square land math question
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Re: square land math question
 
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What? --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Thu, Jul 23, 2020, 2:56 PM uǝlƃ ↙↙↙ <[hidden email]> wrote: Ha! No way. If that were true, then to mow my lawn, I'd only have to mow the little part in the corner and voilá all the other patches would also be mowed. - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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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We used to have this argument all the time about the apt use of relational vs. OO databases. As in Ed's conception, the same square can be associated with multiple locations. Then to update all the renderings of that 1 square, say, change its color from red to blue, all you need do is change the object and all its renderings change as a result. That's pretty handy.
But what if you really did want multiple squares so that changing the color of this square over here didn't change the color of that square over there? You might want "square" to be a class but have color be an instance property so you could change each square to a different color. Or you might even have a concept of *scope* so that all the squares in a neighborhood changed, but no those far away ... or only the squares that are also rotated 90° (invisibly) would change color, but those that haven't been rotated stay whatever color they are. To my mind, computationalists tend to think like the latter (collections of instances) whereas analysts tend to think like the former ("normalized" or "unified"). I'm agnostic and like both teams. But when I see one team winning, I tend to traitoriously jump from one side to the other. On 7/23/20 2:26 PM, Frank Wimberly wrote: > What? > > On Thu, Jul 23, 2020, 2:56 PM uǝlƃ ↙↙↙ <[hidden email] <mailto:[hidden email]>> wrote: > > Ha! No way. If that were true, then to mow my lawn, I'd only have to mow the little part in the corner and voilá all the other patches would also be mowed. > > On 7/23/20 1:52 PM, Frank Wimberly wrote: > > "is the same sized square, e.g. at {0.5,0.5}, the same square as the one at {10.5-10,10.5-10}" > > > > If you agree that 10.5 - 10 = 0.5 then same square, different name. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/
uǝʃƃ ⊥ glen
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Re: square land math question
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OK. As long as you grok the difference between the mathematical concept and the OO concept. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Thu, Jul 23, 2020, 3:41 PM uǝlƃ ↙↙↙ <[hidden email]> wrote: We used to have this argument all the time about the apt use of relational vs. OO databases. As in Ed's conception, the same square can be associated with multiple locations. Then to update all the renderings of that 1 square, say, change its color from red to blue, all you need do is change the object and all its renderings change as a result. That's pretty handy. - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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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No, I don't. What's the difference?
On 7/23/20 2:46 PM, Frank Wimberly wrote: > OK. As long as you grok the difference between the mathematical concept and the OO concept. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/
uǝʃƃ ⊥ glen
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In reply to this post by Frank Wimberly-2
There really does not need to be a difference, Coordinate free geometry is much like vector analysis. You have the equivalent of axioms and I suppose if you so desire you can bring in formal proofs and all the other concepts you like. But what it does for me is give a unified view of linear algebra, odes and geometry as just different instantiations of the same objects and their methods.
Ed _______________________ Ed Angel Founding Director, Art, Research, Technology and Science Laboratory (ARTS Lab)
Professor Emeritus of Computer Science, University of New Mexico 1017 Sierra Pinon
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Re: square land math question
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In reply to this post by gepr
The mathematical concept of a point in R^2 is that a it is completely determined by the values of its coordinates. Same coordinates, same point. A square per se Is determined by the length of its side(s). There is no information about it's location. If I were writing a Square class for a graphics application I would include two member variables: LocationOfLowerLeft point; LengthOfSide double; I haven't written code for years so beware. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Thu, Jul 23, 2020, 3:58 PM uǝlƃ ↙↙↙ <[hidden email]> wrote: No, I don't. What's the difference? - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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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In reply to this post by Edward Angel
I agree. I think Frank is simply prejudiced toward his way of thinking about math. Both relational (normalized) databases and OO databases can be mathematically well-founded. I don't know, but suspect, they're even dual.
