Re: [FRIAM] square land math question

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 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

Re: [FRIAM] square land math question

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 505 670-991

Re: [FRIAM] square land math question

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.

Re: [FRIAM] square land math question

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. -- ↙↙↙ u

Re: [FRIAM] square land math question

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 nicel

Re: [FRIAM] square land math question

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

Re: [FRIAM] square land math question

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 radic

Re: [FRIAM] square land math question

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 p

Re: [FRIAM] square land math question

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

Re: [FRIAM] square land math question

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 def

Re: [FRIAM] square land math question

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

Re: [FRIAM] square land math question

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

Re: [FRIAM] square land math question

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 graphi

Re: [FRIAM] square land math question

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 alge

Re: [FRIAM] square land math question

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 Friday

Re: [FRIAM] square land math question

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 ↙↙↙ wrote: > We used to have this argument all the time about the apt use of r

Re: [FRIAM] square land math question

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

Re: [FRIAM] square land math question

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 ↙↙↙ 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 >

Re: [FRIAM] square land math question

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}"

Re: [FRIAM] square land math question

"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. On Thu, Jul 23, 2020 at 2:47 PM uǝlƃ ↙↙↙ wrote: > Well, we're talking about sub-squares, not just any old reduction. So, > this woul

Re: [FRIAM] square land math question

Well, we're talking about sub-squares, not just any old reduction. So, this would be the reductions where both elements of the tuple are reduced by the same scalar. But, more importantly, 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}? I think most p

Re: [FRIAM] square land math question

In geometry, I find it better to think in terms of objects. A point is an object that has a location, dimension 0 (no measurable property) and no other properties; a line segment is an object with one dimension, has dimension one, and is defined by two points and so on. For each object, we have

Re: [FRIAM] square land math question

"While a point and a vector in R^n might be described by the same tuple, dividing the numeric elements of the tuple does not "partition" the point..." Good point, Steve. There are infinitely many ways of resolving a vector. E.g. (1, 1) = (1, 0) + (0, 1/2) + (0, 1/4) + (0, 1/4) etc. On Thu, Jul

Re: [FRIAM] square land math question

Nice challenge! ... Wel, the original question was basically how Cody might respond to the kid's suggestion that a point is a square with no area. My suggestion to Cody would be to answer the kid with a discussion about the actuality or potentiality of infinity ... or intermediately, disting

Re: [FRIAM] square land math question

Glen - Can you illuminate us as to what treating the *location* of a point as a *quantity* and demonstrating that the quantity can be divided arithmetically adds to the meaning of a point?  While a point and a vector in R^n might be described by the same tuple, dividing the numeric elements of th

Re: [FRIAM] square land math question

So, apparently, 1/ω ≠ 1/(ω+1) in surreal numbers. But if I understand correctly, which is unlikely, we still don't have a definition of integration for surreal numbers. So, I'd hesitate to rely on that as an authority. I now wonder if all infinitesimals have the same size in the hyperreals? And

Re: [FRIAM] square land math question

Doesn’t that depend on how finely you can pick a nit> On 23 Jul 2020, at 12:28, Frank Wimberly wrote: > points are indivisible.  Pardon the tone of authority. - . -..-. . -. -.. -..-. .. ... -..-. . .-. . FRIAM Applied Complexity Group listserv Zoom Fridays 9:30a-12p Mtn GMT-6 bit.ly/v

Re: [FRIAM] square land math question

Zeno had several paradoxes, all intended to expose questionable assumptions. On Thu, Jul 23, 2020, 1:58 PM Frank Wimberly wrote: > A lot of it has to do with using a cell phone keyboard and not wanting to > get too technical here. But maybe Jon is right about "the List can take > it." > > I sho

Re: [FRIAM] square land math question

A lot of it has to do with using a cell phone keyboard and not wanting to get too technical here. But maybe Jon is right about "the List can take it." I should have said that aleph(n) is the cardinality of the power set of a set with cardinality aleph(n-1). That's slightly different from what I

