Some discrepancies in the wiki

Discussion of shapes with curves and holes in various dimensions.

Some discrepancies in the wiki

Postby Kwiitope » Thu Mar 31, 2022 12:31 am

Hello. New member here, although I first stumbled upon this site a few years ago. I thought I had posted this during my lunch break at work but it didn't seem to have "taken." Please forgive my choppiness here as I re-compose this. I'm actually adding a second discrepancy here.

1) (What I tried to post during my lunch break)
From the "Rotatope" article in the wiki ( http://hi.gher.space/wiki/Rotatope ): "Rotatopes of two dimensions or higher also function as expanded rotatopes: a rotatope which is (at its minimal frame) homeomorphic to a set of toratopes of lower or equal dimension." (Notice that there's nothing about open vs. closed toratopes here.)

From the "Expanded rotatope" article in the wiki ( http://hi.gher.space/wiki/Expanded_rotatope ): "The expanded rotatope of a closed toratope is the unique rotatope that is homeomorphic to the toratope." (Emphasis mine)

On the "List of toratopes" in the wiki ( http://hi.gher.space/wiki/List_of_toratopes ), every toratope listed, open and closed, is listed as being homeomorphic to an expanded rotatope.

So what gives? (I also wonder if the the list of toratopes should begin at dimension 0 like the lists of tapertopes and bracketopes, and if the "toratope statistics" table in the "Toratope" article should begin with dimension 1. The fact that there aren't both open and closed rotatopes in those dimensions could make that more complicated though. I'm assuming the line segment/digon is an open rotatope, and probably the point to although maybe the point wouldn't qualify as either open or closed. It would still be a (trivial) rotatope though, right. Everything in this paragraph after the "what gives?" could be considered as issue "1a".)

2) Bracketopic products and bracket notation
The brackets [] in bracket notation are clearly linked to the "rectangular" shapes (or rectangular cross-sections of shapes), the parentheses () to the round shapes and the chevrons <> to the "diamond" shapes. That is assuming the "List of bracketopes" ( http://hi.gher.space/wiki/List_of_bracketopes ) is accurate. But if you look at the references of those symbols to the bracketopic products in the "Bracket notation" article ( http://hi.gher.space/wiki/Bracket_notation ), and then look at the descriptions of those bracketopic products (which are ordered differently) in the "Bracketopic product" article ( http://hi.gher.space/wiki/Bracketopic_product ), the parentheses still go to the circular shapes but the brackets go to the diamond shapes and the chevrons go to the rectangular shapes. So some correction of one of these pages is probably needed. The order being consistent for those two articles would also seem to be ideal (and I'd say brackets before parentheses (since it's bracket notation) before chevrons as in the "Bracket notation" article makes sense).

Okay, that's all for now. Thanks in advance to anyone who can address/respond to this.
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Re: Some discrepancies in the wiki

Postby wendy » Fri Apr 01, 2022 8:59 am

I fixed the paragraphs up to agree with what they should say, as well as added the symbols to the titles.

As to your posts not appearing directly, the first few posts must be approved by a moderator before they are visible. This is to reduce certain problems seen in the past.

Thanks for your attention.
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Re: Some discrepancies in the wiki

Postby Kwiitope » Fri Apr 01, 2022 4:27 pm

Okay, thanks. I think the chevrons go with max and the diamond shapes, though, while the brackets go with sum and the rectangular shapes. That's what it says in the so far unchanged "Bracket notation" article ( http://hi.gher.space/wiki/Bracket_notation ) and the actual text on the sections in the "Bracketopic product" article ( http://hi.gher.space/wiki/Bracketopic_product ) as you edited it today. The brackets [] going with square-type shapes and the chevrons going with diamond-type shapes also jives with the "List of bracketopes" article ( http://hi.gher.space/wiki/List_of_bracketopes ).

