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Date: Sun, 9 Jul 2017 04:55:10 -0700 (PDT)
From: guskant <gusni.kantu@gmail.com>
To: lojban <lojban@googlegroups.com>
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Subject: [lojban] Re: bridi mathematics
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Le samedi 8 juillet 2017 22:07:17 UTC, Vincent Broman a =C3=A9crit :
>
> coi guskant
>
> I agree that part of PA3 is reducible.
> The "fihu" and "cehi" are not very productive, and several others could b=
e=20
> dispensed with, but at a cost in verbosity.
> Peano showed how all arithmetic could be reduced to "pa", "sumji", and=20
> "pilji", and the later two could be reduced to just "baihei".
> Still I'm disposed to see the convenience of most of PA3 for practical=20
> purposes in constructing numbers.
>
> The distinction between common functions in VUhU and more technical=20
> functions in brivla preserves the old grey area where you debate about ho=
w=20
> common or how technical each cmavo is, but you still have to support both=
=20
> kinds of functions separately.=20
> I wished to push the limits, to see how much can be done with the least=
=20
> means.
> Every part of speech has a complexity cost and has to justify the cost=20
> with expressive productivity.
> VUhU looked disposable.
>
> Vincent Broman mihe bremenli
>
>>

Yes, VUhU and PA3 are disposable. I appreciate using bridi math for all=20
expressions of math. VUhU math is still worth preserving especially when it=
=20
is applied to non-math objects.

Let us consider the following examples parsed by an experimental grammar.

[1. VUhU math in non-math sumti]
la galaksis cu gunma lo gei papa vei repimu suhi jonai vuhu papimu tarci .i

[2. VUhU math for counting non-math objects]
lo tarci cu gei papa vei repimu suhi jonai vuhu papimu mei .i

[3. bridi math in non-math sumti]
la galaksis cu gunma lo tarci noi zilkancu lo nihai dektefpihi lo nihai=20
sumji jonai se sumji li repimu li papimu kei li papa .i

[4. bridi math for counting non-math objects]
lo tarci cu zilkancu lo nihai dektefpihi lo nihai sumji jonai se sumji li=
=20
repimu li papimu kei li papa

#note 1. The above statements are parsed by zantufa=20
(http://guskant.github.io/gerna_cipra/zantufa-1.9999.html ) only. The=20
official grammar of mekso doesn't permit even those natural expressions.
#note 2. {zilkancu SUMTI} in the examples of bridi math may be replaced by=
=20
{me SUMTI (mehu) mei}, just like {zilkancu li PA} that may be replaced by=
=20
{PA mei}. The definition of {PA mei} and its difference from {zilkancu li=
=20
PA} are mentioned here:=20
https://mw.lojban.org/papri/gadri:_an_unofficial_commentary_from_a_logical_=
point_of_view#Inner_quantification=20
.

Syllable count:
VUhU expression: 47
bridi expression: 79
ratio: 0.59

Discussions.
1.=20
Besides the syllable count, the important thing for the language being=20
practical is the simpleness of structure that will help listeners'=20
understanding of the meaning. The bridi math requires three layered=20
sub-clauses in the example 3, two layered sub-clauses in the example 4,=20
while the VUhU math requires only one {vei} clause both in the examples 1=
=20
and 2. The difference comes from the fact that VUhU math {gei papa vei=20
repimu suhi jonai vuhu papimu} is grammatically separated from the non-math=
=20
parts of the statements, while bridi math is naturally merged in the=20
non-math structure.

Using the bridi math is quite meaningful for expressions of pure math.=20
However, more layers of sub-clauses are used, more difficult for listeners=
=20
to grasp the structure of the statement. That annoyance is remarkable=20
especially in non-math statements.

2.=20
{zilkancu SUMTI} in the example 3 and 4 may be replaced by {me SUMTI (mehu)=
=20
mei}, but the number of layers will be augmented by {me ... mehu}. The VUhU=
=20
structure of the official grammar has the same annoyance because it does=20
not permit VUhU math in MOI structure without {me li ... (loho mehu)}.=20

However, as I have already pointed out in the last message, the grammar=20
around VUhU can be much simpler as shown by Zantufa grammar. If you accept=
=20
that simplification, then the VUhU math can be harmonized with MOI=20
structure as shown in the example 2, which seems to me not so abominable as=
=20
the official VUhU math.

