[FRIAM] Tweet from MathType (@MathType)

[Jon Zingale]

Steve, Tom,

The Kronecker delta (or Dirac delta or indicator function depending on
context)
appears in the technical machinery of mathematics and so does not usually
show
up meaningfully in the target science of the mathematical theory. The delta
is
a lot like a projection map (likely dual for those playing at home) in that
it is useful
for selecting data out of larger data, but not in any magical way. It is
exactly like
when we select a column in a Google doc, maybe I move the mouse over to the
column and then click the mouse button. This process is internal to how I
work with
the data mechanistically and does not really tell me anything about the
content.
Seeming exceptions do arise, like when one is working with expectations in
probability
theory, but even these cases just make the process of 'counting' easier. The
reason
we perhaps wish to use something like the Iverson bracket is so that we can
keep track
of types. By mapping a truth value to a number, like claiming True to be 1,
we can count
how many people have their hands raised, say. Many people don't really
concern
themselves with these differences and are somehow ok with it when we write
stuff like
3 * True = 3, but they are usually javascript programmers. Knuth advocates
for the use of the Iverson bracket (see Concrete Mathematics) because
concerning
oneself with types often leads to more clear and powerful expressions of
thought.

Jon



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