Analog Between Learning Mathematics And Doing Person Development

[Guest username]

The following quote is about learning mathematics and the strange phenomena of gaining insight in unforeseeable ways, building intuition as you stumble along.

Quote

Here's a phenomenon I was surprised to find: you'll go to talks, and hear various words, whose definitions you're not so sure about. At some point you'll be able to make a sentence using those words; you won't know what the words mean, but you'll know the sentence is correct. You'll also be able to ask a question using those words. You still won't know what the words mean, but you'll know the question is interesting, and you'll want to know the answer. Then later on, you'll learn what the words mean more precisely, and your sense of how they fit together will make that learning much easier. The reason for this phenomenon is that mathematics is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you'll never get anywhere. Instead, you'll have tendrils of knowledge extending far from your comfort zone. Then you can later backfill from these tendrils, and extend your comfort zone; this is much easier to do than learning "forwards". (Caution: this backfilling is necessary. There can be a temptation to learn lots of fancy words and to use them in fancy sentences without being able to say precisely what you mean. You should feel free to do that, but you should always feel a pang of guilt when you do.)

Credit for this goes to Ravi Vakil .

 

I like this quote because it really hits upon the intricacies of delving into vast fields of knowledge that can't be handled in a systematic fashion. This is crucial when doing research with your personal development work. Learning about various fields such as spirituality, human psychology, metaphysics, epistemology, ontology, logic, math, science, relationships, health,etc. is a never ending journey.

While it is important to focus and prioritize your work, such as we do by choosing just one thing at a time as a path to mastery, it is also important to contextualize that in the big picture, that is keep in mind that the systems of working you create to organize your life can be misleading. While you should focused and organized, you should always be open and adaptable as well, aware of the fact you an exploring an infinite field of possibility, unaware of what lessons you are yet to learn.

You must somewhat paradoxically be stable and orderly while acknowledging that your journey is limitless, chaotic, and mysterious. 

Here's another relevant quote from Sir Isaac Newton:

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I do not know what I may appear to the world; but to myself I seem to have been only like a boy playing on the seashore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me.

 

Recommended Sources:

Mastery by George Leonard

Mastery by Robert Greene

https://www.scotthyoung.com/blog/articles/   Scott's blog is rich with perspective on how to optimize the learning process.

http://calnewport.com/  Cal Newport is also a top-tier productivity/ learning optimization writer, an acclaimed author, and a friend of Scott (from the previous link).

How I Do Research & Develop Big Picture Understanding by Leo

Edited April 6, 2017 by username

[Joseph Maynor]

I once had a teacher tell me that mathematics is more like a bush than a tree.  You should read some Wittgenstein.  He talks about mathematics being a bunch of independent theories with family resemblances rather than a single logical structure resting on a foundation of logic and set theory.  This is like personal development.  You gotta make little hacks where you can find them and get stuff wired-in where you can.  As you change, so does the theory and practice for you.  You shed skins like a snake as you get older, and stuff that you occupy your mind with will change as you change.  Even the way you practice will change as you get older.  Even your idea of relevant theory will change as you get older.  I like the idea that personal development is like a logarithmic function like Leo talks about.  If you look at a logarithmic function, the negative numbers have a very slow ascent to 1, which is the value at 0.  After 0, the function starts to ascend very rapidly.  Personal development is like that.  You put in a lot of time learning the theory and getting hung-up on theoretical issues, which is necessary to get your practice wired-in, but you're not seeing many results.  This is like being on the side with the negative numbers.  But once you get the theory handled, and your focus becomes almost exclusively on practice, now you're at the 0 and the value of the function is 1.  From this point on, the function starts to blast off as you get your practice hacks wired-in: Morning routine (including meditation), work routine, evening routine, overcoming addictions, optimizing schedule, diet, and working on my philosophy are my practice hacks.  7 in all.  These practices done on a routine are gonna get me further on the positive side of the logarithmic function, and my results are gonna blast off!  Right now, I'm right at the boot of the curve, like at 1 or 1.5 on the X axis.  I'm positioned to get to 2.  So I'm excited to be finally getting some results after all this time, after all this investment and ingraining I've done.  You gotta pay your dues with this personal development stuff.  Just like a jazz musician doesn't just pick up an instrument and start playing jazz.  He's gotta woodshed and practice for years before he sounds great on the bandstand.  But once he gets there, he sounds amazing and you see the smiles on everyone's face, including his own.  What nobody sees is the work he put in to get there -- years of solitary practice with results few and far between. 

Edited June 19, 2017 by Joseph Maynor