Received: from mail-pf0-f183.google.com ([209.85.192.183]:33486) by stodi.digitalkingdom.org with esmtps (TLSv1.2:ECDHE-RSA-AES128-GCM-SHA256:128) (Exim 4.87) (envelope-from ) id 1dTxsp-0007UC-6s for lojban-list-archive@lojban.org; Sat, 08 Jul 2017 15:07:24 -0700 Received: by mail-pf0-f183.google.com with SMTP id v88sf7236626pfa.0 for ; Sat, 08 Jul 2017 15:07:22 -0700 (PDT) DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=googlegroups.com; s=20161025; h=sender:date:from:to:message-id:in-reply-to:references:subject :mime-version:x-original-sender:reply-to:precedence:mailing-list :list-id:list-post:list-help:list-archive:list-subscribe :list-unsubscribe; bh=qGYlklxjm/Q2+K/XAYnK7QHj+dZxXueDdi0jTv6BJ7s=; b=G4iEDQ6nEe5eTKf27jvGanvnfs71NjRn7OwU6hSXbL9dhC9RrurxxndXOf8t5omvE3 Zai1aZJDyfU3rCrQYPwLfA4BTrYRraDa0nj6/c7coccWTDNBIQSLh1iTXooVJ8GFO8ho M5cFMdZ8BoawX+sjdIalXOIim2GxoH8oYmqklcjmyznEUcMbIKCrpKhGSvC/gpMkxoNh jn6DfiJibAcwfgu5hR15pjh8lMXphW173TE6hSbx9WId7+4jtcLNmDFx5Zpu53pxBfXD TmLKVxog+qN/tokd4JEy7r6PrCQ3SjGV+/LN5oN8WgAZ5/MWXh3TRVszThY7mL0+vRQW 6HBQ== DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=gmail.com; s=20161025; h=date:from:to:message-id:in-reply-to:references:subject:mime-version :x-original-sender:reply-to:precedence:mailing-list:list-id :list-post:list-help:list-archive:list-subscribe:list-unsubscribe; bh=qGYlklxjm/Q2+K/XAYnK7QHj+dZxXueDdi0jTv6BJ7s=; b=PJkTBpf1+wbjazKSF/Jv1CS6XDO54SUM3Uz37L0TvaUmo7xyiTrH+1UKYCKrzG4ifD CKnkseHGxWnxZZKIBZekALCql7VLTdb46UEeGlJNb+mEGM4QXbRLjB8ywYofOQKUVroG BN1xfArR3trSGw9WsqvFi2QGDUa8ASckjHhcA13v0aXwaZygs0PVqAxSvDMvqyssfJEc NO2Q4s9MZ6DgL9bQBR7D7+BCII/18nQV6ax3N8daioyPop8l44EJnxo0SmZxgUWgty6H HCkSfN4qAKWXGl8W9K3rOrORHvfdizT6m/hABcoGxQ/dFzaUfLeGVN3LMmtg+yXEyfHs Aoaw== X-Google-DKIM-Signature: v=1; a=rsa-sha256; c=relaxed/relaxed; d=1e100.net; s=20161025; h=sender:x-gm-message-state:date:from:to:message-id:in-reply-to :references:subject:mime-version:x-original-sender:reply-to :precedence:mailing-list:list-id:x-spam-checked-in-group:list-post :list-help:list-archive:list-subscribe:list-unsubscribe; bh=qGYlklxjm/Q2+K/XAYnK7QHj+dZxXueDdi0jTv6BJ7s=; b=lOkt4+hcerUmgN2xC75shl3lAtmVhGTYuOE2cEEoBv55dyY4tPT3LaijNKHYkrI7/l NHM/orXB5nPi7jILxQqkd+jHiBogrvFCISKuJoonGsBxUTb4k33DzkurWBH32IZfjRCc 0RgzcOTHzZYZ6n2WUUvD9jzuqZHEi5J+yhpyxNjNF+lG3TnZ8pH9IFoLUgXkshCK6M0i pO8FOkfYZe/hAI+dFvH/4M7BmROT9IY0XbpHyO2RZFDSurDzo4zbyNITGDLvkb0ykuXG MlIL/2aa4GgTtr3QVy+ruBgH2UHCIwJuyFNENOZx4kJN/CoerX0h1NYUyYOThNEw8JfE g+VQ== Sender: lojban@googlegroups.com X-Gm-Message-State: AIVw1106EOKhEVjKjq89Oajn89rUhHvL88wAArEBuFQCr8pb3WouFWLg bWTWyaHgQzZIOA== X-Received: by 10.36.16.207 with SMTP id 198mr185353ity.1.1499551636592; Sat, 08 Jul 2017 15:07:16 -0700 (PDT) X-BeenThere: lojban@googlegroups.com Received: by 10.107.205.141 with SMTP id d135ls1565837iog.41.gmail; Sat, 08 Jul 2017 15:07:16 -0700 (PDT) X-Received: by 10.36.65.25 with SMTP id x25mr195884ita.9.1499551635937; Sat, 08 Jul 2017 15:07:15 -0700 (PDT) Date: Sat, 8 Jul 2017 15:07:15 -0700 (PDT) From: vpbroman@gmail.com To: lojban