The Advent of the Algorithm
The Post and Courier recently printed an unusual column discussing “Deep Reading.” It is an excellent article by Laura Casey discussing a lost art.
“Deep Reading, or slow reading, is a sophisticated process in which people can critically think, reflect and understand the words they are looking at. With most this means slowing down – even stopping and rereading a page or paragraph if it doesn’t sink in…”
Deep reading seems out of sync with today’s “modern” communication tools, like Twitter, and it is. But what does this have to do with the algorithm? As a data guy, the algorithm is my life, and the only way to understand what makes it tick is deep reading! My choice for this subject is The Advent of the Algorithm, by David Berlinski.
We experience the algorithm everywhere in our daily lives – in the operation of the toaster, the dentist’s office, our vehicles and in most, if not all, of the communication tools we use daily. I reviewed definitions of the algorithm online, but none have the elegance of Berlinski, in his book, The Advent of the Algorithm:
“In the logician’s voice:
an algorithm is a finite procedure,
written in a fixed symbolic vocabulary,
governed by precise instructions,
moving in discrete steps, 1,2,3,…,
whose execution requires no insight, cleverness,
intuition, intelligence, or perspicuity,
and that sooner or later come to an end.”
Where did this idea come from? It turns out the algorithm we all know is the brain child of four people: Kurt Gödel, Alonzo Church, Alan M.Turning and Emil Post. Each contributed, in part, to the concept of the modern day algorithm, including functions, calculus of conversion and machines capable of manipulating symbols (computers).
Berlinski describes, in depth, the development of the algorithm concept. In one example, the Euler algorithm, he makes clear how important it is – for an analyst, anyway – to know, not just understand, the magic and flaws behind the algorithm. A case in point is the Numerical Solution For Ordinary Differential Equation, page 245.
“From a mathematical point of view, the original differential equation, contingent as it was upon the concept of the limit, has been replaced by a difference equation, one in which the derivative is approximated by a difference quotient, involving no limits whatsoever.
The Euler algorithm demonstrates this method:
BEGIN Euler
Input xΟ, yΟ, xf, h
x: = xΟ
y: = yΟ
WHILE (x<xf) DO
y: = y+ h* f(x,y)
x: = x+ h
OUTPUT x,y
ENDDO
END Euler
This simple algorithm, however, provides critical insight into the weakness of the algorithm:
“…the difference between an analytic and algorithmic solution to an ordinary differential equation is sharp and it is inescapable. An analytic solution completely penetrates the future or the past; an algorithmic solution acts only over a finite interval of time and space. The analytic solution returns a differential equation to a continuous world; an algorithmic solution, to a world that is discrete.”
Now I understand why the brakes failed in my Toyota. 
Note: some of the reviews of the book were not very flattering, but this is DEEP READING with the good stuff starting on page 205. Do you think you have what it takes to DEEP READ? Have at it!
