The Theory of Stretchy Thingys

[jehovajah]

Ausdehnungslehre continued.
Set down here against this, where the idea is not obscured by extraneous methods! Moreover  through the formulae  i set it down and thoroughly made it shine in full clarity,  also for every  formula development  the basic concept of the forward development of the idea was  labelled.

[jehovajah]

Commentary

By this stage it is clear tha Grassmann did not like obscure formula development!

From the outset he cannot help expressing his discoveries as Laws or rules. The analysis he was doing helped him to see clearly but symbolically!  He felt pleased to see symmetry instead of unsymmetrical formulae. He also liked neatness on the page, with position on the page meaning something in the step by step development of these formulae.

He felt that it was important that the labels communicated the basic concepts, and contrasted his style with other usual arbitrary styles, which he showed obscured the idea and the basic concepts.

Much of this attitude reflects an autistic trait which was probably passed down by Justus his father. However, like a master craftsman it meant he could construct a set of formulae which clearly showed the basic concepts and illuminated the development of those concepts into the greater formula.

Formulae tended to become simpler , symmetrical and less wordy, and more general in scope.

How ironic, that what was as clear as daylight to Grassmann was as dark as mud to his contemporaries! gauss is recorded to have said that the new terminology or labels were so busy on the page that he did not have time to learn what they all meant! Grassmann, unfairly got a reputation of being Obscure!

I have to accept that Grassmanns, dad and 2 sons were onto something when they set down formal rules for everything. However, academics usually prize their academic freedom over all else.

[jehovajah]

Commentary
As I read and absorb Grassmanns words, it is clear that he is using religious or clerical metaphors derived from the theosophy or christology of his times.

Philosophers in Christian Europe were mainly employed in the church as ministers or ecclesiastical functionaries. The churches role in Education especially public education was fundamental. It was the church and church schools that taught most students to read and therefore to think! This form of good works was commandeered by the political powers in an uneasy trial of strength. Historically the pagan Romney empire converted to the holy roman empire on the field of battle! The victorious forces of the roman emperor were immediately converted to the catholic faith, because the emperor had seen a cross in a vision and this had assured him of success in battle!

Thus the church naturally fell into the subsidiary role of educating the state as a political entity and as a demographic region in the faith of Christianity.

This did not mean reading and writing, but over time it became clear that both church and state needed an educated source of functionaries to keep the system going.

The licence to teach or preach was granted through the ecclesiastical arm of the state. In Prussia, every philosopher or teacher was officially a cleric in the church..Kant for example had his license withdrawn for a while because his philosophy was not in accordance with the presiding religious consensus.

I say consensus, but in fact the Theosophical and philosophical scene was riven by heretical theologies! Clerics of one theology were arguing against clerics of another theology. In these arguments pagan philosophers were often cited. These philosopher had to be used with care, because they were deemed pagan! But theosophy claimed to have a sanitizer version of their teachings, one purged of all pagan, anti Trinitarian anti Christian theology. However some classicl scholars( also clerics) objected to this kind of censorship and secretly tried to understand the world in an alternative and frequently alchemical and material way.

However, the thought control was so deep and thorough that they could not express hems elves in any other words, metaphors and paradigms than the prevailing religious ones.

Thus we can see often terms hich have a clear theological meaning, applied theosophically or even philosophically to clear mechanical and material scenarios. More interestingly is their application in dialectic or logical discourse. This old often result in readers bring totally confused! Was this statement an mpirically observation or a religious deduction or a statement of faith?

In many cases it was all three, nd some curious logical inconsistencies arose, some which could never be straightened out by the prevailing view.

Returning to Grassmann, much of his style of writing therefore reflect sermon writing. His long sentences with many clauses and subclasses, adjectival and adverbial phrasing follows a speech pattern rather than a written pattern. The connection between clauses in speech is carried by intonation and emphasis, things which are difficult to convey in writing if a person is unfamiliar with them in speech.


While it is arguable tha Grassmann had only his analytical jsystem in mind, and Arithmetic on the brain, this is not sustainable in my opinion. His seeking for laws is almost a religious affirmation that his method was revealing the secrets of God and his angels! As such they carried not only a purely mathematical interpretation, but also a guide to how to apprehend god's thought process in natural events.

