Saturday, 25 April 2015

What’s stronger than Moore’s law?

Moore’s law turned 50 this week.  In a now famous paper from 1965 Gordon Moore predicts that every 1-2  years the number of transistors on an integrated circuit will double, lowering production cost and increasing its capabilities. Even more, in the same paper Moore predicts that “integrated circuits will lead to such wonders as home computers, automatic controls for automobiles and personal portable communication equipment”. Can you imagine today’s world without them? This technological progress has boosted computational power enormously and enabled us to solve larger and larger optimisation problems faster and faster.  But, even though the progress has been phenomenal, there is even a greater power available. It’s called mathematics.
from : https://www.cis.upenn.edu/~cis501/papers/mooreslaw-reprint.pdf
The impact of Moore’s law is best illustrated by the cost per transistor. This cost decreased from about $10 per transistor in 1970 to less than $ 0.000000001 in 2010. That’s less than the cost of ink for one letter of newsprint. It allowed Google to develop self-driving cars, NASA to send satellites into space and allows us to navigate to our destination using real time traffic information. Moreover, it puts computing power at our fingertips and stimulates the application of techniques from Operations Research and artificial intelligence to real world problems.

When looking at the performance improvement over the years there is a remarkable development. Martin Grötschel (actually it's work from Robert Bixby) reports a 43 million (!) fold speedup over a period of 15 years for one of the key algorithms in optimisation, the linear programming problem. Algorithms to solve linear programs are the most important ingredient of the techniques for solving combinatorial and integer programming problems. They are one of the key tools for an analytics consultant in solving real world decision problems. Grötschel shows that a benchmark production planning problem would take 85 years to solve on 1988 hard- and software, but that it can be solved within 1(!) minute using the latest hard- and software. Breaking the speedup down in machine independent speedup and  the speedup of computing power shows that the progress in algorithms beats Moore’s law by a factor 43.

from http://www.math.washington.edu/mac/talks/20090122SeattleCOinAction.ppt

With trends like big data, decision models will increase in size and will become more optimisation driven. As Tom Davenport puts it “Although Analytics 3.0 includes all three types [descriptive, predictive, prescriptive], it emphasizes the last”. Davenport predicts that prescriptive models will be embedded into key processes and support us in our everyday decision making. This requires the models to be fast and robust. Technological progress is not the only power that enables this, it´s mathematics. And mathematics seems to have the upper hand on this,

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