Polygloss

Higher-dimensional geometry (previously "Polyshapes").

Polygloss

Postby wendy » Tue Jan 18, 2005 2:34 pm

I found this forum while googling for the word "polyteron".

The word (like polypeton, polyecton, polyzetton and polyyotton) is one of my inventions. See my online dimension-dictionaly, the polygloss.

http://www.geocities.com/os2fan2/gloss/index.html [FIXED] [DEAD]

http://www.os2fan2.com/gloss/index.html "The thornless polygloss"

http://www.os2fan2.com/glossn/index.html "The polygloss as nature intended"

It is currently being rewritten to include new ideas.

W
Last edited by wendy on Tue Jan 18, 2005 11:51 pm, edited 1 time in total.
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Postby Keiji » Tue Jan 18, 2005 5:11 pm

Sorry, the page you requested was not found.


Try fixing that first :P
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Postby Paul » Tue Jan 18, 2005 5:57 pm

Hello again Wendy,

Perhaps you were unaware that we already have quite an extensive online Multidimensional Glossary for Hyperspace.

I think you'll find George Olshevsky has put allot of work into his glossary, as he has his many online reference resources.

I've found his glossary, and other online reference resources, like his Uniform Polytopes in Four Dimensions website, most helpful... and I think we're greatly indebted to people like George Olshevsky who make these extensive resources available to everyone... for free.
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Postby wendy » Tue Jan 18, 2005 10:47 pm

The correct addy is http://www.geocities.com/os2fan2/gloss/index.html

I am aware of George's work. It's a pretty good reflection of current usage, but the patterns of current usage does not work that well when you hit six dimensions.

For example, you have "polyhedron" where 'hedron' refers to 2D, but "dihedral" where "hedron" refers to 5D.

The polygloss is considerably more entries in it than George's work (not that i am disparaging his work: he did a good job, just the standard notation is pretty awful)

<wonder if anyone else has filled the list with their own responses?>
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Postby wendy » Sat Jan 22, 2005 10:36 am

A new version of the polygloss is released.

http://www.geocities.com/os2fan2/gloss/index.html

A down-load zip-version is available as

http://www.geocities.com/os2fan2/gloss/gloss.zip

This is a zip-inside-a-zip, which reduces the ordinarily 140k zip to 100k.
The inside zip is called inside.zip.
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Postby Paul » Sat Jan 22, 2005 6:49 pm

Hello Wendy,

How long did it take you to make up your glossary? Did you do it alone?
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Postby wendy » Sat Jan 22, 2005 11:58 pm

The thing you need to understand about the polygloss vocabulary, is that it is intended to make a context-free vocabulary.

The implementation of the PG is mine (ie typing it up). The decisions on what words to use, and what meanings are mine too. I make and pick up lots of tidbits, and see patterns in it. I don't make all the geometric facts, but i try to credit the makers as they come to mind.

I do use other people's names for things, such as stott-vectors, dynkin-matrices, etc, largely because these are natural consequences of deep insights these people had.

One can easily set up a context-system: introduce what j- and k-faces mean, and then talk of j and k faces. The vocabulary of the polygloss, and george's multidimensional glossary are meant to be context-free. That is, you can talk about 'angulochora' or 'aperizetton' and be perfectly understood without contexts.

My polytope stuff is home-grown since the late seventies. I only started to talk with other people in 2000, so the conversation is more of the nature of a talk of equals of different background, rather than teacher/student.

Having seen the current terminology, which George Olshevsky's glossary does a good job of, i decided to document a proposal for the new one.

The basis of the polygloss is an amipro dictionary that i wrote one boxingday. Exporting George's dictionary to pdf format was a bit of an eyeopener, and eventually, i worked here and there (off, off and on) to get the pg into a huge 250k hand-typed pre-markup, which i run through a rexx script to get the web-pages (54 at the mo).

I don't spend a lot of time -on- the gloss, but i do spend a bit of time -using- the gloss.

Something tells me it's about 50% done! There is a lot more stuff i want to put in there, such as descriptions of the Complex Euclidean spaces. the hyperbolic universe in a nutshell, the nature of the hyper-euclidean geometry of the horizon, and a whole lot more.
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Postby wendy » Thu May 12, 2005 3:50 am

Hi

I had a shot at translating the local dictionary into PG style words. This is really important, if you want to have a robust vocab. There are some ideas here that are not in the current PG.

