Getting an overview of all possible partitions of a number poses many of the same challenges as getting an overview of all possible meanings. Though admittedly, partitions are much simpler than meanings, and in that way, it becomes easier to successfully oversee all of them than all meanings. But that is also why, in my pursuit of simplifying and bit-sizing meanings, it remains a great example because numbers are already extremely simple and bit-sized entities.
The main common challenge is their enormous number of 'choices': there are an enormous number of meanings in the world or reasonable sentences that can be said and with that; all ideas they may transmit, I suppose an almost uncountable amount. Similarly, there is an enormous amount of possible partitions; there are over 190 million ways to partition the number 100! Yet, it is possible to oversee all of them at once, requiring only a 100*100 co-ordinate system (For partitions of 1 to 100).
The example, pictured below, shows all possible partitions of the number 10, - which has 42 possible partitions. If I could, I would have shown an infinite list, but it would be too large to show here, and I do not know enough about programming to actually draw such big a structure.
How to read the structure below:
The x-axis presents a sum of x
The y-axis is meaningless (I don't put attention to it) (just there for easier reference)
The slope of a line represents its value
1 line piece (1y length) presents 1 addition of the belonging value. Marked by a dot
New lines spawn from the dots of lines with a higher value than the new
The 1/1 line is not counted beyond the first number, neither are new 1/1s drawn
Getting an overview of just the 42 partitions of the number 10 and transmitting them onto One's mind is already very difficult, and it certainly won't get easier as we approach the 190 million+ of the number 100 and beyond. However, being able to take it all in at once is not my goal either. My goal is dependent on the one thing that remains the same regardless of the numbers, namely, the way that the structure conveys its meanings. As, in this example, because the partitions are shown as lines directly connected to their places of relevancy, it will always be perfectly simple to navigate towards any place of interest. I do not mean that following these lines and their connections with the eyes are particularly easy, but just that it is simple. Anyway, it is a task that could be made infinitely easier if One could make an underlying structure or computer program that could help highlight the connections relevant to One's interest.
Keep that idea of relevancy in mind, because it is at the core of everything my writings are about. Mostly, what I wish to emphasize here, is that it explains what I miss most of all about education and our treatment of knowledge/information in general. You see, if you can imagine each count of a partition found in the structure as somehow, and admittedly quite abstractly, repurposed to be a count of some knowledge/information instead, or more generally, repurpose this map of partitions as a map of all meanings - (not that there necessarily is any inherent meaning to partitions (Hence why the repurposing is abstract). I have reserved that discussion for the page Map of physics) -, then, because of the before-mentioned relevancy, it would be perfectly suited to continue/sustain the flow of an autonomously motivated maintained inquisition. Especially of the type, where answered questions lead to new questions.
Now, this is important for understanding what I find meaningful education-wise in this structure, so let me clarify (invention and theorization-wise will be shortly mentioned after, more 'high-level' description in the specific page mind-structure):
Despite my intrinsic directedness and intuition towards certain topics, fairly put as part of my own autonomy, I was not able to enter a kind of state of 'flow' or commitment when I was in school, nevertheless to sustain it, even when I was being taught about the subject that I regarded as being in the scope of my directedness; physics. The cause being, that I found it too hard to ascertain for myself that everything gripping my attention in school was relevant to my directedness or not. And, when it actually did feel meaningfully relevant, and where new questions following answers were answered swiftly, this 'flow' was capped by the duration of the classes, the teachers' limited knowledge, and the difficulty of finding the correct words to even properly access the teachers' knowledge in the first place when One wants to ask a question, and then, hoping the teacher has a familiar understanding of One's choice of words and the teacher is able to respond meaningfully as well. Not to mention that all of this is only made more difficult by the fact that the teacher has to improvise on the spot, and there is no guarantee for their competence for their job.
The part about accessing the teacher's mind is especially important because that has specifically to do with relevancy and ease of navigation - the key issues. This issue could be extended to libraries or the internet, or even the worlds entire infrastructure of knowledge. In general, any place with lots of information/knowledge. The teacher is mostly just a stand-in for an idea.. perhaps not a good one in this example as a good teacher is not just a transmitter/transferer of knowledge but a good 'guide' as well... But, I only write about the transmission/transfer of knowledge. The other aspects of education are not something I will write about that much. Maybe a little in education.
Anyway, with that said... I like to compare the mind-structure, which is the highest of my ambitions to make, to the mind of an all-knowing teacher, except, there are no barriers to accessing this ''teacher'' 's mind, neither knowledge-wise nor time-wise nor navigation-wise. It would the map of meanings Imagined before. There are no uncertainties about the relevancy of the information gripping One's attention, as Oneself would be able to steer it in the direction One finds interesting. In fact, there is only a single hindrance stopping One to telepathically access the ''teacher'' 's mind and leading through its knowledge as if it were One's own, which is the physical medium the mind-structure has to be made of and our senses ability to oversee numerous elements of it at once. (Which is the same hindrance that makes it difficult to oversee all the possible partitions.)
But otherwise, it would be fair to call it telepathic, as the clarity in communication would be perfect. How? Because of the way, this palpable/tangible mind would convey its meanings, - In the nature of the mind, meanings are defined by their constituting elements through their relatedness to each other. Therefore, as the mind-structure essentially is a mind, but a palpable/tangible mind, each element of it would still be defined by their relatedness/relevancy to each other. Meaning; every possible meaning behind a question exists somewhere in the mind-structure, so what One has to do to navigate towards this interest, is to recognize the meaning(s) and elements of One's inquiring, and then the answers should swiftly be found. And due to the palpability/tangibility of it, this 'mind' would always be open to explore or lead through with One's senses, which would be like taking a peek into the mind of someone all-knowing, or alternatively, as achieving this all-knowing status would require all researchers to deposit their finding onto it, it could be seen as a kind of collective mind instead.
While I have focused on the educational part of these structures, there also is another perk/ability of the mind-structure, but to the mind-structure specifically: As it essentially is like a mind, although a 'dead' mind, the mind-structure still contains knowledge, suspended in all the right places, allowing it to be used dynamically and respond properly to proper interactions with it, like how One can use it to satisfy One's inquiries, but also, dynamic/life-like 'acts' of thinking and finding meanings on its own. especially inventions. Although, as it is 'dead' and there is no consciousness inhabiting this mind-structure, this necessitates Oneself to manifest an organizing element onto it, so 'just the right strings' are pulled for it to present relevant and thought-out ideas/inventions.
What stands left to be talked about, is just how you would go about doing that... The map of partitions is a great example because it is very neatly organized (perfectly?) and it makes the task easy to overcome as it has a very simple organizing element.
I suppose the organizing element of a map of meanings would be based on lived experience, but just how difficult is that to organize neatly? Would you simply be able to make a drawing, like the map of partitions? If then, in 2 dimensions, 3 dimensions, 4 dimensions... 5 dimensions..?
But again, perfect or not, such structures, whether it is a palpable/tangible mind or just a general approximation, could all be part of a great paradigm and etiquette in the meaning-searching facilities.
More in-depth about the specific topics on their specific pages.
Access to the perfect mind
a paradigm of education & invention
The tangible & palpable mind