The 4 Stages of Understanding and Algorithm

I was chatting with a couple of my friends¹ one day, when we realized the singularly depressing state our lives were in. We suffered, we concluded, from a pathetic lack of energy and enthusiasm. The gravity of this situation was deeply disturbing. We need to disturb the very depths of this deeply disturbing state!, we thought. And resolved to immediately commence on a new and exciting project - one that would be worthy of investing our joint genius into. One that would expand our minds, and allow us to illuminate the world with our brilliance!

Alas, it turned out to be one of those bursts of enthusiasms whose sorry fate it is to begin with all the promise and vigor of the Big Bang, only to rapidly settle into the steady state of a spent, stagnant, star that has run out of fuel. But though our project did not give birth to anything quite as spectacular as the Universe, it nonetheless produced what I like to pass for the mildly amusing shimmer of a mediocre meteor...

That evening, I chanced upon an old article describing some odd algorithm. When I had first encountered it several years ago, I'd found to be quite beyond my powers of understanding. But being delusionally optimistic, I'd shoved it into my ever-growing agglomeration of 'stuff-to-look-at-later'. That night, I decided to give the paper another try; and sat down to reflect upon the elusive insights its author had attempted to expound. Deeply absorbed in this reflection, I had one of those moments when the sheer intellectual stimulation of reflective absorption triggers the spontaneous emission of an enlightening, illuminating, radiation. My wavelength matched author's, my understanding was suddenly amplified... and everything became at once coherent. I came to the stunning realization that this now that I was experiencing, was that later that I had been waiting for, all those years. I promptly set about creating an implementation of the algorithm. The program I produced is certainly not worth presenting here, but the exercise did beget one other thing...

It hit me how I had evolved through the process of understanding the algorithm. And the next day, I awoke with a buzzing excitement - eager to convey my new-gained insights to my friends. I started mentally drafting my email to them while standing at the bus stop, waiting for my bus to office. Through the ride, it continued to mature, and during the course of a relatively slow day at work, evolved into the following reflection on the evolution of my understanding. So here are The 4 Stages of Understanding an Algorithm, as they apply to me.

[Note: The 'you' in the following lines really refers to me.]

Looking through my experience

Of trying to make sense

Of this Algorithm...

The rhythm…
Of this flow of consciousness -

Of what is now, and what was then -
Prompted me to pen:
The 4 Stages of Understanding an Algorithm

These 4 successive st-ages then,
I thus present to thee.

(I know the mighty William penned 7
But then that was William... and this is just me.)

In the first stage - the problem is perplexing:

And let me tell you that it is rather vexing

As you set upon your mental muscles flexing

Concatenating cantankerous strings; ever-kinking lists, linking

Expanding exotic exponentials; confounded combinations, combiniking
You wonder what the heck the guy who wrote this was thinking
And keep blankly blinking….

With insight, quite out of sight; 
You ‘rith, read, 'rite – but fail to find the direction right;
You try procedures heavy and light – but do not see at the end of the tunnel, light;
But you muster all your might – and fight – in the faint hope that you just might.

Thus does the first stage age...

In the second - the solution is impress-ing:

As you sit upon the problem, with it about messing,
Guessing and second-guessing, progressing and regressing -

In an inspired instant most mind-expanding
you  suddenly hit upon –
(while you still sit upon –)
that awakening we call under-standing

It takes you into a trance of inspiration,
and the elation calls for celebration! 
A bell starts ringing!  An excitement catches hold to you!
In joyous exhilaration, you start singing!  And dancing, if you can dance, too!

The second stage is conquering complexity, and it sits high and mighty...


In the third stage – the understanding is transcending:

This is where those innumerable hours, mind-bending,
Finally come to a  most mellow ending.

For when understanding transcends, the trance ends, for one
(to use a very much intended pun).
And the impressive complexity crumbles to such humbling simplicity
that you wonder how else but this way, it could be done.

The problem appears to daunt us much less.
The solution acquires a sense of obviousness.
What was once forced – now flows naturally.
What was an invention, becomes – a discovery.

The third stage is the return to the wisdom of innocence...


And in the fourth and final stage – the feeling is depressing:

As cometh to light a matter most distressing
I find my mind, into melancholy mood regressing

For how come I had to be so tortuously taught,
That which other minds had originally "got"?
And while these heads, an infinity of  incredible ideas, sprouted
How come mine remained immaculately droughted?

Thus thinking,
Dispirited strokes inking,
I start again blinking…
And into misery sinking

…Sans problem, sans solution, sans inspiration,
Sans everything but the eternal depression…

________________________

1. Ragavendran Madhusudanan and Prasanna.Murthy - and 3 blogs I highly recommend.