Re: [FRIAM] square land math question

Thanks for putting in a little more effort. So, in your definitions, 1/aleph0 = 1/aleph1. That's tightly analogous, if not identical, to saying a point is divisible because point/2 = point. But before you claimed a point is indivisible. So, if you were more clear about which authority you were c

Re: [FRIAM] square land math question

Glen, I am aware of the hierarchy of infinities. Aleph0 is the cardinality of the integers. Aleph1 is the cardinality of the power set of the integers which is the cardinality of the real numbers (that's a theorem which is easy but I don't feel like typing it on a cellphone keyboard). Aleph2 is

Re: [FRIAM] square land math question

Again, you're making unjustified claims. This argues that all infinities are the same and leaves someone to stew in their juices about whether infinities are actual or potential. If they're potential, then 1/∞ is *undefined* and we only *approach* 0. If they're actual, then 1/∞ is an actual numb

Re: [FRIAM] square land math question

Frank, I will send my regards. Because of the kinds of conversations that occasionally heat up around ideas like electron wave-particle duality, I feel that it is important to include definitions that extend to more general concepts. This list can take it :) -- Sent from: http://friam.471366.n2

Re: [FRIAM] square land math question

1/infinity is the limit of 1/x as x goes to infinity, which is zero. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Thu, Jul 23, 2020, 11:16 AM uǝlƃ ↙↙↙ wrote: > Maybe. But how do we handle things like reciprocals of infinities? Is > 1/aleph0 the sam

Re: [FRIAM] square land math question

Maybe. But how do we handle things like reciprocals of infinities? Is 1/aleph0 the same as 1/aleph1? On 7/23/20 10:02 AM, Jon Zingale wrote: > How about, "Points are maps from terminal objects?" -- ↙↙↙ uǝlƃ - . -..-. . -. -.. -..-. .. ... -..-. . .-. . FRIAM Applied Complexity Group

Re: [FRIAM] square land math question

OK with me. Unlike you, Jon, I don't assume my reader is a graduate level mathematician. Did you see my discussion of infinite series? That was approximately sophomore level. When Cody said that limits were a mysterious or magical concept to him I could have launched into a set of formal defini

Re: [FRIAM] square land math question

Well, as I tried to point out, I have a tough time understanding nonstandard math. The actuality of infinities seems to have been handled by Cantor and infinitesimals seem to have been fully justified by Conway and Robinson. But I don't understand much about *how* they built up that infrastructu

Re: [FRIAM] square land math question

How about, "Points are maps from terminal objects?" -- 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/list

Re: [FRIAM] square land math question

Yes! That is of interest. I've been trying to understand a claim I've heard that *actual* infinities are required for full 2nd order math. I.e. potential infinities (which I suppose are necessary for intuitionism and/or program-as-proof) limit the 2nd order operators you can use. I shouldn't be

Re: [FRIAM] square land math question

On 7/23/20 10:47 AM, Frank Wimberly wrote: > In R2 a point is an ordered pair.  How can (1,1) be decomposed into > other points. > > I am correct, goshdarnit.  When I was about 9 I said that word in the > presence of my Southern Baptist grandfather.  He said, "Say Goddamit.  > It means the same th

Re: [FRIAM] square land math question

Well, at least in this post, you *try* to define things such that you'd be right. Although normally considered a rhetorical fallacy, programming into the premises the conclusion you seek is a perfectly reasonable thing to do in math. As long as you actually *do* it ... make the definitions, then

Re: [FRIAM] square land math question

Glen - > Ha! I can't pardon the tone because the authority is simply wrong. Besides, > asserting such things with no justification is not merely a tone. Can you unpack that in the light of Euclid's definition of a point, to whose authority I presume Frank was deferring/invoking. I'm curious if

Re: [FRIAM] square land math question

maybe of interest: In the 1630s, when the Roman Catholic Church was confronting Galileo over the Copernican system, the Revisors General of the Jesuit order condemned the doctrine that the continuum is composed of indivisibles. What we now call Cavalieri’s Principle was thought to be dangerous

Re: [FRIAM] square land math question

In R2 a point is an ordered pair. How can (1,1) be decomposed into other points. I am correct, goshdarnit. When I was about 9 I said that word in the presence of my Southern Baptist grandfather. He said, "Say Goddamit. It means the same thing and it sounds better." On Thu, Jul 23, 2020 at 10:

