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just0
Joined: 22 Jan 2006 Posts: 603

Posted: Fri Jul 27, 2007 1:25 pm Post subject: 


Very well put Peter, you've got a way with words.
And the support is much appreciated,
Seems we're all making it happen in our own strange
ways and we all have a part to play. It's like we're
experiencing a phase shift on all levels too. (<and planes )
It's exciting stuff, so lets keep the momentum. _________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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duane
Joined: 07 Mar 2007 Posts: 554 Location: western pennsylvania

Posted: Tue Jul 31, 2007 12:13 pm Post subject: 


hi just0 and peter'
this is a very interesting thread
my questions are chicken and egg ones
which came first  the shapes or the formula?
is a circle round because it is or because pi r sq?
is pi a mystical thing or an artifact of circles being round?
this goes for all math
do diatoms take these shapes because space on this side of the veil happens to expand that way or because of formulas programmed into them I'm reminded of the square watermelons, grown in frames and sold to a gullible public. the expansion into space determines shape
the real question is : is it Sacred Geometry or Sacred Nature? i feel studying math as a way to understand nature is fine but many lose their way by thinking math is an end unto itself.
. 

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Peter
Joined: 26 Jun 2007 Posts: 2457 Location: The Canadian shield

Posted: Tue Jul 31, 2007 1:03 pm Post subject: Math is the opiate of the intelligent? 


Hi Duane. Welcome to the exchange.
Indeed, c+e questions are often the start of interesting and even vital energy descents that can lead to heightened awareness in this duality filled universe.
Energy came first and always comes first (the male of the duality perhaps....rofl) but the form that it creates and that contains and/or represents it is not diminished. We too are constructs of our sourceselves and our forms have the power to manipulate energy to our own ends.
It is easy to confuse a formula with instigation but the FORMula is just that, another form. The abstruce nature of energetic manifestations is only confusing while you are limited to the apparent and restrictive definitions of what the form actually is. Once you become able to capture the vibration that the descendant energy releases to and inhabits the form with.....it all gets easier AND more useful.
Peter _________________ The grand design, reflected in the face of Chaos. 

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just0
Joined: 22 Jan 2006 Posts: 603

Posted: Tue Jul 31, 2007 6:15 pm Post subject: 


