correctness of the set out equation.  

You see,  mathematics is not accepted merely on the authority of the teacher of mathematics; every individual accepts mathematics because he gradually acquires knowledge and understanding of the fundamentals.

The construction of concepts and representations in mathematics gives the student of mathematics the ability to use correct judgment acting on the strength of what he knows.

And with this, as Dave said in the end the math and logic vanish, we see here it is the exercise of the science which leads to this point by cultivating the powers of understanding and our faculty of judgment. And indeed it is not a matter of becoming an expert in the science (although it is helpful) the discipline opens the all-embracing knowledge of the Spirit.

And with this the soul will be filled with a gladness which is not superficial good cheer, but has its part in the life-giving seriousness that increases our strength.

As you said Vajra “Intellectual/conceptual thought as Plato held is nevertheless an important step in moving us beyond blind instinctive emotionalism - to bring head as well as heart into our decision making”.  

Also Vajra what you said here;
"20th century history though has rather amply demonstrated the pitfalls and limits of heartless intellectual thought - our cult of the intellect has created a  world without heart. Fortunately there's been a considerable rising of compassion more recently - the Age of Aquarius and all that implies".

In my understanding;
At the beginning of Earth-evolution, the human being was part of a group-soul — as expressed in race, blood, family and so on — to a far greater extent than was the case later on. As evolution continues he becomes more and more of an individual, develops his individuality. We have heard what an important part certain forces play in the development of the individuality during Earth-evolution: consciousness that is dependent on the physical body; memory and remembrance which are dependent upon the ether-body; and karma, whereby a man can make real progress, in that his imperfections and faults do not remain but can be overcome by him as he passes through one incarnation after another.

This stage of our evolution is very important in that it developed our Intellectual soul and with this the incorporation of our Ego (not selfish egotism, a clear distinction must be made from this - not selfish controlling egotism – the Ego being the I AM)

And with this incorporation of the Ego consciousness, like you say, arises compassion.  Compassion because the ego consciousness is Christ like.  This is stage of our epoch named the fifth post-Atlantean period is very important to prepare us for the sixth post-Atlantean period as you rightly called the Age of Aquarius which is in preparation now.

We must reach the vantage-point of the true Buddhist who says that the Individuality in the Buddha was that of a “Bodhisattva” who was born as the son of King Suddhodana, rose in his twenty-ninth year to the rank of Buddha, thereby attaining a height whence he need no longer return to a body of flesh. That, therefore, was the final incarnation of the Bodhisattva Individuality who does not reincarnate in the era following the founding of Christianity.

Contemplating the Buddha we see a very special mission in the universe devolves upon an Individuality as sublime as the Buddha. The Individuality who became the Buddha had been sent from the hosts of Christ on the Sun to the 'Venus men' before they came to the Earth; the Individuality of the Buddha, therefore, had been sent forth by Christ from the Sun to Venus, as His emissary. This Individuality came to the Earth with the Venus men and had thus reached such an advanced stage of development that through the Atlantean, on into the Post-Atlantean era, he was able to attain to the rank of Buddhahood before the coming of Christ. He was in very truth a Christian before the time of Christ. We know, too, that later on he revealed himself in the astral body of the Jesus-Child of St. Luke's Gospel — since he need no longer return in a body of flesh. United as he is with the Christ Stream.

Gloria.

Spooky, I hear what you say and I do believe this is the challenge we are faced with today again relating to the very marked difference between the I AM and the egotistic way of thinking.

People often say that rising to the spiritual worlds is a fantastic illusion. They do not see that it is the loss of this knowledge which has brought materialism upon us, with the incapacity for social understanding to which it is allied, with the materialistic way of living, and attitude towards life.

This is the double edged sword.  On the one hand we needed to develop our Individual Intellectual soul and on the other hand we need to stay in touch with our spiritual origins.

This is where the art of mathematics comes in the objective training of the thought process in order to transcend above materialism with the abstractness of mathematical conceptulisation and at the same time transcending above the fantastic illusion the spiritual world often tends to play on us.

However, not everybody is a mathematical genius or whiz and here philosophy comes in;  philosophy does not comprehend the Inexpressible Word, but it can nevertheless still have a feeling for the soul element in the world when it reveals itself in the soul of man as the expressed word. Philosophy does not find the Unmanifest Light, but can sense it from afar, inasmuch as it appears, in its last activity, in human thinking, — that is to say, in that portion of the human spirit which is turned, to begin with, to the external world. Body, soul and spirit.

Spiritual study through philosophy is a helpful discipline, as studying any disciplined Theosophy order such as the teachings of Buddha and Christ wherein the Unmanifested Light comes to be manifested within.

Spooky, I haven’t heard of phaenomenologic but I hear what you saying in connection with language. It is a wonderful approach you have with this.  To contemplate not the dry unalive letters and words but the living essence of the language of words and spiritual meaning thereof. Beautiful! my approach is astrology wherein I find the discipline of the science together with the living word.