Message-Id: <59981656-0038-4db5-975c-161f79cc5f31@googlegroups.com> In-Reply-To: <6ea24494-0b24-406e-9b9f-284081589bc8@googlegroups.com> References: <2c13e620-c697-46aa-ab20-46f4cd5671c2@googlegroups.com> <6ea24494-0b24-406e-9b9f-284081589bc8@googlegroups.com> Subject: [lojban] Re: bridi mathematics MIME-Version: 1.0 Content-Type: multipart/mixed; boundary="----=_Part_5359_646698093.1499551635586" X-Original-Sender: vpbroman@gmail.com Reply-To: lojban@googlegroups.com Precedence: list Mailing-list: list lojban@googlegroups.com; contact lojban+owners@googlegroups.com List-ID: X-Spam-Checked-In-Group: lojban@googlegroups.com X-Google-Group-Id: 1004133512417 List-Post: , List-Help: , List-Archive: , List-Unsubscribe: , X-Spam-Score: -4.1 (----) X-Spam_score: -4.1 X-Spam_score_int: -40 X-Spam_bar: ---- ------=_Part_5359_646698093.1499551635586 Content-Type: multipart/alternative; boundary="----=_Part_5360_2130679006.1499551635587" ------=_Part_5360_2130679006.1499551635587 Content-Type: text/plain; charset="UTF-8" Content-Transfer-Encoding: quoted-printable coi guskant I agree that part of PA3 is reducible. The "fihu" and "cehi" are not very productive, and several others could be= =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 how= =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 with= =20 expressive productivity. VUhU looked disposable. Vincent Broman mihe bremenli On Tuesday, July 4, 2017 at 8:54:30 AM UTC-7, guskant wrote: > > ...but I always think that it would be better if people can freely create= =20 > mathematical functions without adding new cmavo to the grammar.=20 > > ... > However, I think there is one disharmonious point in your examples of=20 > bridi math. In my opinion, cmavos in PA3 have property of functions rathe= r=20 > than numerals. For example, {fihu} is a function of two variables, {nihu}= =20 > is a function of one variable, etc. The functions in the official grammar= =20 > should be in VUhU, but they are in PA only because of the Lojban designer= s'=20 > misunderstanding that PA is easier to use than VUhU for those frequent=20 > functions. Actually, the VUhU math grammar can be much simpler as shown i= n=20 > https://mw.lojban.org/papri/zantufa_mekso . In that grammar, cmavos in=20 > PA3 will be able to moved to VUhU without any difficulties. > > Considering the meaning of PA3, why don't you abandon PA3 while you=20 > abandoned VUhU?=20 > > Considering the shortness of VUhU math, it is pragmatic that we keep some= =20 > frequent cmavos in VUhU, which should be augmented by cmavos moved from= =20 > PA3, and create freely more technical functions in brivla rather than in= =20 > VUhU. > > mihe la guskant > > > Le mardi 4 juillet 2017 05:08:49 UTC, Vincent Broman a =C3=A9crit : >> >> *The fact that lojban mekso represents a subset of the language that is= =20 >> complex, little-used, and** a burden to learn, makes me as a=20 >> mathematician wonder whether we could could still express ourselves **in= **=20 >> math**ematical terms** with much simpler verbal tools, and let the=20 >> complex cruft either get decommissioned, or just die of benign neglect.