This would be a later development as his method gave him more and more insight into the relationship in space between Geometry, Mechnics and Optics.

Many of his explosive iights derive their power from a crossover from religious expressions . The spirit is lifeless is an example or the spirit performs nothing is another. This is tantamount to demonising a particular spirit which is a powerful condemnation.

Grassmann is therefore making powerful statements which are lost if the translator takes a narrow view.  At the same time they obscure the mathmatical or geometrical reference they relate to!

Really?

Yes if you take the view the Ausdehnungslehre 1844 is a mathmatical text book, but no if you understand that like Newton, Grassmann was writing a metaphysics and a metamathmatical treatise, from which to derive his formulations.

The 1862 redaction is a more mathematical treatment in which the symbols play the role described in this section. However, without the metaphysics and metamathematics these long combinations of products and the construction of labels from them seems whimsical and abstract or as mathematicians like to say, completely general or arbitrary!

They are not.

[jehovajah]

Ausdehnungslehre Vorrede p. vi

Through these pursuits i held myself to the hope by right, that i had the unique, the nature measured method  discovered in this new Analytical Method, by following which all branches of mathematics applied to Nature must advance, and which the Geometry , by its identities would be treated if they would lead to general and richly fruited revelatory results!

I raised in myself, therefore the emphatic decision to dedicate my life to the presentation, the enfurthering and the application of this analytical method, as my life's work! Consequently I undividedly applied my spare time any kind of  way that filled the gaps, to these contents, which the the earlier laid aside projects had left.

Specifically it revealed the wisdom , and with the modifications how I presented them in the work itself, I was able to set out  how to apprehend the sum of multiple points as the Schwerpunkt, and the product of points as follows: 2 points:- the joining line; three points:- the enclosed flat figure space(fletch, a kind of arrow feather); four point :- the pyramid or tetrahedron( the body or 3d space)

[jehovajah]

Ausdehnungslehre

The apprehension of Schwerpunkt ( weight point) I was intrigued to compare with the title of a calculus of Möbius., the Barycentric calculus. I knew it in Title only down until that time  so I was not a little overjoyed to discover Möbius used the same notational labels For the summation of points which the process of development  had lead me to.
"Also sprach Zarathustra!"
And it was so!
 with the first (part),

but I lectured the succeeding parts;

and also measured the unique points of tangential contact, which the new method of Analysis already with the  differently understood way could present!

While digesting that calculus(method) certainly there was no label or handle of Product Of Points  forthcoming, but in this labelling of the new Analysis, in which the Sum stepped in combination with it , it begins first  the   unfolding revelations  of the new Analysis. So could I from that( Möbius) start No more extensive  basic assumption,  more fundamental mindset(Förderung) , more inclusive Axiom,  more wider postulate envisage!

[jehovajah]

Commentary

This video by Norman is relevant, but it is the more refined treatment  alluded to by Grassmnn, who literally was initially caught between 2 schools of thought: his own And that of Möbius. It seems that  he realised he had developed a successor to Möbius treatment because Möbius point of view was fundamentally different to Hermann's. They did not share the same Förderung he lrealised. Invention and development did not seem possible using Möbius mindset!
<a href="http://www.youtube.com/v/aN5qULIFuBs&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/aN5qULIFuBs&rel=1&fs=1&hd=1</a>

[jehovajah]

Commentary



The theological reference kept chiming until I recognised it! I substituted Zarasthustra because that is also a famous German poem, and I think Hermann would perhaps have used that allusion for Möbius rather than God, but I might be wrong. In any case I feel the allusion is conveyed. Even the Berührungspunkte seems to be an allusion to the Sabbath day! Ruhe means rest while rühren means to stir or contact with some energy, the opposite of resting!

The Schwerpunkt I left as a distinct label. It has been associated with he centre of gravity or mass, but I think it is confusing to think of it that way. It is an aggregation point, and it has magnitude, which is why it fits in the Strecken scheme of things. Magnitude with no direction? It would initially seem so until you realise this point moves with each new point added to the aggregation. It can therefore be represented by a sequence of lines.

It is all deep thinking by Hermann.

The Berührungspunkte deserve to be highlighted. The Barycentric  is a point derived by his new method which is general, and represents a point of symmetry! Thus it can be taken as a centre of symmetry, mass or gravity! Also a centre for rotational and translational kinetic energy, and a centre of force, momentum and velocity and displacement!
The Berührungspunkte are associated tangential contact points.