mihe la guskant
=20

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<div dir=3D"ltr"><br><br>Le samedi 8 juillet 2017 22:07:17 UTC, Vincent Bro=
man a =C3=A9crit=C2=A0:<blockquote class=3D"gmail_quote" style=3D"margin: 0=
;margin-left: 0.8ex;border-left: 1px #ccc solid;padding-left: 1ex;"><div di=
r=3D"ltr">coi guskant<br><br>I agree that part of PA3 is reducible.<br>The =
&quot;fihu&quot; and &quot;cehi&quot; are not very productive, and several =
others could be dispensed with, but at a cost in verbosity.<br>Peano showed=
 how all arithmetic could be reduced to &quot;pa&quot;, &quot;sumji&quot;, =
and &quot;pilji&quot;, and the later two could be reduced to just &quot;bai=
hei&quot;.<br>Still I&#39;m disposed to see the convenience of most of PA3 =
for practical purposes in constructing numbers.<br><br>The distinction betw=
een common functions in VUhU and more technical functions in brivla preserv=
es the old grey area where you debate about how common or how technical eac=
h cmavo is, but you still have to support both kinds of functions separatel=
y. <br>I wished to push the limits, to see how much can be done with the le=
ast means.<br>Every part of speech has a complexity cost and has to justify=
 the cost with expressive productivity.<br>VUhU looked disposable.<br><br>V=
incent Broman mihe bremenli<br><blockquote class=3D"gmail_quote" style=3D"m=
argin:0;margin-left:0.8ex;border-left:1px #ccc solid;padding-left:1ex"><div=
 dir=3D"ltr"><blockquote class=3D"gmail_quote" style=3D"margin:0;margin-lef=
t:0.8ex;border-left:1px #ccc solid;padding-left:1ex"><div dir=3D"ltr"><p></=
p></div></blockquote></div></blockquote></div></blockquote><div><br></div><=
div><br></div><div>Yes, VUhU and PA3 are disposable. I appreciate using bri=
di math for all expressions of math. VUhU math is still worth preserving es=
pecially when it is applied to non-math objects.</div><div><br></div><div>L=
et us consider the following examples parsed by an experimental grammar.</d=
iv><div><br></div><div>[1. VUhU math in non-math sumti]</div><div>la galaks=
is cu gunma lo gei papa vei repimu suhi jonai vuhu papimu tarci .i</div><di=
v><br></div><div>[2. VUhU math for counting non-math objects]</div><div>lo =
tarci cu gei papa vei repimu suhi jonai vuhu papimu mei .i</div><div><br></=
div><div>[3. bridi math in non-math sumti]</div><div>la galaksis cu gunma l=
o tarci noi zilkancu lo nihai dektefpihi lo nihai sumji jonai se sumji li r=
epimu li papimu kei li papa .i</div><div><br></div><div>[4. bridi math for =
counting non-math objects]</div><div>lo tarci cu zilkancu lo nihai dektefpi=
hi lo nihai sumji jonai se sumji li repimu li papimu kei li papa</div><div>=
<br></div><div>#note 1. The above statements are parsed by zantufa (http://=
guskant.github.io/gerna_cipra/zantufa-1.9999.html ) only. The official gram=
mar of mekso doesn&#39;t permit even those natural expressions.</div><div>#=
note 2. {zilkancu SUMTI} in the examples of bridi math may be replaced by {=
me SUMTI (mehu) mei}, just like {zilkancu li PA} that may be replaced by {P=
A mei}. The definition of {PA mei} and its difference from {zilkancu li PA}=
 are mentioned here: https://mw.lojban.org/papri/gadri:_an_unofficial_comme=
ntary_from_a_logical_point_of_view#Inner_quantification .</div><div><br></d=
iv><div>Syllable count:</div><div>VUhU expression: 47</div><div>bridi expre=
ssion: 79</div><div>ratio: 0.59</div><div><br></div><div>Discussions.</div>=
<div>1.=C2=A0</div><div>Besides the syllable count, the important thing for=
 the language being practical is the simpleness of structure that will help=
 listeners&#39; understanding of the meaning. The bridi math requires three=
 layered sub-clauses in the example 3, two layered sub-clauses in the examp=
le 4, while the VUhU math requires only one {vei} clause both in the exampl=
es 1 and 2. The difference comes from the fact that VUhU math {gei papa vei=
 repimu suhi jonai vuhu papimu} is grammatically separated from the non-mat=
h parts of the statements, while bridi math is naturally merged in the non-=
math structure.</div><div><br></div><div>Using the bridi math is quite mean=
ingful for expressions of pure math. However, more layers of sub-clauses ar=
e used, more difficult for listeners to grasp the structure of the statemen=
t. That annoyance is remarkable especially in non-math statements.</div><di=
v><br></div><div>2.=C2=A0</div><div>{zilkancu SUMTI} in the example 3 and 4=
 may be replaced by {me SUMTI (mehu) mei}, but the number of layers will be=
 augmented by {me ... mehu}. The VUhU structure of the official grammar has=
 the same annoyance because it does not permit VUhU math in MOI structure w=
ithout {me li ... (loho mehu)}.=C2=A0</div><div><br></div><div>However, as =
I have already pointed out in the last message, the grammar around VUhU can=
 be much simpler as shown by Zantufa grammar. If you accept that simplifica=
tion, then the VUhU math can be harmonized with MOI structure as shown in t=
he example 2, which seems to me not so abominable as the official VUhU math=
.</div><div><br></div><div>mihe la guskant</div><div>=C2=A0</div></div>

<p></p>

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