[FRIAM] Tweet from MathType (@MathType)

[Frank Wimberly]

Not at all.

---
Frank C. Wimberly
140 Calle Ojo Feliz,
Santa Fe, NM 87505

505 670-9918
Santa Fe, NM

On Mon, Jun 8, 2020, 5:30 PM cody dooderson <d00d3rs0n at gmail.com> wrote:

> 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
>
>
> On Mon, Jun 8, 2020 at 4:00 PM Frank Wimberly <wimberly3 at gmail.com> wrote:
>
>> 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
>>
>> On Mon, Jun 8, 2020, 3:33 PM Jon Zingale <jonzingale at gmail.com> wrote:
>>
>>> 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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