On 7/23/20 3:08 PM, Edward Angel wrote: > There really does not need to be a difference, Coordinate free geometry is much like vector analysis. You have the equivalent of axioms and I suppose if you so desire you can bring in formal proofs and all the other concepts you like. But what it does for me is give a unified view of linear algebra, odes and geometry as just different instantiations of the same objects and their methods. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/
uǝʃƃ ⊥ glen
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In reply to this post by Frank Wimberly-2
You keep talking in terms of implementations rather than the abstract object.
Here you say a square does not include information about its location but then you add the location in the class definition. In coordinate-free geometry, you have only three basic entities: scalars, points and vectors. You can use them to define all the standard geometric objects and write code purely in terms of these entities. Ed __________
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) [hidden email] 505-453-4944 (cell) http://www.cs.unm.edu/~angel
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In reply to this post by Frank Wimberly-2
I don't think either of those are necessarily true. Math, like so many other things, is not a unitary thing that writes its definitions in stone for all time. Yes, a point can be defined that way. There are other definitions, some more general, some very different. And a square has alternate definitions, too. Just because you have 1 you like does not mean it can't be defined in a different way.
I really like defining square in terms of right angles, myself. That allows me to know what my woodworking friend is asking for when he asks me to hand him the square. He has many different squares of different side lengths (one of which is shorter than the other!), made of different materials, having different widths, etc. But one thing is constant, they all have that 90° angle staring you in the face. On 7/23/20 3:09 PM, Frank Wimberly wrote: > The mathematical concept of a point in R^2 is that a it is completely determined by the values of its coordinates. Same coordinates, same point. A square per se Is determined by the length of its side(s). There is no information about it's location. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/
uǝʃƃ ⊥ glen
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Re: square land math question
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In reply to this post by gepr
Sorry. I only took math courses in grad school until I was 29 years old and at that time OO didn't exist as far as I know. Databases were just coming into prominence as an area of study. The dissertations that were published in my department the year I finished were all in database topics except mine, which was in numerical analysis. I did teach data structures for many years. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Thu, Jul 23, 2020, 4:21 PM uǝlƃ ↙↙↙ <[hidden email]> wrote: I agree. I think Frank is simply prejudiced toward his way of thinking about math. Both relational (normalized) databases and OO databases can be mathematically well-founded. I don't know, but suspect, they're even dual. - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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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This post was updated on .
In reply to this post by gepr
SDG is a rather cool example of where the point notion can be radically
different than classically handled by Euclid. From the man himself, Anders Kock[1]: "Euclid maintained further that R was not just a commutative ring, but actually a field. This follows because of his assumption: for any two points in the plane, either they are equal, or they determine a unique line. We cannot agree with Euclid on this point. For that would imply that the set D defined by D := [[x ∈ R | x^2 = 0]] ⊆ R consists of 0 alone, and that would immediately contradict our Axiom 1. For any g : D → R, there exists a unique b ∈ R such that ∀d ∈ D : g(d) = g(0) + d · b" Gotta love Kock. [1] Synthetic Differential Geometry: https://users-math.au.dk/kock/sdg99.pdf Also, the paper of his I am currently entrenched in to investigate further some ideas in the Instrumental Goal versus Evolutionary Function discussion: https://arxiv.org/pdf/1105.3405.pdf -- 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/ |
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Spot on! And my cognitive disability prevents me from remembering who or where someone used that as an argument against the law of the excluded middle ... arguing for intuitionist logic.