It is a big deal!

[jehovajah]

Commentary

This is a meditative translation so I would encourage you, if you are following to return to see corrections, not only to typos!

My praxis is to read the text and give an impressionistic free spirited translation/ interpretation. This is verY exciting, and generates lots of ideas and connections.

I am surprised some of ou ngerman speaking members have not joined in, because all are welcome, and it is a lot of fun!

Then I come back to the text with some ideas in mind after I have let it stew for a while, and look up words I do not know the meaning or significance of. I try to pay attention to the tense, the case and the prepositions and conjunctions. That is when I find how far off the mark I was, and I correct the translation.

Sometimes I might do 2 translations of the same text , it depends.

So , please if you want to, engage with the text. I have posted a link to it. It would be nicer if you do to do your own translation rather than critiquing someone else's, but if you must criticise criticise mine. I can take it!

I want everyone to feel they can contribute without getting their Feelings hurt unnecessarily. Even if it is necessary to correct a bad translation, it is better to do the correct translation yourself than to offend another member unwittingly.

An open thread can receive all on topic contributions and become a resource for further thought.

[jehovajah]

Commentary
Norman's video clarifies and raises a point about points.
From a arbitrary origin. Point vectors , rather Strecken can be drawn. These are nodal points and uniquely defined by the displacement and direction of these lines.

I called these multicompass vectors in earlier posts in the fractal foundation of mathematics, a different thread. It is as if the line is more fundamental than the point!

In fact this duality of point and line is fundamental to get right. We cannot envisage one without the other.

I usually start with a scatter of points as an arbitrary starting frame, but I cannot process the frame without establishing any arbitrary sequence  and as soon as I sequence I can use a line to represent that process.

There is a notion of contiguity and continuity. They are both continuous states but one captures only smooth things while contiguity models everything.

Straight lines are special, and in fact much of Grassmans method applies to curved Arcs too!

Whatever we use we must admit that this Förderung is not connected to reality, but Is a  tool for measuring and counting space.
<a href="http://www.youtube.com/v/Nu-YPJSNFpE&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Nu-YPJSNFpE&rel=1&fs=1&hd=1</a>

[jehovajah]

Commentary.

Now here is a real revelation to me and a resetting of my Förderung!

Until just a few minutes ago I thought that the Schwerpunkt concept was an Anomally. Grassmann, I thought included it in his method because he could, and it produced the marvellous Berührungspunkte.

But then it suddenly dawned on me that Hermann had said that the product in combination with the sum was the first concept he understood from the beginning! Yes A x B was defined as the joining line between the points(2) A and B, yes yes ... And I have seen that before.( in Norman's presentation) Yes and it is straight forward but what does that have to do with the Schwerpunkt? And why did he say mehrer punkte?

Slowly it dawned that the law of 3 points, the law of 2 Strecken was not what I had teased out of the confusion created by vector math! It was something altogether more straight forward!

I had come to Hermann hoping to understand what vectors really are. I had not been disappointed. When I realised that vectors are an alien word to Grassmann and that he dealt simply with geometrical terms, the line segment a lot of BS fell away!

I just finished grasping that the fundamental object of our geometrical processing was the Begränzte Linie, a line segment with 2 points marking the start and the finish. I said that normally the point is the fundmental object of our Logical Processing, and our dynamic modelling( after Newton) . I knew the difficulty of going from points to lines. Within that transformation lies Zeno and Parmenides lurking with their paradox traps! But the Pythagoreans avoided these by taking what is called "the method of exhaustion " route. In other words they avoided exactitude generally, and worked with approximating the best they could!

Newton used the notion of time or absolute divine time to overstep these logical difficulties. Until Huygens time was not accurate in any sense and so despite the water clocks of Archimedes and Timaeus, time was not universal or divine. It was a local measurement of duration. Time as in day night etc was a celestial track record of star and planet motion and day And night light variation.

When Huygens clocks were shown to be accurate enough to guide ships across the boiling oceans, then clock time became commercially important and so philosophically important. By creating absolute time as a concept to philosophise by, Newton established the basis for making universal claims.

