An Autodidactic's Quest to Learning Quantum Mechanics

by Chris Stones

First, let me say I'm a normal human being.

I find math challenging. However, I am willing to work. I'm
willing to struggle.

I'll venture a guess that you are normal too. Perhaps, we have
different tastes and motivations but basically we are not
geniuses. No offense or anything. I'm claiming this based on
statistics.

And we shouldn't care either.

We can't leave the achievements to the few folks that somehow
'get it' immediately. They're too rare to rely on. We need to
develop a slow steady and dependable way forward without
assumptions as to the general intelligence of those on the trail.
My friends, if we can figure out how to-figure-out with our own
non-genius-tools and tactics than I grant you we'll have it made.

We'll pull humanity out of the dust once and for all.

That's the motive behind my logic. The logic that tells me to
tell you to get yourself a-learnin' because we need you.

This post isn't just about Quantum Mechanics.

Actually, it's about the process of teaching yourself things. I
figured my algorithm ought to be written down and shared with the
masses. I'm almost certain that at least someone else who has
been down this road before will get a good chuckle at the
similarities of our stories.

You see there are a few truths you uncover when you set out to
teach yourself things.


1. It's going to take a long time.

2. You will be frustrated.

3. You will put it down and pick it up a lot.

4. You will learn patience.

5. You will learn focus.

6. You will learn discipline.

7. You will succeed one day.

This is all about you. This is all about your wants and dreams
and ideas and interests. This quest is yours to own and to
utilize.

So...

What do you want to know and why?


I'd advise a certain amount of wandering around. I'd tell you to
take it all in, go out and play with each subject and notice the
birth of your excitement. The right spark can start the fire
that will light the rest of your life. So start rubbing things
together.

Once, you frame your quest, you ought to size up the challenge.
It's akin to standing at the foot of some vast mountain and
looking it up and down. As your eyes narrow you feel the
impending weight of the task at hand.

That's normal.

It means you're on the right track.

As for me, I've always been interested in Quantum Mechanics. In
fact, I've always been interested in science in general. But it
was physics that won out in the end. I was a kid watching the
Discovery Channel (back when it was still worth it) and reading
about Richard Feynman's crazy stories at Los Alamos. I'd watch
the doc from Back to the Future and Bill Nye and when I was home
sick I'd watch educational programming.

I could always see my mountain. I just never had what I needed to
climb it.

Until now.

One summer afternoon I was meandering along the physics books on
the 3rd floor of HSU's library. (The physics, math and computer
science books are all in the same 3 rows.) I came across a little
book called, "Quantum Theory A Very Short Introduction" and read
through it. To my astonishment I actually felt like I had grasped
what it was saying. It was the first glimmer of hope for me. It
was the book that made me think I could go out and teach myself
Quantum Mechanics.

I walked home grinning.

Fast forward a few years and I'm very sick for a very long time.
There was little I could do but stare at my ceiling for months
actually. And when I was strong enough I'd go to the beach and
meditate. I'd be there long enough to see the sun swim and to
greet the stars. I would leave under the moon's watchful gaze as
the encroaching tide forced my retreat.

I could not stand wasting my time so I decided that I'd get some
math and physics books and spend those hours reading up on the
universe. That's where the small library of QM books began.
Truthfully, I had attempted to learn before but it wasn't until I
was stuck in bed for hours and hours before things began to sink
in. (See Step 4)

My goal specifically?

I wished to know the math behind all the theories in order to
make up my own mind when it came time for folks to present the
next big theory of the universe. I figured that if I knew what
the well worn theories of the day were saying I'd have a front
row seat to understanding reality. Besides, I was tired of having
authors cut up and serve me 'their' metaphors for these theories.
I was tired of hearing the 'quantum-hype' and the application of
the ideas way way out of sync with what the math claimed. [1]

This was the motivation. [2]

Build a Plan.


I had a problem. I'd read one paragraph and it would look like a
Mad Libs fill in the blank. Every other word was gibberish in
the beginning. But I was not deterred. I knew I needed a plan
and a system to handle it.

I realized one day that it was all a matter of organizing
definitions. So, I created a wiki that allowed me to link terms
to definitions and then those definitions had terms that I would
link to more definitions. This progresses until I get all the
way back to something familiar. [N]

My point is now that you have a destination you need a road map.
You need a plan. I laid down a bibliography. I had a feeling it
would be necessary to prove what I knew one day so I wanted my
reference handy for quoting.