Re: [FRIAM] square land math question

> So, we’ve finally come to the essential question: > >   > > How many points can dance on the head of a point? > We've come full circle again... https://friam-comic.blogspot.com/2017/10/truthiness-games.html - . -..-. . -. -.. -..-. .. ... -..-. . .-. . FRIAM Applied Complexity Group

Re: [FRIAM] square land math question

Ha! I can't pardon the tone because the authority is simply wrong. Besides, asserting such things with no justification is not merely a tone. On 7/23/20 9:28 AM, Frank Wimberly wrote: > points are indivisible.  Pardon the tone of authority. > > > On Thu, Jul 23, 2020 at 10:12 AM uǝlƃ ↙↙↙

Re: [FRIAM] square land math question

larku.edu/nthompson/> https://wordpress.clarku.edu/nthompson/ From: Friam On Behalf Of Frank Wimberly Sent: Thursday, July 23, 2020 10:28 AM To: The Friday Morning Applied Complexity Coffee Group Subject: Re: [FRIAM] square land math question points are indivisible. Pardon the tone

Re: [FRIAM] square land math question

points are indivisible. Pardon the tone of authority. On Thu, Jul 23, 2020 at 10:12 AM uǝlƃ ↙↙↙ wrote: > But a *relevant* question for me is whether or not you can divide an > infinitesimal point into an infinity of points? My *guess* is that a point > divided an infinite number of times is li

Re: [FRIAM] square land math question

But a *relevant* question for me is whether or not you can divide an infinitesimal point into an infinity of points? My *guess* is that a point divided an infinite number of times is like a power set and is a greater infinity than the point, itself. But I still haven't read a book I bought awhi

Re: [FRIAM] square land math question

I'm surprised EricC didn't say "it all depends on the definition of 'square'". I regard a point as a degenerate square (also a degenerate sphere, cube, etc.). It's the same sort of object as the empty set or an identity like 0 (for +) or 1 (for *). If all we need for a square is an object with

Re: [FRIAM] square land math question

The point is there is no way to partition a square into two squares. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Thu, Jul 23, 2020, 9:17 AM Frank Wimberly wrote: > Right. When its area reaches zero it's not a square. That is, there is > only one

Re: [FRIAM] square land math question

Right. When its area reaches zero it's not a square. That is, there is only one square then. --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Thu, Jul 23, 2020, 9:10 AM Edward Angel wrote: > Why would you call the limit of the increasing smaller squa

Re: [FRIAM] square land math question

Why would you call the limit of the increasing smaller squares a “square”? Would you still say it has a dimension of 2? It has no area and no perimeter. In fractal geometry we can create objects with only slightly different constructions that in the limit have a zero area and an infinite perimet

Re: [FRIAM] square land math question

p.s. Zeno's Paradox is related to 1/2 + 1/4 + 1/8 +... = Sum(1/(2^n)) for n = 1 to infinity = 1 (Note: Sum(1/(2^n)) for n = 0 to infinity = 1/(1 - (1/2)) = 2) --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Wed, Jul 22, 2020, 8:49 PM Frank Wimber

Re: [FRIAM] square land math question

Incidentally, people are used to seeing limits that aren't reached such a limit as x goes to infinity of 1/x = 0. But there are limits such as limit as x goes to 3 of x/3 = 1. The question of the squares is the latter type. There is no reason the area of the small square doesn't reach 0. On Wed

Re: [FRIAM] square land math question

This is a Zeno's Paradox styled challenge, right? I sometimes describe calculus as a solution to Zeno's paradoxes, based on the assumption that paradoxes are false. The solution, while clever, doesn't' work if we assert either of the following: A) When the small-square reaches the limit it stops

Re: [FRIAM] square land math question

Off the top off my head. As long as the small square isn't of zero area the larger square isn't a square. When the smaller square reaches area zero there is only one square. What do you think? --- Frank C. Wimberly 140 Calle Ojo Feliz, Santa Fe, NM 87505 505 670-9918 Santa Fe, NM On Tue, Jul 2