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.

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.

## 2 comments:

On the 2nd of this month I was in Tel Aviv University and happened to meet a person by the name of Eilon (I don’t remember the family name) who is a graduate student of math in the field of set theory. We had a short conversation about the subject and following some subsequent thoughts I came to be fully convinced that the axiom advocating the existence of an infinite set is not acceptable. – The Russell paradox too is a consequence of assuming the possibility of an infinite number of elements constructing a set. – I might still have some relevant questions but it is inevitable that in actuality the root of all troublesome issues occurring quite strangely in the field of this theory is the attempt of inserting the infinite into analyzable human thought in the field of math. I generally believe the true and correct line-of-thought in set-theory would lead to the unequivocal conclusion that there is (absolutely) no room for non-constructive mathematics. What the apparent contradictions very-roughly-attempted-to-be-solved are telling us is that there is no infinite set to be accepted in mathematics. – Things – I believe – are not that difficult to see should one not be too attached to a mathematical-theory of which very little – apparently, - will be left, or to the emotional wish to have the infinite (should one exist at all) accessible and usable at hand within mathematical research. I am saying all is wrong, fundamentally, - and as it seems (as I said not all is yet clear) we could not speak of the idea of an infinite number in practicality. The explosion created by the subsequent construction of power-sets is demonstrating this impossibility when taken to its entirety.

http://www.israelhayom.com/site/newsletter_article.php?id=32345

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