Note some words are still valid under the PG, but one can give precise meanings by using the technical form:

For example, a "glomohedrix" is a hedrix (2-cloth) shaped in a globe. It refers to the *surface* of a 3-sphere. A glomohedron is a figure *bounded* by a glomohedrix.

Current elements to work on in the PG, based on the present list are as follows.

1. A word meaning "solid in x dimensions".

2. A generic class member for the /hedr/ series. ie, one that means "n dimensional". This would allow translation of the meanings of hypercube and hypersphere here.

Both of these can be solved by dividing /solid/ into /sol/ + /id/. So one has a hedrid = solid in two dimensions. Idiomatic usages of these are to be considered.

3. A generic word or words, to give dimensionality of the tip of a ray. Among the meanings of this word, we find 'hole', 'gully' and 'chasm', but the PG goes to 8d.

4. The use of -bour (being = resident) with stems, eg hedrobour = 2d dweller

The current list is standing at

1. /sol/, such as solid is 'solid in n dimensions'.
cf areas of solid black = 2d.
2. -id eg chorid = solid in chorix (3d)
3. [still awaits formal conseration]
4. bour eg we are chorobours (3d dwellers).


Code: Select all
http://tetraspace.alkaline.org/glossary.htm

  ana        direction +4
  apos       most-direction +4
  area       2-content  =  hedrage
  backwards  direction -3
  ball       glomochoron
  bionian    hedrixbour  (one who lives in a hedrix)
  bulk       4-content = terage
  cardinal directions [different idioms]
             east   west   north   south   garp  marp
             east   west   trop    art
  cell       surchoron
  chasm      2-groove
  circle     glomolatron: sa [disk]
  column     row/column/pillar are arrays in 3 successive directions
  cone       glomolatral pyramid
  crind      <unnamed polyhedron = intersection of 2 cylinders>
  cube       prismos polyhedron
  cubinder   square-circle prism
  delta      direction -4
  direction   [different idioms]
             1   x   left / right
             2   y   down / up
             3   z   back / forward
             4   w   kata / ana  or delta / upsilon or zant / wint
  disk       glomolatron
  dbl rotat  bi-axial rotation, clifford-rotation
  down       direction -2
  duocylinder bi-circular prism
  east        cardinal +1  (against the daywards)
  edge        surlatron  [same meaning]
  equator     [different idiom]
  extrude     make a slab-prism of
  face        surhedron
  fune        planoterix, terix [when no confusion exists]
  garp        cardinal (aganist the yearwards)
  glome       glomochorix
  gongyl      glomochoron
  gully       3-groove
  hole        1-groove  / 2=chasm / 3=gully
  hypercube   prismos polytope
  h,cylinder  <the meaning is not clear here>
  hyperplane  plano - ix
  hypersphere glomo - on
  kata        direction -4
  laptitude   cardinal in the yearward direction
  latitude    cardinal in the climata directions
  laver       a 2-river
  left        direction -3
  line        planolatrix
  linear      long in one direction
  linespace   latrix
  longitude   cardinal in the dayward direction
  multiverse  a set of universes
  north       articwards
  omniverse   all universes in existances
  pentaspace  petix
  perimeter   perilatron.
  pillar      row in direction 3
  planar      falling in the same planohedrix
  planespace  hedrix
  polar equator  artic ring
  pole        =
  polychoron  (borrowed)
  polygon     polylatron
  polyteron   polyteron
  polytope    polytope
  realm       chorix
  realmic     chorical
  realmspace  chorix
  right       direction -3
  rotachoron  a product of glomotopes, including glomoteelons
  rotagon
  rototope    (table)
  row         1-row   also, column, pillar
  sheet       flexi-hedrix
  skring      <meaning not clear>
  solar equator = tropic circle
  south        towards the tropic circle
  sphere       glomohedrix   glomohedron = ball
  spherinder   glomohedral slab-prism
  sphone       glomohedral peakpyramid
  square       prismos polylatron
  string       flexi-latrix
  surcell      surchorix
  swirl        clifford-rotation
  swock        flexi-chorix
  tarrow       narrow 4
  teron        surteron
  tesseract    prismos polychoron
  tetral       teric
  teraspace
              n-space    latrix  hedrix  chorix  terix  petix
              n-plane    latrix  hedrix  chorix  terix  petix
              adject     latric  hedric  choric  teric  petic
  tetrealm     (plano)terix
  tetronian    terix-bour
  trength         1        2      3        4
              length   width    height  trength
              short    narrow   short   tarrow
              long     wide     tall    trong
  trionian    chorixbour
  universe    <unchanged>
  up          direction +2
  upsilon     direction +4
  vertex      surteelon
  volume      chorage
  west        with the day
  wint        direction -4
  zakos       zenith kata
  zant        direction +4
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Postby pat » Thu May 12, 2005 5:40 am