= =20 >> Lispers are confident that all computations can be expressed with lists = and=20 >> functions. Bridi seem general enough to do whatever needs doing. I=20 >> investigated how well we might do just using PA and bridi**, **inspired= =20 >> by** these two essays**, but with less revolution**.* >> >> *http://teddyb.org/robin/tiki-index.php?page=3DLojban%2C+Math%2C+mekso%2= C+and+bridi+cmaci=20 >> * >> >> *https://github.com/RossOgilvie/essays/blob/master/source/fancu%20bridi%= 20mekso.md=20 >> * >> >> *It turns out that without changing the grammar, it's hard to do complex= =20 >> quantifiers (you end up saying **"**poi zilkancu**"**) and nearly=20 >> impossible to do complex subscripts. So, we end up needing bridi, PA, VE= I,=20 >> VEhO, and MOhE, assuming the current grammar. La camgusmis points out th= at **with=20 >> bridi **you **often **get intricately nested BE/BEI/BEhO constructions= =20 >> that **can **become a mess, so a coinage like **"**nihai**"** or **"* >> *poihi**"* *with**in the NU **part of speech* *greatly **simplifies the= =20 >> appearance of nested expressions.* >> >> *Attached are all the **relevant **mekso examples in CLL11 extracted for= =20 >> a comparison test, where I append to each one a restatement achieved=20 >> without most of the mekso grammar, just using my subset** with bridi**.= =20 >> In terms of verbosity, the specialized mekso form in these samples saves= =20 >> about 30% in syllables, compared to bridi math. In my view the simplicit= y=20 >> achieved **by the longer bridi expressions **would be worth **the=20 >> verbosity**, especially since bridi math is easily extensible by coining= =20 >> words, while mekso syntax is fixed**,** and crossing the boundary=20 >> between **mekso and bridi** is **effortful.* >> >> *One should note in addition, that all the bridi equations I cite could= =20 >> be simplified at the top level just like the following example** by=20 >> omitting the "du"**: "li mu cu du lo nihai sumji li re li ci kei"=20 >> becomes "li mu cu sumji li re li ci", saving 5 syllables each time, at t= he=20 >> cost of looking a little different from math**.* >> >> *mihe la bremenli* >> >> mekso-bridi.pdf >> >> https://app.box.com/s/mvasmtp4dmlz9wzfx1jdhu4knkpj4gmb >> >> mekso-bridi.odt >> >> https://app.box.com/s/6nk1ysst94896cobk82i14sc9u6vg9zc >> >> mekso-syllables.txt >> >> https://app.box.com/s/qsydv85ska6mc43nx4k2jl1rle9un59h >> >> >> >> --=20 You received this message because you are subscribed to the Google Groups "= lojban" group. To unsubscribe from this group and stop receiving emails from it, send an e= mail to lojban+unsubscribe@googlegroups.com. To post to this group, send email to lojban@googlegroups.com. Visit this group at https://groups.google.com/group/lojban. For more options, visit https://groups.google.com/d/optout. ------=_Part_5360_2130679006.1499551635587 Content-Type: text/html; charset="UTF-8" Content-Transfer-Encoding: quoted-printable
coi guskant

