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 <[email protected]> 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 <[email protected]> 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 <[email protected]> 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 >>> >>> >>> >>> -- >>> Sent from: http://friam.471366.n2.nabble.com/ >>> >>> - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . >>> FRIAM Applied Complexity Group listserv >>> Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam >>> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >>> archives: http://friam.471366.n2.nabble.com/ >>> FRIAM-COMIC http://friam-comic.blogspot.com/ >>> >> - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . >> FRIAM Applied Complexity Group listserv >> Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam >> un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com >> archives: http://friam.471366.n2.nabble.com/ >> FRIAM-COMIC http://friam-comic.blogspot.com/ >> > - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > archives: http://friam.471366.n2.nabble.com/ > FRIAM-COMIC http://friam-comic.blogspot.com/ >
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