Another interesting question would be to what extent different potential routes of inquiry culminate in the establishment of common concepts.
If there is to be discerned some common revelation across different developments of knowledge, it could be read, perhaps among other ways, either as a discovery of some universal source code external to our conception of it but which our conception can apprehend to some degree, or as a discovery of some source code internal to our conception which allows us to approximate the external in ways that enable our survival. I would opt for the latter, but I can't say its clear-cut.Another interesting question would be to what extent different potential routes of inquiry culminate in the establishment of common concepts.
Interesting to see the different mathematics of different cultures and how they differed and to what extent they tended to coalesce and so onA question only addressable to the extent of access that we have to different intellectual traditions, and to the extent of difference between these traditions, how deeply they radically differ.
Which reals could possibly be “missing” from our universe? Every real you can name—42, π, √e, even uncomputable reals like Chaitin’s Ω—has to be there, right? Yes, and there’s the rub: every real you can name. Each name is a finite string of symbols, so whatever your naming system, you can only ever name countably many reals, leaving 100% of the reals nameless.
How did I do?
And for the record, as I got into with @IdleRich in an earlier thread, there is a distinct strategy in forcing yourself into a new course, in order for certain movements and dynamics to become instinctual, or to gauge how well they become instinctual.
That is, there will always be some degree of forced interest in these subjects, in order to spend enough time with them for the interests to start feeling natural and thus not having to be forced as much.
As I mentioned with the sheer amount of lecture material I watch. It started out as forcing myself to withstand material I didn;t understand, because my previous experiences has already started to show me that if I can break the ground, then I can start the cultivation.
Rather than immediately expecting the topic to be fruitful, without having broken any ground beforehand.
And also, if I don't find a subject interesting, I don't always just take that as a sign to move on. In some cases, yes.
In another sense, there is something sublimely vocational about this, albeit in a paradoxically secular way. A process of willing extropy into consciousness with ever greater robustness. I would go as far as to call myself a zealot in this sense, but I am unsure how long I would hold this assertion, due to primarily semantic reservations.
It seems once one becomes more or less convinced that meaning is dynamic and relative, one then has an easier time assuming responsibility for the sustenance of this meaning.
I tend to rely on the metaphor of crop rotations. Some days my interests lay more in favor of calculus, other days in statecraft, and if I can manage to conform focus to interest, and vice versa as a negotiation, the learning experience will prove to be more robust than if I focused on a topic that was remote from where the interest is located.
So one half is conforming topic to interest, which I go about by way of dynamic scheduling, and the other half is conforming interest to topic, which involved forcing myself to become interested in it in order to absorb as much of it as I can.
Yeah I think so. There is no systematic way to list the reals - as Cantor proved - so our language really struggles.I like where this is going.
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Seems like no matter how many points we put down on the line, there's always hella more, our language might be of issue perhaps?
I think so. What I got recommended in that matter is Paul R. Halmos' Naive Set Theory, which I started reading a short while.This is when you get into set theory isn't it? You can't list all real numbers but you can work with a set that contains them all
Similarly, I feel like most of advanced maths are a no-go unless you cover the set theory base.In fact that is where I lost the mathematical thread, trying to multiply one set by another with completely incomprehensible results
I assume what @woops is talking about is the carthesian product?Would that be vector multiplication? Resulting in a matrix?
As much as I am sympathetic to your project, I think you might have to go deeper than the basics of advanced maths, physics, or blockchain tech for that sort of insight.As an aside for the record, much of this project at this phase can be considered a sort of reconnaissance, a scouting out of the landscape to inform later developments.
And even this phase can have its application. Having even a cursory familiarity with this niche topic may lend insight valuable to that niche topic, especially if there tends to be little communication between the two topics/zones.