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Algorithmus infinitesimalis

By Mimi Dionne posted 03-25-2012 02:37

  

Books on algorithms make me especially happy. My latest read is Donald E. Knuth’s “Art of Computer Programming” series.

You know the history of the word, “algorithm”, right? Abū ‘ Abd Allāh Muhammed ibn Mūsā al-Khwārizmī and all that? He wrote the text Kitāb al-jabr wa’l-muqābala (“Rules of restoring and equating”). In the strange way of all things lingual, “al-Khwārizmī” begat “algorism” which in turn begat “algorithm”. An 18th century German mathematical dictionary Vollständiges mathematisches Lexicon defined them as “combined the notions of the four types of arithmetic calculations, namely additional, multiplication, subtraction and division.” Algorithmus infinitesimalis, a Latin term, meant “ways of calculations with infinitely small quantities”. Apparently, algorithms were only used by human computers until the second half of the 20th century[1], when they began to be linked to Euclid’s method of finding the greatest common divisor of two numbers, as it appears in his Elements. Knuth illustrates:

Given two positive integers m and n, find their greatest common divisor, that is, the largest positive integer that evenly divides both m and n.

Step 1: [Find remainder.] Divide m by n and let r be the remainder. (We will have 0 ≤ r ˂ n)

Step 2: [Is it zero?] If r = 0, the algorithm terminates; n is the answer.

Step 3: [Reduce.] Set m ßn, n ßr, and go back to Step 1. |

In other words, it looks like this:

Mr. Knuth states, “an algorithm must be seen to be believed, and the best way to learn what an algorithm is all about is to try it.” So, Records colleagues, time to try one. 

By the way, has anyone ever shared with you how few of our Records programs run comprehensive disposition? Informally surveyed resources employed by global Big Box Storage Companies confirm the same percentage: less than 10% of their clients. So few that it’s completely understandable why our Tech partners wonder at our complicated retention rules, but that’s a post for another day.  

Question for you: in order to construct a presentation to senior management, would you know what disposition data to request from your offsite storage vendor?

At a very high level, Knuth offers some tips on what your disposition algorithm should look like.  Remember five elements.

1.       Finiteness. For any given value of n, your disposition algorithm must terminate after a finite number of steps.

2.       Definiteness. Each step must be very precisely defined; the actions to be carried out must be rigorously and unambiguously specified for each case.

3.       Input. An algorithm has zero or more inputs; quantities that are given to it initially before the algorithm begins, or dynamically as the algorithm runs.

4.       Output. An algorithm has one or more outputs; quantities that have a specific relation to the inputs.

5.       Effectiveness. An algorithm is also generally expected to be effective, in the sense that its operations must all be sufficiently basic that they can in principle be done exactly and in a finite length of time by someone using pencil and paper.

In other words, “an algorithm must be specified to such a degree that even a computer can follow the directions”. Simple is elegant and it must be good and short.

As to what data you should request to calculate disposition, only you know the history of your program and what’s appropriate for your industry. But I’m curious—have so few records storage companies dispositioned that you could teach your account managers and analysts a thing or two about how  to build the request?



[1] Another great book: David Alan Grier’s “When Computers Were Human”. FASCINATING read. ISBN: 0-691-09157-9.



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