On 7/23/20 3:32 PM, Jon Zingale wrote: > SDG is a rather cool example of where the point notion can be radically > different than classically handled by Euclid. From the man himself, Anders > Kock[1]: > > "Euclid maintained further that R was not just a commutative ring, > but actually a field. This follows because of his assumption: for any two > points in the plane, either they are equal, or they determine a unique > line. > > We cannot agree with Euclid on this point. For that would imply that > the set D defined by > > D := [[x ∈ R | x^2 = 0]] ⊆ R > > consists of 0 alone, and that would immediately contradict our > > Axiom 1. For any g : D → R, there exists a unique b ∈ R such that > ∀d ∈ D : g(d) = g(0) + d · b" > > Gotta love Kock. > > [1] Synthetic Differential Geometry: https://users-math.au.dk/kock/sdg99.pdf > Also, the paper of his I am currently entrenched in to investigate further > some > ideas in the Instrumental Goal versus Evolutionary Function discussion: > https://arxiv.org/pdf/1105.3405.pdf -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/
uǝʃƃ ⊥ glen
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Re: square land math question
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In reply to this post by Angel Edward
That's because I was trying to illustrate the difference between the abstract mathematical definition and an implementation suitable for computer graphics. I had just asked Glen if he grokked the difference and he said no. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Thu, Jul 23, 2020, 4:27 PM Angel Edward <[hidden email]> wrote:
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In reply to this post by gepr
<tangent> I have 8 chickens in my courtyard which is roughly 10.5x10.5 meters (varas since this landscape was first surveyed by the Spanish). Once I showed them (when we first released them) that the grass in a .5x.5 meter (vara) square was tasty they proceeded to mow the entire 10.5x10.5 yard down nicely. I don't know if this qualifies since the remaining ~400 squares of grass were not identical (mathematically) to the one I introduced them to, but from my idiosyncratic point of view, I had "mowed" the whole lawn by showing the chickens the one square? Of course, the chickens didn't need showing and would have figured it out for themselves (as they figured out how tasty virtually everything in my gardens were too), and they left the longer, tougher grass-stems, moving their focus to any and all tender shoots the grass root-clumps decide to splurt out every day. Have we agreed on what a "square" is and by whose "authority" we
declare that we are talking about the same description? I don't
think that nit has been picked over yet. And are we doing it in
Cartesian or spherical or ellipsoidal coordinates? I'm not sure
if there is a conventional "ovoid"
coordinate system but my guess is that the chicken's would prefer
those. And I don't think these chickens care for analytic or
computational paradigms, they just want to eat, play grab-ass with
the squirrels and jays invading their territory and lay single
cells the size of a chicken-egg for me to steal and treat as my
personal property to consume, sell, trade or gift. I should have
gone for the golden (or palladium) chickens instead methinks... If we can't even square a square, how can we expect to square a circle, or more interestingly tessellate a sphere uniformly? Let's change the value of Pi to 3.0 and deal with the resulting distortion of space later. </tangent> Carry On, - Sieze
On 7/23/20 3:41 PM, uǝlƃ ↙↙↙ wrote:
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Ha! Speaking of π, this was hilarious:
https://www.youtube.com/watch?v=7LKy3lrkTRA Apparently my TI-36X Pro is simply not as smart as the Casio FX-83. On 7/23/20 3:40 PM, Steve Smith wrote: > Let's change the value of Pi to 3.0 and deal with the resulting distortion of space later. -- ↙↙↙ uǝlƃ - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/
uǝʃƃ ⊥ glen
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Huh, that's fun. I love that my TI-86 correctly evaluates:
(10+6√3)^(1/3) + (10-6√3)^(1/3) to 2, just saying :) -- 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/ |
Re: square land math question
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This is my final comment on this topic. Admitting points as squares makes these square covering problems uninteresting. By placing the point-squares on the boundary you can cover a square with an arbitrary number of them. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Thu, Jul 23, 2020, 6:07 PM Jon Zingale <[hidden email]> wrote: Huh, that's fun. I love that my TI-86 correctly evaluates: - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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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Yeah that's an appropriate response to a child. You are boring so just, whatever.
On July 24, 2020 3:42:37 PM PDT, Frank Wimberly <[hidden email]> wrote: >This is my final comment on this topic. Admitting points as squares >makes >these square covering problems uninteresting. By placing the >point-squares >on the boundary you can cover a square with an arbitrary number of >them. -- glen - .... . -..-. . -. -.. -..-. .. ... -..-. .... . .-. . 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/
uǝʃƃ ⊥ glen
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