Again thanks for the replies, and the read.

Lots of love to all.

Caryn
Ubuntu




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dave_a_mbs
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Re: Mathematics & the Solstice
Reply #6 - Jun 22nd, 2007 at 2:09pm
 
You've got me thinking Caryn (a dangerous pastime?)

Actually, the core of math is application of logic. The core of logic is the expression of consistency under various contingencies. The core of consistency is oneness, so that all contingencies vanish. And when we get to that in our personal selves, we have "awareness", but nothing in particular of which to be aware. It all devolves into It Is - or, as Jesus put it, "I Am." - or in the words of Nisargadatta Maharaj (and a lot of other rishis), "I am That".

I have the distinct impression that all the rest of what we do here, with our careful differentiations and distinctions and discussions about the whichness of whatever is very much like a dog chasing its tail.  But at least we aren't bored. Aha - that's what you were saying about useless activities ...

PUL
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augoeideian
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Re: Mathematics & the Solstice
Reply #7 - Jun 26th, 2007 at 3:28am
 
I think therefore I am!  I don't think therefore I also am!

Yes, I see the core of math is application of logic.  Another thought I had was one can reach highest complex equations/thoughts/ideals and from there it goes into a simplistic equation/thought/idea.  And this is well expressed in math and numbers.  Although I can't say quantum physics is simple for me!  But possibly if we look at numerology and numbers 1 to 9 we see the simplisty of the idea.  Another thought; reducing the complex into simplist is Love  Smiley possibly Love is the number 0.

So that's what Plato was doing!





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dave_a_mbs
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Re: Mathematics & the Solstice
Reply #8 - Jun 26th, 2007 at 2:53pm
 
Hi Guys-
I'm going to be the last one to try to equate the "experience of a green patch" with a numeric equation. Spooky is right, the phenomenology differs in kind. People and minds cannot be reduced to "nothing but numbers", although number can express the same factors that pertain to people. Plato seemed to be grasping at this through harmonic series, and essentially discovered the exponential operations by which the placement of frets of a guitar etc are calculated.

However, just as we can only have "a + b = c" and at the same time force "a - b = c" to occur under the conditions that "b" is trivial or zero; then we cannot have the sum of situations to add to a new experience, and at the same time obtain the same experience from the difference of two situations unless one of the experiences is trivial or null. 

The logic is of the same "equivalence class" (which is math-speak for "similarity" at some level). Or more generally, just as the logical relationships of a system of numbers that add etc must be consistent to make sense, in the same way, the logical relationships that describe inter-personal relationships must also be consistent in order to make sense.  When they aren't, then there is a natural tendency to correct the errors of our perceptions (karma) which corresponds somewhat to the red marks a professor makes on an exam paper to point out  inconsistencies.

If we are willing to really get abstract, then we can summarize all of the dynamic aspects of  expression as a "functional", a collection of all possible functions that might fulfil that definitions.  In my own work I usually call this a "process" and symbolize it as P. We can then collect all the various dimensions and comparisons that give attributive identity to situations and stuff into a generic term R, for "relational". And we can collect all the stuff that has an enduring nature into a common collection called "substantives" or "quons", abbreviated by Q. Using this we can say that all cases can be exemplified by an equivalence class that has the generic description:
P(Q1) = Q2, where Q1 <R> Q2
- which tells us that if a process acts on a substantive to change it into a new substantive, the two substantives will have a well-defined relationship. This is an absolute statement tht refers only to abstractions, but it is similar to the way that reality actually works, because they share the same "equivalence class".

Or in Platonic terms, the tone of a string is multipied by some amount when the sting is stopped at the midpoint. (That's fret 12 on a guitar.) That amount is one octave higher. If the strong is again stopped at it's midpoint we get a second octave higher. These two facts form the equivalence class of "how to generate the second harmonic". Yet the logic itself has nothing to do with the actual tone as we perceive it.

I feel that if one is to truly define everything in abstract terms, the first thing is to define God in sbatract terms. That task will give job security to philosophers fo the next several millennia!  Smiley

For some reason that reminds me of a priest who gave me a rapid "proof of the immaculate conception" - he said "God is ineffable."

PUL
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Re: Mathematics & the Solstice
Reply #9 - Jun 27th, 2007 at 5:11am
 
Thanks for the numerical writings (I asked for it didn't i!)  Totally agree; it's not a case of reducing people and minds to numbers blah awful matrix way of thought - it is, as you said, as Plato (must have been) teaching the harmonics and resonating to the harmonical vibration or octave .. music of the Spheres really.

So, there are two concepts here;

1.  Studying math to train the mind into logic thinking.
2.  Tuning into the octave (expressed in numbers its simplist form)

I do think we all vibrate on certain notes, octaves, numbers which maybe in turn creates the colour of our aura?
In keeping with consistency one resonants harmonically with ones octave, sometimes we hit a flat, to high, or low note and to adjust and realign we concentrate on 0. Out of the 0 comes the harmonics.

