## Information and Measurement

Measurement system

In any measurement system, information about the object to be measured is ‘transmitted’ from the object, via an instrument, to the operator.

As in any transmission system, information can be altered (measurement error) or lost (measurement uncertainty) at various stages in the passage of information through the measurement system [Pendrill 2011].

### Amount of information

The amount of information can be quantified for example in terms, not only of how many characters are observed but also how meaningful each character is. The three following signals have the same number of characters, but clearly convey different amounts of information:

“1 0 0 1 1 0 0 0 1 1 0 0 ……”

“a g u r j e r h j j k l ……”

“t h i s   m e s s a g e …..”

One such measure of information is the Shannon information content:

where base ‘2’ corresponds to the two possible states of information: 0 or 1 in the first example of ‘bits’ such as when describing attribute sampling acceptable or rejectable entity [Schneider et al 1986]. According to Shannon, information conveyed by each character increases when the average probability of a character appearing decreases – i.e. there is more information in the ‘rarer’ events – surprisal. The amount of information of a series of characters observed is then the arithmetic sum of each term (thanks to the log term).

### Words and measurement units

Notice how much more information is conveyed by the 3rd signal above. This is done by ‘packaging’ the characters in words. ‘Words’ are patterns of characters which can be repeated a certain number of times as required. By extension, measurement ‘units’  are the ‘words’ of metrology!

[Maxwell]

A – measurement quantity

[A] – measurement unit

{A} – numerical value

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 Element Person Uncertainty Information Communication Object Measuring Man Hazard and Exposure “Ambiguity”:non-specific, one-to-many relation, variety, generality, diversity and divergence Act of measurement (or more generally of transmitting a message) will reduce our ignorance or uncertainty Instrument Man as Instrument Measurement “Vagueness”:fuzziness, unclearness, indistinctness etc Uncertainty reflects certain loss of information when communicating message from transmitter to receiver. Operator Man as operator Measurement Lack of knowledge or skill Act of measurement will reduce our ignorance or uncertainty – Bayes theorem

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### References

Klir G J and Folger T A 1988 “Fuzzy sets, uncertainty and information”, Prentice Hall, New Jersey ISBN 0-13-345984-5

L R Pendrill, B Berglund et al. 2010 “Measurement with Persons: A European Network“, NCSLi Measure, Vol. 5 No. 2 • June 2010, pp. 42 – 54

L R Pendrill, 2011, ”Uncertainty & risks in decision-making in qualitative measurement”, AMCTM 2011 International Conference on Advanced Mathematical and Computational Tools in Metrology and Testing, Göteborg June 20 – 22 2011, Volume 84, Series on advances in mathematics for applied sciences, ISSN 1793-0901, World Scientific, 2012, ISBN 9814397946, 9789814397940

Schneider T D, Stormo G D, Gold L and Ehrenfeuch A 1986 “The information content of binding sites on nucleotide sequences“, J. Mol. Biol. 188, 415 – 31 www.lecb.ncifcrf.gov/~toms/paper/schneider1986

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