WE don't know nothing!
i know Nosthing..
Our best guess is that it is very very small, but our fractal wisdom is increasing, and we know even at the pico level there is something there, maybe even at the femto level of resolution.
So it is a matter of some marveling to me that the notion of Shunya is still promulgated as "nothing". It of course means "something wonderful". That wonderful thing is the fractal nature of space.
Brahmagupta is often misinterpreted, starting with the Arabs who managed to get sine wrong when translating from the indian masters. The indian means "leg", but the latin means "pocket"! Any way that is what i have been told. And i was told that the Arabs used Sifre meaning wind for shunya from which we obtain our word cypher which is now universally called zero, zilch and Nada in popular speech.
Wind is quite good actually. It is better than empty, which is a synonym for wind. The Buddha in this regard is misinterpreted, or at best an alternative set of notions are promulgated to his plainer, simpler meaning of fullness and potential.
For me Shunya will always mean infinite potential, not nothing. The western Philosophers balked at the idea of "nothing" anyway. Their Greek and in fact natural wisdom was that "nothing comes from nothing". This is a universal understanding, so it takes a great suspension of common sense to believe otherwise. Some very influential and misguided individuals actually foisted this idea on the intelligentsia. Talk about the "blind leading the blind".
Wallis and Euler to some extent had problems reconciling this notion of infinite potential with the common notion of decreasing magnitude. As they struggled with Brahmauptas formulation, they adopted the idea that negative numbers, that is misfortunate numbers were somehow infinite. They were certainly mysterious and mystical. It was like looking into another world that is a mirror image, an illusion, not real. All Brahmagupta advised was that this real world and the imaginary mirror world combined to give Shunya.
Shunya for Brahmagupta was a subjective experience of infinite potential. Others looked for an objective referent for it and of course they found none! hence he idea of "nothing", or fruitless search, or wind attaches to shunya.
Brahmagupta is often called wrong when he describes the rules of comparison for shunya. All agree with him until he apparently "divides" by shunya and get shunya, but of course he is not wrong: shunya is everything, so comparisons with it are going to relate back to shunya.
Where the "difference is is in the accepted formulation that 1 – 1 = shunya implying 1 = shunya + 1. This would be a mistake if shunya was infinite magnitude, But Shunya is a subjective experience, and the combinatorics Brahmagupta is advising is that when an object is identified against the background of Shunya, focus on the object. Similarly if an object is removed from the background environment focus on the removed object. In this way we attend to both fortune and misfortune. Multiple forms or part forms of the entire subjective experience become the new background for the subjective experience. This is the essence of scaling to the level of detail one is at, and is akin to fractal "almost" similarity, as Benoit Mandelbrot put it.
Notions of Zero do not originate with the Indians. All cultures at all times have such a notion. What the Indians did was develop the modulo 10 arithmoi to such an extent, with insights and shortcuts and a light complement of numerals, including the shunya symbol which always meant "full, move onto the next level", that they were wizard at mental calculations, and prodigious in arriving at the accurate results. There is no doubt that autistic mathematical prodigies everywhere would recommend the Indian system for its facility and compactness. Wallis for example spent nights calculating pi to tens of decimal places using the system. It was and is a feat of prowess, and indeed fitted one for the life mathematical.
Nowadays we have calculators and computers that can do these things almost instantly. The joy of calculating is thus somewhat of a nerdish thing to do, but their is no finer employment of the organisational functions of the brain than to do a long calculation in your head. Being trained in this art enables long chains of thinking to be correctly assembled, and thus the investigation of mathematical relationships becomes simpler and more subjective. And therein lies the nub of the question about shunya: utility.
If Stephen Hawkings was unable to employ his mind in calculation would he have a use? Clearly because he can do this his use in the physics community is legendary. But of more use to more people is a hunter-gatherer . Their skills of calculation are well employed in the provision of food. So why would we support a "useless" article who can only think in long extended ways? Precisely because of Shunya!
We do not just want food we want wisdom, answers to everything, that is, Shunya. We are prepared to give up some of our food to support an individual who can tackle and engage with shunya providing they bring back from shunya some advantage to us.Thus the subjective results of these mathematical thinkers must be published for public scrutiny to see if there is any advantage. This is not to say that such thinkers must be directed in how they engage Shunya, but rather to say, like any pop star, if we don't like it we won't pay for it.
The guild of mathematicians may well look after its own, by supporting one another through good times and bad, because guild members at least understand that notions that have no current public value may be essential at some future date. However, such an organisation or society introduces , among animates, politicking and factionism, and many ideas may be lost through this human misconduct too. Thus there is no guarantee that notions derived from shunya will advantage any society at the first announcement, and in fact the ideas may be reinvented or discovered several times before they achieve employment. Evolutionary forces shape the development and deployment of ideas derived from shonya too.
What are we to say about Shunya? Nothing? I think not! There is everything to say about shunya!
This picture represents one relation that fell into place because i wss thinking about shunya. I know there is a relationship between trochoids and the mandelbrot. The frequencies of rotation for example are related to the exponentials of the "mandelbrot" vector equation. But what i had not noticed is that the best fit is obtained when the trochoid frequencis sum to 0! Thus we get that infinite potential in the mandelbrot associated with shunya.