Posted by
jon zingale on
Jun 08, 2020; 9:33pm
URL: http://friam.383.s1.nabble.com/Tweet-from-MathType-MathType-tp7596925p7596941.html
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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