  The famous (3n + 1) or Collatz conjecture has admitted some progress over the
last several decades towards the conclusion that the conjecture is true (i.e.
that all Collatz sequences will eventually reach a value of one), but has
stubbornly resisted a proof. Many professional mathematicians have applied an
impressive array of machinery to its analysis, and discovered some limits or
boundaries to where violations of the Collatz conjecture must be, if they
exist. Here we attempt to look at the conjecture differently than most
mathematicians or number theorists, i.e. we will study the conjecture from the
points of view of a statistician/data scientist and of an engineer. As a
statistician or data scientist, we look at Collatz sequences as if they were
sequences found in nature, like a collection of time series produced by some
natural process, ignoring for the time being their completely deterministic
origins. As an engineer, we try to tinker with Collatz sequences to see what
makes them tick, and engineer -- tweak and build -- changes to the sequences
that likewise do interesting things, after first specifying exactly what we
mean by interesting. Although these analyses do not yield a proof of the
Collatz conjecture, like other efforts they present reasons to think that the
conjecture is probably true, and the hope is that the analyses of sequences
similar to Collatz sequences will tell us something about the nature of Collatz
conjecture itself, and/or lead us into interesting and fruitful new directions.
Indeed, many of the phenomenon revealed in the sequences of these Collatz-like
programs are arguably more interesting than, and suggest conjectures that are
as interesting as, the Collatz conjecture itself.