We miss this fact that Tyme is not universal, and is a construct of a measuring tool called a time piece. It as an entity does not exist , but as an experience we can group together many many related experiences around the ticking of a clock, or the swinging of pendula or fundamentally the motions of bodies in the heavens!

Motion and relative motions exist as identifiable experiences. Time does not. It is a subjective consequence of experiencing these relative motions.

So there were several ways of pragmatically voiding Zeno's and Parmnides mind games, but it is hard to over state how many scientists still struggle with these doubts introduced purposely into logic by these 2 philosophers.

There reason was simple. Man's reason is not sufficient to apprehend reality! At the end of the day we have to accept reality is what it is, and I experience it how I experience it. I have to build my apprehensions on that basis not on some handed down, unchallenged axioms or postulates! I have to think for myself and believe for myself, and expect for myself from my own experience.

So Hermann did the following

He took 3 points A,B,C and realised that AB + BC = AC was a sum. He then, in the simplest way possible mentally set this as

                       The sum of 3 points.

Now I would have written A + B + C as the sum of 3 points, and in fact you find this in the Barycentric literature, where the coefficients are set to 1

So what was AB ?

This was the product of 2 points!

And so was BC and so was AC !

Within the " law" of the sum of 3 points Grassmann saw the product of 2 points!

So now he had to modify his Förderung.

The sum which you can construct from 3 points involves first forming the products of any 2 points!

Thus to illustrate for 4 points A,B,C,D there are 12 products of pairs of points
AB,AC,AD
BA,bC,BD
CA,CB,CD
DA,DB,DC

Of these 12,  6 are the lineal negatives!
Considering the points as FACTORS in their respective products, automatically means that you have to accept that switching or commuting the factors introduces a negative sign!

So now for any four points in a plane I can justifiably replace any 3 points by a representative product of points providing the 3 points are in a triangular relation in the figure drawn by connecting the points into a perimeter!!

That difficult passage that I struggled with? This is precisely what Hermann was alluding to. The products, the multiplication, the observation of sign value the pieces of the figure , all come together in this insight!

In addition we can now define parallel and perpendicular in this new analytical sense of point products and point product sums!

These product sums occur everywhere in mathematics, arithmetic, algebra ,Combinatorics trigonometry...do they always refer to point products?

The answer is no. With the scheme laid ot by Grassmann just now we can extend this concept into lineal,planal and spatial forms!

Of course to do this you have to select the correct points relative to one another.

By specifying all the points of a form ,like a crystal or a geometric solid these product sums can be specified analytically and subsequent manipulation and analysis and synthesis done.

The lineal Algebra is but one method derived from his general method of space analysis and synthesis.

I hope you can let go of years of incorrect training and begin to apprehend Grassmans style of spatial analysi.

[jehovajah]

Commentary

I really think that this is a modification of Grassmanns initial impulse. So he did not come to this point view until he started his dedicated work on what until then had been a put downable hobby.

The gaps he filled covered all the deep questions of trigonometry and geometry. And that means tacking the issue of what is a geometrical object?

Sometimes you cannot define something without a tautology. So far I have not found a definition of point, so these I assume are axioms. But then he defines line and then a plane in terms of a product of points.what he does define is a class of points called Schwerpunkt, the sum of these primitive points.

The story of the Schwerpunkt is not finished., but when he started it he was in awe of Möbius, but as he progressed he realised that his simplest concept for three points being summed had an extra point associated with each point. Instead of a point with a fractional coefficient he saw a point multiplied with a neighbouring point, and this product was the verbindungsstrecke, just as the coefficient gave a fraction of this Strecke to a single point.

But then what was a Strecke multiplied by another Strecke?

This was defined as a parallelogram between these Strecke. .

His ideas were still forming?

http://journals.cambridge.org/download.php?file=%2FPEM%2FPEM10%2FS0013091500030923a.pdf&code=abc71143ee5fa3d47ed3eff3d6c22b2f#xml=http://journals.cambridge.org/data/userPdf/

<a href="http://www.youtube.com/v/BC1jft03k6M&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/BC1jft03k6M&rel=1&fs=1&hd=1</a>

Affine combinations or lineal combinations

<a href="http://www.youtube.com/v/FdgMmHIXA_s&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/FdgMmHIXA_s&rel=1&fs=1&hd=1</a>

Note the practice in Barycentric coordinates makes little sense, whereas the Strecken approach makes sense..

