" We aggregate to measure"
The Logos Response provides us with a spaciometry. Since this is a computed result we know more about our reality than we are taught to accept.
For example we do not need to count to measure a quantity. The measurement has been already done. We can access that measurement f we are taught to allow ourselves to do so.In a similar way we do not need to reharse what someone has said, we have computed our perception of it and that too can be accessed.
So if we inherently attribute measures and quantities to our computed reality why count?
Counting is a naming song, and a ritualistic response to our reality and its many many shunyasutras: music, dance, animated forms, pungent odours, tactile pressures etc,
We can use the song to learn many things" one is life is essentially iterative and requires you to deak with that imaginatively in a fun, music and dance way.
Two is that we can and must respond to reality by making distinction between comparisons and naming those distinctions.
Three is that engaging with something simple and iterative helps us to deal with things that are way more convoluted but still iterative, repetitive and ultimately periodic.
We use the song of counting in many ways, including a socialising into the fabric of society, like the alefbet, like the idiosyncratic familial rituals and the social rituals, and we use it as a response as an answer, but surprisingly never principally to measure!
The basis of measurement is apprehension, manipulation physically or mentally to compare! In comparing we ask 1 major question which one is bigger! Our survival imperative drives us toward the maximum. It is only later that we learn to modify that response to find fitness for purpose and expected conditions.
A Squirrel, and famously an ant will store excess for hard times. This is innate by adaption and evolution, thus certain clock cycles of our computational response will be devoted to behaviours which maximise our chance of survival, and these you will note involve aggregation of excess.
So counting is not pricipally to measure, but it provides the paradigm for responding to our sensory imperative to measure, and meets the expected demand for a response or an answer. We could spend our whole life measuring and responding to measurements without ever giving a verbal answer that is direct to an external enquiry. The counting ritual teaches us to expect to do that amongst other things.
So our comparisons mount up upon comparisons and our innate system files them all away, but there is a certain rhythm to this process, and again the counting ritual indicates the euphony of sound and rhythm in our response to the iterative nature of our measurement. For some of us, the internal innate rhythm of the measuring processes are so influential , we find enjoyment in responding and deploying them on our interaction with reality. We become artisans of one form or another, people of rhythm and form and structure.
You may think that such artisans would be natural mathematicians, but alas no! A mathematician is a late 18th century distinction. No, such people would in fact be found in the Arts and sciences, working as skilled artisans et al.
My point is that nearly everyone has these innate fundamental processes, but the vast majority have any chance of demonstrating them in a polymath form socially and familially and educationally stripped away from them.
Nevertheless, those who have been able to pursue it have contributed firs tto language, and then only gradually to notation( a dire move for the most part)
The contribution to language has been in the formalising of the quantitative senses to nouns etc, and then in certain specific notional words for thinking, and empirically exploring, and ontologically ordering the world and objects in the world; and finally in the functional nature of grammar.
These conceptions have governed and ruled both language and mathematical expressions and formalisation, but they have derived in he main from a close and iterative experience of spaciometry and spaviometric structures and dynamism in spaciometry, including rhythm
The couning paradigm also indicates that we need to iteratively aggregate to measure, or iterative aggregation is involved in measuring.
As we observe the processes in he world we notice ierative aggregation, rhythmic aggregation and explosive aggregation with bundled aggregation and immensely bundled, rhythmical aggregation. In amongst the aggregation we notice disaggregatio, and so we see a comparison process going on, and observe which is greater in effect.
These basic, empirical observations are the basis of our spaciometric measuring systems, which we formlly and ritualistically characterise as numbering nowadays, but earlier societies regarded them as measuring and counting, and certainly the Greeks formalised the worlds knowledge in this area on the basis of measuring the "AR" of arithmoi, that is the area. Their foundational science was empirical geometry beginning with area.
The indians, thouh had a different approach, founded principally and securely on Sutras. That is songs of rhythm praising their deities in complex, poetical and metrical forms. But not only praise. Also deep and profound instruction was given in metrical and poetical verse.
The Indians loved the rhythm and it is no wonder they were appreciated by the Arabs as supreme algebraists. By rhythm alone they could establish the binomial expansion of terms into the so called Pascal's triangle. They loved long and intricate calculations as a beautiful and sophisticated song. They understood the rhythms of counting and the structures of counting like no other. The decimal place system was invented in India, but Archimedes apparently used it to answer a question about the size of the known universe, And Napier had established it as part of his project in developing Logarithms,
The provenance or priority i am not currently sure of, but the secret is that all these 3 knew of `indian and greek ways and Indian predilections.
So the song, the language and the specialist writing were the life blood of science so called. The subject of sudy was spaciometric relations and aggregation observations in order to give a response or answer,
From this basis graduallu Aggregation structures arose in written form as prose or poetry, and often these prose poems were delivered as teaching tools to student teachers or learning tools for students. They also formed the basis of many a public demonstration of methods of aggregation to measure to find an answer or a solution to a "problem".
Some poems or prose was deliberately vague to protect secrets, but most was an honest attempt to provide methods of aggregation in an instructional form.
I guess it is hard to think that prose-poems would have been the basis of ones scientific formulary in ancient times, with an intention in the main to elucidate pragmatic practice not abstract conception!