I wanted to revise spherical harmonics in Quantum mechanics, then came to nice this representation theory based definitions:

Spherical harmonics - Wikipedia

and this:

Spin representation - Wikipedia


hmm its because I were studying to abstract algebra and before not any finishing chapters, I moved to checked last chapter of Galois theory to see how these composition series e.g. would be utilized later. 

I had not studied yet those Galois chapters but just checked. 

hmm. then came up to my mind queries of hamiltonian operator mathematics, and wondered abstract algebra applicability or benefits to such domain,  then but then directly observed usage of Legendre polynomials and spherical harmonics in angular momentum alike topics. which I remembered that in both spin/angular momentum discussions from 3 years ago read qm chapters slightly. Hmm then i think its nicer to assess with representation theory based constructs and figuring out polynomial base solutions. 


So my study in abstract algebra is in chapter 14 and had not finished the book (since I had not studied last weekend and in holiday I only studied last night)  but I also last day started to think, which chapters I urgently need to finish before moving to topology RDF definition language. I mean, the project could iterate in tandem to this group theoretic and representation theoric studies in some pace with agile iterations. 

so I think I decided on following methodology:

I continue this book and finish even also integral domain /fields alike chapters and galois theory chapters. since without those knowledge its not having the higher expression capability for the specific RDF/grammar. but then after that, I could start async studies where I iterate on RDF/grammar of topological language and plus I go get expertise in group theory/ representation theory. but the latter wont be mandatorily necessary for agile iteration of RDF/grammar definition.


ayy there is a lot to learn to get expert in representation theory imho. but at least after this books ends, I could move that study to be accompliushed in tandem to RDF design task which would not initially necessitate being knowledgeable/expert inm group theory/representation theory but initial slight such knowledge is enough. 

but one can not emphasize enough how important such fields are. (I mean representation theory/group theory/abstract algebra).

 E.g. It created very newer understanding to see the spin's homomorphism  to SO3 group in the representationt theory as kernel of it being +1 -1 set (spin directions). 

so its like I should really get expert in group theory/topology/representation theory sides to accomplish this task of building such ai. hmm but at least I can move that to an async learning task that is accomplished in tandem to RDF studies. 


so its like :D I mean consciousness increase when studying these topics of topology/abstract algebra / group theory / representation theory is alike to this funny image of such meme :D


just a funny blog section this time :D  (with a lot exaggeration )  ---------------------------------------------

e.g. learning about galois theory example solutions is the second level consciousness level in such meme's picture :DDD

and e.g. spin directions being kernel of such homomorphism being maybe 3rd of 4th level consciousness increase :DDDDDD (of seeing the universe in new perspective this representation theoretic topics are imho :D ) 





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:DDDDDDDDDDDDDDDDDDDD

Ok when I saw composition series in chapter 13, I got to understand that would be used in solving polynomials. but seeing fastly moving to Galois Theory shown its very elegant methods (not in detail, I just checked very fastly without studying to Galois chapter yet) but this really indicates an increase in consciousness level which made me do inquiry same logic for quantum mechanics there which I checked and came to see representation theoretic definitions of spin direction there, that were like i think 3rd or 4th level reach out in consciousness in this funny meme :D  of course I have lots to learn. I mean I am not any expert in representaiton theory nor group theory vbut I would become in following months along with accomplishing ai project software tasks I would continue to study. but first I need to get expert in initially entire concepts of abstract algebra. That still not accomplished yet but in progress. :DDDDDDDDDDD



ayyyy this meme is one of the funniest memes and very very very exaggerated wise shows the situation here in my studies to these topics of abstract algebra/topology/group theory etc etc :DDDDDDDDDDD

ayyyy so much funny :DDDDDDDDDDDDDDDDDDD


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now lets resume abstract algebra study asap. there is no resuming software tasks until getting very expert in this abstract algebra book is accomplished. then software tasks/RDF/grammar design parts would resume (those tasks are postponed until this learning task is accomplished) .

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