Constitution and arrangement in sequencing
To constitute something is to bring it together. A like word, consist also means to bring to bring things into a common relationship, but usually by unpacking the relationships first.
Despite the similarity of idea the process of determination or distinguishing are usually opposite. Consistent, the adjective emphasises the usual relationships, the expected and harmonious related forms. Thus it implies we start with a usual experience, unpack it and find the usual constituents. Consist then means to apprehend the constituents of a thing by analysing the thing into its constituents, and then resynthesising them back into the thing.
To constitute means to bring things together to synthesise a whole. This created whole may not be judged to be consistent by some criteria. However it may form a new criterion for the judgement of consistency..
I therefore want to distinguish a whole by its parts with the understanding that the parts together constitute the whole
However, the bringing together of the parts may not be consistent with the original whole. We can experience that with so many things. For example. I place my shoes on my feet. That feels right and comfortable. I take my shoes off and swap them around to replace them on my feet. That does not feel right or comfortable. It is not consistent with the original arrangement, the original form or process I used. The constituents are the same.
There are many lessons in this simple observation. The main one is that underpinning all these experience are processes of action and motion which are fundamentally sequenced.
My experience of sequence is often limited, often confused by being renamed time.
Sequencing is unavoidable for me as a subjective processing centre. I have dealt with this topic before, and the question was do" I "impose sequencing on my experience, where I is very loosely the subjective processing centre, and " my" is the pronoun relative to it. In other words, the concept of conscious volition is not being invoked by this question. Rather the question ask me to accept or reject the idea that my experience only generates from a subjective processing centre.
I chose to accept that sequencing in a greater external something imposes sequencing in me as a part of this something. I call it Shunya.
So my experiencing of sequences is learned . What I learn is that I first must have a whole made up of parts. Thus I must bring constituents together physically and or mentally to constitute a whole!
This is the part of sequencing usually ignored in any discussion about entropy or just sequencing. To sequence we need to have a prior order, arrangement, and prior constituents or parts.
Let me take a pack of cards! Such a pack exists because some manufacturer has constituted them! They have a prior order, because some manufacturer has ordered them. They have a distinguished set of constituents because the said manufacturer has so chosen and decided.
Now can we say that the external something , Shunya has manufactured it's arrangement and constituents? The answer is we can, but we do not know that by empirical observation, we give our assent to an analogy that makes sense, based on our experience. That is fine, as long as I do not become dogmatic and absolutist, and particularly if I am aware that as my experience grows I will have to change the analogies I give assent to.
The laws of dynamics have become dogmatic, further they are unwilling to change or even recognise that they are an analogy of some precise set of circumstances that need to be reviewed and revised.
NRp is how many differently constituted node sequences with a node count of p can we lay out if repetition is allowed?
NSp is how many differently constituted node sequences with a node count of p can we lay ot if we have to choose each option only once!
The "number" of arrangements of a sequence with p nodes, each node being unique is p!
If I take a sequence where each constituent is not unique, but it has p nodes the number of arrangements that can be distinguished falls from P!, but in fact the brute quantity is still p!, I just cannot distinguish whole collections of them.
What this means is that, despite seeming impossible, in a certain restricted set of motions or processes, entropy does not increase in a closed system beyond a certain value, but fluctuates relative to the original arrangement.
In a closed system order can spontaneously occur in a cyclical dynamic. We call these types of relationships stochastic or homeostatic.
Even with this clarification the number of sequences with different constituents is a hard concept to grasp in the case of a sequence with N nodes and N constituents. For example a 2 node of 2 constituents. Ask yourself hoe many different sequences can you have, and your mind wants to count the permutations! What does it mean that for this sequence we only have 1?
There is only one set of 2 constituents, we generally ignore this
Pint and go straight to the permutations.