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How long does it take to find the factors of a really big integer? Before you ask, “Who cares?” let me translate that into IT terms: “How secure is your encryption, and for how long will it stay that way?”
At the beginning of this month, the integer produced by multiplying 3,079,640,632,433 by 33,450,397,200,631 (primes with binary lengths of 42 and 45 bits, respectively) would have taken me more than 12 minutes to factor back to its two components. Today, I can do it in 49 seconds. All I did was upgrade from the 4.1 to the 4.2 release of Mathematica, the Wolfram Research (www.wolfram.com) product that almost defines what computers are good for.
Its not just a matter of having an immensely powerful calculator and a graphical rendering tool kit. What really binds me to Mathematica are my “notebooks,” which tell me how I did something before and let me quickly update my past answers to often-asked questions.
Every year, for example, the same groups call to ask when I can do an astronomy night for them. To answer, I open my Mathematica notebook that begins with my location, adds a range of dates and shows an animated view of how the sky will appear on those nights. I pick the date with the best chance of something worth seeing, grab the corresponding animation frame and make copies that Ill be able to pass out that night as visual aids. There are lots of things you can do with just a spreadsheet, but I dont think Excel can manage this.
Im making two points here. First, the state of the art is still rising, more quickly than people might think. The speedup that I describe above would take six years at the Moores Law rate of doubling every 18 months. A better algorithm does it today. When someone asks, “How long will it take?” the answer has to begin with “When will you start?”
Second, whether were talking about an individual or an organization, its easier to be smart tomorrow if you remember how you did it yesterday. If youre answering questions today that you will have to answer again, are you doing everything you can to capture those answers in a form that gives you a running start the next time?
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