Hi Duane, welcome,
And thanks for helping me to give thought to thoughts
which I would've never given thought to before... LOL
Duane wrote:  my questions are chicken and egg ones
which came first  the shapes or the formula? 
As peter touched upon, form (FORMula) imples a structural entity (shape).
Two sides of the same coin.
Form can describe physical shape, catigorical distintions and is also
'tied' to conceptual thinking. Not that we need to get away from all
that, but we need to recognise what the implications of concepts are.
In a strange way, this relates to the chicken and egg paradox.
Rational concepts are FORMal and confined to logical systems of
evaulation, but in order to 'build' a system of logic, there must
be something predicteable in the system. (eg. Axioms, foundations etc.)
So to have a logicical system, you need to able to infer something
from what has gone before, or to refer back to what you 'know' from
experience. In the study of logic this evaluating of the past tense
is called an antecedent.
Wikipedia wrote:  Antecedent (logic)
An antecedent is the first half of a hypothetical proposition.
Examples:
If P, then Q.
This is a standard logical formulation of a hypothetical proposition. In this case, the antecedent is P, and the consequent is Q.
If X is a man, then X is mortal.
"X is a man" is the antecedent for this proposition.
If men have walked on the moon, then I am the king of France.
Here, "men have walked on the moon" is the antecedent. 
As far as I can tell, this is the blind spot for the intellect,
because not everything we experience has a causaul relationship
linking it to the past.
There is spontaneity, a random element that creates without needing
a logicallypredicteable reason. This aspect is 'invisible' to the rational
intellect. So, logic becomes self limiting by it's very nature (as is form).
Even bigbang cosmology has this chicken and egg paradox, the infinite
regress of 'what came before the BB' etc. This rationale is why modern
science fails to address what really needs addressing, a true science
should take note of aspects which are nondefineable or irrational. It's
this randomness or freedom from predicteable limits that describes life.
Allowing that the spontanous, irrational and unpredicteable things do have
value, you can see why I've been caught up in this 0²=2 exploration.
It defies mathematical logic, it shows that rationality has it's limits,
(in a similar way to what Noncommutative algebra would describe) it gives
value to the spontaneous. But at a deeper level, it also says that the cause
of thingness is nothingness.
It's kind of like an end to the infinite regress loop of logic and
simultanously defining a limit to what can be rationally interpreted.
So, to me, the question of which of the two comes first,
Always boils down to, well, neither ...or nothing, really.
You could also relate this chicken/egg paradox to a sphere, it would make
no sense to ask the question;
Which part of the sphere came first?
The Convex side or the Concave side, (inside or outside)
It's easier to ask the question, where did the sphere come from (both inside
and out), what was it when it's radius was zero?
Duane wrote:  is a circle round because it is or because pi r sq? 
Paraphrasing 'Bucky' Fuller;
"I don't think nature is calculating Pi every time she makes a bubble" lol
Duane wrote:  Is pi a mystical thing or an artifact of circles being round?
this goes for all math
do diatoms take these shapes because space on this side of the veil happens to expand that way or because of formulas programmed into them I'm reminded of the square watermelons, grown in frames and sold to a gullible public. the expansion into space determines shape 
IMO, space deterimes everthing. but not in the sense that it can be predicted
and determined, because it's nature is spontaneous i.e. the chaos factor. But
the resulting forms have an element of predictability, this is reflected in
our systems of math and geometry.
As far as math and Pi is concerned, I don't see the numbers or the
formulae as being anything more than formal language/symbols. But they
do 'point' to something special.
It's the habit of the western mind to take symbols, words, numbers,
concepts etc. to be totally and literally true. Of course they're not,
but even though there are limits to what these tools (or forms) can be
used for, we have the oppurtunity to recognise them for what they are
and to use them to 'point' to what is beyond the literal. Just as the
archytypes of mythologies have done.
Duane wrote:  the real question is : is it Sacred Geometry or Sacred Nature? 
Maybe it's neither
Duane wrote:  i feel studying math as a way to understand nature is fine but many lose their way by thinking math is an end unto itself. 
I agree, and it's understandable that this happens, seeing as
the tools of mathematics and number are the most precise forms
of language available. But as always, not seeing the forest for
the trees can blind you to whats really important.
Peter wrote:  Energy came first and always comes first (the male of the duality perhaps....rofl) but the form that it creates and that contains and/or represents it is not diminished. We too are constructs of our sourceselves and our forms have the power to manipulate energy to our own ends.
It is easy to confuse a formula with instigation but the FORMula is just that, another form. The abstruce nature of energetic manifestations is only confusing while you are limited to the apparent and restrictive definitions of what the form actually is. Once you become able to capture the vibration that the descendant energy releases to and inhabits the form with.....it all gets easier AND more useful. 
Nice1 Peter, energy is primal, but it's not energy in that everyday
sense of something with 'powerful' energy, it's more like potential
like light it is purpose itself, which, just like the sperm,
always takes the shortest path (or geodesic) to reach it's goal in the
shortest time.
This potential energy takes on different substances, differnent forms,
but it is not any of the forms which it takes on. So at the risk of
labouring the point, this energetic potential lacks the quality of
'thingness' and is beyond duality. This is what many spiritual
traditions have recognised, they called it 'void' and it is energetic.
OK hang on, let me start over.. what was the question again _________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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Peter
Joined: 26 Jun 2007 Posts: 2457 Location: The Canadian shield

Posted: Tue Jul 31, 2007 7:12 pm Post subject: The more you use, the more you have...intelligence 


And the more people that pipe up and chip in, the greater the effect (potential) that can be realized (brought to earth, like electricity) as we integrate this form.
Just0's contribution provide the springboard for multiple lines of endeavor. How you "feel" about an issue or statement is not about emotion, it's about what that input engenders in you and how you bring it to life.
You cannot be wrong, you can only be silent. _________________ The grand design, reflected in the face of Chaos. 

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just0
Joined: 22 Jan 2006 Posts: 603

Posted: Thu Aug 02, 2007 8:42 am Post subject: Who Knows ? 


