EXPLORATION IN TRUTH-SEEKING
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Pure curiosity, in this context, is defined as the drive to explore knowledge out of the pleasure of the knowledge-seeking process itself. All else equal, such a drive is not necessarily irrational and is often rational. Why?
At any point in our knowledge, we cannot know with certainty where potentially useful knowledge may be found. However, we know for a fact that (1) reality exists independently of consciousness and (2) there exist things in reality whose existence we know but do not understand. These facts indicate a wider objective existence that is potentially valuable (i.e. useful, productive or constructive in some way) to explore in the long-run to keep expanding our cognitive context. Furthermore, this wider existence also indicates that we may not know what area of exploration may turn out to be promising. This is reason enough to explore even arbitrary claims within a limit (i.e. within the framework of our values as well as within the scope of our existing knowledge).
For example, it may be rational to explore an obscure topic of no clear relevance in leisure, whereas it is irrational to explore the same topic in favour of goals you have validated as valuable in your context. Similarly, it may be rational to imagine the opposite of your validated conclusions as a thought exercise, whereas it is irrational to devote undue time and resources to proving it — at least without enough evidence that it may be worth pursuing in some form.
If mathematics is the science of measurement, then statistics is the mathematics of data; it is the science of measuring — i.e. quantifying — the aspects of data. Data is the main resource in understanding a random process or a seemingly random process, i.e. a process with one or more factors that — for practical or other reasons — cannot be accounted for.
NOTE: A process is identified from a sequence of events based on the common factors underlying their results, outcomes or samples. Even a so-called “pure” random process is identified as a unique process based on the common factor or set of factors (known or unknown) that lead to a constant probability for any outcome.
Furthermore, when observing the distribution of samples from a process as frequencies of occurrence across time, space or some other metric, observing a convergence in the patterns of occurrence suggest common factors that may be generalised (though not yet, for certain); this is because in a random process, we expect the effect of one or more of the unaccounted variables to keep changing across samples, so convergence to a pattern indicates that there are constant, universal factors (universal to all possible samples of the process) that cause these aggregate similarities despite the constant changes (at least in the long-run) in many other factors. We can try to generalise this pattern by omitting deviations from averages over time to arrive at theoretical distributions, mathematical objects that are essentially abstractions of the observed distribution(s) of a random process or a class of random processes.
However, statistics does not by itself grant any certainty to a process of induction; by its nature, statistics can only indicate promising leads. This is because statistics measures data, but data as such are particulars; to move from conclusions on particulars to conclusions on universals requires conceptual integration, i.e. the process of identifying and integrating the concepts and previous generalisations underlying a process. This is beyond the scope of statistics as such.
Nevertheless, knowing where to look for answers and knowing how and why the data offer promise are invaluable in the search for knowledge. Since statistics quantifies and systematises such a search, it is a vital tool in automatising learning. This points to the relevance of statistics and statistical principles in indicating promising areas of potential knowledge and truth-seeking.