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So my question is how I can penetrate deep into any topic to understand it profoundly? Does Buddha share any such techniques to sharpen my thinking abilities?
Yes, anapanasati is suitable for this. Itβs detailed in the satipatthana sutta:
https://www.accesstoinsight.org/tipitaka/mn/mn.010.than.html
Comments to the sutta can be read here:
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Well for the '''higher knowledges'' the buddha says that the concentrated must be turned to them, like here http://www.buddha-vacana.org/sutta/anguttara/03/an03-102.html
currently nobody knows how to turn the concentrated mind to the higher knowledge. And Just having a concentrated mind seems very hard....
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Iβm starting to see crosses in most of the default SE avatars, maybe Iβm getting started.
I think there is a right way and a wrong way to do it. Ask yourself if you think so and you will have an answer.
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How to think deeply and penetrate its core? How to think critically? Or how to gain insight?
Regardless a good place to start is to attempt to know something by understanding its binary opposite. You think you know what something is? Every detail of what it is? U memorized it? Backwards and forwards? Now do the same for understanding what it is not. Every detail of what it is not. Or what is there in its absence. Or what is absent in its presence and absence. And what about a non-binary opposite?? Write it all down. Memorize it. until you can repeat it backwards.
Take this example: You are a man and you want to be popular with women so you learn as much as you can. You worship them you pray fr them you protect them you do everything you can but still they dont notice you.
But you only started learning about women with learning about women. Did you learn about men too? Should you? Are they the same? What are the differences anyways? Genetics? Ok so youre a man and you know eveyrthing about men. Do you know about trans women? Trans men? Nonbinary afabs? Binary amab transsexuals?
Maybe youll never know about women. So do give up or do you continue to train in true understanding? Better to be a monk then?