Keep questioning, it's a lie to think there is something wrong with not
knowing something. Not knowing leads to learning... through Trial and error.
Anyway, back to putting math on trial
Mathematicians are in the habit of taking their interpretation of numbers
to be the only way to go.
A lot of what we've described in the articles suggests that there is
more to number than what the counting up of bananas can show us.
One example is that the simple method of summing digits can reveal
orderly patterns.
Applying this to Prime numbers and Perfect numbers proves (IMO) that
there is more to number than what literal interpretations suggest.
The method of summing digits seems to suggest that;
Quote:  ~ None of the prime numbers will add to nine.
~ All perfect numbers (excluding the first) add to one.
(I've not had infinite time to verify this for all numbers, besides, infinity
gets a bit boring especailly near the end. lol ) 
Whether there is anything to this or not is'nt the point, because to me,
It suggests that maybe the Mathematicians have been too concerned with
the 'bits' to notice anything special about the whole.
Anyway, I don't know what all of this means, but I don't need to. _________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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just0
Joined: 22 Jan 2006 Posts: 603

Posted: Fri Aug 03, 2007 9:18 am Post subject: Mathematics & Reality 


This is an interesting piece, quoted from an essay entitled
'Mathematics & Reality' by Arthur M. Young.
A lot of it seems to tie into what we're exploring here,
(don't let the technical jargon put you off.)
Quote:  It is possible that cantor had a valid insight but, as is often the case, distorted it by misinterpretation? Essentially what he says is that there is something beyond infinity.
Perhaps by introducing some ideas I've had for a long time together with the conclusions we've reached here we can arrive at a speculation that would account for Cantor's inspiration and justify some of the acceptance he has been accorded. However, these ideas, while reasonable and straightforward, are even more foreign to what is accepted in mathematics than were Cantor's  in fact, we could say that Cantor's error was to accommodate to the usual thinking.
The ideas to be put together are;
1. Numbers can better be defined as successive divisions of unity rather than as additions to unity as Peano's axioms assume. (This is a point developed in "The Queen and Mr. Russell." I have recently noticed that Eddington says the same thing in 'The Philosophy of Physical Science':"Where mechanics thus brings the integers (which form the whole material of our ordinary arithmetic) into it's purview as the eigenvalues of one of its symbolic operators. Introduced in this way the integers are concepts unassociated with the procedure of counting."
2. There is but one transcendental number, Pi, or two if you count e as independent of pi. (e is related to pi by the formula: e^(pi*i) + 1 = 0. I should acknowledge the fact that there are large classes of numbers that have been proved to be transcendental in the sense that they cannot be expressed as roots of equations, such as 1/n^2! + 1/n3!....Others, such as a^b where b is irrational, are neither constructible nor do they possess the same empirical status as pi or e. It can be argued that neither of the above classes of number "exists" apart from their definition. A theoretical number such as a transcendental, I would argue, must have some foundation in nature. In fact, if the prescription for a number were sufficient to affirm its existence, one should include unicorns, griffons, manticores, and other fabulous animals in zoological classifications, of which animals found in nature would be a subset.)
3. The line or continuum does not consist of an infinity of points, nor of more points than can be put in correspondence with the infinity of natural numbers; rather the point itself makes possible the projection of an infinity of directions.
Proceeding from these assumptions, we will find that the construction that would establish directions depends on our ability to divide the 360degree circleof which pi is the signitureimplied by the point. (The point is a circle of arbitrarily small radius.) Such construction would limit us to rational divisions of the circle.
The circle represents wholeness. In the process of dividing we would discover that each number (or perhaps each prime number) provided a unique division not obtainable by other divisions. For example  1/3 = 1/4 + 1/4"2 + 1/4^3... 1/4^n (~ an infinite series of smaller and smaller terms.
Note that if we replace one of the 1/4's, for however small a term (i.e. however high a power of the denominator), by 1/3, the infinite series collapses into an identity. Thus;
1/3 = 1/4 + 1/4^2 + 1/4^3..... 1/4(n1)x1/3
To define pi in terms of an infinite series we use Euler's formula:
pi/4 = 1  1/3 + 1/5  1/7 + 1/9 ....etc.
In other words, pi is unique. Unlike the integers, which are expressible in terms of one other number, pi's expression requires all the numbers (or all the odd numbers).
Other examples share this propensity;
pi^2/6 = 1/1^2 + 1/2^2 + 1/3^2.....
pi/2 = 2/1 x 2/3 x 4/3 x 4/5 x 6/5 x 6/7 x 8/7 ... etc.
