A Point about Math

- The following I have not read or come across anywhere.


I’d say in mathematics there are fundamentally three or four fundamental forms or structures.

[- We could say three. - The fourth would questionably be relevant for it.]

- Or perhaps I should say in geometry. - But it hardly seems to matter. - To me.


The first is the [single] point. - That would correspond to materialism.

- I am not looking for a definition, [for a single point] and I doubt whether one could be given or is necessary.


The second is the [- infinite, - i.e.] straight line.

Seeing it as reaching the infinite and piercing through it, - (- which is the way it is usually viewed in modern mathematics, - fwiw) would mean it is actually the same as a circle of an infinite radius. - For it is a closed line the convexity of never changes. [- That is to say - if you see it as able to connect to itself through the infinite. - The view is not as if there is a different infinite at each direction you might trod in, - but as if whichever direction you move in there is the same single one [point at the] infinite you encounter, - and cross - following this view - returning from the opposite side. [- i.e. - in the same direction]]

- Though again, - according to the common view - it does have any point you could call its center.^{[- * -]}

That would correspond to idealism.


- That is to say the point would be a geometrical symbol of materialism, - expressing its portion of the spirit in that way; - and the straight line would - in the same way - be an expression of idealism.


The third one would be the graphical description of the function e^x - in the mathematical system or structure known as the real quaternions.

- The real quaternions [- often just referred to as “the quaternions”, - as far as I can remember] form a four dimensional space.

Therefore the form regarded would be an eight dimensional form.

- Therefore, - of course - it can not be imagined. - Not in any way that I could manage to imagine, - at least. - And quite certainly not by very very nearly the whole of humanity.

- What I am about to say - as you might easily predict or expect - is that it corresponds to realism.

Still it might be somewhat meaningless if you haven’t got the faintest idea of what it looks like.

- Still - I will not try to describe.

Its form in the [single dimensional] real field may be quite well known. - However, - on the other dimensions of the quaternion space it might be quite different.

- One who could contribute a link on the comments section where partial views of it could be visualized it might be welcome. - I suppose a software by which 3, - or even 4, - dimensional cuts of it could be displayed could be easily fashioned - but I haven’t come across any such thing that seemed worthy of posting in my view.

- Anyway - I do say this form or structure is the third fundamental form - unique among all others no less than the two others here earlier mentioned - I believe, - and with equivalent importance - both for mathematics itself and as a symbol of philosophical ideas and systems, - and that it would correspond to realism and express it as the two other preliminary ones would express the other two matching views.

I do not know what its value for mathematics would or might be, - and I don’t wish to guess because if I’m wrong it might lead some to assume I was wrong altogether.


The fourth would not be very significant for mathematics, - it is beyond the field of mathematics, - it seems: - It would be just the whole universe as it is. - Simple and dry. - Beyond the sphere of all ideas and the embodiment and inherence of them all. - Not conforming to expectations, but in a way in full accord with them all.


So far as for that. I suspect that different parts of the exponential function (e^x - the third form I mentioned, - the eight dimensional one) might correspond to different parts of realistic philosophy, - but I could say nothing about that.

I can not rationally justify my idea. - Not in its entirety at least. Not for now anyway.

I rely mainly on an inner conviction. - But I believe some of the readers can - and will - grasp my notion and share my confidence.

- Even at the absence of an explicit illustration.


- Still - one other thing: -


- Christianity has its cross. - This is known to all. - Islam has its crescent moon. - Judaism - the Star of David. - Hindu might have its Aum symbol.

- But as far as I recall - from-I-can’t-remember-how-long-ago, - Buddhism did not have a sign or a symbol. - It seems the wheel used today to indicate Buddhism is rather a recent idea, - probably chosen artificially as to liken it to other religions; - perhaps seeing it as necessary - either in a trivial or in a somewhat essential way.

- However - what I want to point here - is - that the third form or shape I related to earlier - is the true [- i.e.: - natural -] sign of Buddhism.

Of course it cannot be drawn on a two dimensional paper. Or presented on a computer screen.


- I also suspect the eight dimensions of this form could be related to the eight lanes of the eight fold path.

- Again - I don’t know how. - Though it seems the four dimensions of the quaternions could easily fit “the four world views”, - or the four dimensions of the world we live in.


So far,
Ran.
_______________________
^{[- * -]} - If you observe the way a circle is usually (chosen to be) “defined”, - as the set of points at an equal distance from a certain one single point, - and if you then choose to examine what would a circle of an infinite radius than be - then for each-point-which-does-not-lie-at-the-infinite (as its center) it would give the point at the infinite exclusively itself alone, - which might still make some sense; - (- though than you would get a circle every-point-in-the-interior-of- which is a center of - a circle with an infinite number of centers - each qualifying for your chosen “definition”) but if we are still to ask what would a circle of an infinite radius be if its center is at the infinite, - than it would follow that such a circle would constitute of all other points in the plain: - the whole of the plain minus the point at the infinite which is said to be its center.

- Given that this is hardly what we would expect or want a circle to be, - it may certainly be that the common definition is faulted and does not reflect the correct and natural view.

Our Mind - Second Post

I suppose a human being, - or any other - in general - can be seen as acting in a sort of a coil, or circle: - First impressions of its “externity” are reflected within it, to the extent it has this ability of reacting in this way to its surroundings. It might then be said to have a “picture” of whatever it has managed to capture features of in this way.

- This would be the most primitive picture of the surroundings, in my view. I would refer to this manner of seeing things as the materialistic view.