wendy wrote:For example, a "glomohedrix" is a hedrix (2-cloth) shaped in a globe. It refers to the *surface* of a 3-sphere. A glomohedron is a figure *bounded* by a glomohedrix.


Hmmm... I'm assuming since you say 2-cloth, that the "glomohedrix" is the surface of a 3-ball. That is, a glomohedrix is what topologists call a 2-sphere. And, a glomohedron is what topologists call a 3-ball (actually, the glomohedron would be a 3-ball plus its limit points).

Yes? No?
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Postby wendy » Thu May 12, 2005 11:45 am

Most of my stuff is home grown.

hedrix is a 2-cloth. glomo- makes it into a sphere-shape. So a glomohedrix is what might be called S2. Note however, that i use it for S2 as all-space and S2 as subspace indifferently.

hedron is a 2-patch. Because we have "polyhedron" = "many 2-patches with closure", it follows that "glomohedron" should refer to the thing that a glomohedrix closes.

In practice, one regards the surface as part of the interior and exterior. So a glomohedron = skin + innards of a 3-sphere, which can not act as an isospace (eg S2 or E3)

Also, in any space, any sphere of lesser curvature can be made a solid thing, like a ball in 3d. In this way, we can translate sphere into two close, but distinct words "glomohedrix [no content] and glomohedron [content]

If you are wondering why i translate into PG, the polygloss has to survive 8 dimensions.

So here one might have to extend the hole / chasm / gully thing to eight terms, or find a regular way of doing this. I do the latter. So i have to write words for teelous / latrous / hedrous / chorous dint, such as made by an object having a 0, 1, 2 or 3 d tip. This extends to 8 dimensions, eg a yottous dint [8d dint].

There are also idomatic issues. The difference between hedrous and hedric is that the latter is always flat, while the latter has a thickness in other dimensions. A slab of foam is hedrous (large extentions in 2d), not a hedrid [entirely flat in 2d].

W

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Postby Keiji » Thu May 12, 2005 3:16 pm

Correct me if I'm wrong, but ~gon is 2d, ~hedron is 3d, and ~choron is 4d... :?
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Postby wendy » Thu May 12, 2005 11:07 pm

The segments for 0d and 1d used to be highly irregular (eg vertex / edge / surhedron / surchoron / surteron ...), but the number of forms on the regular basis expanded so rapidly that a regular form was needed.

The stem -gon means knee, in polytopedom, means "vertex". isogonal means "having identical vertices", the dodecahedron is isogonal.

Attempts have been made to replace polygon (a vertex-count) with something like poly(edge) as a facet-count. This is been done in Germany many times.

In any case, neither "line" nor "edge" passes for the various meanings that a 1d hedron-class stem is put to in the PG, the formal reccomendation is for a new word, ultimately derived from "quadralateral". The etymological backform 'latr' was adopted.
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Postby Eric B » Sun Jul 31, 2005 4:01 am

On the Polyhedron e-mail discussion; I had suggested a few moths ago using "apeirotope" (apeirogon, apeirohedron, apeirochoron, etc). to denote circles, spheres, hypserspheres, etc. Currently, "apeiro-" is only used for flat infinite tilings of d-1 spaces. I had reasoned that this "open" surface would be the result if you fixed the lingth of a facet and increased the number of facets to infinity. Yet, if you fixed the radius instead, you would get a "closed" circle, sphere, etc.
Wendy objected to this, saying that "apeirootope" should have only the one meaning, and circles, spheres, etc. could be called "infinitopes", or something. I objected that this was using an English/Latin prefix, instead of Greek.

