In an affine space (vector space + point), an ant’s position is a point and a path or trail can be described by vectors.
__________ Ed Angel Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab) Professor Emeritus of Computer Science, University of New Mexico 1017 Sierra Pinon Santa Fe, NM 87501 505-984-0136 (home) edward.an...@gmail.com 505-453-4944 (cell) http://www.cs.unm.edu/~angel > On Oct 24, 2021, at 5:27 PM, Frank Wimberly <wimber...@gmail.com> wrote: > > Focusing the application of ant foraging, what is the scalar product of an > ant? What is the sum of two ants. Same questions for pheromone trails. If > the answer is that scalar product and sum are not general enough. What are > the homomorphisms of ants and pheromone trails? > > --- > Frank C. Wimberly > 140 Calle Ojo Feliz, > Santa Fe, NM 87505 > > 505 670-9918 > Santa Fe, NM > > On Sun, Oct 24, 2021, 5:12 PM Jon Zingale <jonzing...@gmail.com > <mailto:jonzing...@gmail.com>> wrote: > I want to clarify what a dual space is. I think it is much more general > than Frank thinks it is: https://en.wikipedia.org/wiki/Adjoint_functors > <https://en.wikipedia.org/wiki/Adjoint_functors> > .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn UTC-6 bit.ly/virtualfriam > <http://bit.ly/virtualfriam> > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > <http://redfish.com/mailman/listinfo/friam_redfish.com> > FRIAM-COMIC http://friam-comic.blogspot.com/ > <http://friam-comic.blogspot.com/> > archives: > 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ > <https://redfish.com/pipermail/friam_redfish.com/> > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/ > <http://friam.383.s1.nabble.com/> > > .-- .- -. - / .- -.-. - .. --- -. ..--.. / -.-. --- -. .--- ..- --. .- - . > FRIAM Applied Complexity Group listserv > Zoom Fridays 9:30a-12p Mtn UTC-6 bit.ly/virtualfriam > un/subscribe http://redfish.com/mailman/listinfo/friam_redfish.com > FRIAM-COMIC http://friam-comic.blogspot.com/ > archives: > 5/2017 thru present https://redfish.com/pipermail/friam_redfish.com/ > 1/2003 thru 6/2021 http://friam.383.s1.nabble.com/
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