abstract number - Thai:
Humans possess language which enables them to utilize concrete numbers to allow them to think about numbers in the abstract sense."
Semiosis, Marginal Signs and Trickster
34 Numbers are generally regarded as a special class of signs, and that the qualities of that special class of signs are particularly relevant to understanding the nature of signs and the problems of the object mystique. Numbers are the most semantically neutral of signs; their semantic carrying capacity is seen as limited to some narrow concept of amount, number or quantity.
46 Zero: The ultimate abstract concept of spatial number is zero because specifically there is no such thing as “nothingness” in nature. As Wilden in System and Structure (1980) argues, the zero, the nought, the not, the negative are all the results of the digital sign system, and apparent live in the Hindus first developed the concept, they viewed it as a spiritual one. Zero, or sunya, was used to represent a spiritual discipline, but pragmatists took the concept and emphasised its quantitative value so it could be utilised to move computational operations from the counting board to the head. It thereby provided European mathematics with a trajectory to modern scientific and mathic thinking, where periodicity has skewed even calculus into new avenues of thought..
The original intent of the zero was to represent the mystical concept of “emptiness”, which the more pragmatic West still has trouble with. However the important point to all this is that these mathematical and spatial concepts can quickly be complicated in their meaning by moving them from one sense of object reference to another.
The literal moving of the concrete object also ought not to be disregarded, as Piaget’s experiments argue or as attempts at modelling demonstrate. The new sense of objects in periodicity is a second-order concept more complex than simple existence in nature. The handling of an object in space and time and moving it, or its parts, around the concept sure way of operating of signs “torqued” into a hypothetical dimension.
It is an abductive way of developing operational signs from pre-concrete and concrete intuitions and of then critically examining the relationships. Part of the magic of numbering is its concreteness and its predictability, and when one begins to play with a Platonic solids an interesting area of hypothetical thinking is opened that is in direct line with the conceptual spacing done by primitive artists.
How Mind Emerged from Matter
Zero – Calculating with Absence
The difficulty we face when dealing with absences that matter has a striking historical parallel: the problems posed by the concept of zero…The symbol designating the lack of quantity was not merely important because of the convenience it offered for notating large quantities. It transformed the very concept of number and revolutionised the process of calculation.
A convention for marking the absence of numerical value was a late development in the number systems in the world...
9 What zero shares in common with living and mental phenomena is that these natural processes also owe their most fundamental character to what is specifically not present. They are also, in effect, the physical tokens of this absence.
Functions and meanings are explicitly entangled with something that is not intrinsic to the artefacts or signs that constitute them. Experiences and values seem to inhere in physical relationships but are not there at the same time.
This something-not-there permeates and organises what is physically present in these phenomena. It's absent mode of existence, so to speak, is at most only a potentiality, a placeholder
Musil, Gödel, Wittgenstein und das Unendliche
Picus Wien 2002
pg 44: Eine der Wahrheit verpflichtete Mathematik müsste über das Unendliche Schweigen, dürfte es nicht mit einem leeren Gerede zu bändigen versuchen. Wittgenstein befindet, dass die Sprache des rationalen Diskurses die Grenze zwischen dem klaren Kalkül, dem sie angemessen ist, und dem Unendlichen nicht überschreiten kann. Jedoch, es gibt noch die Dichtung, die sich zwar nicht auf Antworten zu den Fragen „wahr?“ oder „falsch?“ Zwingen lässt aber uns dennoch anspricht, die - in den Worten des „Tractatus“ - das „Mystische“ anklingen lässt, worüber man nicht reden kann, das sich jedoch „zeigt“.
A (Cybernetic) Musing: Architecture of Distinction and the Distinction of Architecture
Cybernetics and Human Knowing. Vol. 17, no. 3, pp. 95-104
...the mathematical concept of zero. He pointed out that zero is a number with unique qualities, being neither positive nor negative: it is the number between. Zero marks the mathematical space between positive and negative numbers, but is not really a member of either: it creates class of its own with very peculiar behaviours. We recognise this in our calculations of the number of years between a year on the positive side and one on the negative side.
...Then my guide pointed to one of the openings in the front wall of the Temple of the Inscriptions, on top of the Great Pyramid. Walking up the gigantic steps of the pyramid, he asked why the wall was so thick. There is no structural reason to have a wall over a meter thick: structurally, the wall could have been much thinner. Getting no answer, he announced that the wall itself was considered a space. The Maya had, he claimed, taken the wall to embody the number zero, with “positive” space inside and negative space outside.
Wanting us to understand this, the Maya made openings in the thick wall, a wall so thick that you had to step in the space within the wall, the opening—you could not step over it. Thus, you stepped into the space of the wall, the “zero space,” the space between inside and outside
Musement, Play, Creativity:
Cybernetics and Human Knowing. Vol. 16, nos. 3-4, pp. 89-106
Cybernetics and Human Knowing. Vol. 18, nos. 3-4, pp. 111-121
Louis H. Kauffman Eigenforms and Quantum Physics
Cybernetics and Human Knowing. Vol. 18, nos. 3-4, pp. 187-196
Louis H. Kauffman Virtual Logic—Number and Imagination
What is Reality? New Scientist Special Issue 29.9.12