Smiley sorry last sentence sounding a bit abstract ..

PUL
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dave_a_mbs
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Re: Mathematics & the Solstice
Reply #10 - Jun 27th, 2007 at 10:00pm
 
Hi Caryn-
Something else about Plato that I recall is that he felt that our recognition of the furniture of reality arises from prior "ideal images" to which we compare things.  Thus we understand a chair is a chair because we have an idealized pre-existing understanding of chairness built in.

In rational terms this simply is false. We only recognize what we have learned to comprehend. As an example, someone offered me one of the little gelatin square mint things that are becoming popular, and I simply had no idea of what he was holding out.

On the other hand, Don's experience that he calls his "night in heaven", involves primary awareness a long ways deeper and prior to development of speech and rational thought. That level of experience seems to support the Platonic idea. It even begins to make sense if we  view everyone's awareness as part of one big Cosmic Consciousness. Further, while the grossest details of the experience can generally be described, those who have such experiences, such as Don, are unable to capture and describe all the details of their experiences.  So you might have hit on a very valid point by bringing in Plato.

d
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augoeideian
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Re: Mathematics & the Solstice
Reply #11 - Jun 28th, 2007 at 7:48am
 
Hi Dave

Quote:
Thus we understand a chair is a chair because we have an idealized pre-existing understanding of chairness built in.


This sentence makes me think of – awakening – not changing but awakening to the pre-existed understanding.

If we take a tree for example;  A tree is an art of creation from the (post Saturn days)(Steiner spiritual science). When we were in spirit forms before descending into pre-Earth we were part of this creation and we beholded the etheric material take form into a tree, through evolution. The tree and I evolve at the same time. Our thinking receives the concept of the tree because our memory databank within our soul tells us this is a tree.

The framework of the tree is there; inside our soul and outside in the physical. Inside to be released through rational thought identity as matter into the physical plane and as spiritual matter into the spiritual plane released through our carrier and transmitter of memory within our soul.

With this, if you and I had to look at the same tree in the physical it would look the same however, in the spiritual realm, because it is our memory which recalls the tree, the tree would look different for each person because of individual perception of how a tree should look or the emotion we place on our perception of the tree at the time we are looking at the tree, either it is full of leaves (happy emotion) or it is bare of leaves (sad emotion).

Now, somewhere there must be a collective perception of how the tree looks or at least should look and maybe here we could say this is where Don’s  ‘Night in Heaven’ comes in ..

So possibly what Plato was suggesting is to go beyond the ununiformed perception of the tree into the collective uniformed perception of the tree.

Reckon?

ps: how are you Don? long time no write.

Wonderful day to all
Smiley

pps:  We had snowfall last night, the coldest weather in 26 years - snow in Africa! Yo!


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Re: Mathematics & the Solstice
Reply #12 - Jun 28th, 2007 at 8:42pm
 
Good ole philosophical problems! It leads basically to the question if something can occur out of nothing.
You know the reply to Platos teaching of the ideas, that our perception of things is rather a remembering more than learning something new is the "Tabula Rasa" (clear board) theory, coming from Aristotle if I remember right, viewing our initial mind as empty.
When taken radically you have the problem how to get any stability (=things) out of raw data without anything what pre-shapes the data.
So, to take the empty board, at least there is something, the board. So we have our bodies with it's senses we can say, or, more generally and abstract, as Kant said, there are structures which don't stem from experience, but allow experience at all (which he called "trancendental" = condition for making experience possible, in difference to "transcendent" = impossible to experience).
Aristotle repeatedly says in his "Physics" and related articles in the "Metaphysics": "A human comes from a human"- meaning, in nature things come from something similar. Now- haven't we known this all the time already?  Cheesy

Spooky
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Re: Mathematics & the Solstice
Reply #13 - Jun 28th, 2007 at 9:47pm
 
One thing that existed before there was any-thing that existed is potentiality for there to be  existence, so we never realy have nothing. And if you consider potentiality, the totality of all potentiality is all-encompassing, and the basis for all manifestations. That sounds a lot like a definition of God as Creator. Rubbing two potentialities together creates a relationship that is non-abstract, so we actually can get something for nothing. Hawking suggests that the Universe may be the "ultimate free lunch.

However, my reason is somewhat impure, so I Kant critique it.

d
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Re: Mathematics & the Solstice
Reply #14 - Jun 28th, 2007 at 9:59pm
 
Hahaha, pun received Dave!
When I consider your potentiality view I must say strange world! Because I always say potentiality is a strange thing. Before the die stands still you can say the probability for each side to be the upper one is 1/6. Now, when the die is standing still, the probability for this side to be the upper one is 1- or you may say potentiality has turned to reality, but what the heck happens to the potentiality then? The same thing in Quantum mechanics. In one moment you have a potentiality function/wave, the other moment it has "collapsed" into reality. Strange. You just can't get a grip of potentiality, it's slippery- probably, as the name already suggests, because it isn't reality...

Spooky
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