I agree that part of PA3 is reducible.<= br>The "fihu" and "cehi" are not very productive, and s= everal others could be dispensed with, but at a cost in verbosity.
Peano= showed how all arithmetic could be reduced to "pa", "sumji&= quot;, and "pilji", and the later two could be reduced to just &q= uot;baihei".
Still I'm disposed to see the convenience of most = of PA3 for practical purposes in constructing numbers.

The distincti= on between common functions in VUhU and more technical functions in brivla = preserves the old grey area where you debate about how common or how techni= cal each cmavo is, but you still have to support both kinds of functions se= parately.
I wished to push the limits, to see how much can be done with= the least means.
Every part of speech has a complexity cost and has to = justify the cost with expressive productivity.
VUhU looked disposable.
Vincent Broman mihe bremenli

On Tuesday, July 4, 2017 at 8:54:= 30 AM UTC-7, guskant wrote:
...but I always think that it would be better if pe= ople can freely create mathematical functions without adding new cmavo to t= he grammar.=C2=A0

...
However, I think there is= one disharmonious point in your examples of bridi math. In my opinion, cma= vos in PA3 have property of functions rather than numerals. For example, {f= ihu} is a function of two variables, {nihu} is a function of one variable, = etc. The functions in the official grammar should be in VUhU, but they are = in PA only because of the Lojban designers' misunderstanding that PA is= easier to use than VUhU for those frequent functions. Actually, the VUhU m= ath grammar can be much simpler as shown in https://mw.lojban.org/papri/zantufa_mekso . In that gr= ammar, cmavos in PA3 will be able to moved to VUhU without any difficulties= .

Considering the meaning of PA3, why don't yo= u abandon PA3 while you abandoned VUhU?=C2=A0

Cons= idering the shortness of VUhU math, it is pragmatic that we keep some frequ= ent cmavos in VUhU, which should be augmented by cmavos moved from PA3, and= create freely more technical functions in brivla rather than in VUhU.

mihe la guskant


Le mardi= 4 juillet 2017 05:08:49 UTC, Vincent Broman a =C3=A9crit=C2=A0:
=09 =09 =09 =09

The fact that lojban mekso represents a subset of the language that is complex, little-used, and a burden to learn, makes me as a mathematician wonder whether we could could still express ourselves in mathematical terms with much simpler verbal tools, and let the complex cruft either get decommissioned, or just die of benign neglect. Lispers are confident that all computations can be expressed with lists and functions. Bridi seem general enough to do whatever needs doing. I investigated how well we might do just using PA and bridi, inspired by<= span style=3D"font-weight:normal"> these two essays, but with less revolution.<= /span>

http://teddyb.org/robin/tiki-index.p= hp?page=3DLojban%2C+Math%2C+mekso%2C+and+bridi+cmaci

https://github.com/RossOgilvie/essays/blob/master/source/fancu= %20bridi%20mekso.md

It turns out that without changing the grammar, it's hard to do complex quantifiers (you end up saying "<= /span>poi zilkancu"<= b>) and nearly impossible to do complex subscripts. So, we end up needing bridi, PA, VEI, VEhO, and MOhE, assuming the current grammar. La camgusmis points out that = with bridi you often get intricately nested BE/BEI/BEhO constructions that can become a mess, so a coinage like &q= uot;nihai" or "poihi" within the NU part of speech greatly simplifies the appearance of nested expressions.

Attached are all the relevant mekso examples in CLL11 extracted for a comparison test, where I append to each one a restatement achieved without most of the mekso grammar, just using my subset with bridi. In terms of verbosity, the specialized mekso form in these samples saves about 30% in syllables, compared to bridi math. In my view the simplicity achieved by the longer bridi expressions would be worth the verbosity, especially since bridi math is easily extensible by coining words, while mekso syntax is fixed, and crossing the boundary between mekso and bridi is effortful.

One should note in addition, that all the bridi equations I cite could be simplified at the top level just like the following example by omitting the "du": "li mu cu du lo nihai sumji li re li ci kei" becomes "li mu cu sumji li re li ci", saving 5 syllables each time, at the cost of looking a little different from math.

mihe la bremenli

mekso-bridi.pdf

https://app.box.com/s/mvasmtp4dmlz9wzfx1jdhu4knkpj4gmb

=

mekso-bridi.odt

https://app.box.com/s/6nk1ysst94896cob= k82i14sc9u6vg9zc

mekso-syllables.txt

https://= app.box.com/s/qsydv85ska6mc43nx4k2jl1rle9un59h



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