Good article, i discovered it right after i bought my violin (could have been after i got a viola, can't remember). I think you can apply these tips to learning, say, rust programming, or convex optimization. I also think a random beat generator is sort of similar to backing tracks i record in Garage band or ableton, and you should leave pieces/charts you're learning out on the stand next to your computers, and look at them often, 5x/hour.
Another tip, always remember the first time you tried to play a clarinet, cello or violin (if you can). Those for me were special moments.
Here's some other (comprehensive) books about practicing, which go from mechanical prescriptions about washing hands and brushing teeth beforehand, to the zen, in the vein of the motorcycle and archery books, like long tones/long bows/drone notes/son filé (the last is Galamian's term, his violin technique book highly recommended).
I assume you are minimizing -- maximizing
is easily NP-hard.
So, get some supporting hyperplanes
of the convex epigraph and use
linear programming to minimize
subject to those hyperplanes as
constraints. Then add a constraint
and try again. There is also
a cute way to do central cutting planes
that can be better numerically.
So, for many non-linear problems, if are
maximizing, then the dual is a
convex minimization, and that can help.
This can be called Lagrangian relaxation.
I never thought that how to do violin practice
was so tricky -- just work to get the fingers on
the notes, in time and in tune, and then
do it a lot until get a lot of facility
(hear the note(s) just before playing them),
sometimes return and play very slowly and
deliberately, and then work on
expression -- the fun part.
But then I never made much progress.
The best I did was the D major
section of the Bach "Chaconne",
and that was fantastic fun --
I played the repeated notes
that made them sound insistent!
I regard the end of the D major
section as the climax of the piece
and find it fantastic.
That reminds me, somebody borrowed my Galamian and never returned it... I want to read that bit about vowels and consonants again.
I think all of this is about you need to figure out how to practice or learn CUDA or Mandarin or whatever for yourself. My dad's advice on learning math was simple "Stare at the book til something sinks in, do the problems, figure out if the answers in the answer key are right". For some students, that's all they need to be told
What this guy talks about at the bottom of page is similar, i.e. there are people who know the materials and teaching methods that have worked int he past, but the only person who can teach yourself is yourself: http://www.allaboutjazz.com/janek-gwizdala-cooking-up-a-litt...
> "Stare at the book til something sinks in, do the problems, figure out if the answers in the answer key are right"
In Rafe Esquith's classroom, he talks about how they take that a step further. They knock the ball out of the park on standardized testing because they specifically try to come up with wrong answers for a math question. They learn the psychology of making test answers by doing - and don't fall into the traps.
It worked for me, in violin,
As we know, things should
be as simple as possible but not simpler.
My approach to learning mathematics is
quite different from learning to play violin
but also is based mostly in independent study.
In violin, I got started when I was a math
grad student at Indiana University. Of
course there is a terrific music school there,
and at the time my dorm was next door with
a lot of music students. One day one of the
violin students, darned good, a Stern protege, put
his violin under my left chin, and I was off
and running, took a violin course in the
music school.
After some years of work from Galamian's book
and just self-teaching, I went for
some lessons. Sure, I started with the
"Preludio" of the Bach E major partita.
Of course early on there is a fast shift
from 1st position to 5th; I happened
to get the note after the shift right;
and the teacher exclaimed "You could
play in an orchestra!". Gee, that shift
is the main issue for playing in an
orchestra? I doubt that!
Maybe he thought I was sight reading that
music! Not a chance! I'd worked hours
on each note, note by note, checking
intonation over and over, etc. That
shift I'd likely done 1000 times.
I hadn't really been learning just the
piece but had been using the piece
as an exercise to learn to play violin,
starting from very little!
So, that shift to 5th position,
at two places in that music,
was the first I'd learned. Sure,
I could have used that skill with
that shift elsewhere. I learned
the whole piece; the learning was
a lot of fun.
But, I learned it, self-teaching.
