  The advent of modern technology, permitting the measurement of thousands of
characteristics simultaneously, has given rise to floods of data characterized
by many large or even huge datasets. This new paradigm presents extraordinary
challenges to data analysis and the question arises: how can conventional data
analysis methods, devised for moderate or small datasets, cope with the
complexities of modern data? The case of high dimensional data is particularly
revealing of some of the drawbacks. We look at the case where the number of
characteristics measured in an object is at least the number of observed
objects and conclude that this configuration leads to geometrical and
mathematical oddities and is an insurmountable barrier for the direct
application of traditional methodologies. If scientists are going to ignore
fundamental mathematical results arrived at in this paper and blindly use
software to analyze data, the results of their analyses may not be trustful,
and the findings of their experiments may never be validated. That is why new
methods together with the wise use of traditional approaches are essential to
progress safely through the present reality.