Converting to Möbius notation is one of those backward steps that mathematicians impose on their students. This turns the Fórderung into a kind of "trick" , while disguising the fact that Barycentric coordinates are a confusing convention

[jehovajah]

Commentary

The Schwerpunkt episode reveals a source of inspiration for Hermanns work.

It is clear that in 1827 Möbius published his Barycentric coordinate method. This is the year Justus published his treatise on trigonometry and and later on space theory. It is clear that Möbius, a professor in Leipsic would have contributed to the Humboldt reform discussions and collaborations. The fact that he published in the Crelle journal also meant that the young Grassmann would come into personal contact with him, as Hemann published and worked on the editorial board of that magazine.

So both Justus and Hemnn were directly influenced by Möbius, Justus more so. And Justus introduced his ideas on sign into the curriculum of his district . So it was that Hermann came to be acquainting himself with negatives in the first place !

AB + BA = 0 is a pure equation introduced by Möbius!

The Schwerpunkt means the weight point, and is a conception Möbius used to motivate his geometrical proportioning of a line. In a sense a Schwerpunkt becomes a smeared out point !

Now Hermann read many of the great mathematical works in his study to qualify to become a teacher, but he says he only knew of the title of Möbius work. It seems that he absorbed Möbius's ideas by osmosis then, only to find he had come to the same conclusions.

However he makes a bold claim in his 1844 Vorrede to have switched from the student to the lecturer! By this time Mobius had been publishing many articles on various topics and extended his calculus considerably.

This was a bold if not arrogant claim by a primary school teacher who by then had yet to qualify to teach at secondary level. We know that he applied to teach at university level on the strength of this belief, after publishing the Ausdehnungslehre. It was this text and a district commissioners  judgement of it that in fact denied him a Lecturer post at that stage!

It must be said that Möbius recognised the text as an advance on his ideas, but could not apprehend in what way. He suggested sening it to Some academicians he knew including Gauss, and they basically judged it as poorly executed communication of some interesting ideas.

While it seems harsh now, there was a system of accreditation, and clarity of thought and communication was a requirement to teach. Because of the huge scope of his ideas , and the " work in progress"  nature of his presentation. Mathematicians prefer theorems to conjecture, demonstrated proofs to heuristic discussions of how to prove or demonstrate something, and generally a standard format of presentation. Papers were designed to answer specific questions, not to rewrite the whoe of mathematics and science from the ground up!

Newton did it, but from the position of a recognised academic genius asked to solve a problem of orbits by an astronomer, Halley.

As far as anyone knew no one had asked for mathematics to be uprooted, or had a specific problem requiring this kind of solution,( afterwards people began to recollect Leibniz posing this problem). Nor had anyone commissioned an obscure teacher in  to do it! Later Gauss got Riemann to ask for such general solutions in his Habilitation speech in 1854. He asked this of a wider audience than Mathematicians. His scope included physicist, chemists and mechanical engineers .

Gauss felt Geometry had lost its way, specifically because it could not solve the the 5 th postulate Problem.

It is only in this climate that Grassmann's fellow Prussians began  to apprehend what he had singlehandedly achieved, and especially after Riemman died!

Robert his brothers redaction of his work also now had an audience receptive to these kinds of enquiries.
This is when he was rewarded for his life's work , by recognition of his advancement on Möbius' ideas.

[jehovajah]

Commentary

I have completed the survey of Möbius Barycentric calculus, and observe that Hermann drank deeply of its elixir!

As Hermann expressed it , he almost conceded to the master!  If it were not for his concept of product of points his work would have been done at this point.

Möbius could not understand how you could multiply 2 points!. His calculus relied on length as a measurement and sign as a lineal direction in a given line. But his real focus was on the coefficients of the lines. He therefore reduced the line through a point  A that extended to a related point A', as long as it was parallel to a line through a point B that extended to a related point B', to the point A and similarly to the point B.

This was a notational decision, based on notational laziness. The line was crucial to his geometrical proof of his results! But then he cast it away to focus on the points. In this sense he relied on the concept of number and particularly rational fractions as they contain the fundamental notion of Logos Analogos.

Möbius calculus is pure symbolic arithmetic. It looks like algebra but the Greek symbols represent numbers. The points A,B,C etc represent the only reference to space!