and can also be expressed as an infinite nesting of square roots.
Passing beyond technical considerations, such as whether these are the best or most general expressions of the principle, to an interpretation of the principle, we could say pi incorporates (or implies) all the natural numbers. And since each number can be expressed as an infinite series of inverse powers of next higher numbers, pi can be represented as an infinite series of infinite series.
However, pi is not quantitatively infinite. In Euler's expression (given above) addition and subtraction alternate, and the sum approaches a certain value between 2/3 and unity. So pi is quantitatively finite, but includes an infinity of qualifications (natural numbers), each of which is itself "infinite" in the sense that an infinite series is required to express one number in terms of another.
We thus associate pi with an infinity of infinities, and since pi is transcendental, we could say that Cantor correctly perceived that transcendental numbers are "beyond infinity." But two misinterpretations confused Cantor's fundamental insight; 1) that infinity is a very large quantity; and 2) that what is beyond infinity is a still larger quantity  i.e. that there are an uncountably infinite number of transcendental numbers.
To put this in perspective, it could be said we have inverted Cantor and even Peano. Peaon defined number as successive additions to one. This fails to bring out that a number is not just a collection of n units, it is a unity of n parts; that is, any number, say five, is both a collection of five units and a unit of five parts. Once this is recognized, the definition of number as successive divisions can be appreciated.
The inversion of Canto is justified because there does not, in fact, appear to be an infinity of transcendental numbers. Among numbers having any applications to the real world, pi and e alone have proved to be transcendental. These two numbers are intimately related, and it is possible that they are not "different" numbers but aspects of the same "nonnumber." Since we define numbers as divisions of the whole, and pi is not a division but the whole itself, it is not a number.
Thus, while preserving Cantor's distinction between transcendental and other numbers, we can view pi as the transcendental number. It is preeminent not because it is one of higher infinity, but because it is unique.
We may in fact think of pi as a super number, the source of all the other numbers. We can say this because pi represents the circle, a symbol for wholeness. The integers can be defined as the angular divisions of the circle. This also provides a definition for fractions, since given the concept of division _ that the whole can be divided into n parts  each one of these is 1/nth of the whole. The real numbers can be accommodated or defined as trigonometric functions, i.e. Square root 2 is twice the sine of 45degrees, and so on. (This might comfort the ghost of pythagoras) I do not know whether all algebraic numbers could be expressed as trigonometric functions, but a plane surface does accommodate solutions to equations.
Whether or not this approach to number is more correct than the one now in use, it is safe to say that the current interpretation of natural numbers as a mere subset of larger classes of numbers is not a useful one. If the question is one of elegance or aesthetics, which are valid criteria in mathematics especially, then I regard the descent of all numbers from the unity of pi as the more elegant description.
Philosophically, too, it is better to think of the Universe as unity with infinite diversity that as an infinite collection, countable or uncountable. This notion, as we've pointed out, allows for quality as well as quantity. I suspect this issue invoked Bohr's complementarity principle, which generally interpreted to mean that for one measure to made precisely, another measure must be imprecise. We would extend this to read that any measurement must be complemented by a quality that is different from the measure. Measurement of size, for example, is incomplete without a reference to an actual object to provide scale.
In other words, quantitative measurement is in principle incomplete. Applied to mathematics, this implies that if mathematics is the science of quantity, it cannot deal with first principles, or alternatively, if mathematics is to deal with first principles  if it is to be "Queen of the sciences"  it must recognize that which is not quantitative, which we here call quality.
The transcendental number pi is one way in which the limitation of quantity shows up. Pi is neither large nor small, but it cannot be expressed in finite terms.
Cantor's mistake was to find preeminence in quantity of transcendental numbers, whereas it is the quality of the transcendental itself that makes it unique, that makes it the 'origin' capable of any direction. There is a oneness beyond everything that cannot be described because it is beyond everything. This oneness includes all that can be described. 
_________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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duane
Joined: 07 Mar 2007 Posts: 554 Location: western pennsylvania

