topology: Difference between revisions

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I believe the current prescription is that scope follows left-to-right, except for {na} (or NA?), which has maximally wide scope over the bridi.
*[[jbocre: fractal|fractal]]:Pierre Abbat suggests the word frinyselcimde, which is a reference to the fact that some (most) fractals have a fractional Hausdorff dimension in excess of their topological dimension. (For most objects, the Hausdorff dimension is identical to topological dimension) [[jbocre: Jay Kominek|Jay Kominek]] suggests paursmitai and ci'urtolcne as other possibilities.See the short thread on the Lojban list where this originally came up: [http://groups.yahoo.com/group/lojban/message/7845
**] [[jbocre: cein|cein]] suggests rapli fancu.


This exception is a pointless complication that leads to confusion. It should be done away with. (The only defence of it has come from Nora (on jboske & phpbb), hingeing on the interpretation of nago'i. This is addressed on phpbb & will be recapped on the wiki in due course when we get round to writing up something on the interpretation of bridi anaphora.)
*** I think that that would serve as a lay explanation of fractal, but is a far cry from approximating the mathimatically rigid definition of fractal. In particular, 'fractal'ness applies to objects, not functions, as functions cannot have topological dimension. The fact that you can make fractals by the repetition of some functions is more of a defining property of the function in question, rather than of fractals. -jay
**** ok, ''rapli fancu cartu'' then :) {cein}


The scope rules, then, are as follows:
**** A function can exhibit the self-similarity and nondifferentiability required. Also, Hausdorff dimension is a strange concept and has little to do with the idea of an axis, or even an independent variable in an abstract state space, so I am not sure cimde is the right gismu. --xod''
 
* outer has scope over inner
* for two elements at the same level, either (a) the former has scope over the latter, or (b) they have 'coordinate' scope (defined on [[jbocre: Discussion: Three dogs attacked four men]]). Disambiguation between (a) and (b) is done either by glorking or by BAhE-subord/BAhE-coord.
 
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[[User:xorxes|xorxes]]:
 
We also need to consider the scope of quantifiers in tagged terms with respect to the scope of the tag. There seem to be two options:
 
# Since the term appears to the right of the tag, the tag has scope over the quantifier.
 
# Since the tag is essentially an extension of the selbri, the term's quantifier has scope over the tag (as it does over the selbri too).
 
[[User:And Rosta|And Rosta]]: Are you talking about {PA1 ROI PA2 broda}?
 
[[User:xorxes|xorxes]]: Yes, but it applies to other tags as well. Does {di'i ze broda} mean that the event occurs regularly within each of the seven broda, or that the seven broda are regularly distributed? I think the latter has to be {di'i lo ze broda}, and that {di'i ze broda} gives the former, i.e. {di'i} is within the scope of {ze}, just like the selbri of the bridi this term belongs to.
 
[[User:And Rosta|And Rosta]]: OK. So you prefer Option (2), & I agree (cf. {claxu} = {na ponse} with {na} with narrowest scope). But how does one express the reading where PA1 has scope over PA2? Whereas Option (1) offers an obvious way to express both readings, I'm not sure how Opt 2 would express both.
 
[[User:xorxes|xorxes]]: I'd say either {PA1roi lo PA2 broda}, in which PA2 becomes part of the description of the single interval in question, or {PA1roiku ze'a PA2 broda}, i.e. split it into two terms, where PA2 intervals is under the scope of PA1 times.
 
[[User:And Rosta|And Rosta]]: Okay. Then I can't see any reason for Opt 2 not to win.
 
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pc:
 
It is not clear where comments come in the general scheme of things -- after additions (but when) and before discussion.  In any case (since comments seem presently to be reorded in a black hole), the whole notion of scope needs to be looked at again, probably starting with the logical forms and working backward, since the other approach has led to the present mess.  Ideally, the whole preselbri pack -- and the similar BAI phrases -- should go to the front in order.  But that wreaks havoc with quantifiers and can't generally be cured with something like deMorgan, short of making the most common forms {ku}d to death.  If there is a solution that also solves the independent quantifier problem, so much the better (though I don't see the connection).

Revision as of 17:16, 4 November 2013

  • fractal:Pierre Abbat suggests the word frinyselcimde, which is a reference to the fact that some (most) fractals have a fractional Hausdorff dimension in excess of their topological dimension. (For most objects, the Hausdorff dimension is identical to topological dimension) Jay Kominek suggests paursmitai and ci'urtolcne as other possibilities.See the short thread on the Lojban list where this originally came up: [http://groups.yahoo.com/group/lojban/message/7845
    • ] cein suggests rapli fancu.
      • I think that that would serve as a lay explanation of fractal, but is a far cry from approximating the mathimatically rigid definition of fractal. In particular, 'fractal'ness applies to objects, not functions, as functions cannot have topological dimension. The fact that you can make fractals by the repetition of some functions is more of a defining property of the function in question, rather than of fractals. -jay
        • ok, rapli fancu cartu then :) {cein}
        • A function can exhibit the self-similarity and nondifferentiability required. Also, Hausdorff dimension is a strange concept and has little to do with the idea of an axis, or even an independent variable in an abstract state space, so I am not sure cimde is the right gismu. --xod