What I had forgotten, was that before I had even discovered Polygloss, I had found on this multiligual dictionary: http://www.kypros.org/cgi-bin/lexicon, after looking up what "infinity" would be in Greek, the word "apeiro". That is why I instantly recognized it in Polygloss and Polycell. But there was also another word, achanes. I remember wondering which one would be better. Apeiro sounds better, and that seems to be what was chosen here. But perhaps my ideas of the circles and spheres as infinite-faceted polytopes could be called achanetopes? (circle=achanegon, sphere=achanehedron, hypersphere=achanechoron), while "apeiro" would remein for the open tiles surfaces?
(Then, "panda-" was also supposed to be infinity as well.)
What does everytone think of this?
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Postby wendy » Sun Jul 31, 2005 11:13 pm

There are many useful meanings for the concept of infinity. It does little to call both a infinitely sided polygon of vertex-angle (1 radian), and the infinite straight line by the same name (apeirogon).

The polygloss is not so much about "inventing words", but inventing etymological stems. While i try to maintain a classic 'latin/greek' feel in the thing, one must understand that the romans borrowed lots of greek idioms, and used them as if latin words. Likewise, English borrowed many words from many languages, (skip, pork, ham, egg, school, kitchen, church, cathedral) and used them as if they were english words.

The process of taking a word and assigning it one particular meaning (such as german Gift 'poison', from base meaning 'something given') is not new.

The PG is intended to mean a technical vocabulary, not one to ponder over in a literary one. That is, it is intended for use by people not well versed in etymological constructions, but it draws on the power and history of etymology to stabilise its vocabulary.

To this end, there are two useful meanings of endless: without perimeter, and without end of counting. Since we already have words

perimeter, periphery to refer to a boundary,

we then add the greek prefix a- (without), to get aperi- (without boundary).

We also have a latin word 'infinito' meaning "without finish", this being used to form numbers. Since there is a useful distinction between boundless (ie a tiling), and countless (without end of number), the PG makes it by using already existing words aperi- and infiniti-.

One might also understand that there are boundless tilings that are not infinite in number. One of the three branches of iso-geometry (spheric geometry), has boundless tilings with a finite number of cells. There are also modular geometries that feature finite apeirotopes.

The distinction between infinitotopes and apeirotopes is further pressed when one considers that in hyperbolic geometry, one can have an infinite sided and sparse polyhedron, like {8,3}, that is not by any means a tiling. It none the less can feature as a cell of the infinite apeirochoron [boundary-less 3d cells] {8,3,4} or {8,3,5}.

The PG is quite clear on what a perimeter is. A perimeter divides the inside from the outside of a polytope or multitope, the division to occur in the space where the polytope is solid.

So if one draws a pentagon on the surface of a sphere, the space where the pentagon is solid _is_ the surface of the sphere. The perimeter divides the bits of the pentagon from the bits not part of the pentagon.

You can make a multitope (or many surtopes without closure), by adding several pentagons together. The multitope still has a perimeter. (where there divides points in a cell from points outside it). When one completely covers the sphere, there is without boundary. If the closure happens to make a polytope, it is one "without a perimeter", or 'aperi-' [which is greek for 'without perimeter'.

This is why i use /peri/ and /aperi/ only to designate perimeters and tilings.

The PG also distinguishes between "surface" and "perimeter". A perimeter lies between inside and outside, while a surface exists where there is a gradient of density. Surfaces can cross, and the equations for surface are not affected by this definition. The surface of a polytope is the collection of the surtopes, some of which may be interior, but the perimeter is always the solid limit of the polytope (ie where points outside the perimeter are always outside all surfaces).

There are, in six and eight dimensions, way too many different ideas for one to start hassling about using the same 3d word indeterminately for ideas that will in 6d be separated by many dimensions.

I do make my decisions wisely, and welcome comment on these things, none the same.

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Postby Eric B » Tue Aug 02, 2005 2:58 am

OK, so "aperi" means"without perimeter". Still, the question then is what is "achanes" without? I will try to look it up. (So far, I can find neither "chan-" nor "achan-"in the Greek Bible dictionary. Will have to look online). But all the more, it would lead to my suggestion of using this for infinite sided objects. (I know "pan-" is "all", though, so this doesnlt really fit that well either).
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Postby Eric B » Tue Aug 02, 2005 3:55 am

According to this page: http://www.quantavolution.org/vol_13/fi ... own_16.htm, "achanes" is "roofless". There's some place in the Knossos named this.
According to this page: http://www.geocities.com/therapeuter200 ... cs333.html, it seems to mean "yawning". (I take it "chasm" is "gap"). So it just seems to mean "large without bound", and this is basically similar to "aperi". If no word conveying "endless in number" can be found; I would say to still use achane, because at least it still distinguishes from the term you have chosen for perimeterless tilings.
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Postby wendy » Tue Aug 02, 2005 4:14 am

I am not really on the lookout for a word for infinity, because it makes me no sense. Much confusion is caused when people equate differing infinities, when these have clearly different meanings. It is like 'far away'. We have also the silly cantor-infinities, which can easily be proven to be self-in-error.