If I had wiki edit provisions I'd get rid of the "(a,b)", "<a,b>" and "[a,b]" in the section headings, move Sum to the top (since that's the one tied to brackets and is listed first in the "Bracket notation" article), and add a blurb like "Sum is represented by brackets [] in bracket notation." (And similar sentences tying RSS to parentheses () and Max to chevrons <>.) But it won't let me register to edit the wiki for whatever reason.
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Re: Some discrepancies in the wiki

Postby wendy » Sat Apr 02, 2022 1:13 am

The choice was meant to represent the regular solid derived from it, thus [cube] (sphere) <octahedron>.
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Re: Some discrepancies in the wiki

Postby Keiji » Fri Apr 08, 2022 9:11 pm

Welcome to the community, Kwiitope!

I've had a look at the two pages before and after Wendy's latest edits.

Sum is tegmal, i.e. diamond shaped, and uses chevrons < > . If you graph abs(x) + abs(y) = 1, you get a diamond. https://www.wolframalpha.com/input?i=ab ... 28y%29%3D1

Max is square, and uses brackets [ ]. If you graph max(abs(x), abs(y)) = 1, you get a square. https://www.wolframalpha.com/input?i=ma ... %29%29%3D1

This was stated correctly on the bracketopic product before Wendy's edit, which swapped them, so I've reverted the edit, but I have added the bracket notation for each to the page.

Meanwhile, I had indeed gotten them the wrong way round on the bracket notation page when I first created it, and this remained wrong ever since, until Wendy's edit, which corrected them. So that edit rightfully stays. But, to make it less confusing, I've reordered them on this page to match the order used on the bracketopic product page.

I think the difference in order simply came from the fact that to me, when talking about the operations, "rss, sum, max" seems like the natural order, while when talking about punctuation, "brackets, parentheses, chevrons" seems like the natural order.
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Re: Some discrepancies in the wiki

Postby Klitzing » Fri Apr 08, 2022 10:03 pm

<>   or   "sum"   is just the   ||.||1 norm
()   or   "rss"   is just the   ||.||2 norm
[]   or   "max"   is just the   ||.||oo norm

--- rk
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Re: Some discrepancies in the wiki

Postby Keiji » Fri Apr 08, 2022 10:15 pm

Indeed they are!

Though I would argue that these three norms deserve their special names, compared to all the other norms > 2 and < ∞.
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Re: Some discrepancies in the wiki

Postby wendy » Sun Apr 10, 2022 7:45 am

When the crind product became available, the general proposition of \(\sum x_i^n=r^n\) was considered. Most of the shapes are not the sort of things people considered anyway, but the lingering suspicion is that they could all represent coherent products (in the sense of the product of the volumes is the volume of the product).

In any case, it's a painful thing to have to support out in the field, and so we cut it back to simply the regular solids (ie cube, sphere, octahedron). Two of these aready give in-use units, eg square-inch vs circular inch, and the volume of the simplex corner inside a sphere is somewhat between 1 and \(\sqrt{n/4}\) tegum-radii.

Fun fact, a sphere of radius 1 has the surface and volume equal in tegum-units.
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Re: Some discrepancies in the wiki

Postby Kwiitope » Mon Apr 11, 2022 2:54 am

After getting wiki edit privileges but before checking this topic for replies, I swapped the order from rss/(), sum/<>, max/[] to max/[], rss/(), sum/<> in both articles (and then noticed I had missed the opening sentence in the bracketopic product article so I fixed that too. But if Keiji or anyone else wants to change the order back (provided they do so consistently and correctly, like Hayate/Keiji had done in his edits on Friday, I'm fine with that and won't change it again. Not being as familiar with the bracketopic products themselves, I went with my sense of natural order in punctuation, which was the same as Keiji's (I'd normally put parentheses before brackets but the title of the notation puts brackets ahead by a nose; chevrons definitely would go last) although he prioritized what he saw as the natural order of the bracketopic products, which probably makes more sense. But what good are wiki edit privileges if I can't have the two articles they way that seems best to me at least once? :D
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