- Second - one might reflect on the possible error within the process here described. Given that this is a realistic process there would undoubtedly be some. Then such data would be integrated into the first. - While the first phase would give an unequivocal single possibility picture, - though perhaps dim or unclear at places, - the second would fundamentally give as if an array of possibilities. - Possible wrongness is recognized and several possibilities may be related to a certain phenomenon, - in awareness of the impossibility of a definite-single-one pointed-out as corresponding to the actual reality originally reflected.

- I would refer to this as the idealistic view. - I intend to clarify the reason for using this word in just a couple of paragraphs: - This is still a limited and incomplete view, - though quite unmistakenably not as obviously as the first one.

- Further, - as one is always in continuous action, - and to the extent one sees purposes and objectives in his life, - and most [people] certainly do, - according to the picture perceived and processed as above, - one may see or view the data received and moderated in its relation to a possible action taken [in the future] according to it.

No longer are things viewed in a dumb manner unrelated to any consideration, - or idealistically - (- which would undeniably actually be to say emotionally) as if their knowledge is of its own value - devoid of its use and unrelated to it, - but - one might dare say - their value would be seen in a way as a derivative of their actual possible effect - in reality, - and on it.

(- Many might imagine this to be a materialistic attitude. - But this is not the way intended. - It is not meant in a short sighted way but as a matter of principle. It is in no way meant to be intellectual.

- But I will leave it at this with regard to this point now.)

However, - this sight - which would see phenomena - or - rather - its knowledge of it, - [- for - anyway - all you know of any phenomenon is your knowledge of it, - never further and never beyond] as content within its possible application, - and further, - even absorbed in it, - that is to say - goals would be viewed primarily, - and knowledge of facts would only be integrated into their structure and follow their course; - this form of management I would refer to as the realistic view.

Still this is incomplete.

Further there is still the recognition that this reality you originally reflected - however rightly or wrongly, - plus all the additional data regarding its possible wrongness, - plus all the goals of action you may or may not consider worthwhile - according to whichever standards existing and being manufactured within your personal and arbitrary mind, - all of these - this universe out here - as being revealed to whichever extent moment by moment, - are just yourself: - Master Tendo Nyojo’s bottle gourd vine continually entwining with a bottle gourd.

And a bottle gourd being entwined with a bottle gourd vine.

- This closes a circle. - So to speak. - Or rather ties up all sides of reality.

I’m sorry I can’t speak of experience.

Still there is not a man whose day will not come.

- At this final stage one is not separated from that which he perceives, from the ideas arising and noticed throughout the action of his faculty of thinking, from his intentions, - and from the action he ever carries out. It could be defined as full integration, - I might guess.

So far as for the main structure I wanted to present in this post.

Still I might make a few remarks:

First I would assume this would correspond to what is usually referred to as “the Four Noble Truths”. I would even assume this is the principle which lies behind them and a clearer and purer version of the natural structure of their constitution. - The Buddha at his time was of course interested in the convenience of understanding of the audience present at the time and place of his teaching.

Of course this is Nishijima’s idea, - not mine. - Though undoubtedly my presentation is different from his.

- Still, - one teacher you have probably never heard of, - [else than by me, - that is] by the name of Kalo, - refers to those - more correctly I believe - as “the Four Principles of Buddhism”.

- I have once written to Nishijima Roshi about that.

As for his statement that Buddhism is not a religion but a philosophy - it sure seems to make more sense if you view it that way. (I don’t know if my comment about Kalo’s terminology effected his view or gave rise to it, - but it seems to have effected his translation of the Mulamadhyamakakarika - as the little I’ve glanced at it at his blog at the time)

Viewing it that way it is not some arbitrary, - however wise, - means someone has picked for a particular religion he established for whatever reason, - but universal principles of absolute natural existence - independent of one’s choice of a path, or of one’s so called “religious beliefs”.

It is to be remembered in Greece philosophy was a thing to be practiced. And viewing things as suggested Buddhism seems to be the natural and complete philosophical system aimed at nothing but the one true purpose of all religions.

I would also mention Kalo refers to the Six Paramitas as the Six Loftinesses, and to the Three Treasures as the Three Pillars of Buddhism.

Second, - I am not versed in physics, - far from it - but I imagine the first phase described would correspond to classical physics, - while the second would correlate to quantum physics. - I tend to believe a third model - which might relate in its complexity to quantum physics as it (- quantum physics) does to classical physics - might or could be in accord with the third one, - while the fourth of course will or could never be described by the existing or future tools of science.

- Thirdly, - at the beginning I mentioned a coil or a circle, and I never made myself clear as to what I was referring to, - it seems: - So my idea is as follows: - First we perceive, - second we sort the perceived information according to what we consider to be our needs - i.e. - “think” - as we normally call it and see it. - Thirdly, - we act upon whatever or whichever objects we may, - and fourthly, - the independent existence of the consequences of our action has its own place in reality, - and could again of course be perceived by us, - as the coil, or circle, - I was referring to earlier takes its place.




Thus the second post is complete.




So far.




Ran.

Words - First Post

I suppose if one deals with words the place to begin is to put words in place. - In proportion.

Our path is of course not constructed of words. Nor is comunication in general its very heart and essence.

They have their place, but beside being of a somewhat secondary position, they are of course limited in their ability of description. Not only that, - our imagination is limited in its ability of description. And the best words can reflect, - it seems, - is our imagination.

The fact may not be obviouse or significant in every day life, - as we know it these days, - but with regard to the path it is often mentioned.