In any case, the nature of infinity is unproven, and it serves well to avoid it. Some models exist where infinity is 71.

The approach taken is to look at what remains finite: for example, consider the PG entries like "peice-wise finite", "discrete", and a number of entries under "peicewise" [except "~ constructable"], all of which deal with what would elsewise be infinities.

None the same, the PG provides infinito- as a stem, which allows for people who feel the need for it. As with you, i am not overfussed with the word.

It is also worth the recall that neither the Latins nor the Greeks wondered around in 4d, and the borrowings from these languages has more to do with what happened in 535 than that these people were wizzards at what they do.

I normally wrangle in six dimensions, because in there things are much clearer, and the notion that the same stem holds true for two and five, or three and six, is somewhat obscene. Since i want to set up a system of essentially self-defining words, it is very much with care i pick what words mean.

Even words like 'delineate' come under question: delineate is about setting borders for something, which for animals that walk at the bottom of a 3d ocean of air, happen to be 1d (or lines). So the reccomended PG idiom is 'demark' (which means to set out marks, [PG = N-2 dimensions].

The dictionary from this site has been looked at for ideas, i borrowed the notion of -id / -ous from here [ hedrid = solid in 2d, hence flat elsewhere], vs [hedrous = lumpy hedrid.] Likewise, we have 'glomous' being globish, in the sense of 'topologically globe-shaped'.

The PG isn't about giving polytopes names, either. I do name a few here and there, and some considerations exist for extending these, but for the main, some other symbol stands for the name.

It should also be borne in mind that i use a different base (twelfty), so the idea of naming polytopes by their face-counts do not me curry favour. Something that in decimal might have 576 sides, might in twelfty have 496 sides. There are entries that have entries like (twe: 3:16E8 E2 ...), or (dec: 3.14159...), which convert numbers into twelfty and decimal. Some calculations are still done only in base 120.

A name like 'twelftychoron' is fairly base-neutral, since it is 12ty, or 120. while the name 'fifhundchoron' is 500, twelftywise = 600 decimal.

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Postby wendy » Sat Aug 13, 2005 11:57 am

A new version of the polygloss is uploaded. There are no links on the page, because it's only a beta-release.

Anyway. Here goes. It's pretty much thorn-free (ie it does not have þ in it for the most part (except where it comes from `f and `F in the source).

http://www.geocities.com/os2fan2/pglossth.zip

It's currently an interim release.

Added some new words and ideas.

radiant field, radial function, radial product, tegum product , prism product, torus, torus product, pyramid product, comb product, coherent, spheric product, sphere.

Not much work has been done on the rest of it, but some themes have been extended,

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Postby quickfur » Sun Aug 14, 2005 10:30 pm

wendy wrote:A new version of the polygloss is uploaded. There are no links on the page, because it's only a beta-release.

Anyway. Here goes. It's pretty much thorn-free (ie it does not have þ in it for the most part (except where it comes from `f and `F in the source).

http://www.geocities.com/os2fan2/pglossth.zip

Nice work, wendy! Unfortunately I won't have much time for the next long while, so it will be a while before I can comment on it.
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Postby wendy » Sat Jan 28, 2006 8:56 am

A new release of the polygloss is out. It's still vers 2, but up to date.

The zip file hight http://www.geocities.com/os2fan2/gloss/pgloss2.zip .

It mainly brings words up to date, and a few interesting ideas from different places. Worþ þe read.

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Re: Polygloss

Postby wendy » Sun Mar 16, 2014 9:39 am

The polygloss is largely updated in the 'reading matter' section. New sections include the circle (for pi-day), up and down (based on talking to Anton Sherwood), and a few other random stuff. I keep a live tape of the very up to date thing, and every now and then update one or the other of the gloss versions. This time it was "as nature intended".

It has a new home, http://www.os2fan2.com/gloss/index.html or http://www.os2fan2.com/glossn/index.html . I just have to fix up all of the links to external sites now.
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