Re: Tweet from MathType (@MathType)
Posted by
Frank Wimberly-2 on
Jun 09, 2020; 1:25am
URL: http://friam.383.s1.nabble.com/Tweet-from-MathType-MathType-tp7596925p7596947.html
Not at all.
---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505
505 670-9918
Santa Fe, NM
I have only seen them inside of summations,
Σs, but I'm sure they are used elsewhere. They are used like a filter. For instance, if you want to sum weights of butterflies in an insect database you would say "for every insect in X, if it is a butterfly then add it's weight to the sum". When it gets translated into an equation, the part "if its a butterfly" gets turned into a Kronecker delta function where it outputs 1 when it is a butterfly and 0 otherwise.
So in some sort of pseudo equation, it might look like y=Σ
_of_i_in_X( Kron_delta( Label(i), "butterfly") * Weight(i) )
I hope this doesn't muddy the water too much,
Cody Smith
OK. The Kronecker delta on a set A is a function or set of ordered pairs. The arguments of the function are ordered pairs of the elements of A. The elements of the function are defined by <<x,y>, z> where x and y are elements of A and z is in {0, 1}. In other words the domain of the Kronecker delta is the set of ordered pairs of elements of A and it's range is the set {0, 1} and the function is evaluated as delta(x, x) = 1 for all x and delta(x, y) = 0 if x != y.
Is that better?
I stand by my original post
---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505
505 670-9918
Santa Fe, NM
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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