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I really like to study a subject like philosophy, discrete mathematics and some others because the topics fascinate me, but having a full-time job as a system analyst and programmer it is really very hard to find some application in my job. I study some times but really becoming an expert in it will not do me any good other then being knowledgeable in it(well that's also very great). But over time if you don't apply it you will forget it. How can I find enough motivation to really study these subjects I like?

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What is your main question? Are you asking about motivation, about remembering things you want to study or about finding topics that are useful for your job? – THelper Jul 11 '13 at 8:15
i am asking about motivation and remembering things i want to study – maz3tt Jul 11 '13 at 8:44

I understand your position. I am also a full time programmer, but I still find time to learn piano, compose music, and see my friends/girlfriend etc.

There's not one single key to being able to learn the subjects, the process of learning to get motivated is a process in itself, but there are many, many things that you can do to increase your chances.

First of all forget the time you don't have, you don't have it anyway. Next focus on the time you do have. In Commutes, at home, lunch break etc.

Zig Ziglar has a huge body of work on Spotify, Seth Godin has some great books and posts. I'm sure there are many more but for motivation, these two guys and the collective Rocky soundtrack are my mentors.

Next, find a community. Find others interested in the subject, talk to them, learn from them. Philosophy is not the words in a thesis, it's the ideas in a mind. If possible, consider finding a teacher that can guide you through the beginning phase. In my mind being aware of why you want to do something, and formulating it into a goal makes success more likely. Write it down so that when you hit the rough patch you can look at your reasioning and say "this is tough, but I'm going to push through because x" and if your reasoning is no longer valid, then why continue anyway?

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good answer. just a quick curiosity question do you want to be recognized as a great piano player(maybe in your subconscious) ?. or are you doing it just for your love of pianos. recognition is secondary to you?. – maz3tt Jul 12 '13 at 7:18
Both! I want to be a great piano player, composer and I'm already a very technical guitarist, but great is a highly subjective word ;). One of the toughest things is to accept the slower learning rate, but at times where I accept it and don't push beyond my limits, Ironically, I learn and retain information faster. It's to do with the ability to relax helping you retain info. – Alexander Troup Jul 12 '13 at 8:39

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