Herrmann's introduction of the product therefore needs some explanation, but it's simplification in communicating and organising the labels or notation on the page is demonstrable and understandable!

[jehovajah]

Commentary

This is , perhaps the clearest section so far in which Grassmann directs a course of study! We must study Möbius Barycentric calculus as the entry level preparation into his own Barycentric  method!

This is of interest to me, because Möbius is an old school geometer. He has developed along the lines set down by Legendre in his redaction of the Stoikeia of Euclid. Thus, like DesArgues, Poncelet and Chevas, and Steiner he rejected the coordinate geometry of DesCartes!

For us, brought up on Cartesian geometry and mathematical descriptions of lines and curves, we have no apprehension of any other way to describe space! We certainly lose sight of what the Arithmoi are , and how they measure and count space in a mosaic. This becomes an alternative description of surfaces and edges.

What distinguishes Möbius is his use of sign. His use of sign is mathematical, in that it is applied according to the formulary by inspection. The notion of a direction is what Grassmann uses, which encompasses orientation and travel in an orientation. Contra comes out of this process as a specific reversal of direction Of travel.

Studying Möbius I suddenly realised that length and sign were of equal importance to him, and this attitude of mind was reflected by Hermann in terms of length and direction. Suddenly AB + BC  must actually be "equal" to AC . These 2 directions were equivalent to the third direction. These 2 displacements were equivalent to the third displacement. These were " equivalence" relations not numerical sums.

However, Möbius formulae were numerical sums! These numerical sums encoded a mentality to space. That is we can count its quantity and sum its magnitudes by area or volume. These sums recorded the process by which they were obtained, and this was by traversing or tracing out a surface or line.

[jehovajah]

Commentary

I never thought I would ever criticise numbers and elementary arithmetic, but my research has found nothing but practices that need to be criticised!

The unfortunate thing is that some critics have not gone deep enough, and so their attempts at a correction lead only to a new misdrection.

Why did Hermann intuitively look for the product or multiplication of points?

Some would say that the aggregation of points naturally leads to the multiplication of points, but this reasonable line of thought is in fact counter productive.

There is no fundamenta physicall multiplication!

The fundamental physical actions are aggregation and disaggregtion. It is within disaggregation that we locate the notion of multiple form.

Thus a single form divides into a multiplicity of forms, and we recognise these as factors of the single form.

So why do we not locate multiple form in aggregation? We do, but an aggregating form has no goal form, so we do not sense a multiple form is aggregating to anything in particular. It is that sense that aggregation has a goal which gives us the sense the sum has a solution or an answer or a definite form!

So we develop our mathematics in the division of a single form. In that division we can do aggregation and multiplication of aggregates , division and subtraction all with the sense they have an ultimate " meaning".

  Given this nursery approach, we then extend it to aggregation of forms where the numbers as forms are potentially limitless!

Thus the Arithmoi cover these forms as shards of space, that is a large chunk that has been disintegrated, and we are somehow putting it back together again.

Number bonds in this context are cloely linked to block mosaic patterning, or tessellation of space. The full geometry of the Arithmos is then evident.

The relation of the Arithmoi is precisely that parallel displacement of forms , in order to calculate centres of symmetry  and gravity. The proportioning( logos analogos work)  is precisely descriptive coordination of the observer interacting with the form and its environment to measure it and manipulate it , in order to help synthesise it Abstractly, in our heads, and physically in substance.

Start with the bricks, the pebbles, the apples and herd animals, and learn the knots, the cusinaire rods, the sticks, and the schematic or sketch patterns. Declare their names and dance rhythmically with them, singing and swinging, twirling and hopping. Balance them on your arms and with the balances of commerce, and look at their reflections in the mirror, understanding what is yours and what belongs to some other.
Pay what you owe and collect what is owed to you.
Measure what is your land and know your boundary and your neighbours. Know how to travel to and fro , to what is yours and from what is yours, learn how to see these things through your neighbours eyes.

Hopefully you will find that these processes are ingrained in your soul and your spirit, your very being.
Maybe then you will apprehend that Shunya is everything!

Maybe the mystery that all is one or that dynamically all things balance may cast light into the darkness of "Nothing"! For it is a profound ignorance, not easily got rid of!

If you have ears to hear, listen to what I am saying to you.

Shunya is everything!