I had a good ugrad math major but didn't
like what the IU math department had me
doing: Of the three courses they started
me with, two of them had just what I'd already
learned in ugrad school, and the third
started with what I'd learned in an NSF
summer program the previous summer.
But there was other material I wanted
to learn. So, IU and I didn't get along,
and I went, got a job, and studied on
evenings and weekends, independently.
That study worked out well and was,
really, except two graduate courses
all I needed for my Ph.D. I did the
research for that independently in my
first summer after the two courses.
So, my approach to learning has worked.
Computer science and programming? I've
taught college and grad courses in it,
but I never really took one.
What I'm saying did work for me.
Of course if you want then you can
try more complicated ways.
For the OP, she was concerned that
her playing sounded mechanical.
Well, once she has the notes on time
and in tune and practices until
they are "in her fingers" well enough
that she can concentrate on the expression,
then she should, just think about
how she wants it to sound.
For convex minimization, once a guy
had a 0-1 integer linear program
with 40,000 constraints and 600,000
variables. He'd tried simulated
annealing without much luck.
I looked at his constraints, and
16 of them were special, and I put
them in the objective function
with Lagrange multipliers.
Then the dual problem was
to maximize a concave function, and
I did the linear programming and
supporting hyperplane approach
I outlined. After about 500
primal-dual iterations in 900
seconds on a 90 MHz PC, linear programming
via the IBM OSL, I found a feasible
solution, guaranteed from the
duality, to be within 0.025%
of optimality. It was fun!
But I do recommend the central
cutting plane idea.
Kenny Werner's philosophy if you can summarize it in one sentence - is if you are a trumpet player - you must master breath control, fingering so by the time you are in performance - you are truly playing without thinking of the mechanics.
There are many analogies to really focused coding, Kenny Werner's philosophy, and Mihály Csíkszentmihályi's concept of flow [1]. You must master the syntax, the grammar, the idiosyncrasies, the rules and unwritten and written customs, and the is-isms of the language before you can "effortlessly" write code in a given platform/language. This is one of the reasons beginners to programming may stumble on the hike - they are so focused on the writing of the lines of code that they are often pushed by themselves or their otherwise well-intentioned teacher to produce code. The building blocks of code are not the lines of code - it is the concepts and the system and framework and mental model behind it (the whiteboard so to speak).
"This year, forget about the year as a whole. Forget about months and forget about weeks. Focus on days."
An excerpt from Kenny Werner's book that I just pulled out of my giant stack of books Jenga style (p.85).
> Practice
Perhaps music feels great as long as you're fifteen feet away from the instrument, but as you move closer, a different energy takes over and your connection dwindles...
How can we retain the bliss of freedom as we approach our instrument? We must let go off all desires and focus on love. To have the nectar flow through us, we must honor our inner being, and practice receiving what is being given. We must practice and strengthen this conviction daily. We may even have to go outside of music to do it. This is really important, because playing, being so addictive, pulls us easily from the true goal and draws us back into more mundane realms.
But when you have made the inner connection, playing becomes more like taking dictation from within. Work with the thought, I am the master, I am great. Then just put your hands on the instrument, trust them, and eventually it will be so.
"Do not fear mistakes. There are none."
-Miles Davis
Another tip, always remember the first time you tried to play a clarinet, cello or violin (if you can). Those for me were special moments.
Here's some other (comprehensive) books about practicing, which go from mechanical prescriptions about washing hands and brushing teeth beforehand, to the zen, in the vein of the motorcycle and archery books, like long tones/long bows/drone notes/son filé (the last is Galamian's term, his violin technique book highly recommended).
Kenny Werner, http://www.amazon.com/Effortless-Mastery-Liberating-Master-M... (recommends pianists practice long tones ?!)
Sterner: http://www.amazon.com/The-Practicing-Mind-Developing-Discipl...
Bruser: http://artofpracticing.com/book/ (Gerald Klickstein' book is also good, i remember)
Julie Lieberman has soem good violin-specific eg http://www.halleonard.com/product/viewproduct.do?itemid=6954...