Posted: Mon Aug 06, 2007 1:48 pm Post subject: 


one could say that man's problems stem from trying to use mathmathics to build his world. as we investigate nature more and more the formulas become more complicated as we try to define the shapes drawn by nature. fewer and fewer people can pretend the understand the math and so most build things with simpler maths (less variables) which usually ends badly when one of the excluded variables "varies"
perhaps nature draws "freehand" and does not use a grid or graph paper and math and number are illusions of the human mind
i think i'm starting to return to my old back to nature hippie days 

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Peter
Joined: 26 Jun 2007 Posts: 2457 Location: The Canadian shield

Posted: Mon Aug 06, 2007 2:11 pm Post subject: Peace and love.....it would be a start... 


Things that really count (your appreciation of beauty, your level of satisfaction, your understanding of yourself and your surroundings) need only be defined qualitatively. This ensures that you are able to determine quickly and adequately whether or not further action by you is required.
The vibrational nature of your being and the energy that it deals with can be described mathematically, but that is insufficient and wasteful of your time and efforts. This does not mean that math is either useless or lacks application. On the contrary, its utility to man is how we appreciate the results of its application. _________________ The grand design, reflected in the face of Chaos. 

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just0
Joined: 22 Jan 2006 Posts: 603

Posted: Mon Aug 06, 2007 6:25 pm Post subject: TWOness 


The formalities of Math and number are constructs of the human intellect and they change.
But the underlying principles are of the universal (and human) mind and they are eternal.
Number is what it is, but we struggle to undertsand it because it is not
simply a quantitative matter.
A general analogy for this can be seen in the ways in which we communicate.
There are words, which represent the specifics or parts of an experience. i.e. bits
Quantiative.
Then there is the overall meaning which the whole sentance is meant to imply.
Qualitative.
A classic example of finiteness and seperation coupled with integrated and wholeness.
These are two sides of the same coin and are therefore inseparable.
Another case of not being able to have one without the other.
Similarly, this applies to number.
But suprisingly enough, when it comes to science math/number/geometry, we've been highly
successful in payin little or no attention to the overall meaning which the language
of number impies. We've been taking the parts to be all that matters.
Science  in general  is the cornerstones of all civilsations (religion is a science)
and it's clear to me that what our modern culture has focused on is the quantitative 'bits'.
But even so, just look at what has been achieved.
The question is, can we integrate the intellectual understanding of quantity with the
experiential understanding of quality?
It appears that this dual natured situation is what is dominating on the planet today, we
have intellectuals saying it's all objective and spiritualists saying that it's all subjective.
IMO, either one alone is a reversion to the past. _________________ ~"“True observation begins when devoid of set patterns, and freedom of expression occurs when one is beyond systems.”"~ 

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duane
Joined: 07 Mar 2007 Posts: 554 Location: western pennsylvania

Posted: Wed Aug 08, 2007 1:35 pm Post subject: 


http://www.youtube.com/watch?v=uAluyt5_kic
the trap
what happens when "science" tries to apply math model to people
'A simulacra is an image perceptable to the human mind and seen as a life form resulting from a combined mental process whereby our brains process patterns of shadow and light reflected from physical objects'
from Maureen Palmer "Sacred Stones" in The Golden Thread of Time by Creighton E.M. Miller an excellent book by the way
a modern day simulaca would be people seeing the virgin mary in a grilled cheese sandwich, we laugh at these people
the right brained people see images that are not there
the left brained people see formulas that are not there, but instead of laughing at them, we let the rule our lives
this is my basic problem with numbers and formulas 

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Peter
Joined: 26 Jun 2007 Posts: 2457 Location: The Canadian shield

Posted: Wed Aug 08, 2007 2:08 pm Post subject: feelings have the merit that we allow them to have 


Strangely, many of the best mathematicians and scientists have a preternatural "feel" that leads them to the right conclusion etc. It also adds immensely to their enjoyment of solving an equation or discovering a relation that is useful or just abstractly beautiful.
Free yourself to make use of the tools at hand and you will be able to fulfill your promise. _________________ The grand design, reflected in the face of Chaos. 

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