But no number of sources will ever help you if you don't put the
time aside to read them. I ran a few calculations and realized
that learning this is a several year endeavor. Developing and
keeping a schedule separates the laid back "sorta going to
understand this one day" types from the "no I'm dead set on using
quantum mechanics to invent The Matrix' types.

If you see the value in your subject you'll realize how important
it is to get on the trail. That is, with a carefully set goal,
the task becomes easier because you'll find motivation to work at
it everyday.

Maybe, your objective isn't to redesign reality and that's fine.
In fact, sometimes I'm just happy figuring out how to pronounce
all those odd esoteric mathematical terms. But it's still easy to
get lost until you have a measure of how far you've gone.

That's why you have to...

Track your progress


In my case, I practice explaining what I find out over and over
again. Sometimes I write this down and it becomes article fodder
or later a movie.[3] I also have several notebooks full of
mathematical equations I've jotted down and worked over. You
might consider taking audio notes. Chances are you'll need to
pick up where you left off and listening to your own recap is far
more helpful than having to review a scattered collection of
sources.

Lately, I've been harping on this flash card system I've grown
fond of. Because after all success is 3 by 5. I
like the way I can add notes and observations to flash cards. I
smile when I see them in my day pack. I enjoy just flipping
through them. I'm often surprised how fast I remember things in
card form.

As it turns out, if you don't have all the details you don't have
anything. For too long my understanding of things has been hazy
all because I wouldn't put the time into properly memorizing
things. The proper vehicle for my effort just happened to be 3 by
5 index cards.

Rewriting them and referencing where the data came from becomes a
ritual. The upkeep helps me focus on the specifics. The one
problem? Sometimes information doesn't card-i-tize[4]

My favorite thing is to sit back and watch a stack of my
knowledge grow. Visualize your progress and watch your
motivation rev.

Motivation comes in handy because you should..

Expect to be puzzled... Endlessly


Don't worry too much about not 'getting it' because you won't.
That's normal. How well (and how long) you can handle gibberish
is a key factor of success here. Settle in because chances are
it will be a long time before clarity shines down upon you.

I heard QM had something to do with Hilbert Spaces. So naturally,
I decided to go find a math book on Hilbert Spaces. Somewhere, in
the later section of the book it decided to explain a bit of
Quantum Mechanics all by itself. That's when I found out what
"taking a measurement" means in the quantum world. I saw the math
behind it all.

I still recall where I was when I learned that. I can see myself
standing on the 3rd floor of the library looking at that Hilbert
book and flipping to that point somewhere in the latter two
thirds of the book.

Moments of clarity are burnt into my memory. It's just a another
small piece of the picture. But piece by piece we move on. Each
door unlocking yet more doors until material that once was stone
cold glows with new warmth.

Do the work.


Memorize. Maybe you have memorized lines for a play. Or the
multiplication table. Or even a human language.

The fact remains that knowing what the symbols mean is crucial.
Even if your reading slows to a crawl. Crawl through it because
rushing the reading won't get you to the finish line sooner. It
will only make you tired.[6]

If you have to spend an entire night on 2 pages. Then spend an
entire night on 2 pages! That's 2 pages closer to the dream.
That's a 1000 feet to the next base camp.

That's just how it has to be.

It's important to note how different this is from passive
learning. We learn a lot of things by just existing and
interacting. But once we expend the energy, once we stretch our
mental muscles we feel the strain.

Try to solve the problems authors give you. Try a little each
day.

You'll need a lot of days so...

Have Patience.


You get excited. You want to rush it. Don't. That's not going
to work.

The problem here is that I can't just tell you not to rush. You
have to come to the realization that it won't work that way.
What you're embarking on here is a huge time investment. It's
going to be a process. A growth process.

Of course, I had to learn this the hard way. I had to get sick
and put my life on hold for a long time before I realized just
how much better off I was. I had to make it a part of the week
before I could cover ground.

Growing takes time. "You just can't force force a flower to
bloom."[5]

There just isn't a substitute for careful thoughtful research.
The goal is clarity and accuracy not top speed.

Over all it helps to have...

