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The success of mathematical physics led the social scientist to be jealous of its power
without quite understanding the intellectual attitudes that had contributed to this power.
The use of mathematical formulae had accompanied the development of the natural
sciences and become the mode in the social sciences. Just as primitive peoples adopt the
Western modes of denationalized clothing and of parliamentarism out of a vague feeling
that these magic rites and vestments will at once put them abreast of modern culture and
technique, so the economists have developed the habit of dressing up their rather imprecise
ideas in the language of the infinitesimal calculus ...
Difficult as it is to collect good physical data, it is far more difficult to collect long runs
of economic or social data so that the whole of the run shall have a uniform significance ...
Under the circumstances, it is hopeless to give too precise a measurement to the
quantities occurring in it. To assign what purports to be precise values to such essentially
vague quantities is neither useful nor honest, and any pretense of applying precise formulae
to these loosely defined quantities is a sham and a waste of time.
From a modern perspective, Norbert Wiener's assessment now seems too
pessimistic. Yet it highlights the difficulties inherent in these disciplines, and the
role of mathematical theories in economics in particular is still a subject for debates
today, usually each time after the Nobel Prize for economics is announced.
Recommendation engines are used primarily in retail, which also has a complex
environment. Where data mining is used in industrial quality assurance, for example,
environmental conditions are relatively constant (temperature and lighting conditions
in the factory, output speed, etc.), whereas in retail they are changing all the time.
We have already touched on this as an argument in support of realtime analytics.
Control is even more difficult. Empirical evidence shows that recommendation
engines change user behavior significantly. The skill, however, is to convert this
into increased sales. In many cases, the use of REs simply leads to the purchase of
alternative products, and this can even result in down-selling and a loss of sales. We
will look in detail at the subject of down-selling in mathematical terms in Chap. 5 .
Fortunately, user behavior in the areas in which REs are used can generally be
predicted fairly reliably, albeit within strict limits in terms of time and content. And,
unlike the case with economics as described above, the primary and realistic aim of
REs is to control and direct user behavior. As such, the use of realtime methods
makes absolute sense. Nevertheless, to avoid unrealistic expectations, it is important
to stress the complexity of the retail environment (unlike the earlier example of the
electromagnetic wave). For that reason, having rigorous methods of gauging success
is of paramount importance, so we have devoted an entire chapter - Chap. 11 - to this
subject (although this does not relate solely to realtime analytics systems).
Finally, we mention that the topic covers different mathematical disciplines that
sometimes require complex notations. To make the notation more understandable
and to reduce possible confusion, we included a summary of notation at the
beginning of the topic. Nevertheless, the authors could not avoid that some symbols
are used for different representations. In these cases, the meaning should be clear
from the context.
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