Checkpoints

There is a real danger of learning this
stuff wrong. It's a fact of the trajectory. But we can check
ourselves. And that is the most important part.

But it is also the tricky part. You have a few options:

One. You can find a mentor. Someone that you can ask to help tie
you back to reality. They might be online. If you're lucky you
might find someone in person.

Two. If you wish to remain 100% solo go find a question and
answer bank. Go write software and test run it. Go solve
problems in text books. Cross check facts in multiple sources.

You can grind and claw your way to confidence with your growing
knowledge base. Each new concept a hard won trophy shined by the
effort to polish it.

Synthesize.


Create. It is only in the act of creation that we find
ourselves. This might mean solving problems you find in
different quantum textbooks or writing programs to simulate
quantum computing or even writing out the proofs yourself.
Regardless, attempting to create highlights the holes in your
knowledge and it is the quickest way to generate questions.

And the research cycle continues. Research. Work out. Refine
your questions. Research. Repeat. The objective is to build a
real skill. A real skill is something you can use when you want
to, a mode you can switch your mind into.

For me, a particular by-product of this quest was that I was
suddenly very aware of a lot of esoteric higher dimensional
mathematics. I would find myself trying to solve other problems
with my new knowledge. (One of which was the split check
problem.)

You'll be there when you start to use the higher math to solve
other mundane things. It's not just "doing the work" this is
going somewhere else with it. Playing with the ideas. Applying
them.

You'll have to...

Trust Yourself.


You can do it.

A long time ago I was just a little kid writing the same variants
of algebra equations on my driveway all summer. Eventually, I had
more meaningful things to write down but by then I had moved on
to chalkboards on a college campus. The point is that over time
you evolve.[G]

Confusion is a passing phase. So long as you stick to the logic,
follow the math and keep traveling you'll get there. You might
have to wander out and then come back and wander back out and
then return again but eventually the trail will grow familiar.
You'll recognize those symbols. You'll start to draw connections
between Hilbert Space and your everyday life.

Well, maybe not exactly like that but the point is the power is
in you. Trust me, it is.

Oh, and Hang in there.


It's tough that's for sure but for the hour after hour of
frustration it's worth the moment when something clicks. It's a
lot like solving a jigsaw puzzle. They're long periods of
searching punctuated with Ah Ha!s. And then you ride the
endorphins until you can get your next fix. (Assuming you
haven't thrown in the towel just yet.)

In those challenging times, it's a good idea to go sit at the
beach and take in the sunset. Watch the prism of the sky rotate
into that deep blue and greet the stars as they open their eyes.
The quest is understanding the world. Do you think it would be as
wonderful if it wasn't for all it's delicate complexities?

I find it important to maintain that it's only messy when it hits
the math on the page but the perception and the beauty is ready
to be savored while strolling on a warm summer's day. After all,
you're still alive and it's still out there. If you decide to
pack up shop and come back at some future date then that's fine.
Just clear your mind and venture back when you're ready.

I will say this though. If quantum is your game then maybe you'll
start to find wonder in the once mundane world of everyday
things.

I find myself smiling at the patterns of color in soap bubbles or
the heating up of the iron on the stove. I smile and whisper to
myself, "Ah, Quantum Mechanics."

And then I go find my flash cards.

Good luck.




Notes:

[1] I wanted to get to a point where I could take an
experimental setup and write down the matrices that
represented the system Quantum Mechanically. That's
the finish line in my mind.

[2] It wasn't entirely a pure knowledge quest. I was
intending to use it to give myself the edge regarding
quantum computing.

[3] ;)

[4] Turns out, it's hard to spot exactly what you need
to remember sometimes. (I can't fit entire theorems on
cards. ) You can't memorize facts you don't understand
the meanings of very well.

[5] Don't know who said this. There was a guy I knew
back in college that used to work in the mail room and
he said this to me after I told him how stressed out I
was.

[6] Literally. When I rush though text I don't grasp,
it all blurs and I fall asleep.

[N] The problem was that my web wiki was too slow
loading for me to make quick use of it. I haven't
gotten around to bringing it back but I have a feeling
I will.

[G] Much like the way some fighting monks will punch
iron their whole lives to become as strong as iron you
too will forge new talents.

ps. I wrote this article after looking for something
like it and not finding it out there.




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